how to develop critical thinking skills in math

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How To Encourage Critical Thinking in Math

By Mary Montero

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Critical thinking is more than just a buzzword… It’s an essential skill that helps students develop problem-solving abilities and make logical connections between different concepts. By encouraging critical thinking in math, students learn to approach problems more thoughtfully, they learn to analyze and evaluate math concepts, identify patterns and relationships, and explore different strategies for finding the solution. Critical thinking also involves a great deal of persistence. Those are critical life skills!

When you think about it, students are typically asked to solve math problems and find the answer. Showing their work is frequently stressed too, which is important, but not the end. Instead, students need to be able to look at math in different ways in order to truly grasp a complete understanding of math concepts. Mathematics requires logical reasoning, problem-solving, and abstract thinking.

What Does Critical Thinking in Math Look Like?

When I think about critical thinking in math, I focus on:

• Solving problems through logical thinking . Students learn how to break down complex problems, analyze the different parts, and understand how they fit together logically.
• Identifying patterns and making connections. Students learn how to identify patterns across different math concepts, make connections between seemingly unrelated topics, and develop a more in-depth understanding of how math works.
• Evaluating and comparing solutions. Students learn to evaluate which solution is best for a given problem and identify any flaws in their reasoning or others’ reasoning when looking at different solutions

Mathematician Posters

These FREE Marvelous Mathematician posters have been a staple in my classroom for the last 8+ years! I first started using a version from MissMathDork and adapted them for my classroom over the years. 

I print, laminate, and add magnetic stickers on the back. At the beginning of the year, I only put one or two up at a time depending on our area of focus. Now, they are all hanging on my board, and I’ll pull out different ones depending on our area of focus. They are so empowering to my mathematicians and help them stay on track!

A Marvelous Mathematician:

• knows that quicker doesn’t mean better
• looks for patterns
• knows mistakes happen and keeps going
• makes sense of the most important details
• embraces challenges and works through frustrations
• uses proper math vocabulary to explain their thinking
• shows their work and models their thinking
• discusses solutions and evaluates reasonableness
• gives context by labeling answers
• applies mathematical knowledge to similar situations
• checks for errors (computational and conceptual)

Critical Thinking Math Activities

Here are a few of my favorite critical thinking activities. 

Square Of Numbers

I love to incorporate challenge problems (use Nrich and Openmiddle to get started) because they teach my students so much more than how to solve a math problem. They learn important lessons in teamwork, persistence, resiliency, and growth mindset. We talk about strategies for tackling difficult problems and the importance of not giving up when things get hard.

This square of numbers challenge was a hit!

ALL kids need to feel and learn to embrace challenge. Oftentimes, kids I see have rarely faced an academic challenge. Things have just come easy to them, so when it doesn’t, they can lack strategies that will help them. In fact, they will often give up before they even get started.

I tell them it’s my job to make sure I’m helping them stretch and grow their brain by giving them challenges. They don’t love it at first, but they eventually do! 

This domino challenge was another one from Nrich . I’m always on the hunt for problems like this!!  How would you guide students toward an answer??

Fifteen Cards

This is a well-loved math puzzle with my students, and it’s amazing for encouraging students to consider all options when solving a math problem.

We have number cards 1-15 (one of each number) and only seven are laid out. With the given clues, students need to figure out which seven cards should be put out and in what order. My students love these, and after they’ve done a few, they enjoy creating their own, too! Use products, differences, and quotients to increase the challenge.

This is also adapted from Nrich, which is an AMAZING resource for math enrichment!

This is one of my favorite fraction lessons that I’ve done for years! Huge shout out to Meg from The Teacher Studio for this one. I give each child a slip of paper with this figure and they have to silently write their answer and justification. Then I tally up the answers and have students take a side and DEBATE with their reasoning! It’s an AMAZING conversation, and I highly recommend trying it with your students. 

Sometimes we leave it hanging overnight and work on visual models to make some proofs. 

Logic Puzzles

Logic puzzles are always a hit too! You can enrich and extend your math lessons with these ‘Math Mystery’ logic puzzles that are the perfect challenge for 4th, 5th, and 6th grades. The puzzles are skills-based, so they integrate well with almost ANY math lesson. You can use them to supplement instruction or challenge your fast-finishers and gifted students… all while encouraging critical thinking about important math skills!

Three levels are included, so they’re perfect to use for differentiation.

• Introductory logic puzzles are great for beginners (4th grade and up!)
• Advanced logic puzzles are great for students needing an extra challenge
• Extra Advanced logic puzzles are perfect for expert solvers… we dare you to figure these puzzles out! 

Do you have a group of students who are ready for more of a fraction challenge? My well-loved fraction puzzlers are absolutely perfect for fraction enrichment. They’ll motivate your students to excel at even the most challenging tasks! 

Math Projects

Math projects are another way to differentiation while building critical thinking skills. Math projects hold so much learning power with their real-world connections, differentiation options, collaborative learning opportunities, and numerous avenues for cross curricular learning too. 

If you’re new to math projects, I shared my best tips and tricks for using math projects in this blog post . They’re perfect for cumulative review, seasonal practice, centers, early finisher work, and more.

I use both concept-based math projects to focus on specific standards and seasonal math projects that integrate several skills.

Error Analysis

Finally, error analysis is always a challenging way to encourage critical thinking. When we use error analysis, we encourage students to analyze their own mistakes to prevent making the same mistakes in the future.

For my gifted students, I use error analysis tasks as an assessment when they have shown mastery of a unit during other tasks. For students in the regular classroom needing enrichment, I usually have them complete the tasks in a center or with a partner.

For students needing extra support, we complete error analysis in small groups.  We go step-by-step through the concept and they are always able to eventually identify what the error is. It is so empowering to students when they finally figure out the error AND it helps prevent them from making the same error in the future!

My FREE addition error analysis is a good place to start, no matter the grade level. I show them the process of walking through the problem and how best to complete an error analysis task.

When you’re ready for more, this bundle of error analysis tasks contains more than 240 tasks to engage and enrich your students in critical thinking practice.

If you want to dig even deeper, visit this conceptual vs computational error analysis post to learn more about using error analysis in the classroom. 

Related Critical Thinking Posts

• How to Increase Critical Thinking and Creativity in Your “Spare” Time
• More Tips to Increase Critical Thinking

Critical thinking is essential for students to develop a deeper understanding of math concepts, problem-solving skills, and a stronger ability to reason logically. When you learn how to encourage critical thinking in math, you’re setting your students up for success not only in more advanced math subjects they’ll encounter, but also in life. 

How do you integrate critical thinking in your classroom? Come share your ideas with us in our FREE Inspired In Upper Elementary Facebook group .

Mary Montero

I’m so glad you are here. I’m a current gifted and talented teacher in a small town in Colorado, and I’ve been in education since 2009. My passion (other than my family and cookies) is for making teachers’ lives easier and classrooms more engaging.

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Mary Thankyou for your inspirational activities. I have just read and loved the morning talk activities. I do have meetings with my students but usually at end of day. What time do you

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How to Improve Problem-Solving Skills: Mathematics and Critical Thinking

In today’s rapidly changing world, problem-solving has become a quintessential skill. When we discuss the topic, it’s natural to ask, “What is problem-solving?” and “How can we enhance this skill, particularly in children?” The discipline of mathematics offers a rich platform to explore these questions. Through math, not only do we delve into numbers and equations, but we also explore how to improve problem-solving skills and how to develop critical thinking skills in math. Let’s embark on this enlightening journey together.

What is Problem-Solving?

At its core, problem-solving involves identifying a challenge and finding a solution. But it’s not always as straightforward as it sounds. So, what is problem-solving? True problem-solving requires a combination of creative thinking and logical reasoning. Mathematics, in many ways, embodies this blend. When a student approaches a math problem, they must discern the issue at hand, consider various methods to tackle it, and then systematically execute their chosen strategy.

But what is problem-solving in a broader context? It’s a life skill. Whether we’re deciding the best route to a destination, determining how to save for a big purchase, or even figuring out how to fix a broken appliance, we’re using problem-solving.

How to Develop Critical Thinking Skills in Math

Critical thinking goes hand in hand with problem-solving. But exactly how to develop critical thinking skills in math might not be immediately obvious. Here are a few strategies:

• Contextual Learning: Teaching math within a story or real-life scenario makes it relevant. When students see math as a tool to navigate the world around them, they naturally begin to think critically about solutions.
• Open-ended Questions: Instead of merely seeking the “right” answer, encourage students to explain their thought processes. This nudges them to think deeply about their approach.
• Group Discussions: Collaborative learning can foster different perspectives, prompting students to consider multiple ways to solve a problem.
• Challenging Problems: Occasionally introducing problems that are a bit beyond a student’s current skill level can stimulate critical thinking. They will have to stretch their understanding and think outside the box.

What are the Six Basic Steps of the Problem-Solving Process?

Understanding how to improve problem-solving skills often comes down to familiarizing oneself with the systematic approach to challenges. So, what are the six basic steps of the problem-solving process?

• Identification: Recognize and define the problem.
• Analysis: Understand the problem’s intricacies and nuances.
• Generation of Alternatives: Think of different ways to approach the challenge.
• Decision Making: Choose the most suitable method to address the problem.
• Implementation: Put the chosen solution into action.
• Evaluation: Reflect on the solution’s effectiveness and learn from the outcome.

By embedding these steps into mathematical education, we provide students with a structured framework. When they wonder about how to improve problem-solving skills or how to develop critical thinking skills in math, they can revert to this process, refining their approach with each new challenge.

Making Math Fun and Relevant

At Wonder Math, we believe that the key to developing robust problem-solving skills lies in making math enjoyable and pertinent. When students see math not just as numbers on a page but as a captivating story or a real-world problem to be solved, their engagement skyrockets. And with heightened engagement comes enhanced understanding.

As educators and parents, it’s crucial to continuously ask ourselves: how can we demonstrate to our children what problem-solving is? How can we best teach them how to develop critical thinking skills in math? And how can we instill in them an understanding of the six basic steps of the problem-solving process?

The answer, we believe, lies in active learning, contextual teaching, and a genuine passion for the beauty of mathematics.

The Underlying Beauty of Mathematics

Often, people perceive mathematics as a rigid discipline confined to numbers and formulas. However, this is a limited view. Math, in essence, is a language that describes patterns, relationships, and structures. It’s a medium through which we can communicate complex ideas, describe our universe, and solve intricate problems. Understanding this deeper beauty of math can further emphasize how to develop critical thinking skills in math.

Why Mathematics is the Ideal Playground for Problem-Solving

Math provides endless opportunities for problem-solving. From basic arithmetic puzzles to advanced calculus challenges, every math problem offers a chance to hone our problem-solving skills. But why is mathematics so effective in this regard?

• Structured Challenges: Mathematics presents problems in a structured manner, allowing learners to systematically break them down. This format mimics real-world scenarios where understanding the structure of a challenge can be half the battle.
• Multiple Approaches: Most math problems can be approached in various ways . This teaches learners flexibility in thinking and the ability to view a single issue from multiple angles.
• Immediate Feedback: Unlike many real-world problems where solutions might take time to show results, in math, students often get immediate feedback. They can quickly gauge if their approach works or if they need to rethink their strategy.

