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Best Math Books

Unlock the secrets of mathematics with these celebrated math books. whether for academic study or personal interest, this list encapsulates the most frequently endorsed titles by educators, mathematicians, and leading educational blogs..

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58 Amazing Math Books for Young Mathematicians

You can count on them loving these reads.

Math students often have a hard time understanding abstract math concepts. Enhancing your lessons with books about math for kids will help make connections while having fun in the process. Motivate your students while introducing new concepts, reinforcing ideas, and talking about all things math with some of our favorite books. We have you covered through the year with lots of elementary math topics using these children’s math books.

Sorting & Patterns

1. The Animals Would Not Sleep! by Sara Levine

Marco needs to get his stuffed animals organized before bedtime. He tries sorting them in lots of different ways, but they just won’t settle down. Kids will be clamoring to give him ideas!

Buy it: The Animals Would Not Sleep! at Amazon

2. Seeing Symmetry by Loreen Leedy

A beautifully illustrated book about math that shows how flips, slides, and turns can create amazing symmetrical images.

Buy it: Seeing Symmetry at Amazon

3. Pitter Pattern by Joyce Hesselberth

Definitely add this to your list of children’s math books to introduce patterns. This fiction and nonfiction hybrid covers many types of patterns, including simple visual patterns, sound patterns, patterns in nature, and more.

Buy it: Pitter Pattern at Amazon

4. Math at the Art Museum by Group Majoongmul

A little boy thinks his dad is telling a tall tale when he says elements of math are found in the art world. His mind is blown when he visits his local art museum with his family. Children’s math books help prove math is everywhere!

Buy it: Math at the Art Museum at Amazon

Addition & Subtraction

5. Ten on a Twig by Lo Cole

Ten adorably colorful birds sit happily on a branch—until they begin to fall off one by one! Subtraction is a hard concept to introduce to young kids, but this story makes it nice and concrete.

Buy it: Ten on a Twig  at Amazon

6. Six-Dinner Sid by Inga Moore

If you are a cat person, you know felines are smart little creatures. Sid tricks six separate neighbors into thinking he belongs to each household, receiving six dinners every night. Will they figure out his little secret?

Buy it: Six-Dinner Sid at Amazon

7. Monster Math by Anne Miranda

This cute children’s math book starts with a little monster patiently waiting for guests to arrive at the birthday party. As more and more arrive, kids can use addition skills to keep track. Once there are 50 guests, Monster Mom has had enough, and they begin to leave. This, of course, lends to using subtraction skills.

Buy it: Monster Math at Amazon

8. If You Were a Minus Sign by Trisha Speed Shaskan

This cute, colorful book meets the objective of teaching young students to comprehend their signs in math. This book is a great introduction to subtraction, which is necessary to continue building on throughout students’ math careers.

Buy it: If You Were a Minus Sign at Amazon

9., 10., & 11.: Math Is CATegorical Series by Brian P. Cleary

Rhyming text filled with funny, countable examples introduces basic math concepts for young readers and reveals that sometimes math is easier to show than explain. Pairing clever rhyming verse with comical cartoon cats, Brian P. Cleary and illustrator Brian Gable help children add up just how fun math can be.

Buy it: The Action of Subtraction , The Mission of Addition , How Long or How Wide? A Measuring Guide at Amazon

12. Money Math: Addition and Subtraction by David A. Adler

In this fun introduction to American currency, multiple past presidents introduce themselves and their denominations. Readers will learn about who is on each coin and bill, and what they’re worth—and how many of one it takes to add up to another.

Buy it: Money Math: Addition and Subtraction at Amazon

13. Alexander, Who Used To Be Rich Last Sunday by Judith Viorst

Alexander is given a dollar by his grandparents. As he stretches his imagination on how to spend it, count along with him. Kids will laugh while seeing the obstacles he faces along the way!

Buy it: Alexander, Who Used To Be Rich Last Sunday at Amazon

14. Lemonade in Winter: A Book About Two Kids Counting Money by Emily Jenkins

Follow a brother and sister team as they set out to make some money on a cold winter’s day. While lemonade may not be the best idea for the weather, they learn a good lesson about buying and selling goods. Count along with them as they try to make a profit.

Buy it: Lemonade in Winter: A Book About Two Kids Counting Money at Amazon

15. A Dollar, a Penny, How Much and How Many? by Brian P. Cleary

Learn all about different coins and bills in our currency system. Then count along with the help of fun rhymes and silly mathematician cat characters!

Buy it: A Dollar, a Penny, How Much and How Many? at Amazon

16., 17., & 18. Triangle, Square, and Circle by Mac Barnett

Kids love the humor and whimsical illustrations in the sassy stories in the Shapes trilogy. Great for talking about the attributes of different geometric shapes in a fun context.

Buy it: Triangle , Square , and Circle at Amazon

19. The Greedy Triangle by Marilyn Burns 

Triangle is a busy shape! However, he is bored with the same routines. He asks the shapeshifter for another side and goes on adventures. This pattern continues until he no longer can keep track of himself. This is a great geometry book, and it also teaches a valuable life lesson. 

Buy it: The Greedy Triangle at Amazon

20. Grandfather Tang’s Story by Ann Tompert

This Chinese folktale uses tangram shapes to bring the animal characters to life. Grab a class set of tangram puzzles and have your students create the different animals in the story as you read it.

Buy it: Grandfather Tang’s Story at Amazon

21. Circle Loves Pi: A Pi Day Story by Vea Lewis 

Circle is a tough shape to measure. However, when his buddy Pi is around, circumference, volume, and area are a breeze to compute!

Buy it: Circle Loves Pi: A Pi Day Story at Amazon

22. Which One Doesn’t Belong? by Christopher Danielson

Keep the mathematical talk going by talking about attributes of shapes and how they are the same and different. Observations about the shapes on each page can go in many different directions.

Buy it: Which One Doesn’t Belong? at Amazon

23. Sir Cumference and the First Round Table  by Cindy Neuschwander

Brave knights, a strong ruler, and a dilemma that needs to be solved using math. Great for introducing geometry concepts in a fun and accessible way.

Buy it: Sir Cumference and the First Round Table at Amazon

24. Two of Everything by Lily Toy Hong

Mr. Haktuk is working in his garden when he digs up an ancient pot. He and his wife soon learn it is a magical pot. They fill their hut with gold, excited that their luck has changed. When they both fall into the pot, the real trouble begins!

Buy it: Two of Everything at Amazon

25. How Many? (Talking Math) by Christopher Danielson

This really is “a different kind of counting book”! Each page has a thought-provoking photo in which readers decide what and how to count. If you’re looking for children’s math books to get interesting number talks flowing, this is it!

Buy it: How Many? (Talking Math) at Amazon

26. Billions of Bricks: A Counting Book About Building by Kurt Cyrus

Watch as this busy construction crew creates impressive structures by grouping bricks by twos, fives, and tens. Kids will love the catchy repetitive verse and charming illustrations.

Buy it: Billions of Bricks: A Counting Book About Building at Amazon

27. Counting on Fall by Lizann Flatt

As young readers journey into the natural world, they will discover numbers, patterns, shapes, and more. The colorful, collage style of the book will engage both children and adults.

Buy it: Counting on Fall at Amazon

28. Mrs. Wiggles and the Numbers by Lisa Konkol

Mrs. Wiggles is the best way to introduce children to the world of math. Bold and vibrant numbers combined with catchy rhymes make it easy to keep children entertained.

Buy it: Mrs. Wiggles and the Numbers at Amazon

29. Pebbles and the Biggest Number by Joey Benun

A daring butterfly travels the world searching for the biggest number in a picture book filled with fun and facts. This is an entertaining way to teach kids about numbers larger than they could even imagine.

Buy it: Pebbles and the Biggest Number at Amazon

Measurement

30. Inch by Inch by Leo Lionni

Follow the adventures of an adorable inchworm as he measures different body parts of his animal friends. When a bird threatens to eat the inchworm if he can’t measure an intangible item, he gets creative. Kids love the colorful and whimsical artwork common to Lionni’s books.

Buy it: Inch by Inch at Amazon

31. How Tall? Wacky Ways To Compare Height by Mark Weakland

This wacky, laugh-out-loud introduction to height shows kids an easier way to understand measuring. The rhyming text makes it perfect for a read-aloud or to entertain young ones.

Buy it: How Tall? Wacky Ways To Compare Height at Amazon

Place Value

32. Place Value by David A. Adler

Love the story about monkeys jumping on the bed? You’ll adore this version that tells the story of the monkeys at Banana Cafe making one very large banana cupcake.

Buy it: Place Value at Amazon

33. Sir Cumference and All the King’s Tens: A Math Adventure by Cindy Neushwander 

Sir Cumference and his friends are back! This time, they are busy working with place value and counting by tens. When tens, hundreds, and eventually thousands of unanticipated guests show up for King Arthur’s birthday, they need to figure out how to feed everyone ASAP!

Buy it: Sir Cumference and All the King’s Tens: A Math Adventure at Amazon

Area and Perimeter

34. Spaghetti and Meatballs for All! by Marilyn Burns

Mr. and Mrs. Comfort are having a family reunion and need to arrange the tables so that everyone in the family can enjoy their fabulous spaghetti and meatballs. A witty tale by math guru Marilyn Burns.

Buy it: Spaghetti and Meatballs for All! at Amazon

35. Perimeter, Area, and Volume: A Monster Book of Dimensions by David A. Adler

Let’s go to the movies! Find the perimeter, area, and volume of movie theater staples with assistance from a cast of cute movie monster friends. 

Buy it: Perimeter, Area, and Volume at Amazon

Number Sense

36. Infinity and Me by Kate Hosford

Delightful illustrations and a dreamy young girl pondering the vastness of the universe make a very difficult concept approachable and interesting.

Buy it: Infinity and Me at Amazon

37. A Very Improbable Story by Edward Einhorn

Ethan wakes up one morning with a strange cat on his head, and the only way it will agree to get off is if Ethan agrees to play a game of probability with it. This kooky book will entertain your students as it teaches a difficult concept.

Buy it: A Very Improbable Story at Amazon

38. Zero the Hero by Joan Holub

Kids will love this fun story with delightful cartoon illustrations by Tom Lichtenheld that teach the importance of zero as a placeholder in our number system. Without Zero the Hero, we wouldn’t be able to count beyond the number nine!

Buy it: Zero the Hero at Amazon

39. Equal Shmequal by Virginia Kroll

Mouse and her friends want to play a game of tug-of-war but have a hard time making the sides fair. This charming story teaches the concept of balance and equality.

Buy it: Equal Shmequal at Amazon

40. & 41. One Odd Day and My Even Day by Doris Fisher and Dani Sneed

Two more rhyming tales with colorful, busy illustrations that kids will love. In each of these children’s math books, a boy wakes up one day and finds that things are kookily out of order. Great as read-alouds or for independent readers who will love hunting through the detailed pictures to find the odd or even items.

Buy it: One Odd Day and My Even Day at Amazon

42. How Much Is a Million? by David M. Schwartz

Children’s math books are especially helpful when demonstrating very large numbers since it shows a visual picture. Kids love hearing about the numbers in the millions, billions, and trillions, so this book will add to the excitement. With a mystical main character named Marvelossissimo the Magician and illustrations by Steven Kellogg, this book is beyond memorable.

Buy it: How Much Is a Million? at Amazon

Telling Time

43. A Second, a Minute, a Week With Days in It: A Book About Time by Brian P. Cleary

A playful book with silly characters and perfect rhyming that teaches not just the basics of telling time but the tricky concept of relative time.

Buy it: A Second, a Minute, a Week With Days in It at Amazon

44. If You Were a Minute by Tricia Speed Shaskan

How long is a minute, really, when trying to make sense of time? Kids can look at a clock and read the time, but this book helps them understand what can be done in different amounts of time to build deeper meaning. It is never too early to introduce time management skills.

Buy it: If You Were a Minute at Amazon

Division and Fractions

45. A Remainder of One by Elinor Pinczes

The 25th Beetle Army Corp is trying to solve the problem of how to divide their troops into equal groups for the parade march without leaving any stragglers. A fun rhyming book about math that will get kids thinking about how numbers are put together and pulled apart.

Buy it: A Remainder of One  at Amazon

46. The Great Divide: A Mathematical Marathon by Dayle Ann Dodds

At the beginning of the story, 80 contestants are ready to compete in the Great Divide. Dangers lie ahead at every turn, causing more and more runners to leave the competition. Who will be left at the end and survive the obstacles?

Buy it: The Great Divide: A Mathematical Marathon at Amazon

47. The Hershey’s Milk Chocolate Fractions Book by Jerry Pallotta

Incorporating children’s math books with tasty treats is a surefire way to get kids’ attention. Hershey’s chocolate bars are made up of 12 rectangles. Pass out a chocolate bar to each student. Then, use them with this book for a delicious, hands-on fractions lesson.

Buy it: The Hershey’s Milk Chocolate Fraction Book at Amazon

48. If You Were a Divided-By Sign by Trisha Speed Shaskan 

Celebrate a love of language and math with this book that includes a whimsical cast of characters to engage curious minds. Each set of problems introduces basic concepts using simple text and enhances the learning with silly and unexpected examples.

Buy it: If You Were a Divided-By Sign at Amazon

49. Fractions in Disguise by Edward Einhorn 

If you are looking for a fun way to teach your students about reducing fractions, look no further. When a valuable fraction goes missing, George Cornelius Factor (aka GCF) immediately is on the case. He knows if he continues to reduce fractions, he will eventually solve the mystery.

Buy it: Fractions in Disguise at Amazon

50. Math for Minecrafters: Adventures in Multiplication & Division by Amanda Brack

This kid-friendly workbook features well-loved video game characters and concepts to reinforce the development of 3rd and 4th grade math skills. Puzzles use familiar items from Minecraft like diamond swords, suits of armor, zombies, and magical potions to encourage math practice in gamers.

Buy it: Math for Minecrafters: Adventures in Multiplication & Division at Amazon

Problem-Solving

51. The Grapes of Math by Greg Tang

Good children’s math books hone in on problem-solving, identifying patterns, symmetry, and grouping. This one uses all four concepts to help students count in groups, instead of going one by one. Your students will think out of the box as they come up with ways to solve each math riddle. Watch the enthusiasm grow bigger with each turn of the page!

Buy it: The Grapes of Math at Amazon

52. One Grain of Rice: A Mathematical Folktale by Demi

In this Indian folktale, a greedy raja keeps all of the rice for himself. As the rest of the village starves, a clever girl named Rani devises a plan. She makes a deal to receive one grain of rice, doubled, for 30 days. As time passes, over 1 billion grains of rice become available for all of the villagers to share. Problem-solving, along with multiplication, are a big part of this book. At the same time, the valuable lessons of fairness and sharing shine through.

Buy it: One Grain of Rice at Amazon

53. Seven Golden Rings by Rajani LaRocca

This story of a clever young boy in ancient India can be enjoyed on many levels. Bhagat must figure out how to stretch his family’s only fortune, seven golden rings, as far as possible—which leads to some creative mathematical thinking! To engage older students, use the afterword to introduce how to write numbers in binary.

Buy it: Seven Golden Rings at Amazon

54. Math-terpieces: The Art of Problem-Solving by Greg Tang

Help students master important skills while also gaining exposure to some of the world’s most famous paintings. This book focuses on grouping numbers and creating different combinations using visuals.

Buy it: Math-terpieces: The Art of Problem-Solving at Amazon

55. Math Curse by Jon Scieszka

The main character of this children’s math book wakes up one morning only to find she has been placed under a math curse! Follow her through her day as she faces a different math problem everywhere she goes, while just carrying on with ordinary, daily activities. 

Buy it: Math Curse at Amazon

56. The Chicken Problem by Jennifer Oxley

Peg and Cat are enjoying a picnic lunch on the farm, until it is interrupted by chaos; the chickens have escaped the coop! Help them solve mathematical problems in order to restore the peace. 

Buy it: The Chicken Problem at Amazon

57. Problem-Solving Ninja by Mary Nhin

The Ninja Life Hacks series introduces pint-size characters in comedic books easy enough for young readers, yet witty enough for adults. This colorful book is perfect to teach about a growth mindset.

