instructional strategies for math problem solving

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Free ready-to-use math resources

Hundreds of free math resources created by experienced math teachers to save time, build engagement and accelerate growth

20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

• Draw a model
• Use different approaches
• Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

• The context
• What the key information is
• How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Similarly, you could draw a model to represent the objects in the problem:

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

• Understand the problem
• Devise a plan
• Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

How Third Space Learning improves problem-solving 

Resources .

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking. 

Explore the range of problem solving resources for 2nd to 8th grade students. 

One-on-one tutoring 

Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE :

• 8 Common Core math examples
• Tier 3 Interventions: A School Leaders Guide
• Tier 2 Interventions: A School Leaders Guide
• Tier 1 Interventions: A School Leaders Guide

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies for problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

Related articles

How To Teach Math: 10 Effective Strategies For Teaching Math In The Classroom

Building Thinking Classrooms: Effective Strategies For Your Math Classroom

Differentiation Strategies In The Classroom: 8 Methods For Every Teacher

Retrieval Practice: A Foolproof Method To Improve Student Retention and Recall

Ultimate Guide to Metacognition [FREE]

Looking for a summary on metacognition in relation to math teaching and learning?

Check out this guide featuring practical examples, tips and strategies to successfully embed metacognition across your school to accelerate math growth.

Privacy Overview

You are using an outdated browser. Please upgrade your browser to improve your experience.

6 Simple (But Effective) Instructional Strategies for Mathematics

As a mathematics teacher, it’s easy to dream about the dynamite lessons you could plan and deliver if only you had a little more time up your sleeve.

But we don’t live in a perfect world. With time at a premium, it’s not always possible to prepare cutting-edge resources and coordinate lengthy student-focused activities.

That doesn’t mean your teaching has to suffer. There’s still plenty you can do to drive engagement and foster conceptual understanding in your day-to-day lesson.

Here are 6 simple yet effective instructional strategies for mathematics that you can weave into your daily practice.

1. Make conceptual understanding a priority

For students to use mathematics flexibly and grapple with complex problems, they need more than facts and procedures.

They need a deep understanding of mathematical  concepts  themselves.

Here’s how you make conceptual understanding a priority in your classroom:

Use visual strategies

Making a concept visual allows students to see how an abstract concept translates to a physical scenario. Use illustrated problems or hands-on activities, and encourage students to use visual methods of their own (e.g. drawing) when solving problems.

Seeing a problem in different ways also builds the brain’s neural networks, increasing understanding and retention.

Use the schema approach

The schema is the underlying pattern behind a mathematical concept. All subtraction problems, for example, revolve around a certain amount of something being taken away from an original amount. Once students grasp the schema, they’ll be able to notice it in a diverse array of different problems.

To do this, put similar word problems (e.g. addition ones) side by side and help students discover what they have in common. See if they can express this in words that might apply to other problems of the same type.

Explicitly teach the mathematics vocabulary of a concept

Show the different ways a concept might be expressed in words. Addition, for example, might be expressed as two quantities “together” or a “combined amount”. Once they broaden their math(s) vocabulary, they’ll be able to use concepts much more flexibly.

• Here are some fun ways to build mathematical vocab:
• Display words on posters around the classroom.
• Have students bookmark a mathematics dictionary on their browser (link to ours).
• Have students write down a mathematical word, which they then describe to a partner without using the word itself. The partner has to guess which mathematical concept it is.

2. Set meaningful homework that builds on class learning

You hear the bell ring and – in a last-minute panic – yell out an order to complete exercise 15.2, odd number questions, and every second column.

We’ve all been there. After all your lesson planning, meaningful homework sometimes slips through the cracks.

But if you integrate homework into your lesson plans , you’ll find it much easier to set activities that build deep understanding and engage students that much more.

Think about how your students might reflect on or connect new knowledge at home, rather than just blindly practicing a process.

For example, they could:

• Teach someone else in the family about what they’ve learned
• Find a real-life application of the lesson’s concept somewhere in the home
• Put theory into practice with a hands-on activity (e.g. creating a timetable, cooking)
• Ask qualitative or ‘value’ questions of family members where appropriate.

Mathletics has targeted curriculum activities to ensure your students are progressing within their zone of learning

3. use cooperative learning strategies.

Cooperative learning has three major benefits in mathematics:

• It encourages students to express their mathematical thinking, which in turn gives them greater clarity of thought and self-awareness of their own problem-solving strategies.
• Communicating with others exposes students to different mathematical approaches, which they can use to think more flexibly.
• It mirrors the way mathematics is done outside the classroom, where people with different strengths work together to solve challenging real-world problems.

Here’s how you can use cooperative learning strategies effectively in your classroom:

The “puzzle pieces” approach to group work

Use the “puzzle pieces” approach, where each learner is given a unique piece of information to share with the rest of the group to solve a problem. That way every student has to get involved, and everyone has something to contribute regardless of ability level. (Tip: find some examples of puzzle piece activities in our article on math enrichment .)

Take time to reflect

Build-in reflection time after a collaborative activity for students to reflect on what worked, which strategies they found helpful, and how being exposed to other ways of reasoning has made them think differently.

Be strategic when allocating groups

A mix of ability levels will mean top-level students can consolidate their understanding by guiding the activity, while others can learn from more experienced peers. That way, students never miss out on learning, even if they’re always helping others (in fact, research suggests that teaching others yields the highest retention of any strategy).

4. Use strategic questioning

Strategic questions can help turn a regular ‘chalk and talk’ lesson into a deep learning experience, or scaffold learning acting as students advance into more challenging territory. Try using open-ended questions such as:

“Tell me how you solved that”

Instead of congratulating a student when they get an answer correct and moving on, ask them to communicate their approach. This achieves two things:

• The student is encouraged to reflect on their own thought process in detail. Instead of just “doing the math(s)” automatically, they’ll understand exactly the steps they took – and begin to see how these might be adapted to future, more challenging problems.
• Other students get the opportunity to see how they could have solved the problem, even if they struggled to do so originally.