Enhancing the Learning Environment

To genuinely harness the power of mathematics in developing problem-solving skills, the learning environment plays a crucial role. A student who is afraid of making mistakes will hesitate to try out different approaches, stunting their critical thinking growth.

However, in a nurturing, supportive environment where mistakes are seen as learning opportunities, students thrive. They become more willing to take risks, try unconventional solutions, and learn from missteps. This mindset, where failure is not feared but embraced as a part of the learning journey, is pivotal for developing robust problem-solving skills.

Incorporating Technology

In our digital age, technology offers innovative ways to explore math. Interactive apps and online platforms can provide dynamic problem-solving scenarios, making the process even more engaging. These tools can simulate real-world challenges, allowing students to apply their math skills in diverse contexts, further answering the question of how to improve problem-solving skills.

More than Numbers 

In summary, mathematics is more than just numbers and formulas—it’s a world filled with challenges, patterns, and beauty. By understanding its depth and leveraging its structured nature, we can provide learners with the perfect platform to develop critical thinking and problem-solving skills. The key lies in blending traditional techniques with modern tools, creating a holistic learning environment that fosters growth, curiosity, and a lifelong love for learning.

Join us on this transformative journey at Wonder Math. Let’s make math an adventure, teaching our children not just numbers and equations, but also how to improve problem-solving skills and navigate the world with confidence. Enroll your child today and witness the magic of mathematics unfold before your eyes!

FAQ: Mathematics and Critical Thinking

1. what is problem-solving in the context of mathematics.

Problem-solving in mathematics refers to the process of identifying a mathematical challenge and systematically working through methods and strategies to find a solution.

2. Why is math considered a good avenue for developing problem-solving skills?

Mathematics provides structured challenges and allows for multiple approaches to find solutions. This promotes flexibility in thinking and encourages learners to view problems from various angles.

3. How does contextual learning enhance problem-solving abilities?

By teaching math within a story or real-life scenario, it becomes more relevant for the learner. This helps them see math as a tool to navigate real-world challenges , thereby promoting critical thinking.

4. What are the six basic steps of the problem-solving process in math?

The six steps are: Identification, Analysis, Generation of Alternatives, Decision Making, Implementation, and Evaluation.

5. How can parents support their children in developing mathematical problem-solving skills?

Parents can provide real-life contexts for math problems , encourage open discussions about different methods, and ensure a supportive environment where mistakes are seen as learning opportunities.

6. Are there any tools or apps that can help in enhancing problem-solving skills in math?

Yes, there are various interactive apps and online platforms designed specifically for math learning. These tools provide dynamic problem-solving scenarios and simulate real-world challenges, making the learning process engaging.

7. How does group discussion foster critical thinking in math?

Group discussions allow students to hear different perspectives and approaches to a problem. This can challenge their own understanding and push them to think about alternative methods.

8. Is it necessary to always follow the six steps of the problem-solving process sequentially?

While the six steps provide a structured approach, real-life problem-solving can sometimes be more fluid. It’s beneficial to know the steps, but adaptability and responsiveness to the situation are also crucial.

9. How does Wonder Math incorporate active learning in teaching mathematics?

Wonder Math integrates mathematics within engaging stories and real-world scenarios, making it fun and relevant. This active learning approach ensures that students are not just passive recipients but active participants in the learning process.

10. What if my child finds a math problem too challenging and becomes demotivated?

It’s essential to create a supportive environment where challenges are seen as growth opportunities. Remind them that every problem is a chance to learn, and it’s okay to seek help or approach it differently.

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Khan Academy Blog

Unlocking the Power of Math Learning: Strategies and Tools for Success

posted on September 20, 2023

Mathematics, the foundation of all sciences and technology, plays a fundamental role in our everyday lives. Yet many students find the subject challenging, causing them to shy away from it altogether. This reluctance is often due to a lack of confidence, a misunderstanding of unclear concepts, a move ahead to more advanced skills before they are ready, and ineffective learning methods. However, with the right approach, math learning can be both rewarding and empowering. This post will explore different approaches to learning math, strategies for success, and cutting-edge tools to help you achieve your goals.

Math Learning

Math learning can take many forms, including traditional classroom instruction, online courses, and self-directed learning. A multifaceted approach to math learning can improve understanding, engage students, and promote subject mastery. A 2014 study by the National Council of Teachers of Mathematics found that the use of multiple representations, such as visual aids, graphs, and real-world examples, supports the development of mathematical connections, reasoning, and problem-solving skills.

Moreover, the importance of math learning goes beyond solving equations and formulas. Advanced math skills are essential for success in many fields, including science, engineering, finance, health care, and technology. In fact, a report by Burning Glass Technologies found that 71% of high-salary, entry-level positions require advanced math skills.

Benefits of Math Learning

In today’s 21st-century world, having a broad knowledge base and strong reading and math skills is essential. Mathematical literacy plays a crucial role in this success. It empowers individuals to comprehend the world around them and make well-informed decisions based on data-driven understanding. More than just earning good grades in math, mathematical literacy is a vital life skill that can open doors to economic opportunities, improve financial management, and foster critical thinking. We’re not the only ones who say so:

• Math learning enhances problem-solving skills, critical thinking, and logical reasoning abilities. (Source: National Council of Teachers of Mathematics )
• It improves analytical skills that can be applied in various real-life situations, such as budgeting or analyzing data. (Source: Southern New Hampshire University )
• Math learning promotes creativity and innovation by fostering a deep understanding of patterns and relationships. (Source: Purdue University )
• It provides a strong foundation for careers in fields such as engineering, finance, computer science, and more. These careers generally correlate to high wages. (Source: U.S. Bureau of Labor Statistics )
• Math skills are transferable and can be applied across different academic disciplines. (Source: Sydney School of Education and Social Work )

How to Know What Math You Need to Learn

Often students will find gaps in their math knowledge; this can occur at any age or skill level. As math learning is generally iterative, a solid foundation and understanding of the math skills that preceded current learning are key to success. The solution to these gaps is called mastery learning, the philosophy that underpins Khan Academy’s approach to education .

Mastery learning is an educational philosophy that emphasizes the importance of a student fully understanding a concept before moving on to the next one. Rather than rushing students through a curriculum, mastery learning asks educators to ensure that learners have “mastered” a topic or skill, showing a high level of proficiency and understanding, before progressing. This approach is rooted in the belief that all students can learn given the appropriate learning conditions and enough time, making it a markedly student-centered method. It promotes thoroughness over speed and encourages individualized learning paths, thus catering to the unique learning needs of each student.

Students will encounter mastery learning passively as they go through Khan Academy coursework, as our platform identifies gaps and systematically adjusts to support student learning outcomes. More details can be found in our Educators Hub . 

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How to learn math.

Learning at School

One of the most common methods of math instruction is classroom learning. In-class instruction provides students with real-time feedback, practical application, and a peer-learning environment. Teachers can personalize instruction by assessing students’ strengths and weaknesses, providing remediation when necessary, and offering advanced instruction to students who need it.

Learning at Home

Supplemental learning at home can complement traditional classroom instruction. For example, using online resources that provide additional practice opportunities, interactive games, and demonstrations, can help students consolidate learning outside of class. E-learning has become increasingly popular, with a wealth of online resources available to learners of all ages. The benefits of online learning include flexibility, customization, and the ability to work at one’s own pace. One excellent online learning platform is Khan Academy, which offers free video tutorials, interactive practice exercises, and a wealth of resources across a range of mathematical topics.

Moreover, parents can encourage and monitor progress, answer questions, and demonstrate practical applications of math in everyday life. For example, when at the grocery store, parents can ask their children to help calculate the price per ounce of two items to discover which one is the better deal. Cooking and baking with your children also provides a lot of opportunities to use math skills, like dividing a recipe in half or doubling the ingredients. 

Learning Math with the Help of Artificial Intelligence (AI) 

AI-powered tools are changing the way students learn math. Personalized feedback and adaptive practice help target individual needs. Virtual tutors offer real-time help with math concepts while AI algorithms identify areas for improvement. Custom math problems provide tailored practice, and natural language processing allows for instant question-and-answer sessions. 

Using Khan Academy’s AI Tutor, Khanmigo

Transform your child’s grasp of mathematics with Khanmigo , the 24/7 AI-powered tutor that specializes in tailored, one-on-one math instruction. Available at any time, Khanmigo provides personalized support that goes beyond mere answers to nurture genuine mathematical understanding and critical thinking. Khanmigo can track progress, identify strengths and weaknesses, and offer real-time feedback to help students stay on the right track. Within a secure and ethical AI framework, your child can tackle everything from basic arithmetic to complex calculus, all while you maintain oversight using robust parental controls.

Get Math Help with Khanmigo Right Now

You can learn anything .

Math learning is essential for success in the modern world, and with the right approach, it can also be enjoyable and rewarding. Learning math requires curiosity, diligence, and the ability to connect abstract concepts with real-world applications. Strategies for effective math learning include a multifaceted approach, including classroom instruction, online courses, homework, tutoring, and personalized AI support. 

So, don’t let math anxiety hold you back; take advantage of available resources and technology to enhance your knowledge base and enjoy the benefits of math learning.

National Council of Teachers of Mathematics, “Principles to Actions: Ensuring Mathematical Success for All” , April 2014

Project Lead The Way Research Report, “The Power of Transportable Skills: Assessing the Demand and Value of the Skills of the Future” , 2020

Page. M, “Why Develop Quantitative and Qualitative Data Analysis Skills?” , 2016

Mann. EL, Creativity: The Essence of Mathematics, Journal for the Education of the Gifted. Vol. 30, No. 2, 2006, pp. 236–260, http://www.prufrock.com ’

Nakakoji Y, Wilson R.” Interdisciplinary Learning in Mathematics and Science: Transfer of Learning for 21st Century Problem Solving at University ”. J Intell. 2020 Sep 1;8(3):32. doi: 10.3390/jintelligence8030032. PMID: 32882908; PMCID: PMC7555771.

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5. Teaching Mathematical Reasoning: Critical Math Thinking Through Problem-Solving and Modeling

• Mathematical problem-solving : This approach makes students think conceptually about problems before applying tools they’ve learned.
• Mathematical modeling : Modeling projects give students experience in weighing several factors against one another and using mathematical knowledge to make decisions.

I. Mathematical Problem-Solving

An emphasis on open-ended mathematical problem-solving can help develop mathematical reasoning skills and address a problem teachers have long been concerned about: too much “rote” learning in math. 

Too often students spend time in math class memorizing procedures and applying them mindlessly to problems. This leads to errors when students are confronted with unfamiliar problems. It also contributes to a widespread misperception of math as boring and lacking relevance to everyday life. 

On the other hand, attempting to remedy this problem by giving students open-ended problems has its own drawbacks. Without the conceptual and methodological tools to solve these problems students become frustrated and disengaged. It can end up being an inefficient way to spend class time.  

Although learning fundamental math skills like algorithms for adding, subtracting, multiplying, and dividing is absolutely critical for students in the early grades, the deeper mathematical problem-solving skills are the ones we really want students to graduate with. How can we ensure they do?

The deeper mathematical problem-solving skills are the ones we really want students to graduate with.

Evidence suggests that skills in mathematical problem-solving lead to more general improvements in outcomes related to math. They help students acquire a deeper understanding of mathematical reasoning and concepts. 