Buy it: Problem-Solving Ninja at Amazon

58. The Best of Times: Math Strategies That Multiply by Greg Tang

In this book, author Greg Tang takes on the times tables, teaching kids innovative ways to multiply numbers and derive answers without the need for memorization. This is one of the best children’s math books because it uses a simple, sing-song formula to allow kids to understand clever math strategies.

Buy it: The Best of Times: Math Strategies That Multiply at Amazon

Did you love these books about math for kids? Check out Second Grade Math Word Problems of the Day .

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Great Books Related to Mathematics Content Knowledge, Pedagogy, Leadership, Psychology and More!

Great Reads to Rethink Your Philosophy of Mathematics Education, Build Your Content Knowledge, Sharpen Your Pedagogical Practices and Much More!

This page is the Ultimate Guide Of Math Books For Teachers because it is the list of many books I’ve read to challenge my thinking around mathematics education and education in general, to build my own conceptual understanding around big ideas I was never taught, and to improve my instructional practice from day to day in the classroom. I even have links to books not so math related, but very important along my own personal and financial journey thus far.

The Ultimate List of Math Books

Must Read Math Books

The following books are some that I’m highlighting as “ must reads ” for any math teacher, elementary, middle or high school.

Changing Beliefs

Mathematical Mindsets

Unleashing Students’ POTENTIAL Through Creative Math, Inspiring Messaging, and INNOVATIVE TEACHING

Take a journey with Jo Boaler through the muddy waters of the misconceptions in and around mathematics education. From dispelling the “math myth” of ability, learning how to change our fixed mindsets to growth mindset, and how to teach mathematics to reach every student, this book is a must read for those who have always loved the subject as well as those who have always feared it.

More Great Reads Related to Access, Diversity, Equity, and Inclusion

Developing Teacher Mathematics Content Knowledge

The next section of math books have helped me along my journey to fuel sense making in my students. Despite always believing that I had been helping my students make sense of the math I was teaching, many of these reads helped me to realize that I myself didn’t have a strong enough conceptual understanding in order to meet students where they were along their developmental mathematics learning journey.

Building Teacher Mathematics Content Knowledge

Elementary and Middle School Mathematics

Despite the title of the book focusing in on elementary and middle school mathematics, this is a great book for all mathematics educators from Kindergarten through Grade 12. Had I better understood how big ideas in mathematics develop from a young age into the high school grades, I could have been a much better high school math teacher.

Minilessons: Early Addition and Subtraction

Mathematics for Elementary Teachers

(18 reviews)

Michelle Manes, Honolulu, HI

Copyright Year: 2017

Publisher: University of Hawaii Manoa

Language: English

Formats Available

Conditions of use.

Learn more about reviews.

Reviewed by Kevin Voogt, Assistant Professor, Grace College on 4/20/23

There seem to be subjects missing that are typical of the common core mathematics for elementary teachers texts (e.g., Ratios/Proportions, clear Partitive/Measurement division ideas, percentages, certain ideas in Geometry, Measurement). read more

Comprehensiveness rating: 4 see less

There seem to be subjects missing that are typical of the common core mathematics for elementary teachers texts (e.g., Ratios/Proportions, clear Partitive/Measurement division ideas, percentages, certain ideas in Geometry, Measurement).

Content Accuracy rating: 5

I did not find mathematical errors in the text during my review.

Relevance/Longevity rating: 3

I think there is need for quite a few updates to the text in regards to what is covered in elementary mathematics through the common core. The topics listed in my review of the Comprehensiveness above are just a start. I also see a need to add more activities to each section where prospective elementary teachers could do more exploration of the mathematics rather than what seems to be a more traditional approach of having the text explain it followed by problem sets alone.

Clarity rating: 5

The wording was quite clear and had nice explanations throughout.

Consistency rating: 5

It seems consistent throughout - with recurrent use of the same technical terms as needed.

Modularity rating: 4

There were a few issues with being able to assign the texts at different points within the course, as is the case for many math texts, in that many of the sections rely heavily on prior knowledge. If reorganization were to occur, there would be some need to re-structure how certain sections are taught.

Organization/Structure/Flow rating: 4

The text lacks much of the wonderful mathematical connections that could be made between ideas. While some connections are made, they seem a little outdated at times. I also think it would make more sense to have the properties of operations within their corresponding sections on operations rather than after all 4 operations are introduced.

Interface rating: 5

I did not see any issues with the interface. It was pretty user-friendly.

Grammatical Errors rating: 5

I did not notice any errors during my review.

Cultural Relevance rating: 5

I did not see anything insensitive or offensive in the text.

The text is just a small sampling of the many methods that could be used in teaching these mathematical ideas. I would have liked to see more activities for elementary teachers built into the lessons in each chapter as a means for learning and exploring ideas to facilitate more discussion as this text is used. There also are so many more connections that could be made between mathematical ideas that were lost a bit, especially with the general organization. On the whole, it is a nice resource and I could see it as useful for students studying for their certification exams to get some perspectives on the mathematical ideas they might encounter.

Reviewed by Sandra Zirkes, Teaching Professor, Bowling Green State University on 4/14/23

The text covers whole numbers, fractions, decimals, and operations well, and it provides some topics in geometry and algebraic thinking. However, the topics of ratio, proportion, and percent, as well as a more thorough coverage of geometry and... read more

The text covers whole numbers, fractions, decimals, and operations well, and it provides some topics in geometry and algebraic thinking. However, the topics of ratio, proportion, and percent, as well as a more thorough coverage of geometry and measurement are missing.

All information in the text is mathematically accurate and the writing and diagrams are error-free.

Relevance/Longevity rating: 4

While all of the information in the text is accurate and thought-provoking, some specific approaches are outdated with respect to the current standards and pedagogy. Approaching the concept of place value through the "Dots and Boxes" method, without reference to base ten blocks that are overwhelmingly used in the elementary math classroom, limits the coverage of this important topic. Similarly, approaching fractions using the "pies and kids" scenario is not consistent with the standards which emphasize the understanding of all fractions as iterations of unit fractions.

The text is written using clear and understandable prose that is both mathematically accurate and accessible to college level pre-service teachers.

The text has a clear organization and focus and uses consistent approaches and terminology throughout.

Much of the text is easily divisible into smaller subsections for student use. With respect to reorganization and realignment for a particular course, while some topics are revisited at appropriate points in the text, if those original topics were not covered in the course, revisiting the topic may not provide enough basis for the new topic. For example, the understanding of decimals is highly reliant on a student's understanding of the Dots and Boxes approach to place value earlier in the text.

Organization/Structure/Flow rating: 5

The topics in the text are organized in a logical way that is consistent with the structure of a typical mathematics education course.

Interface rating: 4

Navigating the text itself was seamless and intuitive. However, the videos that I viewed had poor visual quality and there was no audio.

The text is well written with no grammatical errors.

There is no apparent cultural insensitivity in the text.

This text has a problem solving focus and emphasizes deep thinking and reasoning about mathematics. Its approaches are clear and understandable. While its approaches are mathematically correct and thought-provoking, it is missing some key topics such as ratio, proportion, percent, and a more thorough coverage of geometry and measurement, as well as some standards-based approaches such as base ten blocks and understanding fractions as iterations of unit fractions.

Reviewed by Fred Coon, Assistant Professor, Anderson University on 2/16/23

The text covers all major points to help develop future teachers. read more

Comprehensiveness rating: 5 see less

The text covers all major points to help develop future teachers.

Text appears to be accurate.

The content is consist with concepts that elementary teachers should know. The methods are small in diversity.

Topics where well explained.

Text appears to use understandable and consistent terms.

Modularity rating: 5

Units appear to be mostly independent and can be used as stand alone units.

The topics are presented in a manner that build on each other but can be rearrange if desired.

Interface was useful and aided in navigating text.

I found no errors.

The text has no culturally insensitive or offensive items that I noticed.

I would like to have seen more diversity in methods discussed.

Reviewed by Perpetual Opoku Agyemang, Professor of Mathematics, Holyoke Community College on 6/17/21

The content in this text is built to help its readers, especially, pre-service elementary education majors learn to think like a mathematician in some very specific ways. The content addresses the subject framework in a complete yet concise... read more

The content in this text is built to help its readers, especially, pre-service elementary education majors learn to think like a mathematician in some very specific ways. The content addresses the subject framework in a complete yet concise manner. Although it does not provide an effective index/or glossary, LCD was not extensively tackled using factor tree, multiples or tables to express it, I still give props to the author since there are a lot of pictorial examples and a question bank for most of the various concepts. Furthermore, Dots and Boxes game on chapter 1 was very engaging and fun.

This text is very accurate and informative using a variety of felicitous examples to suit a diverse student population.

Conventional concepts are presented in a current and applied manner which allows for easier association with similar organized and retained information. This text could use some updated fraction problems and examples involving mixed numbers. Some of the YouTube videos have no sound at all.

Clarity rating: 4

Content material was presented in an easy to understand prose. Introduction of concepts and new terms were usually done by association or relevant previous knowledge. Some of the concepts like Multiplying Fractions, have YouTube videos embedded in the introductions.

Terminologies and framework are consistent throughout the text. The use of different notations were consistent throughout the various chapters and subunits.

This text has easily divisible content as stand alone subunits. However, numbering these chapters and subunits would have gone a long way to help its readers.

The topics in this text are organized from basic to complex concepts in a logical, clear fashion.

This text has an awesome interface (Online, PDF and XML). Moreover, it is untainted by distractions that may confuse its reader. Hyperlinks should have been included in the content.

I did not spot any grammatical errors in this text.

This content material contains no recognizable cultural insensitivity. It could use more examples involving modern affairs that are inclusive of diverse backgrounds.

I truly love the concise format of this text and how many different examples it uses to explain the concepts. The Geometry of Arts and Science and Tangrams were so informative with fun activities. It's easy to tell when one example ends and another begins, although index/or glossary and a system of links from the table of contents would be greatly appreciated. I did not see Points on a Coordinate Plane. Additionally, the number of exercises per section is too small. Of course this can be remedied by adding more. As with any textbook, the reader will need to supplement certain sections and clarify particular terms and concepts to best fit their situation. Pre-service elementary education majors could transition to this book fairly easily and successfully teach K-6 students in the United States in alignment with current Common Core Math Standards.

Reviewed by April Slack, Math Instructor, Aiken Technical College on 5/13/21

This text covers elementary mathematics strands including place value, numbers and operations, fractions, patterns, algebraic thinking, decimals, and geometry. Measurement and Data and Statistics strands are not included in this particular text. ... read more

This text covers elementary mathematics strands including place value, numbers and operations, fractions, patterns, algebraic thinking, decimals, and geometry. Measurement and Data and Statistics strands are not included in this particular text. The last chapter supplies the audience with problem-based learning approaches that include some measurement, but not in the detail of previous chapters of the book. It does incorporate problem solving strategies and pedagogical techniques teachers may use in the classroom. Examples with solutions and clarifying notes are provided throughout the text. The text does address Common Core Standards as well as the eight mathematical process standards. The textbook also provide teachers with a conceptual understanding of elementary mathematics along with appropriate mathematical terminology. The text does not offer an index or glossary.

The mathematics content provided in this text is accurate and provides thorough examples of teaching elementary mathematics for pre-service teachers. I found the text to build conceptual understanding and procedural fluency rather than just focus on basic algorithms to solve math problems. This is especially important for pre-service teachers, as they need to truly understand the "why" behind the math tricks that are often taught in early grades. The embedded links throughout the text are all in working order, as well.

The problem-solving approach to mathematics is especially relevant for elementary pre-service teachers; the intended audience. The book does expand beyond elementary mathematics, however, this is deemed extremely useful for all levels of mathematics teachers. Knowing the mathematical concepts beyond elementary strands allows teachers to know where there students are going and the mathematical purpose of content standards at each grade level. Many of the pedagogical techniques presented in the text are aligned with current research and instructional strategies for the elementary classroom.

This text provides explanations and defines mathematical terminology and has accessible prose. Beginning with the problem solving chapter before the specific content strands allows teachers to apply and consider strategies throughout the text. Often times, textbooks save problem solving for the end, but this text addresses strategies upfront and spirals nicely throughout the text. Some of the examples and visual representations are intended for an audience with mathematical background knowledge and strengths. A pre-service teacher may need help with content review prior to understanding the selection of particular problems highlighted in the text.

The text is well-organized and consistent with terminology throughout. The text is also consistent with provided examples that are used by mathematics teachers in everyday classrooms. There are multiple examples throughout each of the content chapters for pre-service teachers to reference and use in their own experiences.

This book is an easy read and may be easily broken up for weekly reading assignments and reflections. It seems as if mathematics teachers had a hand in writing this book. Bulleted and numbered lists are used throughout the text. The text also presents examples in clear, colored blocks. Visual models are clear and concise.

The book is well-organized with headings, subheadings, and the use of italics and boldface make this book extremely student friendly. The topics and content presented in this text are clear and in a logical order. Bulleted and numbered lists are reader friendly and easily understood. I found having the problem solving chapter appear first in the text stresses the importance and relevance of helping students become natural problem solvers. Often times texts and even worksheets save problem solving until the end, which poses a problem with students in the classroom.

This book is very easily navigated. The contents tab and drop down menu allows for the reader to quickly navigate to particular chapters and specific content. The previous and next buttons located at the bottom of the text allows readers to toggle between chapters very quickly. All embedded links work as they should and visual models are clear and understandable. There are no distractors present when trying to navigate the text. There is no index / glossary offered with this text.

The text is free from grammatical errors.

Cultural Relevance rating: 4

This text is not culturally offensive in any way. The final chapter of the text is dedicated to problem based learning and is centered around Voyaging on Hōkūle`a. The text provides embedded links to culturally relevant videos and models that help illustrate the cultural practices of Polynesians.

This textbook has a solid foundation and is well-organized for it's intended audience, the elementary mathematics pre-service teacher. This text will help build conceptual understanding of mathematics that will lead to procedural fluency for teachers. The text also provides clear examples of instructional strategies to be used in today's classrooms. Methods courses for pre-service teachers will find this text extremely useful and easy to incorporate in elementary mathematics methods instruction.

Reviewed by Kane Jessen, Math Instructor, Community College of Aurora on 8/13/20

This textbook is intended to cover the mathematics topics necessary to prepare pre-service elementary education majors to successfully teach K-6 students in the United States in alignment with current Common Core Math Standards. The textbook is a... read more

This textbook is intended to cover the mathematics topics necessary to prepare pre-service elementary education majors to successfully teach K-6 students in the United States in alignment with current Common Core Math Standards. The textbook is a mostly comprehensive collection of K-6 Common Core elementary math topics ranging from non-numerical problem solving through summative PBL assessments incorporating algebra, geometry and authentic problem solving. However, several topics related to K-6 CCSS Standards are not covered or minimally covered. CCSS topics with minimal coverage include set theory, logic, integers, probability, graphing and data analysis. At the beginning of the book, there is an effective and accessible table of contents with links included. However, sections and subsections are labeled only with names and page numbers. The text does not contain an index, glossary or appendices. Chapter summaries and links to previous concepts/problems are not included but would support student learning if included. More visuals and historical explorations would increase comprehensiveness.

Content was found to be accurate, error-free and unbiased.

Relevance/Longevity rating: 5

The language and examples of this text are written with a constructivist and meta-pedagogical voice that is both academic and accessible. The author immediately addresses the importance of CCSS and consistently utilizes the “Exploding Dots” curriculum. The “Exploding Dots” curriculum is a brave and differentiated approach to holistically teaching multi-base mathematics to K-12 students. “Exploding Dots” has been a core focus of K-12 Global Math Project and was pioneered by James Tanton . As future teachers, students can expect to teach “Exploding Dots” or similar CCSS curriculum sometime during their teaching career.

The language of the text is well-written, accessible and clear. Some sections and examples could be expanded for clarity/depth. Prior definitions/review concepts are not consistently linked.

The text is internally consistent in terms of its own terminology, framework and graphics. The “Exploding Dots” infusion helps maintain continuity throughout the text but is not present in all modules.