“Is there any other way of solving this?”

Asking students to elaborate on different approaches to the same question highlights that there is no single, correct way of doing the mathematics. Moreover, students might discover some new mental mathematics tips or strategies from their peers that they can use in future activities.

“Does this problem remind you of anything else we’ve done before?”

Before students start shrugging their shoulders in response to an unfamiliar problem, ask them if it reminds them of anything they’ve done before.

They’ll start to notice previously encountered concepts underneath the surface. This habit of checking for familiarity is what produces flexible and agile mathematical thinkers.

“Where could you use this…” or “where would you see this used in the real world?”

These questions drive home the relevance of the learning. Instead of procedural knowledge alone, students will also come away with an understanding of how to apply that knowledge.

5. Focus on real problem-solving and reasoning

In the world beyond the classroom, mathematics takes the form of complex problems as opposed to straightforward questions with just one answer. For this reason, the most effective instruction equips students with the problem-solving and reasoning skills they’ll need for real life.

But this doesn’t mean an arbitrary word problem with apples and oranges. Instead, the best problems are real . That means they:

• Are open-ended. Instead of funnelling students to a particular solution, keep it open to different approaches.
• Approximate relevant real-world scenarios, or (even better) invite students to get hands-on with real items.
• Encourage students to collaborate and explore different perspectives.
• Don’t spell out exactly what students need to do. Let them trial different procedures until they settle on a strategy that works instead.

Use these examples of great problem-solving tasks .

Get access to 700+ unique problem solving and reasoning activities with a free trial

6. use mixed modes of assessment.

A variety of formative and summative assessment types will allow you to:

• Assess conceptual learning, as well as fact recall
• Build on what students know, instead of just assessing what they don’t
• Notice gaps in the learning before the final test

Here are some assessment types that provide an alternative to standard timed testing:

• Reflections
• Peer assessments
• “Teach the class” activities

Tip: Learning doesn’t have to cease for assessment to take place. Try and integrate the two, e.g. by assessing students’ collaborative abilities while they do a group task.

Join millions of students across the globe to celebrate  World Maths Day!

More instructional strategies for mathematics, mathematics activities.

• Fun math activities
• At home math activities
• STEM activities for elementary students

Concept-specific instructional strategies

• How to teach addition
• How to teach multiplication
• How to teach subtraction with regrouping
• How to teach addition with regrouping

Other instructional strategies for mathematics

• Math enrichment strategies
• Strategies to support struggling math students
• Mental math strategies
• Problem-solving strategies

You might like...

• DIVERSITY STATEMENT
• CAREER OPPORTUNITIES
• STEMscopes Science
• Collaborate Science
• Kide Science
• STEMscopes Math
• Math Nation
• DIVE-in Engineering
• STEMscopes Coding
• Mastery Coding
• Tuva Data Literacy
• STEMscopes Streaming
• Math Independent Skills Practice Books
• NATIONAL INSTITUTE FOR STEM EDUCATION
• STEMSCOPES PROFESSIONAL LEARNING
• RESEARCH & EFFICACY STUDIES
• FREE RESOURCES
• TESTIMONIALS
• LMS INTEGRATIONS
• CONTACT SALES
• CUSTOMER SERVICE

Top 6 Instructional Strategies for Math

ALI Staff | Published  June 05, 2024

Effective math strategies deepen students' understanding and enthusiasm for mathematics. These strategies not only boost student engagement but also enhance learning outcomes, providing teachers with the tools to deliver more effective education.

In this blog, you will learn:

• The importance of using proven instructional methods in math.
• How these techniques can transform the approach to teaching math.
• Ways to support teachers in implementing these strategies effectively.

Let's explore how strategic instructional methods can significantly improve math education.

Choosing Instructional Math Strategies to Enhance Learning 

It's important that educators select the right strategies when teaching students math. When teachers focus on methods that are known to be effective, they can significantly boost educational outcomes for their students. This involves:

• Assessing Learning Gaps: Regularly evaluating student performance to identify specific areas where improvement is needed.
• Implementing Proven Methods: Adopting instructional strategies such as the Concrete-Representational-Abstract (CRA) approach, which enhances understanding.
• Adapting Instruction: Continuously refining teaching methods based on student feedback and performance data to ensure effective learning for all.

6 Effective Instructional Strategies for Math

Using a variety of instructional strategies in math education ensures that students understand and retain mathematical concepts effectively.

Here are six effective math teaching strategies that all teachers can implement in their classrooms:

1: Concrete-Representational-Abstract (CRA) Approach

The CRA approach guides students through three stages of understanding mathematics. It starts with using concrete objects to demonstrate a math principle, then moves to pictorial representation, and finally to abstract symbols.

How to implement the CRA approach in the math classroom:

Concrete Stage: Start with tangible items like blocks or counters to solve problems, allowing students to physically manipulate the math.

• Example: In an elementary classroom, students might use counting blocks to solve a problem like adding 5 + 3 by physically grouping the blocks together.
• Example: Students then draw a picture of the five blocks and three blocks they grouped, labeling each group with the correct numeral.
• Move to using the numerals and plus-sign (5 + 3) to represent the addition problem, leading students to write and solve the equation using the abstract symbols.

This method helps students make meaningful connections between real-world situations and abstract math concepts, solidifying their understanding and ability to apply math effectively.

2: Hands-On Learning

Hands-on learning is an effective math learning and teaching strategy that allows all students to grasp math concepts in a way that suits them best. Hands-on methods transform abstract learning into experiences students can touch, feel, and physically interact with, enhancing their understanding and retention of the concepts. Engaging students with interesting manipulatives, like bear counters, also increases student motivation for learning math.

How to implement hands-on learning in the math classroom:

• Elementary Math Example: Base-ten blocks can be used to demonstrate addition and subtraction with a concrete example. This allows young students to physically manipulate and combine units to understand basic operations.
• Middle School Math Example: Utilize fraction circles in class to help students visually compare and calculate with fractions, deepening their understanding of how fractions work.
• High School Math Example: Introduce algebra tiles to facilitate the understanding of algebraic expressions and equations. These hands-on pieces allow students to physically represent and solve quadratic equations by manipulating the tiles.