For instance, the commutative property, which most students learn applies to addition and multiplication problems (changing the order of the operations doesn’t affect the outcome), also applies to other logical and practical situations. A familiarity with some of these situations fosters deeper conceptual understanding, and deeper conceptual understanding leads to better critical thinking.

And learning these skills helps students improve outcomes related to critical thinking more generally. For example, students who become skilled in mathematical problem-solving tend to also:

• Create beneficial habits of mind — persistence, thoroughness, creativity in solution-finding, and improved self-monitoring.
• Break down hard problems into easier parts or reframing problems so that they can think about them more clearly. 
• Some problem solving tactics are applicable to situations well beyond math: making a visualization of a situation to understand it more clearly; creating a simplified version of the problem to more easily address the essence of the problem; creating branches of possibilities to solve the problem; creating “what if” example cases to test key assumptions, etc.
• Elevate the value of discussion and argumentation over simple appeals to authority.

Small-group mathematical problem solving targets skills that traditional mathematics instruction doesn’t. Instead of just finding a match between an algorithm and a question, students must: adapt or create an algorithm; evaluate and debate the merits of different solution paths; and verify their solution through additional evidence.

Small-group mathematical problem solving targets skills that traditional mathematics instruction doesn’t.

This process continues until the class has thoroughly explored the problem space, revealing multiple solution paths and exploring variations on the problem or contrasting problem-types.

Of course, the usefulness of a question like this depends on what students already know. If students don’t already know that chickens have two legs and pigs have four, they’re just going to be confused by the problem (and the explanation of the solution). It also requires some other basic skills—for instance, that if one chicken has two legs, four chickens would have eight.

As a way of evaluating student growth, teachers could also include some of these open-ended problems in homework assignments or as extra credit assignments.

Lesson Plan Outline

An example that might be appropriate for fifth grade is something like the following: A farmer has some pigs and some chickens. He finds that together they have 70 heads and 200 legs. How many pigs and how many chickens does he have? Divide the class into student groups of three to four. Have students spend a few minutes reading over the problem individually. Then let student groups discuss possible solution paths. The teacher walks around the classroom, monitoring the groups. Then the teacher leads a whole-class discussion about the problem.

• So how did you go about thinking about the problem?
• Show us how you got your answer and why you think it’s right. This might mean that a student goes up to the board to illustrate something if a verbal explanation is inadequate.
• And what was the answer you got?
• Does anyone else have a different way of thinking about the problem? If there are other ways of solving the problem that students didn’t come up with, teachers can introduce these other ways themselves.

Developing Math Problem-Solving Skills

Teachers should keep in mind the following as they bring mathematical problem-solving activities into their classrooms:

• Problem selection . Teachers have to select grade-appropriate problems. A question like “John is taller than Mary. Mary is taller than Peter. Who is the shortest of the three children?” may be considered an exercise to older students — that is, a question where the solutions steps are already known — but a genuine problem to younger students. It’s also helpful when problems can be extended in various ways. Adding variation and complexity to a problem lets students explore a class of related problems in greater depth.
• Managing student expectations . Introducing open-ended math problems to students who haven’t experienced them before can also be confusing for the students. Students who are used to applying algorithms to problems can be confused about what teachers expect them to do with open-ended problems, because no algorithm is available.
• Asking why . Asking students to explain the rationale behind their answer is critical to improving their thinking. Teachers need to make clear that these rationales or justifications are even more important than the answer itself. These justifications give us confidence that an answer is right. That is, if the student can’t justify her answer, it almost doesn’t matter if it’s correct, because there’s no way of verifying it.

II. Mathematical Modeling

Another approach is mathematical modeling. Usually used for students in middle or high school, mathematical modeling brings math tools to bear on real-world problems, keeping students engaged and helping them to develop deeper mathematical reasoning and critical thinking skills.

Math modeling is an extremely common practice in the professional world. Investors model returns and the effects of various events on the market; business owners model revenue and expenses, buying behavior, and more; ecologists model population growth, rainfall, water levels, and soil composition, among many other things. 

But, despite these many applications and the contributions it can make to general mathematical reasoning and critical thinking skills, mathematical modeling is rarely a main component of the math curriculum. Although textbook examples occasionally refer to real-world phenomena, the modeling process is not commonly practiced in the classroom.

Modeling involves engaging students in a big, messy real-world problem. The goals are for students to:

• refine their understanding of the situation by asking questions and making assumptions,
• leverage mathematical tools to solve the problem,
• make their own decisions about how to go about solving the problem,
• explain whether and how their methods and solutions make sense,
• and test or revise their solutions if necessary.

Mathematical modeling typically takes place over the course of several class sessions and involves working collaboratively with other students in small groups.

Modeling is not just about getting to a “right” answer — it’s about considering factors beyond mathematics as well.

Modeling also offers the opportunity to integrate other material across the curriculum and to “think mathematically” in several different contexts. Modeling is not just about getting to a “right” answer — it’s about considering factors beyond mathematics as well. For example, students deal with questions like:

• What is a “fair” split? 
• What level of risk should someone tolerate?
• What tradeoffs should a society make?

In others words, students come to see mathematics as the socially indispensable tool that it is, rather than an abstract (and sometimes frustrating) school subject.

Mathematical Modeling and Critical Thinking

Research suggests that the ability to solve abstractly framed academic math problems is not necessarily related to mathematical reasoning more broadly: that is, the ability to use math well in everyday life or to integrate mathematical thinking into one’s decision-making. Students may be able to follow procedures when given certain cues, but unable to reason about underlying concepts. 

It’s also very common to hear complaints from students about math — that either they aren’t “ math people ,” that math is irrelevant, or that math is simply boring.

Mathematical modeling is one approach to resolving both these problems. It asks students to move between the concreteness of real — or at least relatively realistic — situations and the abstraction of mathematical models. Well-chosen problems can engage student interest. And the practice emphasizes revision, step-by-step improvement, and tradeoffs over single solution paths and single right-or-wrong answers.

Mathematical modeling often begins with a general question, one that may initially seem only loosely related to mathematics:

• how to design an efficient elevator system, given certain constraints;
• what the best gas station is to visit in our local area;
• how to distinguish between two kinds of flies, given some data about their physical attributes.

Then, over the course of the modeling process, students develop more specific questions or cases, adding constraints or assumptions to simplify the problem. Along the way, students identify the important variables — what’s changing, and what’s not changing? Which variables are playing the biggest role in the desired outcomes?

Students with little experience in modeling can leap too quickly into looking for a generalized solution, before they have developed a feel for the problem. They may also need assistance in developing those specific cases. During this part of the process, it can be easiest to use well-defined values for some variables. These values may then become variables later on.

After students explore some simplifying cases, then they work on extensions of these cases to reach ever more general solutions.

A key part of this activity is letting students be creative — students will often come up with unusual or especially innovative solutions.

Throughout the modeling process, the teacher may need to point out missing assumptions or constraints, or offer other ways of reframing the problem. For any given modeling problem, some solutions are usually more obvious than others, which leads to common stages students may reach as they solve the problem. But a key part of this activity is letting students be creative — students will often come up with unusual or especially innovative solutions.

A sample problem, from the Guidelines for Assessment and Instruction in Mathematical Modeling Education is below:

This problem involves variables that aren’t necessarily immediately apparent to students. For instance, the size of the gas tank, and how much gas you fill up on per trip. As students manage this specific case, they can take other hypothetical scenarios to generalize their solution: if it’s 10 miles away, how cheap would the gas have to be to make it worth it? What about the time spent in the car — is there a value to put on that?

Many modeling problems can be arbitrarily extended in various directions. Instead of just considering the best gas station to go to for a single car, for instance, students can explore the behavior of a fleet of trucks on set routes or seasonal changes to gas prices.

It’s also possible to include shorter modeling activities, where students work together in pairs or small groups to extend a problem or interpret the meaning of a solution.

These kinds of modeling activities are not reserved solely for older students. One example of a modeling problem for students in elementary school might be something like: what should go in a lunchbox? Students can talk about what kinds of things are important to them for lunch, “mathematize” the problem by counting student preferences or coming up with an equation (e.g., lunch = sandwich + vegetable + dessert + drink); and even explore geometrically how to fit such items into a lunchbox of a certain size.

Teaching Mathematical Modeling: Further Key Factors

Mathematical modeling activities can be challenging for both teachers and students. 

Often, mathematical modeling activities stretch over several class periods. Fitting modeling activities in, especially if standardized tests are focused on mathematical content, can be challenging. One approach is to design modeling activities that support the overall content goals.

The teacher’s role during mathematical modeling is more like a facilitator than a lecturer. Mathematical modeling activities are considerably more open-ended than typical math activities, and require active organization, monitoring, and regrouping by the teacher. Deciding when to let students persevere on a problem for a bit longer and when to stop the class to provide additional guidance is a key skill that only comes with practice.

The teacher’s role during math modeling is more like a facilitator than a lecturer.

Students — especially students who have traditionally been successful in previous math classes — may also experience frustration when encountering modeling activities for the first time. Traditional math problems involve applying the right procedure to a well-defined problem. But expertise at this kind of mathematical reasoning differs markedly from tackling yet-to-be-defined problems with many possible solutions, each of which has tradeoffs and assumptions. Students might feel unprepared or even that they’re being treated unfairly.

Students also have to have some knowledge about the situation to reason mathematically about it. If the question is about elevators, for example, they need to know that elevators in tall buildings might go to different sets of floors; that elevators have a maximum capacity; that elevators occasionally break and need to be repaired. 

Finally, the mathematical question needs to be tailored to students’ experience and interests. Asking a group of students who don’t drive about how to efficiently purchase gas won’t garner student interest. Teachers should use their familiarity with their students to find and design compelling modeling projects. This is chance for both students and teachers to be creative. 

To download the PDF of the Teachers’ Guide

(please click here)

Sources and Resources

O’Connell, S. (2000). Introduction to Problem Solving: Strategies for The Elementary Classroom . Heinemann. A recent handbook for teachers with tips on how to implement small-group problem solving.

Youcubed.org , managed by Jo Boaler.  A community with lots of resources for small-group problem solving instruction.

Yackel, E., Cobb, P., & Wood, T. (1991). Small group interactions as a source of learning opportunities in second-grade mathematics . Journal for research in mathematics education , 390-408. Education research that illustrates how small-group problem solving leads to different kinds of learning opportunities than traditional instruction.

Guidelines for Assessment and Instruction in Mathematical Modeling Education , 2nd ed. (2019). Consortium for Mathematics and its Applications & Society for Industrial and Applied Mathematics.  An extensive guide for teaching mathematical modeling at all grade levels.

Hernández, M. L., Levy, R., Felton-Koestler, M. D., & Zbiek, R. M. (March/April 2017). Mathematical modeling in the high school curriculum . The variable , 2(2). A discussion of the advantages of mathematical modeling at the high school level.

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How to Develop Critical Thinking Skills in Mathematics

Introduction

In the realm of education, mathematics goes beyond memorizing formulas and solving equations. It is a discipline that fosters critical thinking, logical reasoning, and problem-solving abilities. Developing strong critical thinking skills in mathematics is not only essential for academic success but also for nurturing cognitive abilities that are applicable throughout life. In this article, we will explore the significance of critical thinking in math education and provide students with practical techniques to enhance their critical thinking prowess.  

