teaching mathematics strategies essay

• Grades 6-12
• School Leaders

Free printable Mother's Day questionnaire 💐!

21 Essential Strategies in Teaching Math

Even veteran teachers need to read these.

We all want our kids to succeed in math. In most districts, standardized tests measure students’ understanding, yet nobody wants to teach to the test. Over-reliance on test prep materials and “drill and kill” worksheets steal instructional time while also harming learning and motivation. But sound instruction and good test scores aren’t mutually exclusive. Being intentional and using creative approaches to your instruction can get students excited about math. These essential strategies in teaching mathematics can make this your class’s best math year ever!

1. Raise the bar for all

WeAreTeachers

For math strategies to be effective, teachers must first get students to believe that they can be great mathematicians. Holding high expectations for all students encourages growth. As early as second grade, girls have internalized the idea that math is not for them . It can be a challenge to overcome the socially acceptable thought, I’m not good at math , says Sarah Bax, a math teacher at Hardy Middle School in Washington, D.C.

Rather than success being a function of how much math talent they’re born with, kids need to hear from teachers that anyone who works hard can succeed. “It’s about helping kids have a growth mindset ,” says Bax. “Practice and persistence make you good at math.” Build math equity and tell students about the power and importance of math with enthusiasm and high expectations.

(Psst … you can snag our growth mindset posters for your math classroom here. )

2. Don’t wait—act now!

Look ahead to the specific concepts students need to master for annual end-of-year tests, and pace instruction accordingly. Think about foundational skills they will need in the year ahead.

“You don’t want to be caught off guard come March thinking that students need to know X for the tests the next month,” says Skip Fennell, project director of Elementary Mathematics Specialists and Teacher Leaders Project and professor emeritus at McDaniel College in Westminster, Maryland. Know the specific standards and back-map your teaching from the fall so students are ready, and plan to use effective math strategies accordingly.

[contextly_auto_sidebar]

3. Create a testing pathway

You may not even see the results of standardized tests until next school year, but you have to prepare students for it now. Use formative assessments to ensure that students understand the concepts. What you learn can guide your instruction and determine the next steps, says Fennell. “I changed the wording because I didn’t want to suggest that we are in favor of ‘teaching to the test.'”

Testing is not something separate from your instruction. It should be integrated into your planning. Instead of a quick exit question or card, give a five-minute quiz, an open-ended question, or a meaningful homework assignment to confirm students have mastered the math skill covered in the day’s lesson. Additionally, asking students to explain their thinking orally or in writing is a great way to determine their level of understanding. A capable digital resource, designed to monitor your students in real-time, can also be an invaluable tool, providing actionable data to inform your instruction along the way.

4. Observe, modify, and reevaluate

Sometimes we get stuck in a mindset of “a lesson a day” in order to get through the content. However, we should keep our pacing flexible, or kids can fall behind. Walk through your classroom as students work on problems and observe the dynamics. Talk with students individually and include “hinge questions” in your lesson plans to gauge understanding before continuing, suggests Fennell. In response, make decisions to go faster or slower or put students in groups.

5. Read, read, read!

Although we don’t often think of reading as a math strategy, there’s almost nothing better to get students ready to learn a new concept than a great read-aloud. Kids love to be read to, and the more we show students how math is connected to the world around us, the more invested they become. Reading books with math connections helps children see how abstract concepts connect to their lives.

6. Personalize and offer choice

When students are given the opportunity to choose how they learn and demonstrate their understanding of a concept, their buy-in and motivation increase. It gives them the chance to understand their preferred learning style, provides agency over their own learning, and allows for the space to practice different strategies to solve math problems. Give students a variety of options, such as timed exercises, projects, or different materials , to show that they’ve mastered foundational skills. As students show what they’ve learned, teachers can track understanding, figure out where students need additional scaffolding or other assistance, and tailor lessons accordingly.

7. Plant the seeds!

Leave no child inside! A school garden is a great way to apply math concepts in a fun way while instilling a sense of purpose in your students. Measurement, geometry, and data analysis are obvious topics that can be addressed through garden activities, but also consider using the garden to teach operations, fractions, and decimals. Additionally, garden activities can help promote character education goals like cooperation, respect for the earth, and, if the crops are donated to organizations that serve those in need, the value of giving to others.

8. Add apps appropriately

The number of apps (interactive software used on touch-screen devices) available to support math instruction has increased rapidly in recent years. Kids who are reluctant to practice math facts with traditional pencil-and-paper resources will gladly do essentially the same work as long as it’s done on a touch screen. Many apps focus on practice via games, but there are some that encourage children to explore the content at a conceptual level.

9. Encourage math talk

Communicating about math helps students process new learning and build on their thinking. Engage students during conversations and have them describe why they solved a problem in a certain way. “My goal is to get information about what students are thinking and use that to guide my instruction, as opposed to just telling them information and asking them to parrot things back,” says Delise Andrews, who taught math (K–8) and is now a grade 3–5 math coordinator in the Lincoln Public Schools in Nebraska.

Instead of seeking a specific answer, Andrews wants to have deeper discussions to figure out what a student knows and understands. “True learning happens a lot around talking and doing math—not just drilling,” she says. Of course, this math strategy not only requires students to feel comfortable expressing their mathematical thinking, but also assumes that they have been trained to listen respectfully to the reasoning of their classmates.

Learn more: Free Let’s Talk Math Poster

10. The art of math

Almost all kids love art, and visual learners need a math strategy that works for them too, so consider integrating art and math instruction for one of the easiest strategies in teaching mathematics. Many concepts in geometry, such as shapes, symmetry, and transformations (slides, flips, and turns), can be applied in a fun art project. Also consider using art projects to teach concepts like measurement, ratios, and arrays (multiplication/division).

11. Seek to develop understanding

Meaningful math education goes beyond memorizing formulas and procedures. Memorization does not foster understanding. Set high goals, create space for exploration, and work with the students to develop a strong foundation. “Treat the kids like mathematicians,” says Andrews. Present a broad topic, review various strategies for solving a problem, and then elicit a formula or idea from the kids rather than starting with the formula. This creates a stronger conceptual understanding and mental connections with the material for the student.

12. Give students time to reflect

Sometimes teachers get so caught up in meeting the demands of the curriculum and the pressure to “get it all done” that they don’t give students the time to reflect on their learning. Students can be asked to reflect in writing at the end of an assignment or lesson, via class or small group discussion, or in interviews with the teacher. It’s important to give students the time to think about and articulate the meaning of what they’ve learned, what they still don’t understand, and what they want to learn more about. This provides useful information for the teacher and helps the student monitor their own progress and think strategically about how they approach mathematics.

13. Allow for productive struggle

When giving students an authentic problem, ask a big question and let them struggle to figure out several ways to solve it, suggests Andrews. “Your job as a teacher is to make it engaging by asking the right questions at the right time. So you don’t take away their thinking, but you help them move forward to a solution,” she says.

Provide as little information as possible but enough so students can be productive. Effective math teaching supports students as they grapple with mathematical ideas and relationships. Allow them to discover what works and experience setbacks along the way as they adopt a growth mindset about mathematics.

14. Emphasize hands-on learning

WeAreTeachers; Teacher Created Resources

In math, there’s so much that’s abstract. Hands-on learning is a strategy that helps make the conceptual concrete. Consider incorporating math manipulatives whenever possible. For example, you can use LEGO bricks to teach a variety of math skills, including finding area and perimeter and understanding multiplication.

15. Build excitement by rewarding progress

Students—especially those who haven’t experienced success—can have negative attitudes about math. Consider having students earn points and receive certificates, stickers, badges, or trophies as they progress. Weekly announcements and assemblies that celebrate the top players and teams can be really inspiring for students. “Having that recognition and moment is powerful,” says Bax. “Through repeated practice, they get better, and they are motivated.” Through building excitement, this allows for one of the best strategies in teaching mathematics to come to fruition.

16. Choose meaningful tasks

Kids get excited about math when they have to  solve real-life problems. For instance, when teaching sixth graders how to determine area, present tasks related to a house redesign, suggests Fennell. Provide them with the dimensions of the walls and the size of the windows and have them determine how much space is left for the wallpaper. Or ask them to consider how many tiles they would need to fill a deck. You can absolutely introduce problem-based learning, even in a virtual world.