These hands-on activities with manipulatives directly support the math curriculum at each educational level, enhancing students' ability to understand and retain complex math concepts through tactile learning experiences.

3: Inquiry-Based Learning

Inquiry-based learning is an approach that encourages students to pose questions, engage in exploration, and solve problems actively. This method makes math education more student-centered while fostering a deeper understanding of mathematical concepts.

How to implement inquiry-based learning in the math classroom:

• Encourage Exploration: Allow students to explore mathematical concepts through guided discovery, which encourages active learning and critical thinking.
• Develop Hypotheses: Encourage students to form hypotheses based on their observations and to test these as they work through mathematical problems.
• Reflect on Findings: Guide students to reflect on their results and the problem-solving process, enhancing their ability to understand and articulate mathematical concepts.
• Encourage Questioning: Foster an environment where students feel comfortable questioning the how and why of mathematical concepts, further deepening their engagement and understanding.
• Integrate Problem-Solving Activities: Use real-world problems that require students to apply math concepts, analyze data, and devise solutions, mirroring the inquiry process in science.

Implementing these elements effectively in the math classroom ensures that students stay engaged while promoting a deeper and more meaningful learning process.

4: Interdisciplinary Teaching

Interdisciplinary learning links math with other academic subjects, helping to connect mathematical concepts to a broader context. This approach enhances the relevance of math by demonstrating its application across various fields, from science to economics, making learning more meaningful for students.

How to implement interdisciplinary teaching in the math classroom:

• Cross-Curricular Lessons: Organize projects and lessons that integrate math with subjects like science, economics, or art, such as calculating angles for art projects or using statistics to investigate a social studies topic.
• Integrate Technology: Employ digital tools that simulate real-life issues needing mathematical solutions, such as coding for data analysis or creating economic models.
• Relate Math to Current Events: Motivate students to apply math to current events or historical data analysis, like election results or economic indicators.

These methods make math lessons more intriguing for students. They also show students how math is used in the real world, making it more meaningful as a subject.

5: Technology Integration

Teachers can incorporate the use of technology and educational apps into their math teaching to make the subject more engaging to students. The use of technology during math lessons also allows teachers to differentiate instruction more easily.

Best practices for technology integration in the math classroom:

• Select Appropriate Tools: Choose technologies that align with your teaching objectives. For example, use graphing calculators for high school algebra or interactive geometry software for visualizing shapes and angles.
• Incorporate Game-Based Learning: Implement educational games that reinforce math skills. These games can motivate students and provide instant feedback, making learning both fun and effective.
• Utilize Online Assessment Tools: Employ platforms that offer customizable quizzes and tests. These tools can provide immediate feedback to students and detailed analytics to teachers, helping to track progress and identify areas needing improvement.
• Encourage Use of Educational Apps: Introduce students to apps that facilitate practice and exploration of math concepts at their own pace. Choose apps that offer adaptive learning paths to cater to individual student needs.

Using technology as a math instructional strategy allows educators to enhance both the content as well as the delivery of their lessons. 

6: Differentiated Instruction

Differentiated instruction is the cornerstone of effective instructional practice for all students. This instructional strategy is based on the idea that different students need different approaches, different types of practice, and varied amounts of time to achieve the same learning goals.

How to implement differentiated instruction in the math classroom:

• Flexible Grouping: Organize students into groups based on their current understanding or skills. These groups can be dynamic, changing as students progress or as different topics are introduced, allowing for targeted instruction that meets each student at their level.
• Adaptive Technologies: Use technology that adapts to the needs of individual students. Tools like adaptive learning platforms can modify difficulty levels or offer different types of problems based on student responses, providing personalized learning experiences.
• Ongoing Assessment: Regularly use formative assessments to gauge student understanding and progress. This helps in identifying learning gaps and successes, allowing for more targeted instruction and adjustments to teaching strategies.
• Tiered Assignments: Create assignment tiers that challenge students at appropriate levels. Each tier should aim to build on students' current knowledge while pushing their understanding forward without overwhelming them.

Social-Emotional Support

Supporting the social-emotional needs of students is not an instructional strategy in its own right. However, it is a vital component of strong and effective math instruction to help students handle the emotional challenges of learning. This approach not only aids their academic skills but also builds important life competencies.

How to foster social-emotional support in math instruction:

• Promote a Growth Mindset: Encourage students to see challenges as opportunities to grow. Highlight that effort leads to improvement and teach them to view mistakes as valuable learning moments.
• Establish a Supportive Classroom Climate: Build a safe space for students to share their thoughts and questions without fear of judgment. Foster trust and respect through activities that enhance interpersonal relationships among students.
• Encourage Self-Reflection: Incorporate activities that promote self-reflection on both their learning experiences and emotional responses. Use tools like journals or group discussions to facilitate this process.
• Celebrate Effort and Progress: Regularly acknowledge all students' effort and progress, not scores or perfect answers. This encourages students to continue trying and learning.

These strategies help create a nurturing environment that supports every student's emotional and academic development, making math class a place where they can thrive both intellectually and emotionally. 

Why are effective Math strategies so important for students? 

Adopting strategic instructional methods is crucial for improving math education.

Strategies like the CRA approach, hands-on learning, and inquiry-based learning help students grasp math concepts more effectively and increase their interest in the subject.

Supporting teachers in implementing these strategies can drive the changes needed to enhance educational outcomes.

By focusing on these effective teaching methods, schools can ensure math instruction goes beyond numbers, fostering critical thinking and problem-solving skills that prepare students for future challenges.

Share this post!

Related articles.

STEMscopes Texas Math Meets TEKS and ELP Standards!

There is quite a bit of uncertainty out there about the newly established Instructional Materials Review and Approval...

10 Quick, Fun Math Warm-Up Activities

Creating an environment that allows students to engage with fun math activities, versus rote memorization, helps...