This text follows the common sequence that many “Mathematics for Elementary Teachers” textbooks commonly follow. The text is organized into eight modules. The text initially builds upon itself without being overly self-referential. The text’s sections, subsections, definitions, axioms and problem banks are all well delineated but lack sections/subsection numbers/identifiers and links to previous concepts/definitions

This textbook has a solid flow and follows a common sequence shared by most for profit “Mathematics for Elementary Teachers” texts. The text is well organized and builds upon itself.

Minimal issues involving interface were observed. Observed interface issues include, one broken video link and unnumbered sections. Definitions and review topics are not linked or referenced with page numbers/sections, however, this creates minimal usability issues. The text contains adequate procedural visuals and also cultural and historical visuals that enhance the student learning experience.

This text is largely free from grammatical errors. Grammatical errors that were observed were minor and non-persistent.

The text is not culturally insensitive or offensive in any way. It consistently uses examples that are inclusive of a variety of races, ethnicities, and backgrounds. Textbook examples often include references to Hawaiin culture. These references are easily understandable and could be readily adapted for students in other places. In an effort to increase relevance, further additions to the text could be made to provide a more equitable and historical focus on women, minorities and problem based learning cross-sectional explorations similar to the Hōkūleʻa section.

This textbook has a solid structure and great flow, I thoroughly enjoyed reviewing this textbook. I am genuinely excited to incorporate Michelle Manes ‘Mathematics for Elementary Teachers’ into my upcoming semester’s curriculum. With subsequent editions and revisions, this textbook will become a wonderful text for students majoring in primary education, especially those who are either lacking in basic math skills or math confidence.

Reviewed by Reina Ojiri, Assistant Professor, Leeward Community College on 7/27/20

The book begins with a reference to the Common Core State Standards (CCSS) for Mathematics and the eight “Mathematical Practices". Though not all states have adopted and/or are currently using the Common Core Standards, with its incorporation at... read more

Comprehensiveness rating: 2 see less

The book begins with a reference to the Common Core State Standards (CCSS) for Mathematics and the eight “Mathematical Practices". Though not all states have adopted and/or are currently using the Common Core Standards, with its incorporation at the beginning of the text I initially thought that the Common Core standards would be revisited consistently throughout the text.

Though the "Think Pair Share" sections are great additions for discussion to the book they do not include common misconceptions or tips for instructors to use to help guide these discussion prompts. The focus on just one type of discussion "Think Pair Share" also does not give future teachers a broader experience with different cooperative learning strategies in the classroom. There are many strategies in addition to “Think Pair Share” that are also great and seeing the same strategy over and over did not provide variation or keep me engaged as I read through the text.

There are a few key concepts that are not included in the text including Measurement & Data and Statistics & Probability.

The text also does not include an effective index and/or glossary. I have found that students do use the index and/or glossary that is typically in the back of the book to help them find information in the text quickly.

Content Accuracy rating: 3

The content is error-free however some of the images included on the PDF version are blurry and hard to read. There does not seem to be consistency between the different readable versions of the text.

There also seems to be a bias for the dots and boxes strategy throughout the text and the content lacks current practices of teaching concepts.

Just like any text, this textbook needs to be updated to match current best practices and research in math education. Since this text is Attribution-ShareAlike which allows “others to remix, adapt, and build upon your work even for commercial purposes, as long as they credit you and license their new creations under the identical terms” it does seem that updates and instructor/course-specific content will be relatively easy to implement as needed.

Clarity rating: 3

This text is written in a way unique way that makes it easier for students to read through and follow. It is very student friendly however might not be as useful as an instructor text since the instructor needs to fill-in-the-blanks on their own.

Consistency rating: 3

The text is written with consistent terminology however the framework for each chapter is not consistent. Some chapters include Explorations and additional sections while others end consistently with a problem bank.

Modularity rating: 3

The text is divided into smaller reading sections however the titles of each section are not easily recognized by students. Though I imagine the titles were meant to be creative for each section, having something more straight forward to make it easier for students to navigate is more important than creativity especially for future teachers who might be teaching these concepts for the first time.

Organization/Structure/Flow rating: 3

It would be good to organize the material consistently throughout the text (e.g.each section should end with a problem bank). The variation in the different sections can be confusing to both the instructor and student when trying to find something in the text.

I also noticed that the online version does not include page numbers while the PDF version does. This is not helpful when referring students to particular sections of the book. The PDF version also has many completely blank pages. I am not sure if this was meant to be on purpose (for printing purposes) but these pages can be very distracting to the reader.

Interface rating: 2

Navigation throughout the text is fine however, there are noticeable differences between the online and PDF versions of the text. The images in the PDF versions are noticeably blurry and lower quality than those in the online version. In some instances, it seems as though images were screenshot and copied and pasted which could account for the image quality.

Some images, in particular, should not have been included at all and are unreadable, for example, the Hokulea on page 441.

I did not notice grammatical errors.

The connection to the Hawaiian culture was a nice touch.

I would use this text as a reference but would not adopt this book as the main text for my class.

Reviewed by Thomas Starmack, Professor, Bloomsburg University of Pennsylvania on 3/26/20

The book is somewhat dated and does not include current research based best practices like concrete, representational, then abstract. Like most authors, they make assumptions that students have the ability to understand abstract and start the... read more

The book is somewhat dated and does not include current research based best practices like concrete, representational, then abstract. Like most authors, they make assumptions that students have the ability to understand abstract and start the lesson there, which is contradictory to how the brain works and what current research says about effective math instruction and learning.

I agree the content is accurate, but in many areas the learner must have a very strong understanding of mathematical concepts, structures, and applications. There lacks current best practice and current NCTM recommendations to approaching the teaching of mathematical content.

Relevance/Longevity rating: 1

Although mathematical concepts at the elementary level remain the same, the approach to engaging students in learning and the methods of instruction have evolved greatly. The book lacks many of the newer approaches and is outdated. The arrangement of the concepts is okay. I would recommend that the big ideas of teaching math are in the beginning and providing an overview of what is mathematics and best approaches to teaching/learning mathematics. Then scaffold the specific concepts. Fractions is one of the most complex and abstract, and this book starts there as a first topic.

Once again, the book is okay in terms of math learning but dated on best practice approaches. The book does not use jargon per say, but does not provide the best approaches for students to learn how to effectively teach mathematics.

Consistency rating: 4

Yes the book is consistent throughout.

The text is divisible, just not relevant to today nor provides current approaches. The order of the content is not in line with a methods of teaching course I would follow.

Organization/Structure/Flow rating: 2

I think the topics are clear but dated and not in the order as described above.

The text provides a variety of interfaces, none of which are confusing for the student who has a very strong math background. The text does mislead students to think starting with abstract is how to instruct elementary students, which is contradictory to brain research and current best practices.

Grammatical Errors rating: 4

I did not notice any grammar errors.

Cultural Relevance rating: 3

I think the text is culturally appropriate. Not certain about the final chapter as it focuses on one population. Having a chapter or theme woven throughout the text that provides students with a stronger understanding that although mathematics is a universal language, there are cultural differences to teaching and learning as evidenced in the 1999 TIMSS report.

The text is outdated. The text is an okay resource but I would not be able to use as the main guide for learning in a college level methods of teaching elementary mathematics course.

Reviewed by Jamie Price, Assistant Professor, East Tennessee State University on 3/20/20

This book introduces the reader to the standards for mathematical practice (SMP) from the Common Core standards in the introduction. I appreciated this as these standards cover all grades and are a unifying theme of the Common Core standards, yet... read more

This book introduces the reader to the standards for mathematical practice (SMP) from the Common Core standards in the introduction. I appreciated this as these standards cover all grades and are a unifying theme of the Common Core standards, yet many times overlooked. In addition, many states, including mine, that are not following Common Core directly have adopted the SMPs. The book does not cover two of the mathematical strands, namely measurement and statistics/data. Among the strands that are covered, however, the author does a thorough job of explaining the content, using a unified theme throughout, such as dots and boxes introduced in place value that appear again in number operations. I particularly liked the final chapter of the book and its connection to Hawaiian culture. The author could easily incorporate ideas related to teaching and learning measurement into this chapter in order to make the book more comprehensive.

The content was very accurate. I did not come across any mathematical errors or biases. The author did a good job of incorporating "think, pair, share" elements throughout each chapter as a model for future teachers. To further guide future teachers, I would have liked to see the author include information in each chapter about common misconceptions students have when learning the related material and ideas on how to address those misconceptions. In my experience, I find that pre-service teachers are unaware of these misconceptions and it is helpful to make them aware of them so that they can anticipate them in their own classrooms.

The content presented in this book is up-to-date and will remain relevant for a long time. Due to the fact that this book focuses more on content rather than methods, I do not foresee a need for many updates moving forward.

The book is written in a very clear and concise way that is approachable to future and current elementary teachers. The author presents key words in bold throughout the book to draw attention to them. I liked the way that the author included videos as well as written explanations of ideas, such as in the Number and Operations chapter, section titled Addition: Dots and Boxes. The author explains, in words, how to use this method to add multi-digit numbers and follows the written example with a video explanation. This helps to reach a variety of learners and learning styles. The author also addresses common "jargon" associated with particular mathematical concepts, such as proper and improper fractions (section titled What is a Fraction?), and discusses how this jargon can be misleading for students.

Each chapter in the book includes an introduction, multiple opportunities for think-pair-share discussions, and several problem sets to practice. I appreciated the consistency in the Dots and Boxes method introduced in the Place Value chapter and then carried into the Number and Operations chapter.

The book uses a modular approach to present the material. Each module contains numerous sections that help to break up the content into smaller chunks so that the content does not seem overwhelming. The modules are set up in an order that makes sense for the mathematics, but a reader could begin reading at any module and still make sense of the content.

The organization of the topics makes sense according to the mathematics presented and is logical.

I did not find anything distracting or confusing in relation to the interface of the text. The book was easy to navigate, with a clearly defined table of contents. I was able to easily click through the various modules and sections within each module. The book uses figures well to provide engagement to the reader as well as to further clarify content. The use of videos embedded within the modules helps to strengthen understanding of the content. It did take me a minute to find the navigation link that allowed me to move to the next section in a module (right arrow at bottom right corner of the page), but once I found it I was able to navigate seamlessly to each subsequent section.

I did not find any grammatical errors in the text.

In my opinion, this was one of the biggest strengths of this text. The author did a nice job of incorporating Hawaiian culture into the text. For example, the author includes an image in the Place Value chapter (Number Systems section) that references the use of tally marks on a sign at Hanakapiai Beach. In addition, a full chapter was devoted to Voyaging on Hōkūle`a. I particularly liked how the author connected this idea to beginning teaching of elementary mathematics and encouraged future teachers to think about ways to see mathematics outside of traditional mathematical settings.

I am glad that I came across this resource. I primarily teach math methods courses for elementary pre-service teachers, but I found many aspects of this text that I can incorporate into my classes to help students think more deeply about the mathematics that they will teach. I appreciated the author's attempt to challenge students in their thinking about elementary mathematics. Initially, I was surprised to find that there was no "answer key" provided for the many problem sets that were included throughout the text. After reading the quote presented on the introductory page to the Problem Solving chapter, I realized that this may have been an intentional decision made by the author to encourage readers to go beyond "a trail someone else has laid." I find that many pre-service elementary teachers want to "just know the answer" when it comes to mathematics; a no answer key approach will encourage discussion and justification, two elements important to ensuring equity in the teaching and learning of mathematics.

Reviewed by Shay Kidd, Assistant Professor- Mathematics Education, University of Montana - Western on 12/30/19

The content that elementary teachers need to have that is not covered in this book is graphing, probability, statistics, exponents, visual displays of data. The coverage of operations is very specific in the examples and does not cover the wide... read more

The content that elementary teachers need to have that is not covered in this book is graphing, probability, statistics, exponents, visual displays of data. The coverage of operations is very specific in the examples and does not cover the wide range that should be presented in this type of text.

Content Accuracy rating: 4

While the core topics presented are correct, the number of problems that are provided without any solutions is alarming. The majority of problems that are provided are meant for the reader to perform but do not provide any type of answer key for checking the work. In this way, the book seems to assume the reader to have a solid knowledge of the topics already and this book discusses a few different approaches to these topics.

The specific content presented is up-to-date and usable.

The book's prose seem to be more of a teaching guide than a textbook. This is nice for the conversational aspect that a reader may want in their learning, but should be explained more or possibly a change of title for the book. Something more like "Exploring the concepts of Elementary Mathematics" would provide a more reading friendly approach the book offers.

The author has a consistent voice of teaching and presenting the material.

Modularity rating: 2

The break-up of the text with boxes is difficult to follow the purpose of each box. While some of the box styles are clear, such as the think, pair, share or problem boxes, others seem to break up the line of discussion. A problem box may be discussed more directly immediately following the box and the presentation of the problem. Most of the problem boxes are not discussed again in the main text. This cased issues for wanting to read with a specific purpose. When the reader wants to understand a problem more, there is generally not more discussion, but unclear about when that would be provided or not. Other times boxes were used without any "box type" provided and these were just to break up the flow of the text.

Place value was a major topic to start the book and had good coverage, then operations and fractions were discussed, then a return to place value with decimals. It would seem that a connection of place value and decimals would work better to follow the other place value discussion.

Interface rating: 3

There are several pages that have large blank parts or are totally blank. This may be due to the PDF version that I chose. When I did use the internet-connected version, there seems to be a dependence on youtube to help do some of the teaching.

There are a few minor issues that would be resolved with a good proofread.

The book does seem to be written with the Hawaiian culture in mind. This may be difficult for other cultures to connect to or understand but does not present any insensitivities.

The book's title suggests a full discussion of the topics that elementary education pre-service teachers would need to know and teach, but this book is very lacking in the topics required for this. I selected this book to review because I teach classes that would use the textbook, but I would not use this textbook as is. There are a few topics that I plan to add to my own instruction, but the book as a whole needs additional help to be able to stand alone. This really appears to be a teaching guide based on the constant think-pair-share setup. This also is a specific teaching and method that seems to require the students to already have much of the content mastered. It does not teach all the content that is required to the level of the discussion had.

Reviewed by Ryan Nivens, Associate Professor, East Tennessee State University on 10/25/19

The book covers all the expected mathematical strands except for measurement and data/stats. There are some obvious connections to the strands of mathematical practice from the Common Core standards. While the abstract specifically lists MP1, MP2,... read more

The book covers all the expected mathematical strands except for measurement and data/stats. There are some obvious connections to the strands of mathematical practice from the Common Core standards. While the abstract specifically lists MP1, MP2, and MP3, the introduction clearly lists all 8. The chapter "Voyaging on Hōkūle`a" contains activities that will require use of measurement and units, but there is no explanation on how measurement topics should be taught or approached. However, this chapter does provide a good project-based learning set of materials, and is an exceptional resource for navigation. The book also includes a chapter on Problem Solving, which is important for those students who must complete the EdTPA and address the 3rd subject specific emphasis area. All embedded links to Youtube videos or Vimeo videos are working and play within the textbook pages.

I find the mathematics to be entirely accurate. There are many teaching strategies, such as "think pair share" that are found throughout the chapters. This is particularly helpful for future teachers.

This book should last a very long time in terms of relevance.

This book is very clear, with mathematical words in bold and proper definitions provided. The text also addresses common math classroom jargon. For an excellent example of this, see the heading "What is a Fraction" in the chapter on Fractions. Toward the bottom is a sub-heading "Jargon: Improper Fractions" that has students consider the usefulness of proper and improper fractions.

This book is consistently laid out, with multiple examples, problems to try, and diagrams to support the transfer of information.

This book is entirely modular. You can pick it up, and easily start in any chapter and not be lost. The heading, subheading, use of italics and boldface make it easy to locate information. As a mathematics education book, this is quite nice.

A mathematician wrote this, the layout is logical without question.

The book is extremely easy to navigate, with a logical structure to the table of contents that you can easily click through. A drop down menu in the upper left corner allows you to view the outline of the book while still viewing a page, and you can collapse/expand chapters within the menu.

The many figures that are present throughout the textbook are perfectly displayed and fit the reading material.

There is nothing I find distracting in the layout and interface.

I could not find any errors.

An entire chapter is dedicated to Voyaging on Hōkūle`a, with exceptional videos and diagrams to illustrate the cultural practices of the early Polynesians.