17. Play math games

Life Between Summers/Shape Guess Who via lifebetweensummers.com; 123 Homeschool 4 Me/Tic-Tac-Toe Math Game via 123homeschool4me.com; WeAreTeachers

Student engagement and participation can be a challenge, especially if you’re relying heavily on worksheets. Games, like these first grade math games , are an excellent way to make the learning more fun while simultaneously promoting strategic mathematical thinking, computational fluency , and understanding of operations. Games are especially good for kinesthetic learners and foster a home-school connection when they’re sent home for extra practice.

18. Set up effective math routines

Students generally feel confident and competent in the classroom when they know what to do and why they’re doing it. Establishing routines in your math class and training kids to use them can make math class efficient, effective, and fun! For example, consider starting your class with a number sense routine . Rich, productive small group math discussions don’t happen by themselves, so make sure your students know the “rules of the road” for contributing their ideas and respectfully critiquing the ideas of others.

19. Encourage teacher teamwork and reflection

You can’t teach in a vacuum. Collaborate with other teachers to improve your math instruction skills. Start by discussing the goal for the math lesson and what it will look like, and plan as a team to use the most effective math strategies. “Together, think through the tasks and possible student responses you might encounter,” says Andrews. Reflect on what did and didn’t work to improve your practice.

Learn With Play at Home/Plastic Bottle Number Bowling via learnwithplayathome.com; Math Geek Mama/Skip-Counting Hopscotch via mathgeekmama.com; WeAreTeachers

Adding movement and physical activity to your instruction might seem counterintuitive as a math strategy, but asking kids to get out of their seats can increase their motivation and interest. For example, you could ask students to:

• Make angles with their arms
• Create a square dance that demonstrates different types of patterns
• Complete a shape scavenger hunt in the classroom
• Run or complete other exercises periodically and graph the results

The possibilities of these strategies in teaching mathematics are limited only by your imagination and the math concepts you need to cover. Check out these active math games .

21. Be a lifelong learner

Generally, students will become excited about a subject if their teacher is excited about it. However, it’s hard to be excited about teaching math if your understanding hasn’t changed since you learned it in elementary school. For example, if you teach how to divide fractions by fractions and your understanding is limited to following the “invert and multiply” rule, take the time to understand why the rule works and how it applies to the real world. When you have confidence in your own mathematical expertise, then you can teach math confidently and joyfully to best apply strategies in teaching mathematics.

What do you feel are the most important strategies in teaching mathematics? Share in the comments below.

Want more articles like this be sure to subscribe to our newsletters ., learn why it’s important to honor all math strategies in teaching math . plus, check out the best math websites for teachers ..

You Might Also Like

24 Creative Ways to Use Math Manipulatives in Your Classroom

Students learn better when they’re engaged, and manipulatives in the classroom make it easy for kids to get excited. We Continue Reading

Copyright © 2024. All rights reserved. 5335 Gate Parkway, Jacksonville, FL 32256

Classroom Q&A

With larry ferlazzo.

In this EdWeek blog, an experiment in knowledge-gathering, Ferlazzo will address readers’ questions on classroom management, ELL instruction, lesson planning, and other issues facing teachers. Send your questions to [email protected]. Read more from this blog.

10 Teacher-Proofed Strategies for Improving Math Instruction

• Share article

During the summer, I am sharing thematic posts bringing together responses on similar topics from the past 11 years. You can see all those collections from the first 10 years here.

Today’s theme is on Math Instruction.

You can see the list following this excerpt from one of the posts:

1. ‘Beware of Teaching Math Vocabulary Out of Context!’

Three educators share their favorite math instructional strategies, including “Turn & Talk to Your Neighbor.” Read more.

2. Four Teacher-Recommended Instructional Strategies for Math

Four teachers share their favorite strategies for math instruction, including the Concrete Representational Abstract approach. Read more.

3. Don’t ‘Make the Math Classroom a Project-Based-Learning-Free Zone’

Three educators share advice on incorporating project-based learning in math classes, including asking the question “What’s nearby?” Read more.

4. Using Project-Based Learning in Math Classes

Two teachers share practical strategies for using project-based learning in math classes, including one called “Notice & Wonder.” Read more.

5. Twelve Ways to Make Math More Culturally Responsive

Four educators share ideas for using culturally responsive teaching in math class, including by helping students make community connections. Read more.

6. ‘I Am Doing My Best': Teaching Math During the School Closure Crisis

Four teachers offer remote teaching tips for math instruction, including recognizing that nothing they do is going to be anywhere near “perfect.” Read more.

7. ‘Less Is More’ in Math Distance Learning

Four math educators offer advice about remote instruction, including providing more specific targets and cultivating home connections. Read more.

8. ‘How to Assess Students’ Math Skills Remotely

Two math educators discuss how they are communicating student performance during the school closure crisis, as well as how they are taking care of themselves. Read more.

9. Math Instruction in the Age of the Coronavirus

Two math educators share how they design their remote teaching math lessons and what they typically look like in practice. Read more.

10. Elements of an Effective Math Lesson

Teachers explain how creative math lessons can spring from students’ surrounding environments and culture such as the cost of the Thanksgiving meal and the search for “math selfies.” Read more.

More Q&A posts about math instruction:

• Eight Educators Share Their Best Math Lessons
• ‘Nix the Tricks’ in Math Instruction
• ‘It’s Time to Slow Down and Smell the Mathematical Roses!’
• Mistakes That Math Teachers Make
• ‘Tech Does Not Replace Pedagogy—It Complements It’
• Ways to Use Tech in Math Class
• Students Must ‘Engage in Math Problem-Solving’ & Not Just ‘Follow Procedures’
• Best Practices for Teaching High School Math
• ‘Writing in Math Class Is a Win-Win for Students & Teachers’
• Author Interview: ‘Motivated: Designing Math Classrooms Where Students Want to Join In’
• Math Can Be a ‘Hard Sell’
• ‘Challenges Are a Natural Part of Mathematics’
• Differentiating Algebra Instruction
• Effective Math Instructional Strategies—Part Two
• Ways to Teach Math Besides ‘Drill the Skill’
• Several Ways to Become Better at Teaching Math
• Several Ways to Become Better at Teaching Math—Part Two

Explore other thematic posts:

• It Was Another Busy School Year. What Resonated for You?
• How to Best Address Race and Racism in the Classroom
• Schools Just Let Out, But What Are the Best Ways to Begin the Coming Year?
• Classroom Management Starts With Student Engagement
• Teacher Takeaways From the Pandemic: What’s Worked? What Hasn’t?
• The School Year Has Ended. What Are Some Lessons to Close Out Next Year?
• Student Motivation and Social-Emotional Learning Present Challenges. Here’s How to Help
• How to Challenge Normative Gender Culture to Support All Students
• What Students Like (and Don’t Like) About School
• Technology Is the Tool, Not the Teacher
• How to Make Parent Engagement Meaningful
• Teaching Social Studies Isn’t for the Faint of Heart
• Differentiated Instruction Doesn’t Need to Be a Heavy Lift
• How to Help Students Embrace Reading. Educators Weigh In
• 10 Strategies for Reaching English-Learners
• 10 Ways to Include Teachers in Important Policy Decisions

The opinions expressed in Classroom Q&A With Larry Ferlazzo are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.

Sign Up for EdWeek Update

Edweek top school jobs.

Sign Up & Sign In

• Our Mission

How to Engage Students in Meaningful Math Discussions

As middle and high school math students talk through problems, they build camaraderie and gain greater conceptual understanding.

Before I stepped into the classroom as an educator for the first time, I had fantasized about what it would be like. I would lecture from the front of the room while all students diligently hung on my every word, eager to learn what I had to share. Students would have pencils to paper for the entire 90-minute block and would readily digest the material.

Anyone who has been in a classroom, especially a sixth-grade one, can easily find fault with my fantasy—there are very few students who want to be passively lectured at and fewer who plan on silently absorbing information for a full 90 minutes at a time. While I recognized that my fantasy was a bit of a stretch even before I began, I very quickly realized that I needed to make some major adjustments to my instructional planning to create the type of highly engaged and high-performing classroom I wanted.

Over the past three years as a sixth-grade math teacher, I have developed a number of strategies that have catapulted my classroom from the rigid and dry lecture halls of my imagination to the highly engaged and passionate places for deep exploration that they are today. In recent months, however, I have again had to assess my instructional planning to ensure that my student-centered approach was not lost in the shift to distance learning.

While distance learning has certainly altered the way in which I carry out my instructional strategies, I have continued to employ the below outlined strategies to ensure a high level of student engagement through discussions. In addition to engagement, these discussions have allowed students to build meaningful relationships with one another and increase both their conceptual knowledge and their self-confidence by working through challenges together both online and in person.