Overview of Instructional Materials Review and Approval (IMRA) and House Bill 1605

In May 2023, Texas approved a transformative bill (House Bill 1605) that significantly impacts educational funding for...

Effective math strategies deepen students' understanding and enthusiasm for mathematics. These strategies not only...

Is Math A Language: Exploring the Relationship of Language and Math

Perhaps you’ve heard someone make the claim that “math is a language.”

Maybe you’ve made that statement yourself...

The Top 7 Elements of a Highly Effective Math Class

Effective math instruction is key to helping students understand and enjoy math. It's not just about numbers; it's...

Play-based Learning in Preschool: Learning Through Play

Play is a natural part of early childhood development, making play-based learning a perfect fit for preschool...

Strategies For Building A Math Community In Your Classroom

At the start of the school year, teachers have the chance to create a math classroom where every student feels valued...

Math Manipulatives: How Can They Improve Student Learning in Math?

Math manipulatives are a great way to make math more accessible for your students, especially if you know they may...

Why Is Storytelling Important in Early Childhood Education?

Storytelling is one of the oldest forms of communication as a way to share experiences, understand others, and...

How To Make Math Fun: 8 Ways To Teach Math Through Play

Welcome to a space where math is not just about right answers but about sparking joy and curiosity. As we blend play...

Engineering in Elementary School

Integrating engineering concepts into elementary education is a crucial topic in this day and age. It's about preparing...

Top 7 Benefits of Play-Based Learning In Early Childhood Education

The idea of a play-based curriculum may sound counterintuitive.

“Play” suggests giving children free rein to explore...

Exploring the Engineering Design Process for Kids

Introducing the Engineering Design Process for kids can sound like an intimidating concept.

As with any other framework...

31 Fun Preschool Themes for STEM Educators

Preschool themes are a fun, creative way to structure the school year with activities that both meet your needs as a...

Teaching Vocabulary in the STEM Classroom

I love words. More generally, I love language.

7 Easy Science Experiments for Preschoolers

Welcome to a world where curiosity meets discovery, and little hands engage in the joy of learning through play .

Teaching Science in Early Childhood

Teaching science in early childhood exposes young learners to more than foundational concepts in STEM.

It sets the...

Math Skills for Preschoolers: How Play-Based Learning Shapes Math Education

Early childhood math doesn’t just lay the groundwork for future academic success in math and the STEM disciplines .

9 Benefits of Messy and Sensory Play for Preschoolers

Messy and sensory play, often a lively and engaging part of educational settings, plays a significant role in the ...

7 Ways to Promote Equity in Education

Ensuring equity in education is a critical part of creating a thriving learning environment for all students.

20 Best Language and Literacy Activities for Preschoolers

Language and literacy form the bedrock of early learning, crucial for building the skills that children carry...

22 Best Social-Emotional Activities for Preschoolers

Children learn by doing and observing. When it comes to social-emotional learning (SEL), they learn by observing...

25 Preschool STEM Activities: Inquiry-Based Learning

Preschool STEM activities and play-based learning are a great way to engage students in science, technology,...

How STEM Helps Preschoolers Prepare for Kindergarten

STEM, representing Science, Technology, Engineering, and Mathematics, is more than an educational buzzword; it's a...

Exploring the Benefits of Video Games in Education

In recent years, video games have emerged as a significant tool in the educational landscape.

Once seen primarily as...

Measuring The Impact of STEAM Education

STEAM in schools doesn’t have a universal approach, but it’s that dynamic nature that makes it such a powerful tool...

How To Use Brain Breaks in the STEM Classroom

Imagine a classroom where students laugh in a circle, passing a beanbag and counting in multiples of three, or stretch...

10 Quick Ways To Do Formative Assessment

Formative assessment is a valuable tool that provides real-time insights into student understanding.

Mathematical Play: Teaching Math The Fun Way

When you're working with two- and three-year-olds, play is how they learn best. Every time they count toy animals,...

7 Solid Strategies To Improve Math Test Scores

There is no single strategy when it comes to how to improve math test scores in the classroom. A classroom full of...

How To Teach Engineering Concepts In The 21st Century Classroom

The goal of modern education is crystal clear: to ignite students' passion for learning and sustain their interest in...

Risk Assessment: Minimizing Safety Hazards With The “AAA” Method

Lab risk assessments are an important part of the STEM classroom. It’s a way to recognize existing and potential...

Types of Learning: All About Learning Styles

Anyone who’s ever stood before a classroom to teach quickly understands that not all students are created the same....

Good Lab Practices: Lab Safety Rules

As a lab teacher, you never have to question the importance of following laboratory safety guidelines. You are well...

What is Inquiry-based Learning?

Sparking student engagement, no matter the subject matter, often means meeting students where they’re already at.

9 Outdoor STEM Activities That Bring Science Learning Out Into Nature

What is outdoor stem.

You might think STEM is all about experiments in the classroom or working with computers. But...

Bringing STEM to Life: The Role of Hands-On Learning

The old saying “learn by doing” captures the essence of hands-on learning. Let’s dive deep into this learning style to...

AI Education: The Impact of Classroom AI

It’s beyond time to talk about the impact of AI education in the classroom. Artificial intelligence is already here....

Five Ways Virtual Reality is Revolutionizing STEM Learning

As technology continues to change the educational landscape, it’s crucial for educators and decision-makers to be...

Collaborative Learning in Science

Chances are, you have encountered some type of team project at some point in your educational journey or at a workshop.

How To Use Cooperative Grouping In Science

Working together to accomplish shared goals — Isn’t this what any group project in school is all about?

Digital vs Traditional: How Digital Education Is Changing the Educational Landscape

Schools and institutions everywhere experienced an abrupt transformation due to the global pandemic as they quickly...

Critical Thinking in Science: Fostering Scientific Reasoning Skills in Students

Thinking like a scientist is a central goal of all science curricula.

As students learn facts, methodologies, and...

Diversity in Tech: How Coding is a Social Equalizer

Technology is all around us, and its capabilities are becoming more and more impressive.

As the tech industry continues...