I was excited to find this book in the Open Educational Resources library. As a professor who frequently teaches methods courses in mathematics for elementary teachers, I feel that this book may be a terrific book to use to replace previous texts that I've adopted. I would like to see a chapter on Measurement to make the Voyaging on Hōkūle`a chapter more useful. It is obvious from the first page you open to that this book was well planned and thought out. I'm impressed.

Reviewed by Monica Rose Gilmore, Graduate Student, CU Boulder on 7/1/19

This textbook goes into depth about different mathematical concepts that are important for elementary school teachers to understand in teaching mathematics. However, the text is missing a focus on statistics and probability, which are key areas of... read more

Comprehensiveness rating: 3 see less

This textbook goes into depth about different mathematical concepts that are important for elementary school teachers to understand in teaching mathematics. However, the text is missing a focus on statistics and probability, which are key areas of focus in elementary math classrooms. The text is also missing an index or glossary but does define new terms as they are introduced.

The content, mathematical diagrams and depictions are accurate and error-free. Each chapter also accurately shows various ways to understand mathematical concepts. However, the diagrams are geared towards an audience that already has some understanding of advanced mathematics.

The content is organized in a way that necessary updates would be straightforward to implement. More specifically, much of the content reflects current mathematical practices and activities endorsed by up-to-date research in mathematics education.

The text is written in accessible prose and provides context for jargon and technical terminology. Additionally, the text clearly separates different terms for different strategies and concepts. For example, in the Problem Solving Strategy section, the interface is divided into different strategies for the reader to explore. This is helpful in keeping new concepts and strategies organized for the reader.

The text is written with consistent terminology. More specifically, the text consistently gives examples of what concepts are called by mathematicians and teachers. This is helpful for pre-service teachers that might be teaching mathematical concepts and strategies for the first time.

The text is easily divided into smaller reading sections. These sections include not only explanations of mathematical concepts, but also theorems, activities and diagrams which can be referenced by the teacher at any point. Also, the text gives teachers ideas for activities and additional problems to try with students.

Though the topics in the texts are presented in a logical, clear fashion, it might be beneficial for pre-service or elementary teachers to see how to specifically scaffold the different concepts within those topics for elementary students at different grade levels. Additionally, the text could also demonstrate how students typically confuse topics so teachers and pre-service teachers are prepared to navigate new concepts for the class.

The interface is easy to navigate since the content clearly outlines chapters and the topics within them. Sections such as notation and vocabulary, think pair shares and theorems are clearly outlined, organized and conceptually scaffolded. However, it might be helpful to have an index so the reader does not have to click within each topic to find the concept they are exploring.

This text is free from grammatical errors.

This text is not culturally insensitive or offensive and includes examples from the Hawaiian culture. Though the text is mainly made up of mathematical explanations, there are a variety of people's names in different problems that could be attributed to a variety of cultures. Additionally, the text reflects Polya's advice (1945) to try adapt the problem until it makes sense. Though the text includes mainly mathematical explanations, it does call for adapting problems which could potentially be applied to a variety of students of different backgrounds.

Reviewed by Glenna Gustafson, Professor, Radford University on 5/22/19

This is book is fairly comprehensive and I feel could be used by most foundational courses in elementary mathematics. The structure and writing provide a good foundation for students learning the "why" behind the mathematics and becoming... read more

This is book is fairly comprehensive and I feel could be used by most foundational courses in elementary mathematics. The structure and writing provide a good foundation for students learning the "why" behind the mathematics and becoming mathematical thinkers. There were some areas that could possibly use more development. In geometry for example there was no discussion of perimeter, area, and volume. Estimation, measurement of weight, time, and probability also appears to be missing. The text is well organized and written so that the chapters do not have to be completed in the order in which they are presented. While there is not index or glossary, the author uses colored text boxes to explain specific content or terms.

The content of the text is accurate and represented in a variety of formats to support learning, Not only does it provide solutions to problems, but also the mathematical thinking behind those solutions.

The text is very relevant for K-6 elementary pre-service teachers. It would be beneficial to know the specific grade levels that the author considers as "elementary" since this does vary by location. The content is "standard" for most elementary math courses and would not need to be updated often and the consistent layout and formation would make changes easy to make.

The text is written in a conversational tone. The simplicity and straight-forwardness of the text should appeal to those students that have sometimes been overwhelmed by writing in more traditional math texts.

The text is organized consistently from chapter to chapter. The table of contents and chunking of content in the chapters is logical and clear, Each chapter includes graphics as well as sections for: Think-Pair-Share; Definitions; Theorems (when appropriate); and, Problems. This consistent structure makes navigation easy.

The table of contents and chunking of content in the chapters is logical and clear. This also makes it easy to not necessary to move sequentially through the text, but to have the option of reviewing or using only needed topics. Subtitles and graphic captioning are appropriate for the content.

The text is easy to read and the organization within each chapters makes navigation easy.

This text is easy to navigate. The inclusion of graphics, charts, photos, and videos support learning. There are several pages where graphics in the Geometry chapter are skewed in the PDF version, but this does not seem to be a problem in the online version, Not all of the video links work within the PDF version.

There were no obvious grammatical errors. Several of the errors that were found were typos and/or word omissions.

The text is culturally inclusive. One thing that should be noted is that it seems male names are over-represented in the Problem sections. A reference to Hawaiian culture and life is evident. The Hōkūle`a voyage found in the last chapter is a good example of problem based learning and the integration of math with other subject areas.

This would be a wonderful text to use as a supplement or compliment to an elementary math methods course. It is not as overwhelming as other math texts, and would provide pre-service teachers with a good foundational review of math concepts, including vocabulary and some pedagogy.

Reviewed by Karise Mace, Mathematics Instructor, Kuztown University on 5/16/19, updated 11/9/20

This book is fairly comprehensive for a one-semester course, although it does not include much detail about several topics. The section on number systems barely touches on Roman numerals and only mentions Mayan and Babylonian counting systems.... read more

This book is fairly comprehensive for a one-semester course, although it does not include much detail about several topics. The section on number systems barely touches on Roman numerals and only mentions Mayan and Babylonian counting systems. The sections on addition, subtraction, and division would be more robust if the author included other algorithms for these operations. The chapter on Geometry does not address perimeter, area, surface area and volume. The book does not include an index or glossary.

While the book is not error free, it is unbiased. Most of the errors seem to be typographical and/or related to web links or LaTeX. In the section on number systems, the author incorrectly explains how one million would be represented using Roman numerals and incorrectly claims that the Mayans did not use a symbol for zero. Further, the Mayan number system was not a true vigesimal system, as the text indicates.

This text uses a constructivist approach to help students build their understanding of the mathematics included in the book. It is well organized and written so that the chapters do not have to be completed in the order in which they are presented. Because of this, the text should be easy to update. When concepts that are presented earlier in the text are used in later chapters, the author includes a brief but thorough review that would allow students to understand the later chapter even if they had not read and completed the problems in the earlier chapter. The "dots and boxes" approach is timely, as it uses the idea of the "exploding dots" that are part of the Global Math Project (https://www.globalmathproject.org).

The textbook is clearly written and enjoyable to read...even for the math-phobic student. The tone is conversational and is even funny at times. The author defines important mathematical terminology in a way that is both mathematically accurate and accessible to students. The chapter on problem solving is fantastic and really gives students insight into how to think and problem solve like a mathematician. The pies per child model for fractions is not the most effective model for helping students understand fractions and this part of the text would be improved if the author replaced this type of modeling with pattern block modeling.

Overall, the text is consistent in its chapter structure and terminology use. However, there is inconsistent notation when using "dots and boxes."

The text is well-organized but can be reorganized in order to suit an instructor's preference. However, it would be best to complete the chapter on problem solving first, as it sets the stage for the rest of the book. Most of the chapters are structured more like an activity book with lots of great problems and thought provoking questions that will help students think deeply about the mathematical concepts being presented. With the exception of the chapter on problem solving, there is not a whole lot of text for students to read.

Although the topics presented could be reorganized to meet student needs, the order in which they are presented is logical and clear.

With only a few exceptions, the images it the text are clear. In the section titled "Careful Use of Language in Mathematics: =" some of the scale images need to be modified so that the items on the scale appear to actually sit on the pans. The same issue occurs in the section titled "Structural and Procedural Algebra." Some of the images in the sections titled "Platonic Solids" and "Symmetry" spill off of the page. The image that appears on page 89 and then again on page 144 would be more clear if a different font was used to label the line segments.

No grammatical errors were noted. However, there were a few typographical errors that could cause confusion for students as on page 219.

The text was culturally sensitive and nothing offensive was noted. As the focus of the text is purely mathematical, there are not many cultural references at all, unless they are references to historical cultures. The author does use names for hypothetical students that are diverse and represent a variety of ethnicities. The last chapter is an integrated unit that focuses on the Hawaiian culture. Unfortunately, the links and web addresses in this chapter do not work and/or are no longer active.

The book includes three sections at the end of the problem solving chapter in which the author articulately explains the language that mathematicians use to succinctly and precisely explain their problem solving and solutions. These sections will help students who may not think of themselves as mathematicians learn to think like mathematicians. So many mathematics textbooks are full of exercises but no true problems. On the other hand, this text is full of wonderful problem solving and critical thinking problems that are embedded in the sections as well as in the problem banks. The author also includes many "Think/Pair/Share" exercises and questions that will facilitate mathematical thinking and conversation among students. The constructivist approach used by the author will help students build deep understanding about the mathematics covered in the text. While there is some room for revision and improvement, this is a very good text to use with elementary education majors, and I definitely plan to use this book the next time I teach them.

Reviewed by Desley Plaisance, Associate Professor, Nicholls State University on 4/29/19

This textbook seems to be appropriate for the first course typically taught for elementary teachers which usually includes topics of problem solving, place value, number and operations. Most books are able to be used for a second course which... read more

This textbook seems to be appropriate for the first course typically taught for elementary teachers which usually includes topics of problem solving, place value, number and operations. Most books are able to be used for a second course which focuses on geometry. This book could not be used for the second course.

Content seems to be accurate.

Topics are somewhat static for a course like this, so the textbook will not become obsolete within a short period of time.

Appears to be clear.

The flow from topic to topic is consistent in presentation.

Divided into clear sections.

Topics are presented logically and in a similar order to most books of this type.

Easy to navigate with clear images and other items such as tables.

Book is written in simple language and appears to be free of grammatical errors.

Appears to be culturally diverse.

This book could definitely be used for a first course of elementary math for teachers with the teacher providing resources. As with many open books, the print and layout is very simple without cluttering pages with unnecessary items.

Reviewed by Lisa Cooper, Assistant Professor, LSUS on 4/26/19

This text covers many concepts appropriately; however, a few concepts are missing, such as; data analysis and statistics. For more than ten years, data-driven instruction has been a major focus in education along with many other uses. This text... read more

This text covers many concepts appropriately; however, a few concepts are missing, such as; data analysis and statistics. For more than ten years, data-driven instruction has been a major focus in education along with many other uses. This text has a table of contents but not an index and/or glossary; however, does define words in chapters when needed.

The content is well organized and accurate. Multiple representations and diverse examples are provided throughout the text which supports an unbiased approach to those entering elementary education.

The text is quite relevant to the classroom today, incorporating such resources as YouTube, varied strategies to promote differentiated instruction, scaffolding between concepts, and problem-solving opportunities. Some states may find issues with Common Core standards being addressed; however, mathematical practices could be interchanged with the "standards."

The text is written free from educational jargon; it is straightforward and easy to understand.

The text is consistent in its structure; color is not distracting, problems, strategies, diagrams, charts, and definitions are provided throughout.

The text is appealing with the page layout; it's not too busy or distracting. Colors are attractive and text is broken down into appropriate amounts.

The text has a well-organized flow with the layout of each topic/chapter.

The text has charts, pictures, diagrams, real-world examples throughout; several different versions of the text are offered too.

No grammatical errors were observed in my review of the text.

The text provides a variety of backgrounds, races, and ethnicities while providing learning experiences and pedagogical approaches to support student engagement and learning.

Reviewed by Demetrice Smith-Mutegi, Instructor/Coordinator, Marian University on 3/6/19

This text covers place value, numbers and operations, fractions, patterns, algebraic thinking, decimals, and geometry. However, elementary teachers are expected to also know and understand statistics and probability. This text does not address... read more

This text covers place value, numbers and operations, fractions, patterns, algebraic thinking, decimals, and geometry. However, elementary teachers are expected to also know and understand statistics and probability. This text does not address this mathematical concept.

The text makes non-traditional, yet, accurate representations of mathematical concepts. In some sections, different solutions are presented and explained. This eliminates bias and provides a diverse representation of ideas when solving math problems.

The text is representative of common core problem-solving standards, however, it does require mathematical knowledge beyond elementary school. The problem-solving nature of the text is very relevant to elementary pre-service and in-service teachers (the audience for the book).

The text language is clear and accessible. There is a section on terminology, which is very helpful. Additional diagrams would help to improve the clarity in some cases.

I was expecting to see videos embedded throughout, after seeing them in the first section. It would be great to have a consistent format throughout the text, however, I understand that it is not always feasible to do so. There were other obvious and clear patterns presented, color-coded sections (think/pair/share), problems, examples.

The chapters and subchapters can be easily accessed, breaking the material into smaller sections.

The topics were presented in a logical, clear fashion, however, not all of the chapters would end with a problem bank. In some cases, there were additional sections after the problem bank. It would be great if each section included key objectives or goals of the section.

The text comes in pdf, XML, and an online web version. The search feature on the online version was a valuable addition.

I did not observe any obvious grammatical errors.

Cultural awareness was very obvious in this text. While it was more relevant to Hawaiian culture, it also included cultural awareness of other cultures and backgrounds.

Overall, this text assumes that the student has successfully completed mathematics through basic calculus. There should be more support in this area, as some elementary math students are not prepared to complete problems with this focus.

This a great "discussion" text.

Reviewed by Kandy Noles Stevens, Assistant Professor of Education, Southwest Minnesota State University on 12/28/18

This text covers the areas applicable to elementary mathematics extremely well (with the exception of omitting probability and data analysis) and provides graphically visual boxes within the text to define terms and instructional strategies. ... read more

This text covers the areas applicable to elementary mathematics extremely well (with the exception of omitting probability and data analysis) and provides graphically visual boxes within the text to define terms and instructional strategies. Additionally, the text provides thinking routines that support understanding more than just the concept, but also, the how's and why's of conceptual understanding.

The content is accurate and organized in a way to supports student learning for those training to become elementary teachers of mathematics.

The content of the book is relevant to today's elementary classroom in that it provides future elementary educators with the content knowledge, but also pedagogical approaches that would support student learning. Additionally, the text is organized in a way that is consistent and provides scaffolding support for those who might struggle with any one of the concepts. For Minnesota standards the only item of note is that there is not a section devoted to probability or data analysis, but the latter is touched upon in other chapters. There are three mentions of the Common Core standards in the text. Minnesota is not an adopter of the CC mathematics standards, but the references to the CCSS are in regards to the practices of mathematics and not on standards specifically.

While a great text for training future math teachers, this book does not read as a "typical" mathematics textbook. Students who have struggled in the past with mathematics might find the authors' writing style to be approachable and accessible for all levels of mathematics competence and confidence.

The text is consistent in its terminology and the structure of the framework is uniform throughout, relying on supporting student learning through exercises, think-pair-share activities, and continuous dialog and reflection.

A majority of the chapters begin with a section that introduces the strand of elementary mathematics covered. Not all chapters have this introduction which may pose challenging to interrupt the mathematical progression of some established courses.

The text is very well organized and has an easy-to-read format and flow.

The text is graphically rich with succinct advanced organizers, diagrams, and photos to support learning.

The text is written with professional level writing and is free of grammatical errors.

A variety of races, ethnicities, and backgrounds are present in the exercises used to support student learning throughout. The end of the text involves a Hōkūle`a voyage as a part of a problem-based learning (integrated curriculum) experience. This was something that really made this text stand out in that it gave future elementary teachers an example of using mathematical concepts in authentic (and exciting) learning experiences. This Polynesian voyage would provide many students with an introduction to life culturally different from their own.