Strategy 1: What Do We Think About That?

When a student provides the correct answer to a posed question, it is easy to simply respond with “Yes!” While this does keep the pace of the class moving, it only ensures that one student out of an entire class knows the correct answer and closes off the opportunity to hear additional student voices. Instead, we as teachers can respond with “What do we think about that?” in response to a given answer. This generates an open-ended question, which allows multiple students to weigh in on the given answer: agreeing, disagreeing, providing additional evidence, etc.

This strategy can easily be applied during a synchronous session of distance learning in the same way as in person. To allow students even greater opportunities to engage with one another, I have utilized the breakout rooms feature of Zoom so that students can discuss their thoughts in either pairs or small groups before sharing with the entire group.

To employ this strategy in an asynchronous session of distance learning, I have utilized Google Docs to pose a question on a collaborative document and required students not only to add their own individual response but also to assess the responses of their classmates by using the comments feature. Additionally, I have utilized Flipgrid to allow students to record themselves providing responses to questions. Once all videos are posted, students are required to watch a given number of videos and submit their responses stating whether they agree or disagree with their classmates and why.

Strategy 2: What Do You Mean I’m Wrong?!

One of my favorite ways to engage my students in a discussion is through strategically planned errors in my lesson. Once I have introduced a topic and am confident that my students understand the solving process, I will guide them through a problem and intentionally make common errors. I will then wait for students to point these out. However, I will not immediately accept that they are right. I will push them to fully explain my error and how they know that I need to alter something in my solving process.

To employ this strategy in a synchronous session of distance learning, I have utilized the whiteboard feature on Zoom as well as shown images of completed problems that have specific mistakes. Once students are able to see the work, they are able to openly discuss mistakes and how to fix them.

In an asynchronous session, I have utilized Google Docs in order to show students an incorrectly completed problem and have asked them to identify and correct the errors using the comments feature. Additionally, I have employed this strategy by posting a video of myself solving a problem incorrectly and have asked students to identify the mistakes and provide the necessary corrections to reach the appropriate answer. I have relied on the platform Edpuzzle to accomplish this. It allows me to post videos with embedded questions, so that students can either respond in a short answer at the end of the video to assess my entire solving process or respond to questions throughout the video to state whether they agree or disagree with each step and why.

These strategies provide a starting point for any teacher to begin to implement a more discussion-based approach to teaching mathematics. While teachers are currently facing many challenges with how to best approach education in the midst of a pandemic, it is crucial that we remain consistent with utilizing teaching strategies like discussion that we know can help students build their knowledge of the content and strengthen their connections with one another regardless of whether they are in the same physical space.

ChatGPT for Teachers

Trauma-informed practices in schools, teacher well-being, cultivating diversity, equity, & inclusion, integrating technology in the classroom, social-emotional development, covid-19 resources, invest in resilience: summer toolkit, civics & resilience, all toolkits, degree programs, trauma-informed professional development, teacher licensure & certification, how to become - career information, classroom management, instructional design, lifestyle & self-care, online higher ed teaching, current events, research-based math teaching strategies.

Math can be challenging for many students. At the same time, integrating research-based teaching strategies can significantly improve their understanding of the material throughout their primary and secondary education.

Research-based math strategies, such as using hands-on manipulatives or incorporating real-world examples, can make basic mathematical concepts more accessible and engaging for students of all ages.

Adapting these numeracy strategies to the needs of individual students can have a significant impact in helping them build a strong foundation in math and set them up for ongoing success.

Basic math teaching tactics

A simple strategy teachers can use to improve math skills is repetition. By repeating and reviewing previous formulas, lessons, and information, students are better able to comprehend concepts at a faster rate.

According to Professor W. Stephen Wilson from Johns Hopkins University, the core concepts of basic math must be mastered before students are able to move into a more advanced study. Repetition is a simple tool that makes it easier for students to master the concepts without wasting time. According to the University of Minnesota, daily re-looping or reviews will bring the previous lesson back into the spotlight and allow teachers to build on those previous skills.

Timed testing

When teachers are moving beyond the simple concepts of numbers into addition, subtraction, multiplication and division, it is important to incorporate timed tests that review the previous class or several classes.

Taking a short test and then grading the test in class will help teachers assess student understanding. When the test shows that students are answering more questions correctly within the time period, teachers are able to determine that students have mastered the basic skills.

Mathematics is not limited to learning from a textbook, lessons, or testing strategy. Students have different learning styles and need to have lessons that help improve all styles of learning to get the best results.

Group work is a simple strategy that allows students to work and problem-solve with a buddy. When a teacher has provided the basic instruction, it’s helpful to split the class into pairs or groups to work on problems.

Since the pairs are working as a team, the students can discuss the problems and work together to solve the issues. The goal of pair work is to teach students critical thinking skills that are necessary for future math problems and real life.

Manipulation tools

The use of blocks, fruits, balls, or other manipulation tools help students learn the basics of place value, addition, subtraction, and other areas of basic math. According to Kate Nonesuch on the National Adult Learning Database of Canada, manipulation tools help slow down the process of problem solving so that students are able to fully understand the information.

Manipulation tools make it easier for students to learn and understand basic skills. These are ideal when students learn best through hands-on experience and building, rather than traditional lessons and repetition.

Reinforcing the information learned in class is not always the easiest task for teachers, but math games provide the opportunity to make the lesson interesting and encourage students to remember the concepts.

Depending on the class size, computer availability, and the lesson being taught, games can vary. Teachers can use computer games for the particular skills or can opt to use class games to make the lesson more fun. Teachers should be sure to incorporate a strategy into games to help students learn the material.

Fundamental mathematical concepts students should learn by 12th grade

Though the specific curricula may vary by location and school district, typical mathematical concepts students are expected to have learned upon completing secondary education include:

• Algebraic expressions and equations . Graduating students should be able to understand, manipulate, and solve algebraic expressions and equations.
• Functions . Seniors should be able to understand and work with linear, quadratic, and exponential functions.
• Geometry . By the completion of 12th grade, students should have a working knowledge of geometric concepts such as points, lines, angles, triangles, quadrilaterals, circles, and three-dimensional shapes.
• Trigonometry . Graduates should be fluent in trigonometric functions and able to solve problems involving angles and lengths in triangles.
• Statistics and probability . Graduating seniors should be able to understand and analyze simple statistical data and the concepts involved in the calculation of probabilities.
• Calculus . Though mastery of this subject is generally beyond the scope of secondary education, graduating seniors should have a functional understanding of calculus concepts such as limits, derivatives, and integrals.

Early education: research-based math instruction for kindergarten

The youngest students are at the onset of their math literacy, and teaching strategies for kindergarten math must be developmentally appropriate. Start with imparting basic ideas such as counting and number recognition before moving on to more advanced concepts.

It is well established that younger students are concrete learners and can more easily grasp mathematical concepts through hands-on and visual approaches. The use of manipulatives, such as counting bears of different colors, can be used to teach basic counting and sorting concepts.

Unifix or linking cubes are effective methods for teaching the fundamentals of counting, addition, and subtraction. Similarly, the use of base ten blocks efficiently introduces students to the concepts of units, tens, and hundreds.

Connecting mathematical concepts to real-life examples can make them more meaningful and easier to grasp for kindergarten students, while incorporating games or activities has the added benefit of making math instruction more fun and engaging.

Counting or shopping games involving bills and coins of different values supports an increased understanding of counting, addition, and subtraction. Likewise, cooking games involving ingredients can help teach concepts of measurement such as weight and volume.

Encouraging students to work together on math activities in pairs or small groups can help them develop problem-solving skills and the ability to communicate mathematical concepts.

Ongoing support and reinforcement of new ideas are essential to help kindergarten students retain what they have learned. Regular and consistent review of learned material can reveal whether individual students need additional instructions or practice.

Essential mathematics topics for primary school: research-based strategies for grades 1-6

Continuing elementary math strategies should build on what early childhood students have already learned. Games and real-world examples continue to be effective, as are hands-on and interactive activities involving manipulatives. These should gradually become more complex and involve more functions with variable solutions.

Activities should be combined with visual aids like pictures and diagrams. These visual aids help introduce students to abstract representations of concepts that they first encountered via concrete methods.

The use of repetition and review becomes developmentally appropriate and can help students comprehend and retain essential functions more rapidly. 

Young students develop at different rates and respond better to various approaches. Numeracy strategies in the classroom should draw on an assortment of methods during early primary education.