Professional Development For Teachers: Leveraging PD At Your School

The value of teacher professional development in facilitating student achievement cannot be overstated.

Here we discuss...

Student-Centered Instructional Strategies For Science

Teaching science requires more than merely imparting knowledge; it involves encouraging students' critical thinking...

The Impact of Literacy in Science

In today's rapidly advancing world, science literacy is more important than ever. It empowers students to understand...

Engage Students with Science: 5 Project-Based Learning Activities

Learning about alternate teaching strategies is always exciting, especially when they can demonstrate proven results to...

The Importance of Science Safety

The science lab is a fun and exciting place for students. It’s where they get hands-on with science and learn how to...

Solving Problems in Science: How the Driving Question Motivates Students In PBL

Teachers using the project-based learning approach generally agree that creating the driving question for a project is...

Equity In The Classroom: Making Science Accessible For All Students

All teachers want to see their students succeed.

They don’t want to see students fall behind, but everyone learns...

Teach Engineering: Engineering projects for kids

Children are natural engineers who are curious, inventive, and ready to create things out of the most unexpected...

Data Science Education: Making data work in math and science class

Staying relevant to students while preparing them to be successful in the future is the winning formula that all...

What Is Coding For Kids?

At the heart of today’s tech-driven world is coding – the way we interact with computers. As technology becomes...

Bolstering Creative Thinking in Science Education

Being a scientist and being told to think creatively automatically sound contradictory.

Science is about the facts, the...

Project-based Learning vs Problem-based Learning in Science

Crafting a science curriculum that engages students isn’t always easy.

While there are plenty of examples of...

Rise of the Educational Robots

Robotics education can prepare children for the jobs of the future, foster essential skills and competencies, and make...

What Is RTI (Response To Intervention) In Education?

Let’s explore the key features of Response to Intervention (RTI), a proactive multi-tiered approach to providing...

The Importance of Data Literacy in the Classroom

In today’s information age, we all want to claim we’re data-literate, but what does that really mean?

The Top 7 Benefits of Phenomenon-Based Learning

Phenomenon-based learning takes students’ questions and turns them into learning opportunities. The premise may seem...

Providing Equity in Math Through Small Group Instruction

Keeping students engaged in math isn’t always easy, but differentiated instruction within a single class period can...

Time Management Tips for Teachers

Ask teachers what resource they need more of, and chances are most of them will say, “Time!”

For teachers, managing...

Exploring the Connection Between Math and Art

Combining art with traditional STEM subjects (Science, Technology, Engineering, Math) creates STEAM education, which...

STEM Career Spotlight: Women In STEM

In honor of Women’s International Month, we would like to spotlight some amazing women scientists who have made...

How Autonomy Can Transform Your Classroom and Empower Students

Giving students autonomy over their learning doesn’t just engage and motivate them; it gives them the skills to achieve...

Math Strategies For Struggling Students: A New Approach to Challenges

Mathematics can be a challenging subject for many students, requiring schools to have effective strategies in place to...

Math in the Real World

“Why do I need to know this?”

AI In Education: The Impact of ChatGPT in the Classroom

ChatGPT, a language model that uses deep learning techniques to generate human-like responses, has garnered significant...

How to Support Multilingual Learners in Math

Multilingual learners often require tailored educational strategies to support their language development and academic...

Interactive Math: How To Make Math More Interactive

Interactive math isn’t a new concept. The idea of engaging students in more active learning experiences to enhance...

STEM Career Spotlight: The Impact of Black Scientists and Innovators

Throughout history, many Black scientists have made tremendous contributions to the advancement of STEM and positively...

How To Teach Math Vocabulary

Even for students with an intuitive sense of math, its specialized vocabulary often gets in the way, but that doesn’t...

The Top 8 Tips First-Year Teachers Need To Know

Whether fresh out of college or entering teaching as your second career, these tips will guide you in making the most...

Game-Based Learning vs. Gamification: Using Gaming In The Classroom

Games are highly motivating for everyone, including students. But you don’t have to turn your classroom into a game...

Overcoming Math Anxiety and the Fear of Math

Remember the first time you noticed a student's hands shake during a math test? Or that student who suddenly had to...

Taking A Fresh Look At STEM Professional Development

Professional development for STEM teachers is a tall order these days. 

As the pace of scientific advancement has...

STEM Integration from Kindergarten to High School

STEM education benefits students of all ages. Students as young as kindergarten can begin reaping the positives just...

The Challenges of STEM Education: Barriers to Participation

Incorporating new instructional strategies into your teaching practices is always challenging at first, but it gets...

The Pros and Cons of STEM Education

Introducing any new curriculum into an existing educational system always has pros and cons. There’s often a learning...

Any Classroom Can Be a STEM Classroom: Tips for Creating a STEM Learning Environment

You too can create a STEM classroom where students are actively engaged in collaborating to solve problems using...

How STEM Education Can Shape the Future

The future is ultimately uncertain. We can never completely predict what will happen to the economy, the job market,...

Why STEM is Important for Students, Schools, and Society

The buzz around STEM education continues to grow as teachers discover how it builds creative problem-solving through...

Cooperative Learning in STEM

STEM and cooperative learning strategies go hand-in-hand. If cooperative learning is the teaching method to engage...

All About The Concrete Representational Abstract (CRA) Method

Think back to your earliest memories of math class...

Do you remember using blue graphing blocks or cut-outs of...

How STEM Education Contributes To Career and College Readiness

We've previously discussed the benefits of STEM in early childhood education – but what about its benefits for students...

5 Reasons the Productive Struggle Belongs in STEM

It may be hard to watch students struggle, but facing the challenges of learning with the right attitude and seeing how...

Why is STEM So Important in Early Childhood Education?

STEM in early childhood education isn’t a new approach to teaching, but it is gaining traction as an important piece in...

STEM Spotlight: Katherine Johnson

Katherine Johnson, a mathematician and aerospace technologist at NASA, made significant contributions to the first...

There’s Nothing Ordinary About the STEM Everyday Podcast

Host chris woods brings fascinating interviews with a fantastic array of authors, makers, educators, and stem....