The Significance of Critical Thinking in Math

Critical thinking is the ability to analyze, evaluate, and synthesize information to make well-reasoned decisions and solve problems effectively. In the context of mathematics, critical thinking is the driving force behind understanding concepts deeply, approaching problems from multiple angles, and devising innovative solutions. It encourages students to question assumptions, think logically, and develop a genuine understanding of mathematical principles rather than merely memorizing procedures.  

Analyzing Problems

Encourage students to approach mathematical problems with a critical eye. Emphasize the importance of reading problems carefully, identifying the given information, and understanding the context. Encourage them to break down complex problems into smaller, manageable parts, making connections between different components. This analytical approach lays the groundwork for a structured problem-solving process.  

Asking Questions

Incorporate a culture of curiosity in the math classroom. Encourage students to ask questions about concepts, procedures, and problem-solving approaches. Asking “why” and “how” questions fosters a deeper understanding of the subject matter and challenges students to think beyond the surface. Teachers can create an open and supportive environment where questioning is welcomed and encouraged.  

Making Logical Deductions

Students can enhance their critical thinking by making logical deductions from given information. Encourage them to draw inferences, make predictions, and explore relationships between mathematical concepts. Engage students in discussions that require them to justify their answers and provide evidence for their conclusions. This practice strengthens their ability to think logically and reason through mathematical challenges.  

Exploring Real-World Applications

Connect math concepts to real-world applications, illustrating how critical thinking is integral to problem-solving in everyday life. Show students how math is used in various professions, such as engineering, finance, and technology. Engaging with real-world scenarios helps students recognize the relevance of critical thinking in their future endeavors.  

Encouraging Collaborative Learning

Promote collaborative learning environments where students can engage in discussions, share ideas, and learn from one another. Collaborative activities challenge students to think critically, consider different perspectives, and defend their reasoning. Peer-to-peer interactions can foster a supportive learning community that encourages critical thinking and intellectual growth.  

Critical thinking is a cornerstone of mathematics education, empowering students to become independent and proficient problem solvers. By analyzing problems, asking questions, and making logical deductions, students can develop their critical thinking skills and apply them to various academic and real-life scenarios. As educators, parents, and mentors, we play a pivotal role in nurturing these abilities in our students. By cultivating a culture of curiosity, fostering collaborative learning, and highlighting the relevance of critical thinking in everyday life, we can equip our students with invaluable skills that will serve them well beyond the boundaries of the math classroom.  

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How Math Can Help Children Develop Critical Thinking Skills

• 1.1 Thinking Deeply About Questions
• 1.2 Breaking Down Problems
• 1.3 Developing Logical Thinking
• 1.4 Encouraging Patience and Persistence
• 2.1 1. Mathematician Posters
• 2.2 2. Critical Thinking Math Activities
• 2.3 3. Fraction Lessons
• 2.4 4. Logic Puzzles
• 2.5 5. Math Projects
• 2.6 6. Error Analysis
• 3 Conclusion
• 4.1 1: What is critical thinking for math?
• 4.2 2: Can math improve critical thinking skills?
• 4.3 3: What are some activities that promote critical thinking skills in math?
• 4.4 4: How can parents support critical thinking for math at home?
• 4.5 5: Does math help with critical thinking in other areas?
• 4.6 6: What are some real-world applications of critical thinking skills in math?

Did you know that math can do more than just teach your child how to add and subtract? It can also help children develop critical thinking skills, which are super important for solving problems and making good decisions in life. Let’s understand how math can help your child become a better thinker and some fun activities you can try at home.

How Math Helps Children Develop Critical Thinking Skills

Math isn’t just about numbers and equations; it’s a way to help kids think more deeply and critically. Here’s how:

Thinking Deeply About Questions

When children tackle math problems, they have to think carefully about what the question is asking. This helps them understand the problem fully before jumping to a solution. By practicing this, they learn to approach all kinds of problems with a thoughtful mindset.

Breaking Down Problems

Math teaches kids to break down big problems into smaller, more manageable parts. For example, solving a complex equation often involves handling simpler steps first. This skill of breaking down problems is crucial for critical thinking, as it makes complicated issues easier to handle.

Developing Logical Thinking

Logical thinking is a big part of math. Kids learn to follow a series of steps to reach a conclusion, which helps them think logically about other types of problems too. 

Encouraging Patience and Persistence

Solving math problems can be challenging, and it often requires patience and persistence. Kids learn that it’s okay to make mistakes and that they can learn from them. 

Fun Math Activities to Boost Critical Thinking

Here are some easy and enjoyable activities to help your children develop critical thinking skills through math:

1. Mathematician Posters

What They Are: These are free posters with fun math facts and problems.

How to Use Them: Print them out, laminate them if you can, and put them up in your child’s room or study area. They’ll remind your child of important math concepts and encourage them to think critically.

2. Critical Thinking Math Activities

Square of Numbers: Give your child some tricky math problems that involve finding the square of numbers. This helps them learn persistence and teamwork if they do it with friends.

Domino Challenge: Use dominoes to create math problems. This game helps children develop problem-solving and logical thinking skills.

Fifteen Cards: This is a card game where your child has to make combinations that add up to fifteen. It encourages them to consider all options and think strategically.

3. Fraction Lessons

Activity: Have your child write down their answers to fraction problems and explain why they think they are correct. This promotes debate and a deeper understanding of fractions.

Benefits: Discussing and visualizing fractions helps your child understand and think critically about abstract concepts.

4. Logic Puzzles

What They Are: These are math puzzles that require logical thinking to solve.

How to Use Them: Give your child puzzles that match their skill level. These puzzles are fun and challenging, helping them think critically while having fun.

5. Math Projects

What They Are: These projects connect math to real-world situations and involve group work.

How to Use Them: Pick projects that are interesting to your child and do them together. These projects help children see how math applies to everyday life and develop their critical thinking skills.

6. Error Analysis

What It Is: This activity involves looking at mistakes to understand why they happened and how to avoid them in the future.

How to Use It: When your child makes a mistake, help them analyze what went wrong. This helps them learn from their errors and think more critically about their approach to problems.

Math is not just about numbers and equations; it’s a fantastic way to help your child develop critical thinking skills. By doing fun math activities and using simple resources, you can help your child learn to think deeply, solve problems, and make better decisions. You can consider Mathema for math resources for your children to score higher on their next test!

1: What is critical thinking for math?

Critical thinking for math involves using logic and reasoning to solve problems. It means not just finding the answer but understanding why it’s the right answer and how to approach similar problems in the future.

2: Can math improve critical thinking skills?

Yes, math can improve critical thinking skills. By working through math problems, children learn to think deeply, consider multiple solutions, and justify their answers.

3: What are some activities that promote critical thinking skills in math?

Activities like logic puzzles, fraction lessons, and error analysis are great for promoting critical thinking skills in math. 

4: How can parents support critical thinking for math at home?

As a parent, you can support critical thinking for math at home by engaging your children in fun math activities. You can encourage them to explain their reasoning and provide resources like mathematician posters and logic puzzles to stimulate their thinking.

5: Does math help with critical thinking in other areas?

Yes, math helps with critical thinking in other areas like science, reading, and even everyday decision-making.

6: What are some real-world applications of critical thinking skills in math?

Real-world applications of critical thinking skills in math include budgeting, planning trips, cooking (measuring ingredients), and solving everyday problems that require logical thinking and analysis.

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Projects selected for dB-SERC Course Transformation Awards

The Discipline-Based Science Education Research Center (dB-SERC) has awarded 12 Course Transformation Awards to faculty in natural sciences.

Since 2014, dB-SERC has supported natural sciences faculty members in developing projects to transform the way classes are taught by adopting evidence-based teaching practice to improve student learning outcomes.

Award recipients receive funds for equipment, student support or summer salary for faculty. Two mentor-mentee awards also were given out to support classroom innovation projects conducted by students and faculty working together.

Course Transformation Awards

Young Ahn, Department of Biological Sciences: Designing a high-structure course combining frequent low-stakes assessments with inclusive teaching for a large-enrollment introductory biology class

This proposal aims to test the “heads and hearts” hypothesis which suggests that both students’ cognitive (heads) and affective (hearts) learning experiences must be purposefully constructed in classroom environments. This project will investigate whether a course structure that combines frequent low-stakes assessments (heads) and inclusive teaching (hearts) can improve student performance and reduce achievement gaps in a large-enrollment introductory biology course thereby promoting retention in STEM.

Anusha Balangoda, Department of Geology and Environmental Science : Use of a Collaborative Online Reading Platform for Pre-class Reading Assignments in a Large Enrollment First-Year Undergraduate Class

The proposed work seeks funding to implement pre-class reading assignments through a social annotation platform allowing active reading on assigned course materials outside the class. A free social platform, Perusall, provides an interactive experience for students to engage with peers asynchronously and facilitates a space to teach and learn from peers. This collaborative social platform allows students to work on assignments outside the classroom to promote productive discussions and produce high-quality peer interactions.

Seth Childers, Department of Chemistry: Development of Interdisciplinary Courses for a New Chemical Biology Major

In the Department of Chemistry, the PI is proposing a chemical biology major, including two new lecture courses and one laboratory course, proposed to launch in Fall 2025 or 2026. This timeline allows them to craft a curriculum while deploying evidence-based learning practices to enhance job readiness. Based on student surveys, the program aims to accommodate approximately 48 majors annually and engage non-majors as a desirable scientific elective campus wide.

Russell Clark and Aidan Payton, Department of Physics & Astronomy: Gender Equity in Introductory Physics Lab Group Roles

This is a continuation of a dB-SERC award from 2020 (Development of Teacher Guides and Rubrics for Introductory Physics Labs). The original plan for that award was to develop better rubrics and other materials to help the TA graders provide more valuable feedback to the students. However, the University was forced into quarantine midway through the first semester of the project, and so the character of it changed.  They know from a previous study that student groups tend to have gender bias in which men tend to work with the experimental apparatus and women are relegated to secretarial roles (recording data, writing the report, etc.). They attempted to mitigate this by asking the students to cycle through the roles week to week so that each student would get to participate in each role multiple times.

Erika Fanselow, Department of Neuroscience: Incorporating digital and physical 3D brain models into interactive online and in-class activities to enhance student engagement and mastery in neuroanatomy courses

The goal of this course transformation is to develop interactive, online and in-class exercises that incorporate digital and printed 3D models of nervous system structures. These 3D model-based exercises and in-class activities are intended to enhance students’ visualization and conceptualization of neuroanatomical structures. The rationale for this course transformation proposal is based on the fact that neuroanatomy students are commonly overwhelmed by the complexity of the nervous system, resulting in a condition Jozefowicz (1994) referred to as “neurophobia,” which he concluded actually keeps students from choosing fields such as neurology.