The continued use of manipulatives and visual aids is most effective when employed alongside traditional methods such as worksheets and classroom instruction. Technology-based instruction, which often involves online math games, virtual manipulatives, and videos, can further help keep students engaged and actively learning.

Ongoing primary education: research-based math strategies for middle school

Middle school typically refers to grades 6-8, though some schools may include Grade 9 students. This is a time of significant transition and developmental growth for students as they tackle increasingly advanced coursework, greater responsibility, and more independence in their ongoing instruction.

Linking mathematical concepts to the real world remains an effective teaching method. However, real-world examples should reflect the growing sophistication and abilities of older primary school students. Budgeting and financial planning exercises help reinforce concepts such as decimals and percentages.

Games and activities continue to help engage middle school students but should reflect their increased capabilities. More complex card or board games can help students practice new math skills. Virtual games using technology-based methods are similarly effective.

Collaborative learning furthers critical thinking and problem-solving skills. One excellent way to keep students involved is by encouraging them to work in pairs or small groups using educational apps or online resources.

Ongoing review of learned material is essential to greater understanding and retention. Students should be provided with individual support and tailored practice to reinforce concepts that may be challenging.

Secondary education: research-based math strategies for high school students

As students progress through high school and prepare for a university education, independence and individual responsibility become essential. Encouraging  students to take ownership of their ongoing education and math studies will help enable them to successfully meet the expectations and demands placed on them in higher education. 

Provide opportunities for the personal exploration of mathematical concepts through individual study and solo projects. This can be especially effective when coupled with collaborative efforts, such as having students review each other’s work and discuss any errors or differences in understanding.

Using increasingly complex real-world situations, such as statistical analysis of sports or finance, emphasizes the utility of mathematical concepts in everyday life. Similarly, algebra teaching strategies incorporating technology such as loan calculators and online stock trading simulations increase engagement and retention of learned concepts for secondary school students.

Intervention strategies for learners experiencing barriers in mathematics

Numeracy intervention strategies are useful to help students struggling with math. Practical approaches will depend on each student’s specific needs. They should be tailored to individual learning styles and the concepts with which that student is experiencing difficulties.

Individualized instruction and one-on-one tutoring may be effective for single students having difficulty with concepts understood by most of a class. Forming small groups for instruction and collaborative study is a more efficient and targeted method for students struggling with similar or related concepts.

A math intervention strategies list should include tools that address the needs of individual students. Visual aids like graphs and diagrams and adaptive software that responds to a particular student’s performance are effective techniques. Students who need to solidify their understanding of specific topics or improve individual skills will benefit from additional practice opportunities.

For students struggling with previously introduced concepts, reviewing the material using different approaches, examples, and explanations can be helpful. The most effective math intervention strategies will vary depending on each student’s specific needs and learning style. Students may require different approaches to find what works best for their challenges.

Final thoughts: a tailored approach to individual needs

There are many proven, research-based strategies for teaching math . Approaches involving the incorporation of real-world examples to make concepts more relatable and the use of technology and online resources to enhance learning remain effective throughout primary and secondary education. Of course, these should be adapted to ensure they’re developmentally appropriate for students as they progress.

Overall, teachers should encourage students to persevere through the challenges they may face in understanding math concepts while promoting a growth mindset and providing ongoing support. The ultimate key to success lies in balancing traditional and modern methods and using various approaches to suit each student’s individual needs and learning styles.

You may also like to read

• Effective Teaching Strategies for Adolescent Literacy Teachers
• Effective Teaching Strategies for Special Education
• ESL Teaching Strategies for Educators
• Teaching Strategies for Preschool Educators
• Tips in Teaching a Hands-On Math Curriculum
• 6 Strategies for Teaching Special Education Classes

Categorized as: Tips for Teachers and Classroom Resources

Tagged as: Math and Science

• Certificates in Trauma-Informed Education and...
• Online Education Specialist Degree for Teache...
• Online & Campus Bachelor's in Elementary Educ...

• Mathematics
• Reading and Writing
• Intervention
• Professional Learning
• Virtual Events
• What is Phonics?
• Teaching Grammar
• Vocabulary Games
• What is Virtual Learning?
• About Sadlier
• Find a Sales Representative
• International Distributors
• International Programs
• Online Catalogs
• Sadlier School Site Map
• Pricing & Ordering Information
• Sadlier’s W-9
• Sadlier’s Sole Source Letter
• Sadlier’s Credit Application
• Privacy Policy
• Return Policy
• Terms & Conditions

Sadlier's Math Blog

• Counting and Cardinality
• Operations and Algebraic Thinking
• Number and Operations in Base 10
• Measurement and Data
• Math Practices
• Number and Operations Fractions
• Statistics and Probability
• The Number System
• Ratios and Proportional Relationships
• Expressions and Equations
• MP1—Problem Solving
• MP2—Abstract <−>Quantitative
• MP3—Reasoning
• MP4—Modeling
• MP5—Using Tools
• MP6—Precision
• MP7—Structure
• MP8—Repeated Reasoning
• Kindergarten Math Activities
• First Grade Math Activities
• Second Grade Math Activities
• Third Grade Math Activities
• Fourth Grade Math Activities
• Fifth Grade Math Activities
• Sixth Grade Math Activities
• Seventh Grade Math Activities
• Eighth Grade Math Activities
• Professional Development
• Test-Taking Strategies
• Classroom Posters
• Writing In Mathematics

July 23, 2020 k-2-math-practices , 6-8-math-practices , other-professional-development , 3-5-math-practices

5 ways to update methods & strategies in teaching mathematics, by: jeff todd.

Moving from onsite instruction to remote instruction (or a blend) has forced teachers to assess their methods and strategies in teaching mathematics. Teachers can use this new educational landscape to breathe new life into their teaching! In this post, I explore how incorporating new strategies into instruction is the quickest way to kick the digital disconnect some students may experience and keep them building their conceptual understanding of mathematics.

Adjusting Your Methods of Teaching Mathematics for Distance Learning

Summers spent assessing whether you're stuck in the same instructional routine or experiencing a teaching slump are gone, 2020 has ushered in the "age of Covid-19".

Social distancing measures flipped the education world upside down and educators have been called to adjust, innovate, and restructure.  A new school year is quickly approaching and math teachers are having to discover (and rediscover) new methods of teaching mathematics for distance learning. In order to effectively teach math in virtual instructional settings (or a hybrid schedule), teachers need to put in place both old and new strategies that will maximize student learning. 

Despite the whirlwind of change, I want to share a  tip sheet that outlines five timeless ways teachers can enhance their K–8 math instruction. Even if you are going to be teaching remote this new school year, this tip sheet is still relevant to you and a valuable resource to have in your teaching toolbox. Download it now! 

hbspt.cta._relativeUrls=true;hbspt.cta.load(95641, '1543e221-7be0-4ef4-9ba1-4ee951d1ba8d', {"useNewLoader":"true","region":"na1"});

Ways to update your methods and strategies of teaching mathematics, #1 improve your use of classroom discourse.

Creating rich classroom discussions is essential for your in-person or virtual classroom. To offset some of the harmful effects of long periods of social distancing, students need interaction with their teacher and with their peers. Classroom discourse will give students the interaction they need while also helping them improve their ability to communicate mathematics. A win for everyone!

Here are some things to remember:

To promote quality mathematics discussions, students need to understand why discourse is important.

• Students need reassurance that although it can be unnerving to participate in discussions about mathematics, it is beneficial to their learning!

Establishing a learning environment that welcomes student involvement is the key to engaging students in discourse.

• Teachers need to set the expectation that every student will contribute during math talk. Establishing expectations emphasizes that the class is a community of learners.
• Active listening is an important component of any classroom, but in the math classroom it is crucial to comprehension! Without active listening, students will not be able to critique the reasoning of their peers or analyze how their understanding aligns with or differs from their classmates.

A challenge ALL teachers will face when working to promote classroom discourse is that many students, especially in during virtual lectures , tend to take on an observer role. 

When in an in-person classroom setting students are more likely to stay interested (or feign interest 😂), pick up on cues that they are required to participate, and be active listeners. Onsite instruction also makes it easier for teachers to assess which students are struggling to fully engage. Regardless of these benefits of teaching in-person, classroom discourse does not happen overnight and will have obstacles.

Creating rich classroom discussions will breathe life into your in-person or virtual math instruction!