Using Inquiry-Based Learning With STEMscopes Math Activities

Traditional methods of teaching math only work for a handful of students. The majority of students struggle trying to...

Simple Strategies to Teach Math Through Play

Research indicates that attitudes towards mathematics, especially at a young age, can significantly influence a child’s...

Celebrating Hispanic Heritage: Walter Alvarez's Contributions to STEM

Walter Alvarez is known for having formulated the theory that the impact of an asteroid extinguished dinosaurs, an idea...

Bringing NASA’s DART Mission into the Classroom

Double Asteroid Redirection Test (DART) is a method of planetary defense against near-Earth asteroids, which changes...

How To Foster A Growth Mindset in the Classroom

Do you ever wonder why some students embrace making mistakes while others shy away from them?

Using The 3 Little Pigs To Teach 5E STEM

Let’s take a closer look at the classic children’s story, The Three Little Pigs, and how it serves as the foundation...

Integrating ICT Into STEM Education

Information and Communication Technology (ICT) is used everywhere in the world and has become an integral part of our...

Top 10 Tips for an Effective STEM Classroom

Today's students are coming of age in a world vastly distinct from the one their educators experienced during their own...

Tips from Former Teachers at STEMscopes (Part II)

Many STEMscopes employees come from a teaching background. In this 2-part blog, we draw on their past experiences to...

Tips from Former Teachers at STEMscopes (Part I)

Thanks to our teachers

All of us have had teachers that have touched our lives. For some of us, it’s been a few simple words of encouragement...

Best Practices for Remote Learning

The world can be an unpredictable place. We’ve all experienced that recently. And one of the hardest adjustments many...

Teaching Student Confidence

Can confidence be taught? Of all the questions math teachers ask when thinking through ways to improve instruction,...

Accelerate Learning STEMscopes and Google Classroom Integration

Today we are announcing that your favorite science and math curriculum can now be used with Google Classroom LMS. We...

Teaching Problem-Solving In Math

Problem-solving is essential in math education.

Black History Month Hero: Katherine Johnson

February is recognized across the US as Black History Month. In keeping with this tradition we like to look back on...

Math Teacher Writer Highlight: Helen Squire

Helen Squire’s love for STEM can be found in all areas of her life—from her job as a math teacher at a charter school,...

What is Computational Fluency?

Let's explore computational or mathematical fluency, a key component of STEM education.

Math fluency is a combination...

Fact Fluency in Math: Everything You Need To Know

Fact fluency is a skill that allows students to naturally solve problems with little to no conscious effort. The ease...

SEL for Teachers

Introduction

Across the country, school districts are adding social emotional learning (SEL) to their curriculum. SEL...

National Native American Heritage Month Hero: Matthew Yazzie

National Disability Employment Awareness Month Hero: Temple Grandin

Teacher Writer Spotlight: Rachel Neir

Hitting her one-year anniversary as a STEMscopes writer, Rachel Neir brings her bright smile and big ideas to...

SEL in Math: Promoting Social-Emotional Learning in Math Class

Integrating social-emotional learning (SEL) into math instruction is more than a trend; it's a meaningful shift in how...

STEMscopes Celebrates the Achievements of Hispanic STEM Pioneers

September 15th through October 15th marks National Hispanic Heritage Month, a time of year where we honor the...

Solving Word Problems With Three Reads

Teacher Writer Spotlight: Susan G. Galvan

It’s all about the science for Susan G. Galvan. Not only has she worked in science education practically her whole...

Math Teacher Writer Highlight: Steve Baker

Steve Baker writes for STEMscopes Math on the go. After teaching elementary math and science for years, Baker and his...

Math Intervention and Tutoring: Helping Struggling Students

In education, not all students progress at the same pace, especially in mathematics.

For those facing challenges in...

Teacher Writer Spotlight: Danielle Porterfield

New to science writing, Danielle Porterfield is making an impression with her commitment to tackle new things. She puts...

Going the Extra Mile: Acceleration and Intervention

The learning needs of one student are often not those of their classmates. To meet each student where they...

Teacher Writer Spotlight: Stephanie Even

Stephanie Even has been with STEMscopes since June of 2017, making this her fourth year with the curriculum writing...

Understanding Focus, Rigor, and Depth

When it comes to math education, we all want the same thing: students who are confident critical thinkers and problem...

Which Way is Right? Problem-Solving in Mathematics

The Mona Lisa is surprisingly, almost shockingly, small. Yet its far-reaching influence has made it synonymous with...

Teacher Writer Spotlight: Katy Grose

After teaching fifth-grade science for over six years, in addition to teaching multiple other subjects to third-,...

The American Rescue Plan and What It Includes

How Schools Will Spend HR 133 and ARP Funding

Announcing our STEMscopes Coding Contest Winners

This month we celebrated two special holidays, Mother’s Day and Teacher Appreciation Day. We invited students and...

Meet Jenny Stallworth

Jenny Stallworth is a dynamo of an educator. She has taught almost all STEM subjects, homeschooled her four children...

A Better Understanding of Mistakes Brings More Growth and Development for Both Students and Teachers

Throughout this past year, COVID-19 has reminded us that things don’t always go according to plan. The pandemic has...

How To Scaffold In Math

Scaffolding is a powerful educational strategy that provides temporary support to help students grasp new concepts and...

Meet our Writers: Kimberly Pardue

With a Bachelor’s in Early Childhood Education, a Master’s in Administration, and extensive experience teaching...

Understanding HR133

The effects of the pandemic have left almost no one untouched, and education is one area in particular that has...

Celebrating women in stem

Focusing on Social and Emotional Learning: Making a Pandemic Comeback

The coronavirus pandemic has changed a lot for students across the country. They’ve spent time learning virtually,...

Teacher Writer Spotlight: Lisa Culberson

After a whopping 23 years of being a science teacher, science department head, science teacher trainer and a summer...

Learning Loss and Its Impact on Math Education

What is learning loss? 