I have been a STEM educator for more than two decades and I come from a long line of mathematics educators. While wrapping up my reading of this text, I happened to have my father (a 46 year veteran mathematics educator) here visiting. I shared the text with him and several times I heard him utter, "I like the way this problem is set up". We both found the book to be very knowledgeable for mathematical conceptual understandings, but even more so for introducing ideas for instructional strategies and classroom discourse to help future teachers become equipped with speaking the "language of mathematics" to guide their future students.

Table of Contents

I. Problem Solving

• Introduction
• Problem or Exercise?
• Problem Solving Strategies
• Beware of Patterns!
• Problem Bank
• Careful Use of Language in Mathematics
• Explaning Your Work
• The Last Step

II. Place Value

• Dots and Boxes
• Other Rules
• Binary Numbers
• Other Bases
• Number Systems
• Even Numbers
• Exploration

III. Number and Operations

• Addition: Dots and Boxes
• Subtration: Dots and Boxes
• Multiplication: Dots and Boxes
• Division: Dots and Boxes
• Number Line Model
• Area Model for Multiplication
• Properties of Operations
• Division Explorations

IV. Fractions

• What is a Fraction?
• The Key Fraction Rule
• Adding and Subtracting Fractions
• What is a Fraction? Revisited
• Multiplying Fractions
• Dividing Fractions: Meaning
• Dividing Fractions: Invert and Multiply
• Dividing Fractions: Problems
• Fractions involving zero
• Egyptian Fractions
• Algebra Connections
• What is a Fraction? Part 3

V. Patterns and Algebraic Thinking

• Borders on a Square
• Careful Use of Language in Mathematics: =
• Growing Patterns
• Matching Game
• Structural and Procedural Algebra

VI. Place Value and Decimals

• Review of Dots & Boxes Model
• Division and Decimals
• More x -mals
• Terminating or Repeating?
• Operations on Decimals
• Orders of Magnitude

VII. Geometry

• Triangles and Quadrilaterals
• Platonic Solids
• Painted Cubes
• Geometry in Art and Science

VIII. Voyaging on Hokule?a

• Worldwide Voyage

Ancillary Material

About the book.

This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations. The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will: • Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more. • Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete). • Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students. Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.

About the Contributors

Michelle Manes, Associate Professor, Department of Mathematics, University of Hawaii

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14 Best Books for Math Teachers

By Med Kharbach, PhD | Published: June 18, 2023 | Updated: November 8, 2023

Books for math teachers is the topic of our blog post today!

Now, I know what you’re thinking—I’m more at home dissecting sentence structures than quadratic equations. That’s right, my wheelhouse is language, but I’ve donned my researcher cap to curate a list that’ll have every math teacher reaching for their “#1 Teacher” mugs. Why? Because great teaching knows no boundaries and I wanted to delve into what makes math classrooms tick.

After sifting through top-ranking lists, diving into reviews, and even picking the brains of some math-savvy colleagues, I’ve put together a collection of books that are making waves in math education. These reads range from exploring the cognitive science behind math learning to giving you hands-on activities that even Pythagoras would high-five you for.

So even if you, like me, have felt that math is like a foreign language, these books aim to make it a universal one. Whether you’re a math teacher, or just math-curious like me, you’re going to find something in this list to spark your interest and maybe even improve your craft.

[ Related: Best Project-based Learning Books for Teachers ]

Books for Math Teachers

Here are our top picks for books for math teachers:

1. Building Thinking Classrooms in Mathematics , by Peter Liljedahl

Building Thinking Classrooms in Mathematics by Peter Liljedah is a guide to help teachers create an ideal setting for deep mathematics learning. It is based on 15 years of research and offers 14 teaching practices that can be used to engage students in meaningful thinking. These practices are designed to improve the way teachers facilitate learning and create an environment that encourages students to think deeply.

2. Making Sense of Math , by Cathy L. Seeley

In Making Sense of Math, Cathy L. Seeley encourages teachers to nurture habits of mind that help students become analytical and adaptive problem-solvers. She stresses the importance of incorporating mathematical building blocks into instruction, as well as turning traditional teaching styles “upside down” by placing more emphasis on discussion and analysis.. Making Sense of Math is a recommended read by the National Council of Teachers of Mathematics.

3. Math Fact Fluency, by Jennifer Bay-Williams, Gina Kling 

In Math Fact Fluency authors Jennifer Bay-Williams and Gina Kling provide a comprehensive guide for teaching, assessing, and communicating basic math facts. This book offers five fundamentals of fact fluency based on research-based frameworks for effective instruction in the basics.

In addition, readers can find strategies students can use to remember facts, over 40 engaging games and 20 assessment tools, as well as strategies for collaborating with families.

4. What’s Math Got to Do with It? , by Jo Boaler 

What’s Math Got to Do with It? by Jo Boaler is an indispensable resource for those looking to improve their children’s mathematical learning. This revised edition includes updated research findings on the brain, mathematics, and the Common Core standards, as well as advice on how to teach mathematics with a growth mindset.

The book also provides teachers and parents with all the practical tools to create meaningful math learning experiences in and outside class.

5. Why Write in Math Class? , by Linda Dacey, Rebeka Eston Salemi, Kathleen OConnell Hopping 

Why Write in Math Class provides ideas to help students construct, explore, and reflect on mathematical ideas. It offers teachers a chance to gain insight into student thinking as well as practical advice for how to support writing in math, along with a variety of examples of writing prompts and tasks.

The stories and samples of student work from K-5 classrooms provide insight into how writing in math class can successfully unfold.  Definitely a good resources for math teachers.

6. Math Recess: Playful Learning in an Age of Disruption , by Sunil Singh, Christopher Brownell 

Math Recess: Playful Learning in an Age of Disruption is a book written by Sunil Singh and Christopher Brownell that encourages readers to explore mathematics in a playful and engaging way.

The book provides parents, teachers, and administrators with creative ideas for mathematical puzzles and problems. Math Recess promotes math as a joyful and meaningful activity that can be enjoyed for many years to come.

7. Real-World Math: Grades 5-8 , by Genene Rhodes

Real-World Math: Grades 5-8, by Genene Rhodes, is a comprehensive educational resource for teachers and students alike. It provides meaningful and relevant learning experiences that make math concepts easier to understand in the context of real-world situations. Real-World Math focuses on the development of critical thinking skills, problem-solving strategies, and higher-order thinking processes.

Real-World Math covers a range of topics, including addition, subtraction, multiplication, division, ratios, graphs and charts, logical reasoning, percents, basic geometry, time, decimals, and fractions, among others.

8. Elementary and Middle School Mathematics , by John Van de Walle, Karen Karp, Jennifer Bay-Williams 

Elementary and Middle School Mathematics provides pre-service teachers with the necessary tools to become effective math teachers. Written by John Van de Walle, Karen Karp and Jennifer Bay-Williams, this book seeks to help teachers create an environment where all students can learn mathematics in a thoughtful and engaging manner.

The authors back up their arguments sample instructional activities, tables and rubrics. with real student work help readers visualize what good mathematics instruction looks like while new common challenges and misconception tables assist in examining student progress more closely. Elementary and Middle School Mathematics: Teaching Developmentally is a valuable resource for any pre-service teacher looking to develop their mathematics teaching pedagogy.

9. Mastering Essential Math Skills Fractions , by Richard W. Fisher 

Mastering Essential Math Skills Fractions, by Richard W. Fisher, is a comprehensive guide to mastering fractions and making math fun and easy.

The book is perfect for students who have struggled with fractions in the past and are looking for an easier way to learn. Each lesson is presented in clear language, with step-by-step solutions and helpful hints.

Additionally, the book includes Problem Solving exercises for students to practice applying their newfound math knowledge to real-life situations. The book also provides free access to video tutorials online, as well as a solutions section with answers to all problems.

10. 5 Practices for Orchestrating Productive Mathematics Discussions , by Margaret Smith, Mary Stein

The 5 Practices for Orchestrating Productive Mathematics Discussions, by Margaret Smith and Mary Stein, provide a framework for facilitating effective inquiry-oriented classrooms.

This framework entails anticipating what students will do and the strategies they will use in solving a problem, monitoring their work as they approach the problem in class, and connecting the strategies and ideas in a way that helps students understand the math.

Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance is also included as an addendum to this book. Productive Math Struggle provides teachers with six points of action for helping students become more comfortable with experiencing and overcoming mathematics challenges. Each point is designed to help teachers build a culture of learning through struggles, where mistakes are seen as opportunities to learn, not failures.

11. Productive Math Struggle , by John J. SanGiovanni, Susie Katt, Kevin J. Dykema 

Productive Math Struggle by John J. SanGiovanni et al., provides teachers with an action plan to value and harness student struggle and make the best of their math learning.

It offers actionable steps, activities, and tools for implementation as well as instructional tasks representative of each grade level along with real-world examples showcasing classroom photos and student work. Productive Math Struggle helps teachers create a game plan for overcoming obstacles.

12. Making Number Talks Matter , by Cathy Humphreys, Ruth Parker 

Making Number Talks Matter by Cathy Humphreys and Ruth Parker is another good math book for teachers. It offers an innovative approach to teaching mathematics in the classroom, applying 15-minute lessons that inspire and initiate math talks.

With vignettes from other teachers, Making Number Talks Matter explains how to listen closely to students and prompt them into finding solutions to problems. The book also provides sample problems, navigational tips, and ideas on how to respond to mistakes.

13. Principles to Actions: Ensuring Mathematical Success for All , by National Council of Teachers of Mathematics 

The Principles to Actions by the National Council of Teachers of Mathematics (NCTM), provides a comprehensive view on what it will take to turn the Common Core standards into reality in every classroom, school, and district.

This initiative articulates specific principles and actions – including specific teaching practices – that are necessary to ensure a high-quality mathematics education for all students.

14. Building a Math-Positive Culture , by Cathy L. Seeley 

In Building a Math-Positive Culture, Cathy L. Seeley provides guidance for school administrators looking to improve their math programs.

She outlines the three components necessary for success – recognizing and supporting effective teachers, moving from ideas to results, and overcoming obstacles – and provides examples of actions that can be taken to accomplish these goals. Seeley’s book is an invaluable resource for administrators seeking to create a math-positive culture in their schools.

In this deep dive into books for math teachers, we’ve covered a lot of ground—from cognitive science and hands-on activities to nurturing analytical thinking and fostering a math-positive culture. What’s clear is that these books offer diverse and research-backed approaches to teaching math, something I find incredibly valuable in our ever-evolving educational landscape.

Whether you’re a seasoned math teacher, a newbie, or even a parent or someone who’s just math-curious like me, this list offers actionable insights and techniques to elevate your understanding of math education. I’m eager to hear which titles resonate with you and if you have any gems to add to this treasure trove of resources. Let’s keep the conversation rolling and continually strive to enrich our math classrooms.

• National Council of Teachers of Mathematics
• Barnes & Noble
• Amazon best selling math books

Related Posts

Meet Med Kharbach, PhD

Dr. Med Kharbach is an influential voice in the global educational landscape, with an extensive background in educational studies and a decade-long experience as a K-12 teacher. Holding a Ph.D. from Mount Saint Vincent University in Halifax, Canada, he brings a unique perspective to the educational world by integrating his profound academic knowledge with his hands-on teaching experience. Dr. Kharbach's academic pursuits encompass curriculum studies, discourse analysis, language learning/teaching, language and identity, emerging literacies, educational technology, and research methodologies. His work has been presented at numerous national and international conferences and published in various esteemed academic journals.

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Early math review

Kindergarten, basic geometry and measurement, pre-algebra, algebra basics, high school geometry, trigonometry, statistics and probability, high school statistics, ap®︎/college statistics, college algebra, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra, 6th grade (illustrative mathematics), 7th grade (illustrative mathematics), 8th grade (illustrative mathematics), algebra 1 (illustrative mathematics), 3rd grade (eureka math/engageny), 4th grade (eureka math/engageny), 5th grade (eureka math/engageny), 6th grade (eureka math/engageny), 7th grade (eureka math/engageny), 8th grade (eureka math/engageny), algebra 1 (eureka math/engageny), geometry (eureka math/engageny), algebra 2 (eureka math/engageny), precalculus (eureka math/engageny), 3rd grade foundations (eureka math/engageny), 4th grade foundations (eureka math/engageny), 5th grade foundations (eureka math/engageny), 6th grade foundations (eureka math/engageny), 7th grade foundations (eureka math/engageny), 8th grade foundations (eureka math/engageny), integrated math 1, integrated math 2, integrated math 3, arithmetic (all content), algebra (all content), geometry (all content), get ready for 3rd grade, get ready for 4th grade, get ready for 5th grade, get ready for 6th grade, get ready for 7th grade, get ready for 8th grade, get ready for algebra 1, get ready for geometry, get ready for algebra 2, get ready for precalculus, map recommended practice, get ready for ap® calculus, get ready for ap® statistics, grade 6 math (fl b.e.s.t.), grade 7 math (fl b.e.s.t.), grade 8 math (fl b.e.s.t.), algebra 1 (fl b.e.s.t.), geometry (fl b.e.s.t.), algebra 2 (fl b.e.s.t.), grade 6 (virginia), grade 7 (virginia), grade 8 (virginia), grade 3 (fl b.e.s.t.), grade 4 math (fl b.e.s.t.), grade 5 math (fl b.e.s.t.), class 9 (od), class 10 (od).

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Science » Math & Statistics

The best books on teaching maths, recommended by alf coles.

What is the best way to teach maths? Maths teacher and author Alf Coles recommends books that offer some clues.

Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos

The Common Sense of Teaching Mathematics by Caleb Gattegno

Calculus by and for Young People by Donald Cohen

Teaching Mathematics: Towards a Sound Alternative by Brent Davis

Starting Points for Teaching Mathematics in Middle and Secondary Schools by Banwell & Saunders and Tahta

1 Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos

2 the common sense of teaching mathematics by caleb gattegno, 3 calculus by and for young people by donald cohen, 4 teaching mathematics: towards a sound alternative by brent davis, 5 starting points for teaching mathematics in middle and secondary schools by banwell & saunders and tahta.

What are these mathematics books you’ve chosen about?

Tell me more.

Within these books there is a sense of mathematics as a subject over which we can actually have some control, as something that is much closer to the humanities and aesthetic subjects where the role of the community plays a part. There isn’t some absolute truth of the matter, because actually mathematicians argue about definitions and about proofs and there’s a human dimension to it.

Following that through into the classroom, in some of these books there is a portrayal of classrooms or classroom cultures where children can be operating as mathematicians. Children can be creative and exploratory in their learning of mathematics, and that doesn’t have to come at the expense of their attainment on standard tests or their learning of those algorithms and procedures that are commonly the focus of maths teaching.

So if you ask “What’s 2+2?” and a child answers “3” is that allowed?

When someone has just made a slip I correct it and move on. But often when people make what might be classified as an error by the wider community, they’re just operating under a different set of assumptions. So rather than just saying “No, that’s wrong,” it’s often quite interesting to explore where their answer has come from. To give you an example from my own teaching, an activity I often organize at the beginning of a class — as a mechanism for everyone to learn each other’s names — is that a first person stands up and says “My name is John.” A second person then has to stand up and say, “You’re John and my name is Fred.” The third person has to stand up and say, “Your name is John, your name is Fred, and I’m Alf.”— and it goes on like that. Maybe there are 28 people in the class and at the end I say, “So, if we consider what’s just happened – how many names have been said altogether?” Clearly, the first person said one name, the second person said two names and the third person said three names and so on up to 28. But doing this activity with 11-year olds, someone will almost always say “The total number is 28 times 28.” That’s clearly wrong, but, in a sense, it’s an answer to a different thing that might have happened. Exploring what might have happened for 28 times 28 to have been the answer is actually a useful thing to do.

Why do they think it should be 28 times 28?

That would be the answer if everybody had said everybody’s name. That distinction is then quite useful and generally helps the class realize what they’ve got to do, which is to add up one plus two plus three all the way up to 28. So the perspective is not so much that there aren’t right and wrong answers, but that, in a sense, the answers are dependent on the set of assumptions you are working under. Obviously there are mistakes. We can just make mistakes in carrying out a process, and I’m not shying away from that. But at a more conceptual level, if there are mistakes that might be considered errors of understanding, rather than seeing those as deficits, it seems to me much more productive and actually a much truer way of viewing the situation to just say that these people are operating under different rules and we can then explore that difference.