Mathematical discourse in the virtual classroom is new territory for teachers and students. Because most K–8 students are use to the traditional classroom setting, we can expect the shift to a virtual setting will increase the number of "observers" in a class. 

So how can educators improve and promote quality classroom discourse?

To have great discussions as an onsite or offsite class, teachers should consider think-pair-share activities, accountable talk strategies, and ways to draw out reluctant class participants.

Download a series of prompts  you can use to improve student interaction in your classroom!

If you are unfamiliar with these techniques, I would encourage you to read this post , which includes easy-to-implement strategies for accountable talk. 

Other strategies include:

The 60-Second Startle– Do something within the first 60 seconds of kicking off classroom discourse that will startle students into paying attention and snap them out of observer mode. Consider sharing a personal story, song, or riddle that highlights the real-world importance of the math topic you will be discussing!

Math Reporters– Make students hard-hitting math reporters in the in-person or virtual classroom. It doesn't matter if students are participating in asynchronous   instruction or synchronous instruction, require them to report on various items in the math classroom. If students know they have to report, recount, or respond to something happening in recorded or live lectures, they are more likely to be active listeners. Students can record and upload 15-60 second clips reporting on various topics. For example, students could report:

• Their response to a prompt
• Showing how they got an answer
• Explaining different ways to get the same answer
• Remark on something in the lesson they learned or are confused about

Finally, use these videos to encourage discourse! Require students respond to each others math news reports with accountable discussion prompts. Their commentary should showcase their ability to construct viable arguments and to critique the reasoning of others. 

#2 Promote Students' Development of Procedural and Computational Fluency

With so much focus recently on conceptual understanding, modeling, and problem solving, it can be easy to forget that both procedural and computational fluencies are foundational to students’ long-term success in mathematics.

There are many online and commercial products available to help students develop these fluencies, but even if you don’t have the technology available, there are still ways to work on them. A couple of my posts provide some of these resources, and I hope that you will take advantage of them:

This Subitizing Powerpoint Activity is great for Grades 1 to 4

This is my version of  Flashcards for Multiplication and Division that combines the use of arrays with fact families.

As you work with students to improve their fluency, remember that the activities you implement should be brief, engaging, and purposeful, and should be distributed throughout the school year. Practicing fluency should not be drudgery for students. It can be made fun! And that kind of fun atmosphere can help liven up your classroom.

#3 Use Real-World Problems

Modeling, reasoning, and problem solving are the goals of higher order thinking in the math classroom. Not only are the modern open response questions on high-stakes tests focused on these areas, but they are also one way that students can become engaged in math. Rich contextual problems can help students see why math is important and answer the question: “Why are we learning this?”

I know that many of the “real-world” problems in textbooks I have used are a bit flimsy such as: “Bob sold ½ of a 16 acre plot. He then sold ⅔ of the remaining piece. How much of the 16 acres remain unsold?” While valuable procedurally and for the purposes of reading, this is not the kind of rich context where students get involved with a personal connection to the problem.

Below are some printable activities that are great examples of real-world problem solving.

If you will be teaching remote, these printable   PDFs can be converted via Google Drive so students can type directly into the worksheet. Check out   Vocab Gal's tutorial for converting PDFs   so they can be completed online. 

Or you can complete these activities when meeting virtually with small groups of students (camp fire groups). 

#4 Using Virtual Instruction Time and Technology Effectively

Right now is a great opportunity to breathe new life into your classroom through the use of computers (most of us don't have a choice 😆 ). But remember, it’s not the fact that you are using technology, it’s how you incorporate it that makes all the difference.

All educators are having to rethink how to incorporate technology strategically and align it to your district grade-level goals. Virtual instruction does not mean abandoning traditional teaching methods, but it does mean we have to be smart about how we teach, assess, and execute activities.

For more ideas on ways to use virtual instruction time and technology effectively, check out this article !

#5 Implement the Standards for Mathematical Practice

I feel that one of the most valuable resources I have provided through the blog is the number of resources you can use to implement the Standards for Mathematical Practice. I hope you have seen these articles and downloadable resources , but here they are all in one place and organized by standard:

PROBLEM SOLVING

• Two Ways You Can Begin to Implement the Math Practice Standards
• How to Make Sense of Problems and Persevere in Solving Them
• Place Value Primary Resources to Promote Flexibility in Grades 1 and 2
• P3: Partner Problem-Solving Protocol and Graphic Organizer
• 3 Ways to Reason Abstractly and Quantitatively in the Middle School Classroom
• How to Express Regularity in Repeated Reasoning with Fact Families At the Middle School Level
• Vocabulary to Construct Viable Arguments and Critique the Reasoning of Others
• Using the Rule of Four Template to Help Middle School Students Model with Mathematics
• Three Ways to Use Appropriate Tools Strategically
• Attend to Precision in the K–8 Classroom
• How to Look for and Make Use of Structure in the Elementary Classroom

If your 2020-2021 school plans have you teaching in the virtual classroom, have students print the anchor charts on   8.5 x 11   copy paper and then put them in the front of their daily math journals (use page protecters). Now they have fabulous reference sheets they can easily access during class or when completing homework! The tip sheets and activities can be used at home by students to develop these practices.

If we can take hold of these elements and put them into practice, or even deepen our use of them if we are already using them, then we will breathe new life into our lessons and build student confidence despite the changes in schools!

I know that when reflect on my own practice and think about how I can take it deeper to reach more students, I get more excited about my work.

By implementing these research-based practices, we will have a profound impact on our students. Just as our personal relationships do, our career can go through ups and downs. Educators can let the current "downs" overwhelm them... or use these circumstances to revitalize their classroom and deepen student comprehension and learning, I hope you can take advantage of the many resources shared in this article.

Good luck! We are in this together! 

This article is a companion piece to the webinar, Need Ideas to Update and Enhance Your Math Instruction? available for free on the Sadlier website. I hope you will take time to listen to Ellen Edmonds’ webinar, but this post will expand on the presentation and point you to some resources that can help you implement best practices and refresh, or even overhaul, your teaching.

7 Concrete Strategies to Teach Conceptual Understanding in Math

These strategies will give you a head start on getting rid of math tips and tricks.

Multiplication is repeated addition.

Keep, switch, flip. 

The butterfly method.

These are all examples of math shortcuts, tips, or tricks that many students learn to rely on from an early age. I taught many students throughout my 16 years in the classroom who quickly pulled out these strategies!

But my students couldn’t explain why these tips and tricks work and would often stumble and become frustrated when they encountered situations where the tricks didn’t work or they forgot exactly what to do.

That’s why math education has transitioned in recent years to focus on teaching deep conceptual understanding rather than encouraging students to rely on shortcuts. Educators know that teaching children to deeply understand math leads to the development of problem-solvers and critical thinkers. 

But how can we ease away from teaching tips and tricks so our students have the opportunity to become true mathematicians?

Don’t worry; we’ve got a few ideas for you! Check out these seven tips for getting rid of the shortcuts and teaching true conceptual understanding in math.

1. Spiral Practice Through a Well-Thought-Out Scope and Sequence

Mathematics is a body of conceptual knowledge made up of interrelated concepts—it isn’t just a list of disconnected topics to check off a list as students move from grade to grade. Using a carefully considered scope and sequence to structure your school year is the first step in avoiding the pitfalls of math tips and tricks.

During my last few years of teaching, my district used the Carnegie Learning High School Math Solution for our Algebra 1 and Geometry classes. For the first time, I saw how much the scope and sequence really matter. Watching my Algebra 1 students pull from their Module 1 experiences in Module 5 to make sense of quadratic functions was a lightbulb moment–for all of us!

A thoughtful scope and sequence incorporating spiral review is key to teaching deep conceptual understanding in math. If we rely on teaching the “easy” shortcuts instead of giving students the time and space to master grade-level skills and see the connections between concepts, they’ll struggle to develop a body of conceptual knowledge that will help them understand more complex ideas in the future.

2. Use High-Order Tasks to Build Critical Thinking Skills

Although many students (and teachers!) love math shortcuts because they lead to quick “success,” having a toolbox packed with critical thinking skills and problem-solving strategies for students to pull from is so much more valuable. These skills will serve your students in various situations, whether they’re in advanced math classes or have to think critically about real-world problems.

One way to help students develop their critical thinking and problem-solving skills is to assign high-order math tasks in your classroom. When working on these rich tasks, they can think about what they already know and test out different ways to complete the task until they identify one that works. In the process, your students fill their toolbox with problem-solving strategies and critical thinking skills, eliminating the need for tips and tricks.