Teacher Writer Spotlight: Kathy Blanton

Kathy Blanton’s instructional experience is vast. Before joining STEMscopes , she taught math, health, and science to...

Learning from My Coworkers

When protests erupted across the country last spring, I was confused as to what they were about. Naturally, I was...

COVID Funding for K-12 Education

To date the federal government has designated funding for COVID-19-related expenses through two major federal bills...

Teacher Writer Spotlight: Jennifer Donovan

It’s no surprise that STEMscopes sought Jennifer Donovan to join the company’s team of curriculum writers. Donovan’s...

Teacher Writer Spotlight: Carri Bevil

Carri Bevil saw firsthand how effective STEMscopes Science was in her district. So when asked to join the new...

Breaking Down Norman Webb’s Depth of Knowledge Model

Learning is a process that entails different levels of understanding. This is the basic idea behind Norman Webb’s Depth...

Teacher Writer Spotlight: Morgan Christiansen

Morgan Christiansen fully commits herself in every aspect of her life. Her daily runs, her nearly decade-long marriage...

Introducing Students to the Future of Coding

The world as we know it is changing every day. With emerging technology shifting more and more toward the digital...

Teacher Writer Spotlight: Bonnie Smith

No task is too complex or unfamiliar for Bonnie Smith, who joined our team of STEMscopes Science teacher writers at the...

Bridging the Opportunity Gap in STEM Education

With new innovations emerging daily, technology seems to be evolving at the speed of light, and increasingly jobs...

Being Good at Math Means Finding a Good Job

Is being good at math necessary to finding a good job? Increasingly so, this is the case. While a discrete math skill...

Teacher Writer Spotlight: Erin Rawlinson

Sometimes things just come together at the right time. Erin Rawlinson was a new mom. She loved her job as a third-grade...

How STEMscopes Works: A Teacher’s Introduction to STEMscopes Math Lessons

STEMscopes is built around an instructional concept pioneered by Rodger Bybee in the 1980s and further refined over the...

Math as the Language of STEM

If we consider science to be the understanding of phenomena, technology the tools used to investigate phenomena, and...

Process Over Answer

3 Easy Steps to Making Math a Daily Routine at Home

We all know that very familiar adage, practice makes perfect —or as my third-grade teacher liked to say, practice makes...

Celebrating the teachers that make it possible: Nicole Blakeslee

How Introducing Coding at the K-12 Level can Help Bring About Equity

While the United States has come a long way in terms of education, there are still gaps in equity. One way to level the...

Providing Equity with Guided Math Small-Group Math Lessons

“When a teacher begins a math lesson with direct instruction they completely disregard and ignore their students’...

Math Teacher Writer Highlight: Taylor Wheeler

A year after Taylor Wheeler resigned from her teaching job to focus on raising her children, a former mentor called to...

What We Believe: The Pedagogical Philosophies that STEMscopes Math was Built On | Part 2

We’ve all heard the expression “practice makes perfect.” Rote math drills, however, have proven to be an ineffective...

What We Believe: The Pedagogical Philosophies that STEMscopes Math was Built On | Part 1

When the STEMscopes math team came together to design our curriculum, we set out to solve a problem that has always...

Science Teacher Writer Highlight: Lindsay Van Wyk

Overnight, COVID-19 created a demand for flexible lessons that can be taught virtually. Teachers everywhere are now...

Preventing the Summer Slide

Teachers and parents alike want to prevent summer slide , which may be exacerbated this year by school closures. As a...

World Oceans Day: 5 Ways to Take Action

Did you know that oceans make up 71% of Earth’s surface? Or that oceans contain 99% of Earth’s area that can be...

Math Teacher Writer Highlight: Alicia Chiasson

When her school district adopted STEMscopes Science in 2016, Alicia Chiasson knew there was something special about it....

10 Climate-Friendly Actions to Support Earth Day

In 1970, 20 million Americans came together for the very first Earth Day to raise awareness of the massive impact...

Nurturing Self-Directed Learning in the Classroom

Self-directed learning isn’t a new concept.

Maintaining Student-Teacher Connections During Remote Learning

Imagine this scenario: a star 5th grader is forced to stay home from school but continue learning. She’s accustomed to...

How to Give Assignments | Part 2

In our preview post , we shared a bit about setting expectations when assigning tasks remotely, along with the benefits...

How to Give Assignments | Part 1

What should be the expectation.

As more schools close due to the unforeseen impact of the coronavirus, districts are...

How Teachers Can Help in COVID-19

The COVID-19 crisis is changing the country as we know it. With cancellations of well-established events like the ...

5 Ways to Boost Student Engagement while Teaching Remotely

Distance learning brings with it many adjustments, from settling into an at-home work environment and keeping kiddos...

Math Chats, Going Beyond the Answer

Bridging the student gap between the problem and the solution .

As teachers, it is easy for us to get caught up in the...

Structure and STEM Resources for Distance Learning

We realize these days look different from our normal routine, especially for students who are used to following a...

Science Learning at Home: K-5 STEM Activity Pack

We’re all in a strange place of uncertainty right now due to the COVID-19 outbreak. Schools have shut down, parents...

COVID-19 Update | Keep the Learning Going

Coronavirus, or COVID-19, has dominated the news, so we’re ready to help you be informed. In this blog, we’ll explore...

5 Fun and Educational Ways to Celebrate Pi Day

Yes, we all know that Pi Day on March 14th is a fun excuse to eat one of the best desserts ever, but it’s also a great...

How to Improve Mathematical Discourse in the Classroom

Fostering mathematical discourse in the classroom is key to helping students understand and enjoy math. It can instill...

6 Take-Home Activities to Engage Your Student in STEM Over Winter Break

While winter break is a special time to spend with family, friends, and plenty of food, it doesn’t necessarily mean...

Teacher Tip: Intellectual Risk Taking

As educators, we are aware that our current students will be redefining knowledge and possibilities in the future, in...

Using Extended Vocabulary Instruction

­­­ We all know the importance of language acquisition , but did you know that how you teach students new science...