Sean Garrett-Roe, Department of Chemistry: Activity redesign and mindset intervention based on growth-oriented testing in Chem-0110 General Chemistry I

“Grading for Growth” is a movement to encourage students to embrace deeper intellectual engagement with their studies by revolutionizing the way that their learning is assessed. Student-focused active learning pedagogies, such as Process Oriented Guided Inquiry Learning (POGIL), are well-established; student-focused assessments, on the other hand, are a new frontier. The PIs have formulated, implemented and assessed a student-focused assessment system that they call “Growth-Oriented Testing.” As successful as the system has been, the assessment results have illuminated ways in which their in-class materials have not optimally supported students, and the student opinion surveys suggest ways in which they have not optimally framed the learning process. As a result, students may not get the full benefits of the learning environment. A long-range goal of their teaching is to help students embrace a life of growth and learning; they want the students to learn both Chemistry and the metacognitive and metaemotional skills they need to succeed beyond the Chemistry classroom.

Sean Gess, Department of Biological Sciences: Supporting richer class-wide discussion and promoting the use of scientific argumentation in Foundations of Biology laboratory courses

This project focuses on class-wide discussion in a guided, authentic research lab. In this course students engage in science education by performing authentic research science to address active research questions being investigated within the department. The course is designed to mimic the research process, including discussions of data to try and understand it better. These discussion-based activities often struggle to support the learning objectives due to low participation from students or students not really listening and engaging with others during the discussions. To improve these discussions, they have previously introduced an explicit framing to attempt to help students understand the norms around this activity, normalize it as a professional practice, and encourage engagement and participation. This approach to science learning has shown gains in critical thinking skills and supports epistemic learning of STEM content.

Burhan Gharaibeh, Natasha Baker and Bridget Deasy, Department of Biological Sciences: Enhancing student engagement in anatomy and physiology courses through regenerative medicine primary science literature

Students of anatomy and physiology in different majors often report difficulty in these courses due to the need for memorizing lists of structures and comprehending complex physiological processes. They have preliminary data demonstrating that adding discussions of current, clinically relevant therapies and biotechnology articles related to regenerative medicine studies were effective in enhancing the biology student’s engagement during anatomy lectures. More importantly, the addition of these discussions to the curriculum appeared to improve exam grades.

Melanie Good and Eric Swanson, Department of Physics & Astronomy: The Use of Comprehensive PACE (Pseudoscience and Conspiracy-theory Education) in Physics and Society

Phys0087: Physics and Society was a course developed by Eric Swanson to help students examine the conceptual foundations of modern science with the goal of understanding how science affects our daily lives and our impact on the environment. At the intersection of science and society lies the issue of popular belief in the claims of pseudoscience and conspiracy theories. These beliefs are fairly common and often can be difficult to dislodge with education in science alone. However, past work has shown that explicit instruction on topics related to pseudoscience and conspiracy theory beliefs may be effective in reducing endorsement of these beliefs. The PIs have seen this among their own students, based on pilot data and data from a previous dB-SERC Course Transformation Award. The success of their earlier work has captured the attention not only of our university media, but also the Lilienfeld Alliance, a group of higher education professionals across the nation that is committed to promoting critical thinking skills in the face of the claims of pseudoscience, who invited them to join their cause. With the momentum they have built, they are inspired to more comprehensively overhaul Phys0087: Physics and Society to expand upon their original transformation. Their new proposed course transformation would extend the pseudoscience module into a comprehensive PACE (Pseudoscience and Conspiracy-theory Education) curriculum in Phys0087–Physics and Society during the 2024-2025 school year.

Edison Hauptman and Jeffrey Wheeler, Department of Mathematics: Contract Grading in Calculus 2

In summer 2024, Edison Hauptman’s section of Analytic Geometry & Calculus 2 (Math 0230) was taught with a different set of assignments and grading structure. The grading structure for the class resembled a contract between the instructor and their students: the instructor provided many different assignments, and for a student to earn a desired grade, they had to score enough points on various assignments of their choice to reach that grade’s point threshold. This course structure can have many variations and is called a “grading contract.” Compared to the current (default) course structure for Calculus courses at the University of Pittsburgh, a grading contract is a more equitable way to evaluate a diverse set of students, allows the instructor to be more accommodating to students without sacrificing the course’s rigor, and encourages more student buy-in. This project develops and evaluates a set of assignments offered to students in  Hauptman’s Summer 2024 12-week section of Math 0230 and focuses on mathematical skills emphasized in each assignment.

Zuzana Swigonova, Department of Biological Sciences: Combining computer visualizations with 3D printed models to engage students in active study of molecular structure and function

All biological processes in a living system depend on proper functioning of molecules. Understanding the principles of molecular structure, the three-dimensional spatial arrangements of atoms and functional groups that allow for intra- and intermolecular interactions, is crucial for grasping the fundamentals of structure-function relationships. Despite the many benefits of physical 3D models, printing intricate biological molecules has several limitations, such as low level of atomic detail in complex structures, depiction of a single static molecular representation, and labor-intensive post-printing processing. Computer visualization allows for the development of abundant resources that complement physical models with no added material cost. They propose to develop teaching resources using computer visualization to supplement the physical 3D models.

Margaret Vines, Department of Chemistry: Learning to learn chemistry

The purpose of this project is to help students learn. Most students come to college with the desire to learn. They want to be successful and learn the material presented to them in their classes. Unfortunately, many of them engage in activities that do not help with their learning. The PI’s goal is to help students begin to learn how to learn. They will do this as part of their regular lecture and recitation in general Chemistry. They will educate them about learning techniques and explain why they will aid in their learning. They will then demonstrate these techniques in class, and the students will be given opportunities to use these techniques inside and outside the lecture and recitation. Finally, they will encourage their students to develop those techniques for use in their other classes.

Mentor/Mentee Award

Mentor: Anusha Balangoda / Mentee: Beth Ann Eberle. Department of Geology and Environmental Science: Use of Cooperative Learning Approach in Recitations to Untangle Pressing Environmental Issues in Introductory Environmental Science Class

Cooperative learning is a student-centered active learning strategy in which a small group of students is responsible for their own success and that of their team by holding themselves accountable for the process and outcomes of the activities. In this project, they propose to use a cooperative learning strategy in the GEOL 0840 Introductory Environmental Science course, which is a large enrollment three-credit class, and both lectures and recitations are required.

Mentor: Ben Rottman / Mentee: Rebecca McGregor. Department of Psychology; Learning Research and Development Center: Using a Consulting Model and Project-Based Learning to Teach Psychology Research Methods

In the field of psychology, research methods form the foundation of students’ knowledge during the remainder of their undergraduate degree and beyond. Students in PSY 0036: Research Methods Lecture at the University of Pittsburgh have three course objectives: learn how to read, interpret and discuss research design and conclusions, learn how to critique research, and learn how to design valid research. There are currently few opportunities for students to apply this knowledge to real-world experiences, as this is an introductory course in which students have not yet developed the skills to analyze and interpret their own data. Thus, this course design through the dB-SERC would provide a semester-long collaborative assignment in which students would develop a project proposal to investigate a real-world research problem for a fictional client.

Introduction to Critical Thinking Skills

• First Online: 04 September 2024

Cite this chapter

• K. Venkat Reddy 3 &
• G. Suvarna Lakshmi 4  

This chapter contains summaries of six articles that are machine generated. The summaries discuss the multitude ways in which the field of critical thinking has been understood and defined. Mostly the summaries included in the chapter project the view that critical thinking is all about certain cognitive abilities belonging to the higher order of thinking. The first summary explains the definition of critical thinking using a meta-level approach; it uses this approach because the problem of defining critical thinking is a meta-problem. The authors argue that the definitions proposed earlier were either subject-specific or skill-specific resulting in definitions that are neither universally applicable nor acceptable. The authors therefore have attempted to propose an approach that has three proper criteria that the definition should satisfy. They are: (1) rely on criteria, (2) self-correcting, and (3) sensitive to context. The summary of the second article on the skills required for the twenty-first-century education is based on the lists of skills proposed by various bodies that are broadly categorized as productive, critical, and creative thinking along with digital skills. The author proposes that the curriculum should incorporate skills that are required as per the current pace of change and the need of the hour.

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Reddy, K.V., Lakshmi, G.S. (2024). Introduction to Critical Thinking Skills. In: Reddy, K.V., Lakshmi, G.S. (eds) Critical Thinking for Professional and Language Education. Springer, Cham. https://doi.org/10.1007/978-3-031-37951-2_1

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Development of ASICC-Based Modern Biotechnology Student Worksheets to Improve Students’ Critical Thinking Skills

This research aims to develop modern biotechnology worksheets to improve high school students’ critical thinking skills. This research uses design research with a development study which consisting of preliminary studies and prototyping. The research was conducted to senior high school in Kediri, East Java. Critical thinking skills scores are taken using a rubric that is integrated with essay test questions. Data was collected using pre-test and post-test questions, then analyzed quantitatively and descriptively. The results of this research reveal that ASICC-based student worksheets can improve the critical thinking skills of students in the medium category. Student learning stages in the form of searching, interpreting, and creating in the ASICC learning model can improve students’ critical thinking skills.

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Developing Critical Thinking Skills: Sample Questions for

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Breaking the taboo of using the nursing process: lived experiences of nursing students and faculty members

• Amir Shahzeydi   ORCID: orcid.org/0000-0001-9095-2424 1 , 2 ,
• Parvaneh Abazari   ORCID: orcid.org/0000-0003-4024-2867 3 , 4 ,
• Fatemeh Gorji-varnosfaderani   ORCID: orcid.org/0000-0001-6830-982X 5 ,
• Elaheh Ashouri   ORCID: orcid.org/0000-0002-7566-6566 6 ,
• Shahla Abolhassani   ORCID: orcid.org/0000-0002-5191-7586 6 &
• Fakhri Sabohi   ORCID: orcid.org/0000-0003-1448-6606 6  

BMC Nursing volume  23 , Article number:  621 ( 2024 ) Cite this article

Metrics details

Despite the numerous advantages of the nursing process, nursing students often struggle with utilizing this model. Therefore, studies suggest innovative teaching methods to address this issue. Teaching based on real clinical cases is considered a collaborative learning method that enhances students’ active learning for the development of critical thinking and problem-solving skills. In this method, students can acquire sufficient knowledge about patient care by accessing authentic information.

The aim of the present study was to investigate the experiences of nursing students and faculty members regarding the implementation of nursing process educational workshops, based on real case studies.

A qualitative descriptive study.

Participants

9 Nursing students and 7 faculty members from the Isfahan School of Nursing and Midwifery who attended the workshops.

This qualitative descriptive study was conducted from 2021 to 2023. Data was collected through semi-structured individual and focus group interviews using a qualitative content analysis approach for data analysis.

After analyzing the data, a theme titled “Breaking Taboos in the Nursing Process” was identified. This theme consists of four categories: “Strengthening the Cognitive Infrastructure for Accepting the Nursing Process,” “Enhancing the Applicability of the Nursing Process,” “Assisting in Positive Professional Identity,” and “Facilitating a Self-Directed Learning Platform.” Additionally, thirteen subcategories were obtained.

The data obtained from the present study showed that conducting nursing process educational workshops, where real clinical cases are discussed, analyzed, and criticized, increases critical thinking, learning motivation, and understanding of the necessity and importance of implementing the nursing process. Therefore, it is recommended that instructors utilize this innovative and effective teaching method for instructing the nursing process.

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Introduction

The nursing process is a systematic and logical method for planning and providing nursing care [ 1 ] that provides an opportunity for nurses to efficiently and dynamically utilize their knowledge and expertise. It also creates a common language, known as nursing diagnosis, which facilitates action, promotes creative solutions, and minimizes errors in patient care [ 2 ]. Clinical education, based on the nursing process, provides an appropriate setting for nursing students to gain clinical experiences and foster professional development [ 3 ].