Why do some of us, like me, do fine with most of our subjects at school, but come out feeling we’re really bad at maths? Is it badly taught or are some of us just not good with numbers?

I would distinguish being good with numbers and being good at maths. It does seem to be the case that some people feel much more comfortable working with numbers than others. But that doesn’t seem, to me, at the essence of what it is to be a mathematician or to be successful mathematically. What is valued and prioritized, particularly in the early years of school, is basically arithmetic and it doesn’t bear a strong relationship to the kind of skills you need to be successful at maths at ‘A’ level and beyond. I’m not suggesting they’ve got things wrong at primary school, you have to develop your sense of number and so on, but I think an emphasis on the quick recall of facts — which is often a characteristic that is used to distinguish between people who are good at maths and people who are not – isn’t a very important skill for higher levels of mathematics. At higher levels, being able to think through complex problems in a systematic way and not jumping to quick conclusions are much more important skills.

In answer to your question about why so many people feel differently about maths than other subjects, I do believe that when maths is presented in a very right/wrong manner, then, if you’re an adolescent and the rest of your experience is very fuzzy, it’s hard to spend time in this world where everything is black-and-white. When you’re interested in negotiating boundaries and navigating uncertainty and the relationships within that, why would you want to bury yourself away in a black-and-white world which clearly has no resemblance to your lived experience? It’s not my idea, but some people have suggested that as an adolescent, to really get into maths you’ve got to have had some kind of psychological damage. For some people, it can be an escape, a safe place. If you don’t need that safe place, why would you be interested in maths?

What do you make of the concern that the West or the US in particular – is falling behind in maths, compared to Asia?

I don’t have a lot of experience of education in the US. What little I do know suggests that the US takes quite a rote learning approach to teaching mathematics, with a focus on memorization. There have been big moves to try and shift that, but I understand that’s been one of the problems in the past. I have been to Japan to see some of the maths teaching there, and there was a much more conceptual focus compared to this image of teaching via memorization. In other words, the lessons I saw in Japan had a strong emphasis on children problem-solving, and on sharing approaches to problems. There is always an interesting balance between developing a conceptual understanding and developing a fluency with procedures, and the Japanese children were developing a high level of skill, but in the context of solving problems that made sense to them. That would be one story for me of why there are some very good mathematicians coming out of Japan. Then of course there are huge cultural differences in terms of what families value and the general approach to education. But I’m not in any sense an international expert, so I’m very hesitant to make these kinds of generalizations…

What about your own pupils – you’ve taught secondary and been involved in primary school teaching as well. What’s your general feeling about why children fall behind at maths?

It’s very easy to conceive of mathematics as this building block subject where if you want to learn something at, say, step 20, you have to have steps 1-19 securely in place. When I work with primary school teachers in the UK that seems to be a very common view of the subject. One of the implications is that if a pupil starts falling behind — you start working on step 23 and they haven’t got to step 20 — then they need to be taken out of that class and supported to try and get to step 20. One of the effects of that in the UK is that it’s not uncommon to have a class of children aged 4-5 already split up into people who are high attaining at maths and those who are not. Those who are not are given special support. But there is evidence that if you are put into one of these bottom groups that actually you never get out of it. While your peers are then going on to steps 21, 22, 23, 24, 25, 26, you’re still struggling around at step 19. You will never then get contact with people who are getting excited about mathematics, and step 19 becomes a bit pointless and meaningless to you. You just flop around there and make slower and slower progress in relation to your peers and that carries on up to age 16. Then, in the UK at least, your life chances are very highly correlated to your attainment at age 16.

It seems to me that an alternative approach is possible. If you think about your learning in almost any other sphere, it doesn’t seem right that it should be this very linear, step-by-step process. Perhaps what’s actually more important than whether you understand step 19 is how you’re feeling about the subject. If you’re actually feeling positive and you’re in an environment where some people are excited about the subject  — and you’re offered images of what you’d be able to do if you did master step 19 — then maybe that’s more important than trying to fill in every single block. Certainly my experience confirms that. When I’ve worked at secondary school with people who have come to the school underachieving compared to the norm, what will get them through is if they actually change their emotional relationship with the subject. If they begin to start seeing themselves as mathematicians, and start feeling they have some control over the subject, that it’s not just this thing that’s outside them where somebody else tells them whether it’s right or wrong, but that they’ve got some agency, then that can completely switch around, in a very rapid period of time, what they’re able to attain. You can actually jump straight from step 19 to step 26 and pretty much fill in all the other steps along the way.

What do you mean by offering images of what you could do with step 19? Can you give an example?

OK let’s find out a bit more about all these ideas by going through your book choices. Your first one is by Imre Lakatos and it’s called  Proofs and Refutations .

I first came across this book at university in a course on the philosophy of mathematics. Looking back, it was one of my first experiences of how maths could be different to how I was taught it. In the book, Lakatos takes a particular area of mathematics to do with shape and recreates an imaginary dialogue where he and the characters in the book go through this extraordinary process of developing what mathematicians would call conjectures. So they are developing predictions about how a particular property of a shape might operate, or which types of shape it might be true for. There’s this amazing description of a process which, for me, is at the heart of doing mathematics, which is coming up with conjectures, coming up with predictions and then the search for counter-examples that don’t fit that conjecture, and, as a result of that, the refinement of the conjecture itself. It’s quite a scientific process: you come up with an idea and you try and refute it.

There’s a phrase, “mathematizing”, which is about trying to capture the process of doing mathematics as a mathematician and this book is just a beautiful description of that. It was very important in the development of my own thinking, just about how mathematics can then become alive. OK, other people may have gone down these steps of logic before, but that doesn’t make the process any less valid. Those ended up being guiding ideas for me as a teacher in my classroom, trying to set up situations where the children can come up with conjectures, can come up with predictions and they can work on testing those ideas, and trying to find examples that don’t work and so on.

On Amazon.com one of the reviewers of this book said it showed how misleading the textbook presentation of maths really is. Another reviewer pointed out that the book shows that even famous mathematicians got some of these things wrong, and that things that seem obvious now, weren’t obvious at all at the time…

Let’s go on to your second book, The Common Sense of Teaching Mathematics.

I could have chosen almost any book by Caleb Gattegno and in fact one of the exciting things is that most of his books are now available for free on a website, www.calebgattegno.org . Gattegno was a maths educator who talked about, in his own practice, teaching the entire five-year secondary maths curriculum in 18 months — and teaching it to mastery. What he meant by mastery was that students were as good at performing these things as he was. Gattegno did a lot of work in teaching languages, and he basically felt that learning mathematics was like learning a language. He looked at how young children learn languages, and he developed a curriculum which, certainly in his own hands, demonstrated it was possible to access all those powers we have as learners, for learning our mother tongue, in the learning of mathematics. Hence the speed and skill which he was able to impart to his students.

He advocated a route through this whole debate about “should I teach for understanding or should I teach rote learning?” What he did was devise activities where children could very quickly gain a symbolic mastery and then through a more creative exploration within those symbols, would develop their own understanding. In a sense, to quote a man called Dick Tahta who is actually the author of one of my other books, the teacher takes care of the symbols, the teacher is there to design activities which will mean the children get a sense of how these symbols work, and the sense takes care of itself. We leave it up to the children to actually make their own connections about how these things work. So it’s not denying the importance of understanding, but it’s suggesting that if that’s what you focus on right from the beginning, that’s quite an inefficient way to learn mathematics. By devising game-like activities which involve these mathematical symbols, you can get children into using symbols in a very sophisticated way, and through that use, develop their understanding.

So to try and ground that suggestion, again going back to working with primary children, Gattegno from a very early age would get children working with very large numbers. He had a chart where it would be possible to get children working with hundreds and thousands and tens of thousands and writing those symbols accurately from a very early age. I don’t think it matters what the children understand by being able to say, age 4, 10,000 plus 10,000 is 20,000. It doesn’t really matter what that means – they can get excited by using these symbols and names. I’ve certainly seen that. They do get very excited. In a sense the understanding or the meaning of those, and the relationships between those words develops over time. It’s not like I need to understand what 10,000 means before I can start using it and playing with it.

This book was written in the early 1970s – has his teaching had a big impact?

At that time he was a well-known figure, he was written about in  Time magazine and I don’t know if you know the Cuisenaire rods ? Cuisenaire was a Belgian teacher. They’re these different coloured rods starting with a white cube, going up to an orange one that is length ten. Gattegno was involved in the promotion of those materials, and I think at one stage every primary school in Canada had them and they were very well used in the UK. He certainly has had influence, but I don’t think many people today would recognize his name. It’s not clear to me why that has happened. Partly, it’s his writing. The book I’ve chosen here is one of his more accessible ones, it’s quite curricular focused. When he writes in a more general way about mathematics, it’s almost impenetrable. He has a whole system of thought about what it is to be human and learning, and really I’ve only been able to access his work through working with it in a group, with groups of people who are interested in the same thing. It’s not an easy approach. What he’s advocating depends a lot on the awareness of the teacher. He developed these materials – like the rods – and I think they can be spectacularly successful, but they’re not easy to use. They’re not the kind of thing that you can just pick up and go into a classroom and from day one expect to be successful…

Isn’t that one of the problems, that for someone to be a really good teacher they have to be rather brilliant themselves? They have to be completely on top of the subject matter, in order to be able to explain it simply to their pupils?

One answer I have to that links with a research project I’ve been involved with at a primary level, where teachers have been getting into this idea of positioning the students as “becoming mathematicians”. This has allowed some of these teachers to let go of their worries about not necessarily knowing what mathematics will come out of a particular activity. The teachers can place themselves alongside the students and say, “Well, actually, as a mathematician I’m not sure what the outcome will be, but maybe as a mathematician this is the question I’d ask, or I’d try to pursue that pattern.” On one level I think you’re right, but there are alternatives. The learning of mathematics can turn into something where the teacher is not needing to offer a very clear explanation, but a process of exploring and discovering things together with the children.

I like this idea of children defining themselves as mathematicians, because I do think a lot of the problems with maths come from people writing themselves off and saying “oh I’m no good at maths” and giving up. Whereas if you say “Right! I’m a mathematician!” you feel good about yourself. “Maybe I could be the next Fermat…”

OK so tell me about Calculus by and for Young People . I love the subtitle: “Ages 7, Yes 7 and Up”

This is a wonderful, very short book by a man called Don Cohen. It’s just an image, for me, of what’s possible. If we do turn the situation around and get children interested in exploring ideas and feeling confident enough to follow through on those ideas, then, actually, things that are said to be incredibly complex and you can’t do them till you’re 16, Don Cohen — as Gattegno did in his own work — has shown that to be nonsense.

So Don Cohen gets children excited about ideas of infinity. One of the activities he does with very young children is getting them to consider what happens if you add 1/2 to a 1/4 and then add on an 1/8 and 1/16 and a 1/32 and so on to infinity. He does this by getting people to imagine a square. Picture a square in your mind and imagine shading half of it. Then shade a quarter — a half of the bit that’s unshaded. Then you shade an eighth – again, a half of what’s unshaded. And then you shade a sixteenth, again you’re shaving a half of what’s unshaded. Quite quickly, even young children can get a sense that they can carry on shading half of what they’re left with forever. They’re filling up more and more of this square, but there’s always going to be a tiny bit left over. They get a sense that there might be this infinite process.

On to your next book, Teaching Mathematics: Towards a Sound Alternative . I have to confess I tried reading it but I still have absolutely no idea what it’s about — please tell me.

This book was an important part of my own research journey. It’s by a man named Brent Davis and it’s a write up of his PhD thesis. What he got interested in was trying to say something about the listening of the teacher. I just found that such an appealing idea. From when I first read it in 1999, the idea of the importance of listening has been a recurrent theme of interest for me, both in my teaching and in my research. In the book, Davis distinguishes an evaluative form of listening — where as a teacher what I’m basically doing is saying this response is right or wrong – and contrasts that to a non-evaluative form of listening. He then further differentiates that, but I don’t think that’s so significant.

What seems to be powerful — from when I started looking into this idea and doing video recordings in classrooms trying to analyse the listening that was taking place — is that it really did seem possible to distinguish between what happened when a teacher evaluated a student comment (basically saying “Yes I agree” or “No I don’t“ or some variation of that) and the dialogue that ensued, compared to when a teacher made a more non-evaluative response, for example, inviting someone else to comment, or writing the answer on the board and asking if anyone had a different answer. In the video recordings I took, the classroom somehow became alive as soon as the teacher stopped evaluating. A space was created for other voices to be heard. If you imagine a whole class discussion going on, very often the pattern of dialogue will go “Teacher-student-teacher-student.” What I got interested in was when it might go “Teacher-student-student” or “Teacher-student-student-student-teacher” and so on. In the small sample of classroom data I took, the only times the ping-pong pattern was disrupted was when the teacher was responding and listening in a non-evaluative way.

Which ties in with your comment at the beginning about making maths more like the humanities, where something is put out there by the teacher but then everybody discusses it. Can you give an example or anecdote?

We’d better get to your last book, Starting Points: For Teaching Mathematics in Middle and Secondary Schools.

This, for many years, was my Bible of teaching. I got to know about it through Laurinda Brown, with whom I have worked and co-researched for many years now. The third author, Dick Tahta, who is dead now, was a close friend of Laurinda’s. I knew him in the last ten years or so of his life and he influenced me hugely. It’s a very simple book on one level. It begins by talking about ways of working in the classroom and there’s a section on the role of the teacher. He asks, “What is the role of the teacher? How can he or she create the conditions in which creative and independent work can take place?” That, in a nutshell, is what I’m interested in in my work in mathematics.

Most of the book is just page after page of starting points for mathematical activity, which generally have something visible or tangible or something the children can just do straight away, but from which they are able to ask questions, spot patterns, make conjectures. Dick Tahta was certainly very influenced by Gattegno in this. They are just very rich starting points for children to get into the process of thinking mathematically. As a teacher wanting to develop a more creative approach to my own teaching, it was just an invaluable resource. Time and again, these activities would end up getting kids energized and excited and engaged and asking questions.

Can you give a specific example?

One is a game called the function game, where he imagines the teacher having some rule in mind. So with quite a young group, the rule I might have in mind is “add one.” So I might write the number three on the board and a little arrow (this is all ideally done in silence) with a four next to it. Underneath, I might write seven with an arrow and then eight. Then maybe I’d write six underneath, with an arrow, and hand the pen over to the children – or motion with my pen towards the class and try and get someone to come up to the board and fill in what they think the answer it. With older children the rule might be square the number – you can make it as complex as you like. I then give them feedback – so if a child comes up and doesn’t write seven, I draw an unhappy face. It’s the kind of activity which children can get very engaged in and can just lead in so many different directions.

Do you feel you’ve had results with your teaching methods?

At the school where I used to teach our results were pretty good age 16. We had a lot of people coming through to do ‘A’ level and it was quite often the most popular ‘A’ level choice [ Editor’s note : in the UK, children after age 16 choose only three subjects for their last two years of school, at the end of which they sit ‘A’ level exams in those subjects]. We were the only school in the local area to teach Further Maths as an ‘A’ level, which at that time was a subject in major decline outside public [private] schools. Those things for me were indicators that we were successful in developing in quite a few children a sense that mathematics was something they could be engaged in and excited about. I was teaching in a school with quite a disadvantaged catchment area, and we had a couple of people getting into Oxford to read maths and quite a lot of people doing maths-related university degrees. So yes, there were some good responses from the children.

April 22, 2013

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Alf Coles studied maths and philosophy at Oxford University. He went on to spend 15 years teaching maths in secondary school, including 7 years as head of a maths department. He is now a senior lecturer in education at Bristol University. He is currently working on a project focused on tackling underachievement in primary school mathematics in collaboration with the charity "5x5x5=creativity" and funded by the Rayne Foundation. His book,  Being Alongside: For the Teaching and Learning of Mathematics ,  analyses the teaching and learning of students and staff at the school where he worked.

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Softening the sharp edges in mathematics.

For everyone whose relationship with mathematics is distant or broken, Jo Boaler , a professor at Stanford Graduate School of Education (GSE), has ideas for repairing it. She particularly wants young people to feel comfortable with numbers from the start — to approach the subject with playfulness and curiosity, not anxiety or dread.