Some of my favorite high-order tasks to use with my Algebra 1 students were in a lesson titled, “Do You Mean: Recursion ?” This lesson is filled with activities that encourage students to think critically about arithmetic and geometric sequences and how to develop and deeply understand explicit and recursive formulas. They’re even asked to compare the pros and cons of using explicit or recursive formulas, using evidence developed over the last series of lessons!

The fact that there’s no “plug and chug” in this series of high-order tasks meant that my students were constantly using and developing their critical thinking skills and problem-solving strategies. 

I was always amazed at the deep conversations I heard around the room as they completed tables of cell divisions and eventually used those observations to understand why explicit and recursive formulas work.

3. Visual Representations for Better Retrieval

Visual aids are powerful tools for helping students to develop a deep, conceptual understanding of mathematical concepts. I loved supplementing as many lessons as possible with diagrams, graphs, anchor charts, manipulatives, and even high-quality math videos . In doing so, every learner had an entry point into even the most upper-level mathematic concepts.

When students visualize math concepts, they can more easily see patterns and make connections that might not be immediately apparent from written or verbal explanations. And when they have a visual cue stored in their brain, it makes retrieving information much more manageable. 

For example, suppose a student can recall that a quadratic function looks like a parabola because they’ve interacted with graphs illustrating a pumpkin catapult or diving into a swimming pool. In that case, they’re more likely to be able to interpret the formula of a quadratic function and apply that conceptual knowledge to different scenarios.

4. Manipulatives and Hands-On Learning

Another way to eliminate the need for tips and tricks (“A negative times a negative is a positive,” anyone?) is with manipulatives such as algebra tiles, counting chips, and even interactive number lines.

And I promise those hands-on materials aren’t just for the younger kids—your high schoolers won’t mind abandoning the paper and pencil note-taking in favor of digging into algebra tiles occasionally! 

I’ll never forget using algebra tiles for various purposes with my high schoolers. From watching a student with complex special needs finally understand the meaning and applications of a zero pair to seeing upper-level students suddenly “get” factoring trinomials, each visual and hands-on learning experience was pure magic!

5. Connect Concepts Instead of Teaching Math Shortcuts

Teaching is all about making connections. And while, yes, connecting with your students is one of the best ways to increase engagement, here we’re talking about making mathematical connections.

Teach your students to look for the interconnectedness of mathematical concepts, so they see how ideas fit together and build on one another, and watch as they develop a deeper understanding of the underlying concepts. Then, it’s time to kiss the shortcuts goodbye!

For example, the scope and sequence I used encouraged my students to apply their foundational knowledge of concrete geometric investigations and reasoning with shapes to formalize their understanding. Circles were also integrated throughout the course, rather than treating them as isolated geometric figures (as many other curriculums do). 

Watching my Geometry students make connections between circles and angle relationships and complete constructions using arcs was a game changer! They retained much more information when they saw the connections between concepts and were able to apply their knowledge and skills in new situations that I never expected.

6. Help Your Students Make Real-World Connections

Another vital connection that will lead to the elimination of shortcuts, tips, and tricks is between the mathematics your students learn in the classroom and the real-world applications of the concepts.

When you help your students discover these links to the real world, math suddenly loses its abstract nature. It becomes relevant, practical, and motivating.

Now your students will be more likely to remain engaged and acquire conceptual knowledge that can be generalized across various situations. Here are some examples using real-world scenarios to model integer subtraction that could be used in a 7th-grade class.

7. Don’t Use Math Tips and Tricks—Collaborate!

Most kids love to work in groups, right? It enhances the social aspect of school that many students value, and when structured correctly, these collaborative learning experiences can be the perfect setting for developing deep mathematical understanding.

Collaborating to create their conceptual knowledge is a powerful experience for your students. They may productively struggle , disagree, and even argue a bit, but these experiences are where the magic happens. 

“Allow students to experience and play and notice and wonder,” writes Tina Cardone, author of Nix the Tricks: A Guide to Avoiding Shortcuts That Cut Out Math Concept Development . “They will surprise you! Being a mathematician is not limited to rote memorization…Being a mathematician is about critical thinking, justification, and using tools from past experiences to solve new problems.”

And I can think of no better opportunity to notice, wonder, think critically, and justify those thoughts than when collaborating with peers. It may be hard to give up that “sage on the stage” lecture style (I definitely struggled!), but hearing your students engage in rich, mathematical conversations and watching them abandon the shortcuts in favor of deeply understanding the math is worth it. The feeling is second to none!

Don’t Let Tips and Tricks Take Away the Beauty of Math

Math is a beautiful, creative, and thought-provoking subject that sets the perfect stage for your students to become critical thinkers, problem solvers, and leaders of tomorrow. Don’t let a reliance on math shortcuts, tips, and tricks rob them of that experience!

I hope you’re ready to ditch the tips and tricks in your classroom, but if you need more convincing, check out this case study from Muleshoe Independent School District in Texas. They were able to teach their students deep conceptual understanding in math and get rid of the shortcuts—with some great results to show for it!

• Karen Sloan
• Content Marketing Specialist
• Carnegie Learning

Before joining Carnegie Learning's marketing team in 2022, Karen spent 16 years teaching mathematics and social studies in Ohio classrooms. She has a passion for inclusive education and believes that all learners can be meaningfully included in academic settings from day one. As a former math and special education teacher, she is excited to provide educators with the latest in best-practices content so that they can set all students on the path to becoming confident "math people."

You May Like

• April 17, 2023

Math is a beautiful, creative, and thought-provoking subject that sets the perfect stage for your students to become critical thinkers, problem solvers, and leaders of tomorrow. Don’t let a reliance on math shortcuts, tips, and tricks rob them of that experience!

Karen Sloan, Math and Special Education Teacher of 16 Years

Filed Under

• LONG + LIVE + MATH
• LONG + LIVE + MATH Classrooms
• LONG + LIVE + TEACHING
• Conceptual Understanding
• Critical Thinking
• Math Classrooms
• Math Confidence
• Math Motivation
• Math Tips and Tricks
• Problem Solving

Teaching Math: The Best Learning Practice Essay

Learning math is not an easy task for many students, especially if they are of a young age. It is not always interesting to deal with numbers and develop various calculating activities to meet educational standards and get high grades. However, students have to learn mathematics as an obligatory part of the elementary school system. Therefore, to facilitate a learning process and raise students’ interest, teachers offer various practices and improve their understanding of children’s needs, abilities, and expectations. The examples introduced on video lessons show that teachers may cooperate with children in a variety of ways. Still, the main task is to involve students in a learning process by giving vivid examples, clear instructions, and options to choose from. In this paper, the attention to three teaching strategies, which are explicit teaching, developmental activities to support a diversity of levels, and reflection, will be discussed and explained through the prism of mathematics classes and teachers’ intentions to improve their classroom work.

Motivation and interest are the two crucial aspects of student education. It does not matter what subject has to be learned or what activities must be developed, teachers have to make sure that their students are ready and eager to participate in classroom activities. In both videos, teachers make use of explicit teaching as the main learning practice for their students to be offered. This type of learning aims at directing student attention towards certain subjects and topics in the already established learning environment. In math classes, it is not enough for teachers to provide students with an opportunity to learn new material and follow the given instructions (Selling, 2016). Explicit learning is used to make mathematical practices interesting to students through real-life representations, generalizations, problem-solving, and justifying (Selling, 2016). When students can use their own examples and explanations of the theoretical material given, it is easy for them to realize why all these tasks cannot be ignored, and what the essence of all these tasks is.

Another significant step in classroom learning is the attention to developmental activities in terms of which a diversity of levels and group work can be taken into consideration. Student learning and achievements depend directly on the teachers’ level of professionalism (Bayar, 2014). On the one hand, following the instructions and recognizing standards cannot be ignored in the classroom. On the other hand, students may easily get bored with all those requirements being set. In both videos, teachers underline the necessity to promote development activities and observe what students can do, want to do, and try to avoid. Sometimes, it is better to observe the work of students in groups or make them work individually and investigate their strengths and weaknesses. In schools, children of different backgrounds should cooperate, demonstrating their ability to use knowledge and their tolerance for other students’ mistakes. Teachers have to underline the importance of development and create the required environment to support but never offense or reproach a child.