Despite the numerous advantages, nursing students face difficulties in implementing this model in various countries [ 4 , 5 ], lack of appropriate knowledge, lack of clinical practice, and insufficient learning are among the most significant obstacles to the implementation of the nursing process by students. This can be attributed to the poor quality of education regarding this important nursing care model. Therefore, it is necessary for educators in this field to use innovative and participatory teaching methods [ 3 , 6 ]. According to research conducted in Iran, 72% of nursing faculty members use passive teaching methods. Meanwhile, 92% of nursing students prefer active and innovative learning methods over traditional and passive methods [ 7 ]. Therefore, the use of modern methods, which aim to stimulate students’ thinking and enhance their responsiveness in acquiring and applying knowledge, can be effective [ 6 ].

Case-based learning is a collaborative learning method that aims to develop and enhance critical thinking and problem-solving skills [ 8 ]. Teaching the nursing process based on clinical and real cases can be very important in terms of promoting critical thinking, simulating real experiences, enhancing clinical judgment, and ultimately improving the quality and effectiveness of education [ 8 , 9 ]. In this method, students gain sufficient knowledge about patient care by accessing real information, improving their skills in patient assessment, and gaining personal nursing experience. This leads to a better understanding of comprehensive care and prepares individuals for future professional roles [ 9 ].

Very few studies have been conducted on teaching methods and their impact on the quality of nursing process [ 10 , 11 ]. In Iran, case-based trainings have mostly focused on hypothetical cases [ 1 , 12 ]. In other countries, most studies conducted on the case-based educational method have not focused on the nursing process. The few studies that have been conducted on the nursing process have either not been based on real clinical cases [ 13 ] or, if clinical cases have been researched, the studies have been conducted quantitatively [ 8 , 9 ] While qualitative research provides researchers with more opportunities to discover and explain the realities of the educational environment and gain a better understanding of many challenging aspects related to the nursing education process. Researchers are able to provide a practical model that helps improve and enhance the current process by gaining insight and a deep understanding of what is happening in the field of study [ 14 ]. This study represents the first qualitative research that describes the lived experiences of nursing students and faculty members regarding the teaching of the nursing process through real-based case workshops.

Study design

This qualitative descriptive study was conducted from 2021 to 2023. Qualitative descriptive studies typically align with the naturalistic inquiry paradigm, which emphasizes examining phenomena in their natural settings as much as possible within the context of research. Naturalistic inquiry, rooted in a constructivist viewpoint, enables a deeper understanding of phenomena by observing them within the authentic social world we inhabit [ 15 ]. In this type of study, researchers provide a comprehensive summary of an extraordinary occurrence or circumstance of interest and its related factors, but they do not delve into deep interpretation [ 16 ]. This study was undertaken to explore students and faculty members perceptions of the effect of the educational workshops on knowledge, skills and attitudes of students to the nursing process.

Setting and sample

Participants were selected from nursing students and faculty members who participated in nursing process workshops (Table  1 ). The criteria for entry into the study included volunteering to participate in the study and attending at least 3 sessions of the workshops.

Workshop details

The workshops were held in the conference hall of the Nursing and Midwifery Faculty. They consisted of 9 sessions, each lasting 2 h, from 16:00 to 18:00. Students from terms 2 to 8 and faculty members participated in these workshops. Each session was attended by an average of 60 members. Despite the inconvenience of scheduling the sessions outside of the official class hours, all the members stayed until the end of the meeting, showing a keen interest in the material and actively participating in discussions. Attendance was open to all students and faculty members, and participants in each of the workshop sessions were not the same.

It should be noted that all workshops were accompanied by a specialized instructor in the field of the nursing process, as well as a specialized instructor in the field of the specific disease being discussed. The details of these workshops are summarized in three stages:

First Stage

Step 1 . The researcher visited one of the inpatient clinical wards of the hospital based on the assigned topic for each workshop. They selected a patient, conducted a comprehensive assessment, and recorded the information using Gordon’s assessment form. This included the patient’s current and past medical history, paraclinical tests, physical examinations, medications, and information gathered from credible sources such as interviews with the patient and their family, medical records, and the patient’s treatment and care interventions documented in their medical file and Cardex.

Step 2 . Preparing the presentation file, which includes the following items:

Writing the comprehensive patient assessment based on step one.

Writing actual and at-risk nursing diagnoses according to PES (Problem/ Etiology/ Signs and Symptoms) and PE (Problem/ Etiology) rules, as well as collaborative problems, and then prioritizing them based on Maslow’s Hierarchy of Needs.

Writing objectives and outcomes for each nursing diagnosis based on the SMART (Specific/ Measurable/ Attainable/ Realistic/ Time Bound).

Writing nursing interventions (based on objectives and outcomes), along with the rationales according to evidence-based, up-to-date, and reliable sources for each intervention.

Step 3 . Sending the presentation file to an expert professor in the field of nursing process for review and implementing her comments.

Second stage

Step 1 . Announcing the date and time of the workshop session to students and faculty members.

Step 2 . Providing students and faculty members with a comprehensive patient assessment.

Third stage (workshop implementation)

Step 1. Presenting all stages of the nursing process based on the case study:

Providing a comprehensive assessment of the patient’s condition. (Giving time for students, faculty members, and presenters to discuss with each other, express their comments, and summarize)

Presenting diagnoses along with the objectives and expected outcomes. (Giving time for students, faculty members, and presenters to discuss with each other, express their comments, and summarize)

Presentation of nursing interventions. (Giving time for students, faculty members, and presenters to discuss with each other, express their comments, and summarize)

Presentation on assessing the level of achievement of expected outcomes and evaluating interventions. (Giving time for students, faculty members, and presenters to discuss with each other, express their comments, and summarize)

Data Collection Tools

Demographic questionnaire.

It included age, gender, Position, degree and number of sessions attended in the workshop.

Semi-structured interview

It included the following questions:

What was your motivation to attend these meetings?

Before entering the nursing process meetings, what did you expect from the meeting?

How many of your expectations were met by participating in the meetings?

How much did these meetings help you in applying the nursing process in the clinical setting?

What do you think about the continuation of such meetings?

Data collection

After obtaining official permission from the university in 2021, the phone numbers of students and faculty members who participated in more sessions of the workshop were collected in 2023. A specific time and location were subsequently arranged to contact and interview participants who had indicated their willingness to take part in the study. Approximately 40 individuals expressed their consent to participate; however, data saturation was achieved after interviewing 16 participants. It is important to note that interviews were conducted through both individual sessions and focus groups. Individual interviews were carried out with 3 faculty members, while two focus groups were conducted separately with 9 students and 4 faculty members.

Individual Interviews

The interviews were conducted in a semi-structured manner and began with a general question to establish initial and closing communication. These interviews were conducted by one of the researchers who holds a PhD in nursing and has published several qualitative articles in reputable journals. In each of these sessions, the interviewer introduced themselves and welcomed the participants. The goals of the session were discussed, and participants were given complete freedom to express their opinions. The interviewer refrained from interfering or reacting to their opinions, and the information discussed was kept completely confidential under the guise of a code. Participants were subsequently asked to provide consent for voice recording during the interviews. Once consent was obtained from the participants, their voices were recorded. Each individual interview lasted between 30 and 45 min.

Focus Group Interviews

All the conditions of these interviews were similar to individual interviews. However, in focus group sessions, an additional researcher acted as an assistant to the main interviewer. The assistant’s role was to determine the order of speaking based on the participants’ requests, observe their facial expressions while speaking, and take necessary notes. Each of the focus group sessions lasted approximately 5 h. It should be noted that participant selection and sampling continued until data saturation was achieved. Saturation of data refers to the repetition of information and the confirmation of previously collected data.

Data analysis

The qualitative content analysis approach proposed by Graneheim and Lundman was used for data analysis [ 16 ]. The recorded interviews were transcribed verbatim (The transcripts were sent to the participants for feedback and were approved by them), and then each word was carefully examined to identify codes Two independent individuals encoded the data. Words that accurately represented thoughts or concepts within the data were highlighted. Then, the researcher added her own notes about his thoughts, interpretations of the text, and initial analysis of the text. With the progression of this process, appropriate names for the codes emerged, and the codes were organized into subcategories. These subcategories were created to organize and categorize the codes within clusters. The researcher reorganized the subcategories based on their relationships, condensing them into a smaller number of organizational categories. And then the concepts of each category, subcategory, and code were developed.

Trustworthiness

Data was managed using the Lincoln and Guba criteria. These criteria include acceptability, which is equivalent to internal validity; transferability, which is equivalent to external validity; similarity, which is equivalent to reliability; and verifiability, which is equivalent to objectivity [ 17 ]. The use of member checks by participants is considered a technique for exploring the credibility of results. In this regard, the interview text and the primary codes extracted from it were made available to several participants to verify the accuracy with their experiences. External supervision was employed to ensure that the criterion of internal consistency was met. For this purpose, the data was given to a researcher who did not participate in the study. If there was agreement in the interpretation of the data, it confirmed the presence of internal consistency. Finally, an audit or verification inquiry was conducted. The researcher accurately recorded and reported all stages and processes of the research from beginning to end. This allows external supervisors to conduct audits and assess the credibility of the findings.

Data analysis resulted in the emergence of 13 subcategories, 4 categories, and 1 theme (Table  2 ).

Strengthening the intellectual infrastructure of accepting the nursing process

Subcategories such as “improving nursing perception,” “strengthening critical thinking,” “evidence-based nursing practice,” and “filling an educational gap” contributed to the emergence of the category “Strengthening the intellectual infrastructure of accepting the nursing process.”

Improving nursing perception

Participants’ experiences indicate the significant positive impact of the workshop on improving students’ perception of the nursing process. Most nurses in departments do not provide patient care based on the nursing process. As a result, students do not have the opportunity to practically experience the real application of the nursing process in the department. Instead, they only perceive the nursing process as a written task.

For me, it was a question of what the nursing process is, for instance. How difficult is it?” and it really helped me overcome my fear in a way. (P3 student) Usually, they would explain the nursing process to us, but it was not practical or based on real cases, like this. (P1 Student)

Strengthening critical thinking

Critical thinking is a fundamental skill in the nursing process that involves various stages and activities. These include questioning to gather adequate information, validating and analyzing information to comprehend the problem and its underlying factors, evaluating interventions, and making appropriate decisions for effective problem-solving. The experiences of the participating students clearly reflected the formation of these stages during the workshop sessions.

I learned in the workshop about the importance of using critical thinking to successfully connect knowledge and practice. It’s a shame that critical thinking has not been cultivated in the minds of students, and these workshops have laid the foundation for it in our minds. (P6 student) Students often come across hypothetical cases in textbooks, but when they are confronted with real cases, the circumstances are different… This is when critical thinking becomes crucial and the art of nursing is demonstrated… These sessions have made a significant contribution to this subject. (P15 Faculty member)

Evidence-based nursing practice

One of the features of the sessions was that in introducing the case from assessment to evaluation, to justify the rationale and process of collecting and formulating nursing diagnoses, establishing expected outcomes, and providing reasons for each intervention, relied on up-to-date and reliable nursing and medical resources

It had a strong scientific foundation, consistently emphasizing the importance of evidence-based practices and a scientific approach, effectively communicating this perspective to audience. (P2 Student). I became familiar with the book ‘Carpenito,’ and it helped me a lot in understanding my shortcomings. (P3 student). In my opinion, one of the factors that contributed to the effectiveness of the work was consulting the references. They emphasized that as a nurse, I should not solely rely on my personal opinion but should instead base my actions on the reference materials (P14 Faculty member).