“Most people have only ever experienced what I call narrow mathematics — a set of procedures they need to follow, at speed,” Boaler says. “Mathematics should be flexible, conceptual, a place where we play with ideas and make connections. If we open it up and invite more creativity, more diverse thinking, we can completely transform the experience.”

“Mathematics should be flexible, conceptual, a place where we play with ideas and make connections," says Professor Jo Boaler. (Photo: Robert Houser Photography)

Boaler, the Nomellini and Olivier Professor of Education at the GSE, is the co-founder and faculty director of Youcubed , a Stanford research center that provides resources for math learning that has reached more than 230 million students in over 140 countries. In 2013 Boaler, a former high school math teacher, produced “How to Learn Math,” the first massive open online course (MOOC) on mathematics education. She leads workshops and leadership summits for teachers and administrators, and her online courses have been taken by over a million users. 

In her new book, Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics , Boaler argues for a broad, inclusive approach to math education, offering strategies and activities for learners at any age. We spoke with her about why creativity is an important part of mathematics, the impact of representing numbers visually and physically, and how what she calls “ishing” a math problem can help students make better sense of the answer. 

What do you mean by “math-ish” thinking?

It’s a way of thinking about numbers in the real world, which are usually imprecise estimates. If someone asks how old you are, how warm it is outside, how long it takes to drive to the airport – these are generally answered with what I call “ish” numbers, and that’s very different from the way we use and learn numbers in school.

In the book I share an example of a multiple-choice question from a nationwide exam where students are asked to estimate the sum of two fractions: 12/13 + 7/8. They’re given four choices for the closest answer: 1, 2, 19, or 21. Each of the fractions in the question is very close to 1, so the answer would be 2 — but the most common answer 13-year-olds gave was 19. The second most common was 21. 

I’m not surprised, because when students learn fractions, they often don’t learn to think conceptually or to consider the relationship between the numerator or denominator. They learn rules about creating common denominators and adding or subtracting the numerators, without making sense of the fraction as a whole. But stepping back and judging whether a calculation is reasonable might be the most valuable mathematical skill a person can develop.

But don’t you also risk sending the message that mathematical precision isn’t important? 

I’m not saying precision isn’t important. What I’m suggesting is that we ask students to estimate before they calculate, so when they come up with a precise answer, they’ll have a real sense for whether it makes sense. This also helps students learn how to move between big-picture and focused thinking, which are two different but equally important modes of reasoning.

Some people ask me, “Isn’t ‘ishing’ just estimating?” It is, but when we ask students to estimate, they often groan, thinking it’s yet another mathematical method. But when we ask them to “ish” a number, they're more willing to offer their thinking.

Ishing helps students develop a sense for numbers and shapes. It can help soften the sharp edges in mathematics, making it easier for kids to jump in and engage. It can buffer students against the dangers of perfectionism, which we know can be a damaging mind-set. I think we all need a little more ish in our lives. 

You also argue that mathematics should be taught in more visual ways. What do you mean by that? 

For most people, mathematics is an almost entirely symbolic, numerical experience. Any visuals are usually sterile images in a textbook, showing bisecting angles, or circles divided into slices. But the way we function in life is by developing models of things in our minds. Take a stapler: Knowing what it looks like, what it feels and sounds like, how to interact with it, how it changes things — all of that contributes to our understanding of how it works. 

There’s an activity we do with middle-school students where we show them an image of a 4 x 4 x 4 cm cube made up of smaller 1 cm cubes, like a Rubik’s Cube. The larger cube is dipped into a can of blue paint, and we ask the students, if they could take apart the little cubes, how many sides would be painted blue? Sometimes we give the students sugar cubes and have them physically build a larger 4 x 4 x 4 cube. This is an activity that leads into algebraic thinking. 

Some years back we were interviewing students a year after they’d done that activity in our summer camp and asked what had stayed with them. One student said, ‘I’m in geometry class now, and I still remember that  sugar cube, what it looked like and felt like.’ His class had been asked to estimate the volume of their shoes, and he said he’d imagined his shoes filled with 1 cm sugar cubes in order to solve that question. He had built a mental model of a cube.

When we learn about cubes, most of us don’t get to see and manipulate them. When we learn about square roots, we don’t take squares and look at their diagonals. We just manipulate numbers.

I wonder if people consider the physical representations more appropriate for younger kids.

That’s the thing — elementary school teachers are amazing at giving kids those experiences, but it dies out in middle school, and by high school it’s all symbolic. There’s a myth that there’s a hierarchy of sophistication where you start out with visual and physical representations and then build up to the symbolic. But so much of high-level mathematical work now is visual. Here in Silicon Valley, if you look at Tesla engineers, they're drawing, they're sketching, they're building models, and nobody says that's elementary mathematics.

Click to enlarge: A depiction of various ways to calculate 38 x 5, numerically and visually. (Image: Courtesy of Jo Boaler)

There’s an example in the book where you’ve asked students how they would calculate 38 x 5 in their heads, and they come up with several different ways of arriving at the same answer. The creativity is fascinating, but wouldn’t it be easier to teach students one standard method?

That narrow, rigid version of mathematics where there’s only one right approach is what most students experience, and it’s a big part of why people have such math trauma. It keeps them from realizing the full range and power of mathematics. When you only have students blindly memorizing math facts, they’re not developing number sense. They don’t learn how to use numbers flexibly in different situations. It also makes students who think differently believe there’s something wrong with them. 

When we open mathematics to acknowledge the different ways a concept or problem can be viewed, we also open the subject to many more students. Mathematical diversity, to me, is a concept that includes both the value of diversity in people and the diverse ways we can see and learn mathematics. When we bring those forms of diversity together, it’s powerful. If we want to value different ways of thinking and problem-solving in the world, we need to embrace mathematical diversity.

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460 Free Textbooks – Math, Science, and More [Online PDF for College and High School]

While you're in school, you will go through a number of textbooks and the cost can add up pretty quickly. Luckily, there are websites that offer free textbooks for high school and college students.

Here is a list of 460 free textbooks, arranged by topic. Once you find a topic that interests you, click that link and it will jump you down to a list of related textbooks.

High School Textbook Categories

Natural sciences, classical novels, college textbook categories, computer science, engineering, social sciences, journalism and communication, high school textbooks (90).

• Advanced High School Statistics - 2nd Edition
• Advanced High School Mathematics
• AP Physics Collection
• Biology for AP courses
• Principles of Macroeconomics for AP courses 2e
• Principles of Microeconomics for AP courses 2e
• Adventures of Huckleberry Finn, The
• Adventures of Tom Sawyer, The
• Aesop’s Fables
• Alice’s Adventures in Wonderland
• Andersen’s Fairy Tales
• Anna Karenina
• Anne of Green Gables
• Around the World in 80 Days
• Beyond Good and Evil
• Bleak House
• Brothers Karamazov, The
• Christmas Carol, A
• Crime and Punishment
• David Copperfield
• Down and Out in Paris and London
• For the Term of His Natural Life
• Frankenstein
• Great Expectations
• Great Gatsby, The
• Grimms Fairy Tales
• Gulliver’s Travels
• Heart of Darkness
• Hound of the Baskervilles, The
• Island of Doctor Moreau, The
• Jungle Book, The
• Lady Chatterly’s Lover
• Last of the Mohicans, The
• Legend of Sleepy Hollow, The
• Les Miserables
• Little Women
• Madame Bovary
• Merry Adventures of Robin Hood, The
• Metamorphosis, The
• Middlemarch
• Northanger Abbey
• Nostromo: A Tale of the Seaboard
• Notes from the Underground
• Odyssey, The
• Of Human Bondage
• Oliver Twist
• Paradise Lost
• Picture of Dorian Gray, The
• Portrait of a Lady, The
• Portrait of the Artist as a Young Man, A
• Pride and Prejudice
• Prince, The
• Robinson Crusoe
• Scarlet Pimpernel, The
• Sense and Sensibility
• Sons and Lovers
• Strange Case of Dr Jekyll and Mr Hyde, The
• Tale of Two Cities, A
• Tales of Mother Goose, The
• Tarzan of the Apes
• Tender is the Night
• Tess of the d’Urbervilles
• Thirty Nine Steps, The
• Three Musketeers, The
• Time Machine, The
• Treasure Island
• Vanity Fair
• War and Peace
• Within A Budding Grove
• Women In Love
• Wuthering Heights

College TextBooks (370)

• Python for Everybody: Exploring Data Using Python 3
• Web Accessibility for Developers
• The Missing Link: An Introduction to Web Development and Programming
• Foundations of Computation
• Algorithms and Data Structures With Applications to Graphics and Geometry
• Think Data Structures: Algorithms and Information Retrieval in Java
• Open Data Structures: An Introduction
• Java with BlueJ
• Introduction to Programming Using Java - Eighth Edition
• A Byte of Python
• Eloquent JavaScript: A Modern Introduction to Programming
• High Performance Computing
• Database Design - 2nd Edition
• Relational Databases and Microsoft Access
• A First Course in Electrical and Computer Engineering
• How to Think Like a Computer Scientist: Learning with Python
• How to Think Like a Computer Scientist: C Version
• How to Think Like a Computer Scientist: C++ Version
• Programming Fundamentals - A Modular Structured Approach using C++
• Think Java: How To Think Like a Computer Scientist - 2e
• Java, Java, Java: Object-Oriented Problem Solving
• Think Stats: Probability and Statistics for Programmers - 2e
• Think Bayes: Bayesian Statistics Made Simple
• Think Complexity: Exploring Complexity Science with Python - 2e
• Digital Circuit Projects: An Overview of Digital Circuits Through Implementing Integrated Circuits
• Introduction to the Modeling and Analysis of Complex Systems
• Physical Modeling in MATLAB
• Spatial Thinking in Planning Practice: An Introduction to GIS
• Introduction to Computer Graphics
• Computer Networks: A Systems Approach
• An Introduction to Computer Networks - Second Edition
• Computer Networking : Principles, Protocols and Practice
• Signal Computing: Digital Signals in the Software Domain
• x86-64 Assembly Language Programming with Ubuntu
• Professional Web Accessibility Auditing Made Easy
• First Semester in Numerical Analysis with Python
• The Crystal Ball Instruction Manual - version 1.1 Volume One: Introduction to Data Science
• An Introduction to Matlab and Mathcad
• Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version)
• Delftse Foundations of Computation
• The Unicode cookbook for linguists: Managing writing systems using orthography profiles
• Implementing a One Address CPU in Logisim
• Embedded Controllers Using C and Arduino - 2e
• Introduction to MIPS Assembly Language Programming
• Think DSP: Digital Signal Processing in Python
• Information Systems for Business and Beyond
• Information Systems: A Manager's Guide to Harnessing Technology
• The Little Book of Semaphores
• Essentials of Geographic Information Systems
• Programming Languages: Application and Interpretation - Version Second Edition
• A Brief Introduction to Engineering Computation with MATLAB
• Introduction to Industrial Engineering
• Fundamentals of Electrical Engineering I
• Sustainability: A Comprehensive Foundation
• Notes on Diffy Qs: Differential Equations for Engineers
• Elementary Differential Equations with Boundary Value Problems
• Developing New Products and Services
• Introduction to Aerospace Structures and Materials
• Building Maintenance & Construction: Tools and Maintenance Tasks
• Direct Energy
• Operational Amplifiers & Linear Integrated Circuits: Theory and Application - 3e
• Manufacturing Processes 4-5
• Electromagnetics Vol 1
• DC Electrical Circuit Analysis: A Practical Approach
• AC Electrical Circuit Analysis: A Practical Approach
• Applied Fluid Mechanics Lab Manual
• Fundamentals of Microwave and RF Design
• Introduction to Probability
• Introduction to Linear, Time-Invariant, Dynamic Systems for Students of Engineering
• Hybrid-Flexible Course Design
• Creating Online Learning Experiences
• Education for a Digital World: Advice, Guidelines and Effective Practice from Around Globe
• Educational Psychology
• Learning to Learn Online
• Sharing Our Knowledge: Best Practices for Supporting English Language Learners in Schools
• Introduction to Curriculum for Early Childhood Education
• Bad Ideas About Writing
• Write Here, Right Now: An Interactive Introduction to Academic Writing and Research
• Elementary Earth and Space Science Methods
• Mathematics for Elementary Teachers
• Trauma Informed Behaviour Support: A Practical Guide to Developing Resilient Learners
• Trauma-Informed School Practices: Building Expertise To Transform Schools
• Wellbeing in Educational Contexts
• Parenting and Family Diversity Issues
• Safety, Health, and Nutrition in Early Childhood Education
• The ELC: An Early Childhood Learning Community at Work
• Building Democracy for All: Interactive Explorations of Government and Civic Life
• Foundations of Learning and Instructional Design Technology
• Ethical Use of Technology in Digital Learning Environments: Graduate Student Perspectives
• Writing Instruction Tips For Automated Essay Graders: How To Design an Essay for a Non-human Reader
• Conventions 101: A Functional Approach to Teaching (And Assessing!) Grammar and Punctuation
• Choosing & Using Sources: A Guide to Academic Research
• WAC and Second-Language Writers: Research Towards Linguistically and Culturally Inclusive Programs and Practices
• WAC Partnerships Between Secondary and Postsecondary Institutions
• Working With Academic Literacies: Case Studies Towards Transformative Practice
• Antiracist Writing Assessment Ecologies: Teaching and Assessing Writing for a Socially Just Future
• Critical Expressivism: Theory and Practice in the Composition Classroom
• Copy(write): Intellectual Property in the Writing Classroom
• Teaching Autoethnography: Personal Writing in the Classroom
• Algebra and Trigonometry
• Calculus Volume 1
• Calculus Volume 2
• Calculus Volume 3
• Multivariable Calculus
• College Algebra
• Open Resources for Community College Algebra
• Elementary Algebra 2e
• Intermediate Algebra 2e
• Fundamentals of Matrix Algebra
• Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students
• A Cool Brisk Walk Through Discrete Mathematics
• Mathematical Analysis I
• Introductory Statistics with Randomization and Simulation - First Edition
• Introductory Business Statistics
• Introductory Statistics
• Statistical Thinking for the 21st Century
• Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics
• Prealgebra 2e
• Precalculus
• Geometry with an Introduction to Cosmic Topology
• Technical Mathematics
• Introduction to Game Theory: a Discovery Approach
• Quantitative Problem Solving in Natural Resources
• Euclidean plane and its relatives
• Proofs and Concepts: The Fundamentals of Abstract Mathematics
• Applied Finite Mathematics
• Linear Regression Using R: An Introduction to Data Modeling
• Applied Combinatorics
• Math in Society - Edition 2.5
• Anatomy and Physiology
• Human Anatomy Lab Manual
• A Mixed Course-Based Research Approach to Human Physiology
• Fundamentals of Anatomy and Physiology - Australian Edition
• Biochemistry: Free For All
• Concepts of Biology
• Principles of Biology: Biology 211, 212, and 213
• Microbiology
• General Microbiology - 1st Edition
• A Primer for Computational Biology
• From Growing to Biology: Plants 1e
• A Student's Guide to Tropical Marine Biology
• Chemistry 2e
• Chemistry: Atoms first 2e
• College Physics
• Foundations of Neuroscience
• Foundations of Epidemiology
• Radiation Safety
• Environmental Toxicology
• Geological Structures: a Practical Introduction
• Physical Geology - First University of Saskatchewan Edition
• Climate Toolkit: A Resource Manual for Science and Action
• Introduction to Climate Science - 1st Edition
• Bending the Curve: Climate Change Solutions
• Chemical Biology & Biochemistry Laboratory Using Genetic Code Expansion Manual
• Biotechnology Foundations - 2nd Edition
• An EKG Interpretation Primer
• Introduction to Oceanography
• Nutrition: Science and Everyday Application - beta v 0.1
• Human Nutrition - 2020 Edition
• Concepts of Fitness and Wellness
• Histology and Embryology for Dental Hygiene
• Nursing Pharmacology
• Nursing Care at the End of Life: What Every Clinician Should Know
• Transitions to Professional Nursing Practice - 2nd Edition
• The Complete Subjective Health Assessment
• Evidence-Based Massage Therapy
• A Laboratory Guide to Clinical Hematology
• Undergraduate Diagnostic Imaging Fundamentals
• Public Health Ethics: Global Cases, Practice, and Context
• Literature Reviews for Education and Nursing Graduate Students
• Health Case Studies
• Supporting Individuals with Intellectual Disabilities & Mental Illness
• Field Trials of Health Interventions: A Toolbox
• Clinical Procedures for Safer Patient Care
• Creative Clinical Teaching In The Health Professions
• Veterinary Epidemiology: Principles and Methods
• American Government 2e
• American Government 3e
• Introduction to Sociology 2e
• Introduction to Sociology 3e
• Principles of Economics 2e
• Principles of  Macroeconomics 2e
• Principles of Microeconomics 2e
• Psychology 2e
• Psychology: The Science of Human Potential
• Abnormal Psychology - 2nd Edition
• Introduction to Community Psychology
• An Introduction to Psychological Statistics
• Human Behavior and the Social Environment I
• Human Behavior and the Social Environment II
• Language and Culture in Context - A Primer on Intercultural Communication
• Intercultural Communication
• Contemporary Families: An Equity Lens
• Child Growth and Development
• Child, Family, and Community
• Interpersonal Communication: A Mindful Approach to Relationships
• Attenuated Democracy: A Critical Introduction to U.S. Government and Politics
• Foundations of Social Work Research
• Introduction to Human Geography - 2nd Edition
• Beyond Race: Cultural Influences on Human Social Life
• Classical Sociological Theory and Foundations of American Sociology
• Speak Out, Call In: Public Speaking as Advocacy
• A Quick Guide to Quantitative Research in the Social Sciences
• The Balance of Personality
• The Art of Being Human: A Textbook for Cultural Anthropology
• Stand up, Speak out: The Practice and Ethics of Public Speaking
• U.S. History
• World History: Cultures, States, and Societies to 1500
• Modern World History
• International Relations
• Becoming America: An Exploration of American Literature from Precolonial to Post-Revolution
• American Literature I: An Anthology of Texts From Early America Through the Civil War
• Spanish I: Beginning Spanish Language and Culture
• Linguistics for Teachers of English
• The Changing Story: digital stories that participate in transforming teaching & learning
• Essentials of Linguistics
• Technical Writing
• Let's Get Writing!
• You, Writing! A Guide to College Composition
• Writing for Success
• College ESL Writers: Applied Grammar and Composing Strategies for Success
• Introduction to Sociology - 2e
• Introduction to Philosophy: Philosophy of Religion
• Introduction to Philosophy: Philosophy of Mind
• English Composition: Connect, Collaborate, Communicate
• Studying the Bible: The Tanakh and Early Christian Writings
• Philosophical Ethics
• Ethics for A-Level
• Steps to Success: Crossing the Bridge Between Literacy Research and Practice
• Exploring Public Speaking - 4th Edition
• Plato's 'Republic': An Introduction
• Decoding the 1920s: A Reader for Advanced Learners of Russian
• An Introduction to Technical Theatre
• Theatrical Worlds
• Understanding Basic Music Theory
• Music Theory for the 21st-Century Classroom
• Music on the Move
• Introduction to Art: Design, Context, and Meaning
• Guide to Ancient Egyptian Art
• Guide to Ancient Roman art
• Guide to Ancient Greek Art
• Moving Pictures: An Introduction to Cinema
• Naming the Unnameable: An Approach to Poetry for New Generations
• Prose Fiction: An Introduction to the Semiotics of Narrative
• Mindful Technical Writing: An Introduction to the Fundamentals
• Explorations 1: Grammar for the Experienced Beginner
• Introduction to Logic and Critical Thinking
• Writing and Literature: Composition as Inquiry, Learning, Thinking, and Communication
• British Literature I Anthology: From the Middle Ages to Neoclassicism and the Eighteenth Century
• British Literature II: Romantic Era to the Twentieth Century and Beyond
• Perspectives: An Open Invitation to Cultural Anthropology
• A Guide to Good Reasoning: Cultivating Intellectual Virtues - Second edition, revised and updated
• Inferring and Explaining
• Exploring Perspectives: A Concise Guide to Analysis
• EmpoWord: A Student-Centered Anthology & Handbook for College Writers
• Introduction to Business
• Business Ethics
• Business Law 1 Essentials
• Entrepreneurship
• Introduction to Intellectual Property
• Organizational Behavior
• Principles of Financial Accounting
• Principles of Managerial Accounting
• Principles of Management
• Business Writing Style Guide
• Financial Management for Small Businesses: Financial Statements & Present Value Models
• Intermediate Microeconomics with Microsoft Excel - 2nd Edition
• Business Computers 365
• Problem Solving in Teams and Groups
• Digital Accessibility as a Business Practice
• Management Communication
• Introduction to Financial Accounting: U.S. GAAP Adaptation
• eMarketing - The Essential Guide to Online Marketing
• Fundamentals of Infrastructure Management
• An Introduction to Cooperation and Mutualism
• Financial Strategy for Public Managers
• Entrepreneurship and Innovation Toolkit
• Business Plan Development Guide
• Project Management
• Introducing Marketing
• Fundamentals of Business - 3rd Edition
• Business Law and the Legal Environment
• Good Corporation, Bad Corporation: Corporate Social Responsibility in the Global Economy
• Guidelines for Improving the Effectiveness of Boards of Directors of Nonprofit Organizations
• Small Business Management in the 21st Century
• The Sustainable Business Case Book
• Advanced Business Law and the Legal Environment
• Electronic Commerce: The Strategic Perspective
• Focusing on Organizational Change
• Human Relations
• Leading with Cultural Intelligence
• Managerial Accounting
• Business English for Success
• Human Resource Management
• International Business
• Strategic Management
• Sustainability, Innovation, and Entrepreneurship
• The Power of Selling
• Principles of Marketing
• The Legal and Ethical Environment of Business
• Money and Banking
• Risk Management for Enterprises and Individuals
• Exploring Business
• International Finance: Theory and Policy
• Law School Materials for Success
• Introduction to Criminal Investigation: Processes, Practices and Thinking
• Ethics in Law Enforcement
• Criminal Law
• Intellectual Property: Law & the Information Society—Cases and Materials
• Wetlands Law: A Course Source
• First Amendment: Cases, Controversies, and Contexts - Second Edition
• The Indigo Book: A Manual of Legal Citation
• Fundamentals of Business Law
• Business Law I Essentials
• Law 101: Fundamentals of the Law
• Liberty, Equality and Due Process: Cases, Controversies, and Contexts in Constitutional Law
• Introduction to the American Criminal Justice System
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• Sources of American Law: An Introduction to Legal Research - 4th Edition
• Basic Income Tax - 8th Edition
• What Color is Your C.F.R.?
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• Introduction to Contracts, Sales and Product Liability
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• Introduction to Basic Legal Citation
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• Digital Foundations: Introduction to Media Design with the Adobe Creative Cloud - Revised Edition
• Humans R Social Media - Open Textbook Edition
• Writing for Strategic Communication Industries
• Open Technical Writing: An Open-Access Text for Instruction in Technical and Professional Writing
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• Be Credible
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Math Lessons for a Living Education: Level 1