Finally, the teachers from both videos agree that reflection has to be one of the main learning activities in the classroom. It helps not only to clarify what students learn but also focuses on the gaps that still exist. The possibility to reflect on the already gained experience and personal progress is the skill that has to be developed through teachers’ and students’ cooperation (Kiemer, Grőschner, Pehmer, & Seidel, 2015). In addition, reflection as a learning activity has a number of crucial benefits for students. First, they learn how to use the classroom material in real life. Second, sharing their thoughts, doubts, and ideas, students are able to comprehend the true importance of mathematics. Finally, students who are able to reflect on their activities demonstrate intentions to learn new information and participate in classroom activities. Therefore, the choice of this practice is not only a sign of a high-level professionalism of an educator, but an example of how teachers should respect and support their students.

To conclude, it is necessary to say that the offered videos help to realize how to improve mathematics classes and how to choose appropriate learning activities. The justification of this choice is based not only on the benefits students may gain in the classroom. The recognition of explicit learning, developmental activities, and reflection as the best practices to study math is explained by the possibility to focus on the merits and demerits of the subject and underline the importance of student participation. Though rules and plans cannot be ignored in teaching, educators should never forget that student motivation, interest, and achievement are the core values. Students may vary in their backgrounds, personal experiences, and skills. The task of teachers is to promote development, organize group projects, and reflect on the achievement made. Math can be one of the greatest subjects for students to deal with in elementary school, and explicit learning alone with group activities and reflections can help to achieve the best results in teaching practice.

Bayar, A. (2014). The components of effective professional development activities in terms of teachers’ perspective. International Online Journal of Educational Sciences, 6 (2), 319-327.

Kiemer, K., Grőschner, A., Pehmer, A. K., & Seidel, T. (2015). Effects of a classroom discourse intervention on teachers’ practice and students’ motivation to learn mathematics and science. Learning and Instruction, 35 , 94-103.

Selling, S. K. (2016). Making mathematical practices explicit in urban middle and high school mathematics classrooms. Journal for Research in Mathematics Education, 47 (5), 505-551.

• Chicago (A-D)
• Chicago (N-B)

IvyPanda. (2021, June 26). Teaching Math: The Best Learning Practice. https://ivypanda.com/essays/teaching-math-the-best-learning-practice/

"Teaching Math: The Best Learning Practice." IvyPanda , 26 June 2021, ivypanda.com/essays/teaching-math-the-best-learning-practice/.

IvyPanda . (2021) 'Teaching Math: The Best Learning Practice'. 26 June.

IvyPanda . 2021. "Teaching Math: The Best Learning Practice." June 26, 2021. https://ivypanda.com/essays/teaching-math-the-best-learning-practice/.

1. IvyPanda . "Teaching Math: The Best Learning Practice." June 26, 2021. https://ivypanda.com/essays/teaching-math-the-best-learning-practice/.

Bibliography

IvyPanda . "Teaching Math: The Best Learning Practice." June 26, 2021. https://ivypanda.com/essays/teaching-math-the-best-learning-practice/.

• What I Can Do to Help People Learn More About Math and Science
• Teaching Math in Charter and Public Schools
• Is Montessori Math a Pathway for Academically Gifted Students to Advance in Mathematics?
• Child-Educator Interactions and Development
• Children Engaged in a Science Activity: Behavior Observation
• Sheltered English Instruction Strategies: Lessons
• Assessment and Teaching Strategies in Nursing Education
• "How to Draw a Dog" Video Lecture Critique

• Prodigy Math
• Prodigy English
• Is a Premium Membership Worth It?
• Promote a Growth Mindset
• Help Your Child Who's Struggling with Math
• Parent's Guide to Prodigy
• Assessments
• Math Curriculum Coverage
• English Curriculum Coverage
• Game Portal

Top 9 Math Strategies for Successful Learning (2021 and Beyond)

Written by Ashley Crowe

• Teaching Strategies

Why are effective Math strategies so important for students?

Getting students excited about math problems, top 9 math strategies for engaging lessons.

• How teachers can refine math strategies

Math is an essential life skill. You use problem-solving every day. The math strategies you teach are needed, but many students have a difficult time making that connection between math and life.

Math isn’t just done with a pencil and paper. It’s not just solving word problems in a textbook. As an educator, you need fresh ways for math skills to stick while also keeping your students engaged. 

In this article, we’re sharing 9 engaging math strategies to boost your students’ learning . Show your students how fun math can be, and let’s freshen up those lesson plans!

Unlike other subjects, math builds on itself. You can’t successfully move forward without a strong understanding of previous materials. And this makes math instruction difficult.

To succeed in math, students need to do more than memorize formulas or drill times tables. They need to develop a full understanding of what their math lessons mean , and how they translate into the real world. To reach that level of understanding, you need a variety of teaching strategies. 

Conceptual understanding doesn’t just happen at the whiteboard. But it can be achieved by incorporating fun math activities into your lessons, including 

• Hands-on practice
• Collaborative projects
• Gamified or game-based learning

Repetition and homework are important. But for these lessons to really stick, your students need to find the excitement and wonder in math.

Creating excitement around math can be an uphill battle. But it’s one you and your students can win! 

Math is a challenging subject — both to teach and to learn. But it’s also one of the most rewarding. Finding the right mix of fun and learning can bring a lot of excitement to the classroom. 

Think about what your students already love doing. Video games? Legos? Use these passions to create exciting math lesson plans your students can relate to. 

Hands-on math practice can engage students that have disconnected from math. Putting away the pencils and textbooks and moving students out of their desks can re-energize your classroom.

If you’re teaching elementary or middle school math, find ways for your students to work together. Kids this age crave peer interaction. So don’t fight it — provide it! 

Play a variety of math games or puzzles . Give them a chance to problem-solve together. Build real-world skills in the classroom while also boosting student confidence. 

And be sure to celebrate all the wins! It is easy to get bogged down with instruction and testing. But even the smallest accomplishments are worth celebrating. And these rewarding moments will keep your students motivated and pushing forward.

Keep reading to uncover all of our top math strategies for keeping your students excited about math. 

1. Explicit instruction

You can’t always jump straight into the fun. Explicit instruction still provides the best foundation for the activities to come. 

Set up your lesson for the day at the whiteboard, along with materials to demonstrate the coming activities. Make sure to also focus on any new vocabulary and concepts. 

Tip: don't stay here for too long. Once the lesson is introduced, move on to the next fun strategy for the day!

2. Conceptual understanding

Helping your students understand the concept behind the lesson is crucial, but not always easy. Even your highest performing students may only be following a pattern to solve problems, without grasping the “why.”

Visual aids and math manipulatives are some of your best tools to increase conceptual understanding. Math is not a two dimensional subject. Even the best drawing of a cone isn’t going to provide the same experience as holding one. Find ways to let your students examine math from all sides.

Math manipulatives don’t need to be anything fancy. Basic wooden blocks, magnets, molding clay and other toys can create great hands-on lessons. No need to invest in expensive or hard-to-find materials. 

Math word problems are also a great time to break out a full-fledged demo. Hot Wheels cars can demonstrate velocity and acceleration. A tape measure is an interactive way to teach area and volume. These materials give your students a chance to bring math off the page and into real life. 

3. Using concepts in Math vocabulary

There’s more than one way to say something. And the more ways you can describe a mathematical concept, the better. Subtraction can also be described as taking away or removing. Memorizing multiplication facts is useful, but seeing these numbers used to calculate area gives them new meaning. 

Some math words are going to be unfamiliar. So to help students get comfortable with these concepts, demonstrate and label math ideas throughout your classroom . Understanding comes more easily when students are surrounded by new ideas. 

For example, create a division corner in your station rotations , with blocks to demonstrate the concept of one number going into another. Use baskets and labels to have students separate the blocks into each part of the division problem: dividend, divisor, quotient and remainder.  

Give students time to explore, and teach them big ideas with both academic and everyday terms. Demystify math and watch their confidence build!

4. Cooperative learning strategies

When students work together, it benefits everyone. More advanced students can lead, helping them solidify their knowledge. And they may have just the right words to describe an idea to others who are struggling.

It is rare in real-life situations for big problems to be solved alone. Cooperative learning allows students to view a problem from various angles. This can lead to more flexible, out-of-the-box thinking. 

After reviewing a word problem together as a class, ask small student groups to create their own problems. What is something they care about that they can solve with these skills? Involve them as much as possible in both the planning and solving. Encourage each student to think about what they bring to the group. There’s no better preparation for the future than learning to work as a team. 

5. Meaningful and frequent homework

When it comes to homework, it pays to think outside of textbooks and worksheets. Repetition is important, but how can you keep it fun?