Filling an educational gap

From the perspective of workshop participants, the workshop has increased their awareness of their limited knowledge about the application of the nursing process. It has also helped them recognize their shortcomings, and motivated them to pursue additional studies in this field.

Exactly, there was a vacant spot for this educational program in our classes. And there should have been sessions that would prove to us that nursing is not just about the theoretical concepts that faculty members teach in class. (P5 Student) The nursing process has a theoretical aspect that students learn, but when they attempt to apply it in practice, they often encounter difficulties. These sessions helped to fill the gap between theory and practice. (P15 Faculty member)

Practicality of the nursing process

Subcategories of “linking the nursing process with team care,” “demonstrating the role of the nursing process in improving care quality,” “comprehensive view in care,” and “student’s guiding light in the clinic,” Created the category “Practicality of the Nursing Process”.

Linking the nursing process with team care

Participants’ experiences indicated that participating in nursing process sessions helped them realize that the nursing process is a model that will lead to collaborative team care. Prior to attending these sessions, nursing students like nurses considered their duty to be solely executing medical orders under the supervision of clinical faculty members and staff nurses.

I realized that in certain situations, I am able to confidently express my opinion to the doctor. For instance, if I believe that a particular course of action would yield better results, I can easily communicate this and provide reasons to support my viewpoint (P7 Student). Teaching the pathway when it’s categorized with knowing what we’re assessing… Let’s go up to the patient; our confidence can really guide them along with us as we progress step by step and systematically. Often, the patient accompanies us, and sometimes they voice their unspoken concerns, which helps improve their care. It means the patient themselves are partnering with us. (P6 student)

Demonstrating the role of the nursing process in improving care quality

Strengthening the attitude and belief in the role and application of the nursing process in improving the quality of care was another concept that emerged from the experiences of the students. Presenting reports on the implementation of the nursing process on real cases led them to believe that providing care based on the nursing process results in organized care planning and enhances the quality of care.

In these workshops, the needs of patients were prioritized, documented, and then organized systematically. This concept remains ingrained in a person’s mind and enables us to deliver comprehensive care to the patient without overlooking any aspect. This has been very helpful for me, and now it greatly assists me in the clinic. (P4 Student) Another great aspect of these sessions was the emphasis they placed on the nurse-patient relationship. I could see that the students had been following up with patients for a while and implementing the process. This was very helpful to me. For instance, diagnosing based on the patient’s current health status was an ongoing process. In my opinion, the connection between the patient and nurse was more important and practical for me.(P1 Student).

Comprehensive view in care

Attention to the patient’s care needs went beyond focusing solely on physiological aspects. It involved a holistic approach that addressed the patient’s needs related to all aspects of biology, psychology, society, spirituality, and economics. This was clearly reflected in the students’ experiences during the nursing process sessions.

…I paid attention to all aspects of the patient. For example, perhaps I overlooked her anxiety issue and never took it into consideration. However, I eventually came to realize that addressing anxiety is crucial, as it is one of the primary concerns and needs of patients. (P2 Student) …that the students had a holistic view of the patient (they had examined the patient thoroughly, including the patient’s skin, etc.) and had compiled a list of the patient’s issues, paying attention to all aspects of the patient (P14 Faculty member).

Student’s guiding light in the clinic

One of the significant accomplishments of nursing process sessions, as evidenced by the students’ experiences, was the role of these sessions in assisting students in overcoming confusion and uncertainty during their internships. These sessions enabled them to establish a mental connection between the theoretical knowledge learned in the classroom and its application in the real clinical setting, also helped them understand how to effectively utilize their theoretical knowledge in a clinical learning environment.

.I was feeling incredibly lost and confused. I didn’t know what steps to take next. Many of us find ourselves in this situation, unsure of what to do. At least for me, as someone who grasps concepts better through examples, the case-based studies conducted during the workshop had a significant impact. (P6 Student)

Supporting a positive professional identity

Two subcategories, “highlighting the importance of nursing science” and “reforming the perception of nursing nature,” have contributed to the development of the category “supporting a positive professional identity.”

Highlighting the importance of nursing science

Based on students’ experiences, the nursing process sessions have been able to answer an important question. Why should they be bombarded with information and expected to possess extensive knowledge in the field of disease recognition, pathophysiology, diagnosis, treatment, and nursing care during their studies? The students believed that the content of the nursing process sessions clarified the necessity and importance of nursing knowledge for them. In these sessions, they came to believe that providing care based on the nursing process requires extensive nursing knowledge.

. In my opinion, this work showcases a significant strength by highlighting the importance of working scientifically as a nurse. Personally, I feel its impact on myself is profound. (P2 Student) In my opinion, it was very touching and captivating because it accurately portrayed the immense power of a nurse. However, amidst the demanding and difficult nature of the job, what specific details should a nurse pay attention to? and it is precisely these details that shape the work of a nurse. It was very interesting and beneficial for me. (P5 student)

Reforming the perception of nursing nature

The student is seeking ways to comprehend and value the practical aspects of nursing as a genuine science, assuming that nursing is indeed regarded as a science. Participants’ experiences have shown that nursing process sessions have been able to address this identity challenge and modify and enhance students’ understanding of the nature of nursing.

I used to believe that nursing was primarily an art complemented by science until I entered term 2 and participated in these workshops. And now I realize that it has the scientific foundation that I expected from an evidence-based practice. (P5 student). . The important point was that lower-term students, who sometimes lacked motivation and thought nursing had nothing to offer, gained motivation and had a change in perspective by attending these sessions. (P2 faculy members)

Self-directed learning facilitator

Subcategories of “stimulating a thirst for learning,” “creating a stress-free learning atmosphere,” and “teaching fishing,” formed the category of “self-directed learning facilitator.”

Stimulating a thirst for learning

Participants’ experiences indicated that the format of conducting sessions, ranging from step-by-step training to training accompanied by multiple examples, had a significant impact on creating a sense of necessity and stimulating learners’ motivation to learn.

First of all, the challenges that you yourself raised (faculty member) for example, why did you make this diagnosis?” Why did you include this action? Why is this a priority? Really, it shook me and made me think that maybe there is more to this, maybe there is more to the nursing process that I haven’t understood yet…. That’s why it became my motivation. (P3 student) …But these sessions helped me a lot. At least, they sparked my curiosity and motivated me to delve deeper into the subject. I began actively participating in these sessions and found them to be highly effective for my personal growth. (P6 student) In my opinion, one of the things that empowered the work was the act of seeking references. They emphasized that as a nurse, I should not solely rely on my personal opinion but should instead base my actions on credible sources. (P14 Faculty member)

Creating a stress-free learning atmosphere

Students believed that the absence of a legal requirement to attend these workshops, coupled with the understanding that their participation or non-participation would not be evaluated for grading purposes, would enable them to engage in these sessions without concern for their academic performance and in accordance with their own volition.

I was more scared… In my internships, for example, we would sit and talk with the instructor. However, the discussions primarily revolved around grades and other academic matters, which created a stressful environment where students were hesitant to freely express their thoughts. But the sessions here are very relaxed, and students no longer have the fear of grades. (P7 student) The essence of these sessions was that they came from the heart and inevitably touched the heart. The beauty of this program was that it was built on love. (P10 Faculty member)

Teaching fishing

Direct reference to teaching fishing in the participants’ experiences points to one of the very important features that effectively prepares the way for self-guided learning. The term “teaching fishing” was repeatedly mentioned in the participants’ experiences. They believed that these sessions served as a roadmap to easily enhance their knowledge and skills in the field of nursing process application.

.And actually, teaching fishing, as mentioned by other students, is important. In my opinion, it has a positive impact both professionally and in terms of the effectiveness of the nursing process. (P2 student) The important aspect was the involvement and full participation of the students, who prepared the materials themselves… The meaning and concept of being a student were more evident, and the talents of the students flourished. They actively participated in discussions about learning and education. (P15 Faculty member)

Planners, in their efforts to help students gain a better understanding of the nature and application of the nursing process, are constantly striving to innovate in teaching this model. The aim of the present study was to describe and explain the experiences of nursing students and faculty during clinical-based nursing process workshops involving real cases.

Hanisch et al. (2020) recommend using data from actual patients [ 18 ], and Yilmaz et al. (2015) suggest providing nursing students with opportunities to apply the nursing process in diverse patient populations during clinical training [ 19 ]. The study conducted by Karimi et al. (2011) demonstrated that organizing nursing process classes as workshops stimulated a sense of competition and superiority both among and within groups. This approach also enhanced participants’ concentration on learning the content of each session. In addition, the workshop fostered a sense of cooperation and cohesion among the students, which was evident in their increased interest and excitement [ 1 ]. The importance of utilizing workshop-based training with real clinical cases is clearly evident. When students receive data related to a real patient, they directly experience the clinical environment. This, in turn, leads to an improvement in their critical thinking and decision-making skills when they encounter similar cases. For this purpose, nursing educators can present the rich clinical cases they encounter during their internships in theory classes based on the stages of the nursing process. They can also ask students to present these cases for their peers to comment on and critique the care provided, in order to stimulate discussion.

The category of " Strengthening the intellectual infrastructure of accepting the nursing process " indicates that the teaching method used in this study has been able to help students better understand and recognize the nature and improvement of insight into the nursing process. In the study by Thuvaraka et al. (2018), 52% of participants strongly agreed on the necessity of having a positive attitude and insight towards the nursing process for its proper implementation [ 20 ]. According to the study by Mert et al. (2020), a lack of insight into the nursing profession and process can even lead students to consider dropping out of their studies [ 21 ]. The importance of reviewing the nursing education process to enhance this perception has been emphasized in various studies. Zamanzadeh et al. (2015) discuss several challenges in the implementation of the nursing process. These challenges include a lack of clarity regarding its meaning, differences in perspectives, and insufficient training leading to a lack of awareness on how to properly implement it [ 22 ]. More than 90% of students (93.5%) in the study conducted by Rajabpoor et al. (2018) [ 4 ] and over two-thirds (75.6%) of students in the study conducted by Sharghi et al. (2015) identified lack of proper training and insufficient time allocated for teaching as the most significant barriers to implementing the nursing process. They attributed this to traditional and routine teaching methods [ 23 ]. This causes students to undervalue the nursing process, perceiving it only at a theoretical level rather than practical. As a result, they become overwhelmed by the routine when working as clinical nurses [ 7 ]. Therefore, by teaching the case method based on real clinical cases, nursing instructors can strengthen students’ positive outlook and ability to apply the nursing process. This increases the percentage of students implementing the nursing process in clinical wards.