For Ages 5-7

Math Lessons for a Living Education: Level 1 is a Christian homeschool math curriculum designed to ignite a love for math in your first-grade level students. The captivating story of the twins continues with the specific purpose of helping your student learn to count to 100, identify place values, number families and more.

Math Lessons for a Living Education is an award-winning math homeschool curriculum series known for helping students love math. Using the Master Books’ method of education, the grab-and-go workbooks help build confidence at a pace that will not overwhelm your student with the typical “drill and kill” approach.

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Math Lessons for a Living Education: Level 1 teaches math through engaging, real-life stories and practical application because math is all around us! This award-winning homeschool math curriculum series uses a story-based approach allowing students to participate in the story, make mathematical connections, explore the world around them with Charlie & Charlotte, and realize the value of math in their own lives.

Math Lessons for a Living Education: Level 1 teaches through:

• Short, story-based lessons
• Real life application
• Hands-on activities
• Engaging, full-color worksheets

Learn Smarter

Students learn best and retain more when they are engaged in the material and actively applying concepts to their lives. Math Lessons for a Living Education engages your student through exciting stories allowing your student to learn smarter instead of harder!

Real Life, Real Math

Mathematical concepts such as addition, subtraction, patterns, and telling time are taught within the framework of an engaging, real-life story while fun worksheets provide your student the opportunity to apply the exciting new concepts. An engaging blend of stories, copy work, oral narration, and hands-on experience brings mathematical concepts to life. First grade level students will explore the world around them discovering why math matters.

Lessons Kids Love

Math Lessons for a Living Education creates a stress-free, tear-free environment for your child to learn, grow, and develop their math skills. Because your student is relating newfound knowledge to everyday life, they’ll retain those skills too!

In Math Lessons for a Living Education: Level 1 your student will learn:

• How to count & write numbers 0-100
• Counting by 2s, 5s, & 10s
• Addition & Subtraction of numbers 0-10
• Place value to hundreds
• Shapes & Patterns
• Simple Fractions
• How to tell time
• and so much more!

* A Math Lessons Readiness Test is available to help you determine if this level is best for your student. You will find it as a downloadable PDF on this page under the product image.

Math Lessons for a Living Education: Level 1 Includes:

• Convenient Daily Schedule—saving you time!
• Short, engaging 15-30 minute lessons
• Full-color worksheets
• Link to downloadable answer key
• Manipulatives section

Course Features:

• Instructional blend of stories, copy-work, oral narration, and hands-on experience to bring concepts to life
• Convenient perforated pages
• Recommended for: Grade 1 / 5-7 years old
• Designed for parent & child to work through together

Table of Contents

• Using This Course
• Lesson 1: The Adventure Begins! We Learn Numbers 0–9
• Lesson 2: How Many Eggs? Review of Numbers 0–9
• Lesson 3: A Bed for Pokey; Introducing Rectangles
• Lesson 4: Circles and Patterns
• Lesson 5: Review of Concepts
• Lesson 6: More Numbers, Patterns, Shapes; Introducing Triangles
• Lesson 7: Learning to Count with Bigger Numbers—Place Values
• Lesson 8: More Work with Place Values
• Lesson 9: Review of Concepts
• Lesson 10: Place Value, Patterns of 10s
• Lesson 11: Practice with Patterns and Shapes
• Lesson 12: Introducing the + and = Symbols
• Lesson 13: Addition + 1
• Lesson 14: Writing & Adding Numbers; Introducing the Days of the Week
• Lesson 15: More About Addition (Vertical Addition)
• Lesson 16: More Addition; Introducing Squares
• Lesson 17: Two by Two (Introducing Skip Counting by 2s)
• Lesson 18: Number Families, Addition to Ten
• Lesson 19: Counting by 10
• Lesson 20: Counting Groups
• Lesson 21: Solving for an Unknown
• Lesson 22: Tally Marks to Make Groups of Five
• Lesson 23: Counting by 5s
• Lesson 24: Telling Time, Part 1
• Lesson 25: Telling Time, Part 2
• Lesson 26: Telling Time, Part 3
• Lesson 27: Introducing Simple Fractions, Part 1
• Lesson 28: Introducing Simple Fractions, Part 2
• Lesson 29: Introduction to Subtraction
• Lesson 30: Subtraction -1
• Lesson 31: Review of Shapes
• Lesson 32: Review of Place Value — Numbers to 100
• Lesson 33: Review of Addition
• Lesson 34: Review of Skip Counting 2’s and 5’s
• Lesson 35: Review of Skip Counting 10’s & Tally Marks
• Lesson 36: Review of Numbers to 100
• Manipulative Section
• Appendix – Bean Sprouting Project Instructions

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Homeschooling a first grade student is fun and exciting because children are naturally inquisitive and curious at this age, eager to develop their skills and learn about the world around them. But what exactly does a first grader need to know? Carrie Lindquist, homeschool mom of 3 and Master Books curriculum author, is here to walk you through the skills your student will be developing during this foundational year.

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SPS aims to boost summer learning with free books, math workbooks for K-5 students

It's that time of year again. Superintendent Grenita Lathan has been visiting elementary classes to pass out bags of free books.

This year, students are also receiving scholastic magazines and workbooks, including puzzles and games meant to boost math skills.

Lathan, an avid reader, started the tradition of giving away books to encourage summer reading and help students build a personal library at home.

"I love to read. Throughout my whole life, reading has been a favorite pastime. It has introduced me to fascinating people, transported me to exciting places and exposed me to memorable experiences," Lathan wrote in a letter to Springfield parents as part of the giveaway.

"The only thing I enjoy more than reading myself is encouraging others, especially children, to experience the joy of reading."

In the letter, Lathan said she hopes the books inspire young students to become confident, independent readers.

"From an educator's perspective, I believe reading is one of the best strategies to promote achievement and prevent students from falling behind," Lathan wrote. "Children who read regularly during the summer will be better prepared to enter the classroom in August."

Lathan's efforts have received strong support from the Springfield school board, which approved buying the books to give away. Board member Maryam Mohammadkhani suggested adding the math workbooks, an idea embraced by the rest of the governing body.

Here is a by-the-numbers look at the books and other materials being sent home:

• 46,657 − Scholastic books, five each for students in grades K-3 and three each for students in grades 4-5;
• 10,769 − Summer express workbooks, one each for students in K-5;
• 7,188 − Scholastic STEM (science, technology, engineering and math) workbooks, two each for students in grades 4-5;
• 3,715 − Math practice books, provided to students in grades K-5 who have scored below grade level.

The workbooks provide a way for students to practice math, reading, writing, phonics, vocabulary and grammar.

In a letter explaining the math practice books, Lathan said the lessons are tailored to the skills students are expected to acquire at their grade level.

More: Two Springfield high school seniors awarded funds in National Merit Scholarship Program

For example, in third grade, a student typically works on multiplication, division, geometry and measurement, fractions and solving problems.

"This math practice workbook will provide your child with ready-to-use, skill-building practice pages with easy-to-follow directions," Lathan wrote. "The practice pages incorporate challenging puzzles, inviting games and picture problems."

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Books at Amazon

The Amazon.com Books homepage helps you explore Earth's Biggest Bookstore without ever leaving the comfort of your couch. Here you'll find current best sellers in books, new releases in books, deals in books, Kindle eBooks, Audible audiobooks, and so much more. We have popular genres like Literature & Fiction, Children's Books, Mystery & Thrillers, Cooking, Comics & Graphic Novels, Romance, Science Fiction & Fantasy, and Amazon programs such as Best Books of the Month, the Amazon Book Review, and Amazon Charts to help you discover your next great read.

In addition, you'll find great book recommendations that may be of interest to you based on your search and purchase history, as well as the most wished for and most gifted books. We hope you enjoy the Amazon.com Books homepage!

Amazon.com Books has the world’s largest selection of new and used titles to suit any reader's tastes. Find best-selling books, new releases, and classics in every category, from Harper Lee's To Kill a Mockingbird to the latest by Stephen King or the next installment in the Diary of a Wimpy Kid children’s book series. Whatever you are looking for: popular fiction, cookbooks, mystery, romance, a new memoir, a look back at history, or books for kids and young adults, you can find it on Amazon.com Books. Discover a new favorite author or book series, a debut novel or a best-seller in the making. We have books to help you learn a new language, travel guides to take you on new adventures, and business books for entrepreneurs. Let your inner detective run wild with our mystery, thriller & suspense selection containing everything from hard-boiled sleuths to twisty psychological thrillers. Science fiction fans can start the Game of Thrones book series or see what's next from its author, George R.R. Martin. You’ll find the latest New York Times best-seller lists, and award winners in literature, mysteries, and children’s books. Get reading recommendations from our Amazon book editors, who select the best new books each month and the best books of the year in our most popular genres. Read the books behind blockbuster movies like Suzanne Collins’ The Hunger Games , John Green’s The Fault in Our Stars , Stephenie Meyers’ Twilight series, or E.L. James’ 50 Shades of Grey . For new and returning students, we have textbooks to buy, rent or sell and teachers can find books for their classroom in our education store. Whether you know which book you want or are looking for a recommendation, you’ll find it in the Amazon.com Books store.

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