Create more meaningful homework by including games in your curriculum plans. Encourage board game play or encourage families to play quiz-style games at home to improve critical thinking, problem solving and basic math skills. 

Sometimes you need homework that doesn’t put extra work onto the parents. The end of the day is already full for many families. To encourage practice and give parents a break, assign game-based options like Prodigy Math Game for homework. 

With Prodigy, students can enjoy a fun, video game experience that helps them stay excited and motivated to keep learning. They’ll practice math skills, while their parents have time to fix dinner. Plus, you’ll get progress reports that can help you plan future instruction . Win-win-win!    

Set an Assessment through your Prodigy teacher account today to reinforce what you’re teaching in class and differentiate for student needs. 

Ready to make homework fun?

6. Puzzle pieces math instruction

Some kids excel at math. But others pull back and may rarely participate. That lack of confidence is hard to break through. How can you get your reluctant students to join in?

Try giving each student a piece of the puzzle. When you’re presenting your class with a problem, this creates necessary collaboration to get to the solution. 

Each student is given a piece of information needed to solve the problem. A number, a unit of measurement, or direction — break your problem into as many pieces as possible. 

If you have a large class, break down three or more problems at a time. The first task: find the other students who are working on your problem (try color-coding or using symbols to distinguish each problem’s parts). Then watch the learning happen as everyone plays their own important role. 

7. Verbalize math problems

There’s little time to slow down in the classroom. Instruction has to move fast to keep up with the expected standards. And students feel that, too. 

When possible, try to set aside some time to ask about your students’ math struggles. Make sure they know that they can come to you when they get stuck. Keep the conversation open to their questions as much as possible.

One great way to encourage questions is to address common troubles students have encountered in the past. Where have your past classes struggled? Point these out during your explicit instruction, and let your students know this is a tricky area. 

It’s always encouraging to know you’re not alone in finding something difficult. This also leaves the door open for questions, leading to more discovery and greater understanding.

8. Reflection time

Providing time to reflect gives the brain a chance to process the work completed. This can be done after both group and individual activities.

Group Reflection

After a collaborative activity, save some time for the group to discuss the project . Encourage them to ask:

• What worked?
• What didn’t work?
• Did I learn a new approach?
• What could we have done differently?
• Did someone share something I had never thought of before? 

These questions encourage critical thinking. They also show the value of working together with others to solve a problem. Everyone has different ways of approaching a problem, and they’re all valuable.

Individual Reflection

One way to make math more approachable is to show how often math is used. Journaling math encounters can be a great way for students to see that math is all around. 

Ask them to add a little bit to their journal every day, even just a line or two. Where did they encounter math outside of class? Or what have they learned in class that has helped them at home? 

Math skills easily transfer outside of the classroom. Help them see how much they have grown, both in terms of academics and social emotional learning .

9. Making Math facts fun

As a teacher, you know math is anything but boring. But transferring that passion to your students is a tricky task. So how can you make learning math facts fun?

Play games! Math games are great classroom activities. Here are a few examples:

• Design and play a board game.
• Build structures and judge durability.
• Divide into groups for a quiz or game show. 
• Get kids moving and measure speed or distance jumped.

Even repetitive tasks can be fun with the right tools. That’s why engaging games are a great way to help students build essential math skills. When students play Prodigy Math Game , for example, they learn curriculum-aligned math facts without things like worksheets or flashcards. This can help them become excited to play and learn! 

How teachers can refine Math strategies

Sometimes trying something new can make a huge difference for your students. But don’t stress and try to change too much at once. 

You know your classroom and students best. Pick a couple of your favorite strategies above and try them out. 

If you're looking to freshen up your math instruction, sign up for a free Prodigy teacher account. Your students can jump right into the magic of the Prodigy Math Game, and you’ll start seeing data on their progress right away! 

Learner-Centered Teaching in Mathematics Education

• Reference work entry
• First Online: 01 January 2014
• Cite this reference work entry

• Michelle Stephan 2  

791 Accesses

8 Citations

Learner-centered teaching is an approach to mathematics instruction that places heavy emphasis on the students taking responsibility for problem solving and inquiry. The teacher is viewed as a facilitator by posing problems and guiding students as they work with partners toward creating a solution.

Characteristics

Intellectual autonomy.

Many researchers have contended that one of the most important contributions that education can make in individuals’ lives is to their development of autonomy (Piaget 1948/1973 ). Autonomy is defined as the determination to be self-governing, to make rules for oneself rather than rely on the rules of others to make one’s decisions (heteronomy). Kamii ( 1982 ) suggests that autonomy is the ability to think for oneself and make decisions independently of the promise of rewards or punishments. In relation to education, Richards ( 1991 ) distinguishes between two types of traditions in the mathematics education of children, what he terms school...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Durable hardcover edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Akyuz D (2010) Supporting a standards-based teaching and learning environment: a case study of an expert middle school mathematics teacher. Unpublished doctoral dissertation. University of Central Florida

Google Scholar  

Anthony W (1973) Learning to discover rules by discovery. J Educ Psychol 64:325–328

Article   Google Scholar  

Barrows H, Tamblyn R (1980) Problem-based learning: an approach to medical education. Springer, New York

Bowers J, Cobb P, McClain K (1999) The evolution of mathematical practices: a case study. Cognit Instruct 17(1):25–64

Chung S, Walsh D (2000) Unpacking child-centeredness: a history of meanings. J Curric Stud 32(2):215–234

Dewey J (1938) Democracy and education in the world of today. Essays (pamphlet series). Society for Ethical Culture, New York

Hiebert J, Carpenter T, Fennema E, Fuson K, Murray H (1997) Making sense: teaching and learning mathematics with understanding. Heineman, Portsmouth

Jonassen D (1991) Objectivism vs. constructivism. Edu Tech Res Develop 39(3):5–14

Kamii C (1982) Number in preschool and kindergarten. National Association for the Education of Young Children, Washington, DC

Kirschner P, Sweller J, Clark R (2010) Why minimal guidance during instruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educ Psychol 41(2):75–86

Kolb D, Fry R (1975) Toward an applied theory of experiential learning. In: Cooper C (ed) Studies of group process. Wiley, New York, pp 33–57

National Council of Teachers of Mathematics (1989) Curriculum and evaluation standards for school mathematics. Author, Reston, VA

National Council of Teachers of Mathematics (2000) Principles and standards for school mathematics. Author, Reston

National Council of Teachers of Mathematics (2006) Curriculum focal points for prekindergarten through grade 8 mathematics: a quest for coherence. Author, Reston

National Governor’s Association and Chief Council of State School Officers (2011) Common Core State Standards for Mathematics (CCSS). http://corestandards.org/the-standards/mathematics . Accessed 14 May 2012

Piaget J (1948/1973) To understand is to invent. Grossman, New York

Richards J (1991) Mathematical discussions. In: von Glasersfeld E (ed) Radical constructivism in mathematics education. Kluwer, Dordrecht, pp 13–52

Chapter   Google Scholar  

Stephan M, Akyuz D (2012) A proposed instructional theory for integer addition and subtraction. J Res Math Educ 43(4):428–464

Stephan M, Cobb P, Gravemeijer K, Estes B (2001) The role of tools in supporting students’ development of measuring conceptions. In: Cuoco A (ed) The roles of representation in school mathematics. NCTM, Reston, pp 63–76

Tarr J, Reys R, Reys B, Chávez O, Shih J, Osterlind S (2008) The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement. J Res Math Educ 39(3):247–280

Thompson P, Lambdin D (1994) Concrete materials and teaching for mathematical understanding. Arith Teach 41(9):556–558

Yackel E, Cobb P (1994) Sociomathematical norms, argumentation and autonomy in mathematics. J Res Math Educ 27:458–477

Download references

Author information

Authors and affiliations.

College of Education, Middle Secondary Department, The University of North Carolina at Charlotte, University City Blvd, 28223-0001, Charlotte, NC, USA

Michelle Stephan

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Michelle Stephan .

Editor information

Editors and affiliations.

Department of Education, Centre for Mathematics Education, London South Bank University, London, UK

Stephen Lerman

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this entry

Cite this entry.

Stephan, M. (2014). Learner-Centered Teaching in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_87

Download citation

DOI : https://doi.org/10.1007/978-94-007-4978-8_87

Published : 31 July 2014

Publisher Name : Springer, Dordrecht

Print ISBN : 978-94-007-4977-1

Online ISBN : 978-94-007-4978-8

eBook Packages : Humanities, Social Sciences and Law

Share this entry

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research