Strengthening critical thinking is one of the concepts derived from analyzing the experiences of the students and faculty who participated in the present study. Based on a review study by Carvalho et al. (2017), the utilization of the nursing process, particularly the stage of nursing diagnosis formulation, enables nurses to employ critical thinking in making judgments and providing clinical care [ 24 ]. This process also helps ensure the delivery of high-quality care [ 25 ]. But if the nursing process is presented in an undesirable manner, it suppresses critical thinking. According to Heidari et al. (2016), the nursing process resulted in students relying on copying from books, which led to a decline in creativity and an increase in their dissatisfaction [ 26 ]. According to the study conducted by Ghanbari et al. (2017), the implementation of collaborative workshops focused on the nursing process resulted in an improvement in critical thinking skills among nursing students [ 3 ]. Therefore, nursing instructors can teach theoretical classes based on the clinical cases they have experienced in the hospital. By doing so, students can immerse themselves in the clinical environment during theoretical classes, which significantly enhances their critical thinking skills.

The evidence-based nursing display was one of the achievements of nursing process educational workshops, which were based on real cases. Mackey et al. (2017) consider evidence-based practice as a means to bridge the gap between theory and practice in nursing education for undergraduate and graduate students [ 27 ]. And likewise, Sin et al. (2017) believe that nursing faculties are obligated to enhance the competence and knowledge of students for evidence-based practice by employing innovative methods [ 28 ]. Therefore, it is recommended that nursing instructors use up-to-date scientific references for nursing interventions when teaching about the nursing process of diseases. This practice helps students feel that the care they provide is supported by scientific evidence and motivating them to carry out nursing care more effectively.

One of the emerging concepts in this study was the focus on the practicality of the nursing process. In the study conducted by Agyeman-Yeboah et al. (2017), participants reported that new students and nurses tend to neglect the implementation of the nursing process when they observe experienced nurses failing to apply it in a scientific and systematic manner [ 5 ]. The lack of implementation of the nursing process by nurses is due to a lack of knowledge and a negative attitude towards it. Zerihun Adraro and Adugna Cherkos (2021) conducted a study in Ethiopia and found that the majority of nurses had inadequate knowledge, and half of them lacked a positive attitude towards the implementation of the nursing process [ 29 ]. In the study by Thuvaraka et al. (2018), only 17% of nurses had sufficient knowledge about the nursing process and implemented it [ 20 ]. One of the important experiences for students in the “Practicality of the Nursing Process” category is the development of their participatory and interprofessional spirit. They are encouraged to express their opinions about the care and treatment process of patients, rather than blindly following the doctor’s orders. According to a systematic review study, the level of physicians’ proficiency in their management systems is a significant issue for the healthcare system [ 22 ]. According to the study conducted by Nakhaee et al. (2017), doctors are the ones responsible for making decisions regarding all patient matters, while the efforts of nurses often go unappreciated. This lack of recognition can result in a decline in their self-esteem [ 30 ]. While according to Adamy et al. (2019), the implementation of the nursing process at a professional level is highly effective in creating an independent nursing role, rather than just serving as assistants to physicians. This implementation also enhances the credibility of the nursing profession [ 31 ]. The recommendation of the present researchers to nursing instructors is to take a significant step in enhancing the knowledge and independent spirit of nursing students by basing their teaching on real clinical cases. When students perceive that they have independence and are not merely following doctors’ orders, their engagement in operationalizing the nursing process and evidence-based care will increase.

Strengthening the holistic perspective was one of the positive experiences for students and faculty members who attended these workshops. According to the study by Hackett et al. (2017), physical problems can result in mental stress among patients. Therefore, it is essential to consider all dimensions of care [ 32 ]. According to Ericsson (1995), humans should be considered as a whole, and nursing care should be tailored to address biological, psychological, social, and spiritual aspects [ 33 ]. The importance of holistic care has been emphasized by Florence Nightingale, who encouraged caregivers to practice it [ 34 ]. Holistic care emphasizes partnership and dialogue between nurse and patient about health care needs [ 35 ]. Adequate training is crucial in ensuring that nurses and nursing students are well-prepared to meet the diverse needs of patients and deliver comprehensive care [ 36 ]. It is recommended for nursing instructors to focus on the mental aspect in addition to the physical aspect when teaching the nursing process and encourage students to apply this approach during clinical internships.

Another advantage of these sessions was the successful implementation of the nursing process in apprenticeship. Work disorder and confusion in implementing the nursing process are significant challenges. According to the study by Korkut et al. (2021), students were unable to collect appropriate data from their patients and were confused when formulating and prioritizing nursing diagnoses, determining goals, and planning care. However, due to the fear of receiving a low grade, they were compelled to present fabricated data [ 37 ]. Therefore, nursing instructors should incorporate real clinical cases encountered during internships into their theoretical classes. This simulation helps students perform better in implementing the nursing process in the hospital environment later on.

During these workshop sessions, the students’ awareness of the professional identity of nursing was heightened. They came to understand that this professional identity is a crucial principle that underpins their comprehension of nursing and scientific care. As a result, they recognized the significance of studying pathophysiology and the fundamental principles of scientific care for different diseases. Professional identity is described as a person’s perception of themselves within a profession or the collective identity of the profession [ 38 ]. In nursing, professional identity plays a crucial role in delivering high-quality services to patients [ 39 ] because it effectively enhances clinical competence, self-assurance, self-esteem, and interpersonal communication skills [ 40 , 41 ]. In this regard, the study by Sun et al. (2016) found that professional identity and education level had the greatest impact on the stress levels of nursing students. The results of that study showed that developing and enhancing professional identity could be beneficial for nursing students in managing stress [ 42 ]. Similarly, according to the study by Sabanciogullari et al. (2015), there was a positive and significant correlation between nurses’ job satisfaction and professional identity. This study found that 15.5% of nurses who intended to leave their profession had insufficient professional identity and lower job satisfaction. Professional identity is a significant factor in job satisfaction [ 41 ]. According to the study by Van der Cingel et al. (2021), a lack of attention to the professional identity of nursing contributes to the departure of nursing students and young nurses from the nursing profession [ 43 ]. Therefore, focusing on professional identity in nursing education is crucial and should be a primary objective [ 38 ], despite findings from Haghighat et al. (2019) indicating that nursing education programs in Iran have not effectively nurtured nursing students [ 44 ]. This highlights a greater focus on teaching based on real clinical cases, which enhances the professional identity of nursing and facilitates the implementation of the nursing process.

“Self-directed learning facilitator” is one of the important categories identified in the present study. It encompasses three crucial concepts: “stimulating a thirst for learning”, “creating a stress-free learning atmosphere”, and “teaching fishing”. The students’ experiences indicated that engaging in discussions, asking questions, and providing answers had a significant impact on motivating them to study and enhancing their motivation for learning. This learning took place in a calm and stress-free environment. Participants were able to analyze the content calmly, as grades were not involved. As a result, they were able to diagnose what to prioritize in a clinical setting, even without the assistance of a clinical instructor. In fact, during these sessions, the instructors focused on teaching the students how to fish instead of simply giving them fish. As a result, the students’ spirit of independent learning increased. Kholmuratovich et al. (2020) stated in their study that independent learning helps students to learn effectively and efficiently [ 45 ]. It increases their independence and critical thinking skills, while also effectively enhancing their self-esteem and motivation [ 46 ]. For this reason, Lau et al. (2017) recommend promoting this teaching method in their study [ 47 ]. Based on the aforementioned studies, independent and self-directed learning leads to improved comprehension and learning, increased motivation, enhanced self-confidence, and critical thinking among students. Consequently, it can be argued that teaching based on clinical cases and workshop-based approaches, beyond aiding students in better understanding and applying the nursing process, has the potential to transform students’ overall learning approach.

Teaching the nursing process through workshops based on clinical cases has broken the taboo surrounding the application of the nursing process. The organization of these workshops in a friendly and stress-free environment, where real clinical cases were discussed, analyzed, and criticized, motivated the students to apply the nursing process in clinical setting. This approach led to a correction in their perception that they considered the implementation of the nursing process as time-consuming and unnecessary, and it also increased the students’ critical thinking abilities. The nature and process of conducting the workshops proved to be beneficial in implementing the theoretical standards in practical settings. The nursing interventions program was evidence based. This approach not only fostered students’ motivation for self-directed learning but also heightened their curiosity for acquiring knowledge. In these sessions, the approach involved teaching students how to fish rather than simply giving them fish. On the other hand, one of the significant challenges in the application of the nursing process in clinical practice by students is the lack of knowledge and skills among nurses to provide care based on the nursing process, it is recommended that these workshops also be conducted for nurses. Furthermore, action research should be employed to evaluate the role of this educational approach in enhancing the knowledge and skills of clinical nurses.

Limitations

Considering that the workshops had to be held outside of the regular class hours of the faculty, which is at 16:00, and taking into account the transportation issues of the students, the workshops could only continue until 18:00. The limitations of this study include the restricted hours and duration of these workshops. Another limitation of this study is the lack of implementation of nursing interventions by the researchers for the patient and subsequently the real evaluation of the interventions performed, due to ethical considerations. In fact, considering that the biggest problem for students is the application of the nursing process related to assessment, diagnosis, and planning, the focus of the workshops was on these stages. However, it seems that by covering all stages of the nursing process in educational workshops, the challenges faced by students in the implementation and evaluation stages can also be addressed.

Data availability

The data that support the findings of this study are available from the cor - responding author upon reasonable request.

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Acknowledgements

The researchers would like to express their gratitude to the students and professors who participated in the workshops and Student Research Committee of Isfahan University of Medical Sciences.

This study was financed by the Student Vice Chancellor for Research of Isfahan University of Medical Sciences (Project number 1400254).

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Parvaneh Abazari

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Faculty of Nursing and Midwifery, Qom University of Medical Sciences, Qom, Iran

Fatemeh Gorji-varnosfaderani

Nursing and Midwifery Care Research Center, Department of Adult Health Nursing, Faculty of Nursing and Midwifery, Isfahan University of Medical Sciences, Isfahan, Iran

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ASH, PA, FG designed the study. ASH, PA, FG, EA, SHA, FS helded the Workshops. PA interviewed the participants. ASH and FG wrote the interviews. PA, EA and SHA analyzed the interviews. ASH, PA and FS prepared the manuscript, and all authors read and approved the final manuscript.

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This study has been approved by the ethics committee of Isfahan University of Medical Sciences (IR.MUI.NUREMA.REC.1400.139) in 2021. Initially, the research purpose was explained to the patients and their caregivers. They were informed that participation in the research is entirely voluntary and free of charge. Not participating in the research would not affect their care and treatment interventions. They were assured that they could withdraw from the research at any time. Furthermore, it was emphasized that their information would be presented in the workshop in a strictly confidential manner, without disclosing their names, photos, file numbers, etc. Subsequently, both oral and written consent were obtained from them. After that, the study’s purpose was also explained to nursing students and faculty members, and informed oral and written consent was obtained from them. Numeric codes were used instead of personal names to ensure the confidentiality of the interviews. The participants were free to withdraw from the study at any time. All methods were conducted following the applicable guidelines and regulations.

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Shahzeydi, A., Abazari, P., Gorji-varnosfaderani, F. et al. Breaking the taboo of using the nursing process: lived experiences of nursing students and faculty members. BMC Nurs 23 , 621 (2024). https://doi.org/10.1186/s12912-024-02233-z

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DOI : https://doi.org/10.1186/s12912-024-02233-z

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