All Students Are Created Equally and Differently: Addressing Diverse Learning Styles in the Science Classroom

Imagine you are a middle school student challenged with the phenomenon, “What causes rainbows?” in your science...

STEMscopes Announces Exciting Fall 2018 Product Updates

Everyone at STEMscopes has been hard at work over the summer to improve the online application, so take a look below to...

What are NGSS Evidence Statements?

The NGSS have undergone numerous evolutions since their inception. Among the most powerful (and most recent) are the...

The Flipped Classroom: Everything You Need To Know

The flipped classroom is an educational model that turns the learning environment into a workshop for concepts...

Accelerate Learning Releases STEMscopes NGSS 3D Curriculum to Help Teachers Engage Students in Three Dimensional Learning and Phenomena-Driven Inquiry

Although the Next Generation Science Standards (NGSS) were released more than five years ago, many teachers still feel...

10 Careers that Use Math You Should Consider

Not everyone cringes at the idea of math class or reacts with panic to memories of algebra, but for people who...

10 More Careers in Science for 2018

When it comes to unique science jobs , professional opportunities aren't in short supply. Many top, high-paying...

10 More Careers that Use Technology

Technology is everywhere. In fact, nowadays it may be hard to imagine life without it, as it's part of every...

ELL Strategies: 7 Teaching Strategies For English Language Learners

English Language Learners (ELLs), or Multilingual Learners (MLLs), bring diverse perspectives and experiences to the...

Five ELL Resources for the Classroom

For a student who does not speak English as their first language, learning is an entirely different experience.

What Defines an English Language Learner?

English Language Learners (ELL) represents a growing population of U.S. students. According to the National Center...

Top 10 Science Jobs in the United States

Astronaut. Marine Biologist. Archaeologist. Every child dreams of what they want to be when they grow up. Often...

STEMscopes Early Explorer Named CODiE Award Finalist for Best PreK/Early Childhood Learning Solution

The 2018 SIIA CODiE Awards have selected STEMscopes™ Early Explorer as a finalist in the Best PreK/Early Childhood...

Top 10 Ways to Thank a Teacher this Week

Another Teacher Appreciation Week is upon us and the STEMscopes team is excited to have so many teachers and former...

What are Cooperative Learning Strategies and How Do They Affect my Classroom?

As a first-time teacher, how do you start aligning a lesson plan and classroom setup with cooperative learning...

How STEM Education Differs from Science Education Instruction

If you are a teacher in the 21st Century, then you know that the education landscape has changed quite significantly...

STEMscopes PreK-12 Digital Curriculum Named Finalist for EdTech Cool Tool Award in STEM Solution Category

Accelerate Learning announces that the STEMscopes™ PreK-12 digital STEM curriculum has been chosen as a finalist...

Accelerate Learning Founder and CEO Honered as EdTech Leadership Award Finalists

  Accelerate Learning announces that Reid Whitaker, founder of the company and creator of the award-winning ...

STEMscopes Dive-In Engineering Named Finalist for EdTech Cool Tool Award

Created by Accelerate Learning and the New York Hall of Science, the hands-on engineering curriculum provides...

Mississippi Approves STEMscopes Digital Science Curriculum for Grades K-12 in State Science Textbook Adoption 

Accelerate Learning announced earlier this week that the STEMscopes™ digital science curriculum has been approved...

How Playing Outside Increases Science Understanding and Real World Learning 

Outdoor play has always been an important part of childhood. Imaginative play, exploratory discovery, and real-world...

STAY INFORMED ON THE LATEST IN STEM. SUBSCRIBE TODAY!

Which stem subjects are of interest to you.

STEMscopes Tech Specifications      STEMscopes Security Information & Compliance      Privacy Policy      Terms and Conditions

© 2024 Accelerate Learning

Classroom Q&A

With larry ferlazzo.

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

Four Teacher-Recommended Instructional Strategies for Math

• Share article

(This is the first post in a two-part series.)

The new question-of-the-week is:

What is the single most effective instructional strategy you have used to teach math?

This post is part of a longer series of questions and answers inviting educators from various disciplines to share their “single most effective instructional strategy.”

Two weeks ago, educators shared their recommendations when it came to teaching writing.

Last month , it was about teaching English-language learners.

There are many more to come!

Today, Cindy Garcia, Danielle Ngo, Patrick Brown, and Andrea Clark share their favorite math instructional strategies.

‘Concrete Representational Abstract’

Cindy Garcia has been a bilingual educator for 14 years and is currently a district instructional specialist for PK-6 bilingual/ESL mathematics. She is active on Twitter @CindyGarciaTX and on her blog:

The single most effective strategy that I have used to teach mathematics is the Concrete Representational Abstract (CRA) approach.

During the concrete step, students use physical materials (real-life objects or models) to explore a concept. Using physical materials allows the students to see and touch abstract concepts such as place value. Students are able to manipulate these materials and make sense of what works and what does not work. For example, students can represent 102, 120, and 201 with base 10 blocks and count each model to see the difference of the value of the digit 2 in each number.

During the representational step, students use pictures, images, or virtual manipulatives to represent concrete materials and complete math tasks. Students are making connections and gaining a deeper understanding of the concept by creating or drawing representations.

During the abstract step, students are now primarily using numbers and symbols. Students working at the abstract stage have a solid understanding of the concept.

The CRA approach is appropriate and applicable to all grade levels. It is not about the age of the student but rather the concept being taught. In 3rd grade, it is beneficial to students to have them use base 10 blocks to create an open-area model, then draw an open-area model, and finally use the multiplication algorithm. In algebra, it is STILL beneficial to practice using algebra tiles to multiply polynomials using an open-area model.

The CRA approach provides students P-12 to have multiple opportunities to explore concepts and make connections with prior concepts. Some teachers try to start teaching a concept at the abstract level, for example, the standard algorithm for multiplication. However, they soon find out that students have difficulty remembering the steps, don’t regroup, or don’t line up digits correctly. One of the main reasons is that students don’t understand this shortcut and they have not had the concrete & representational experiences to see how the shortcuts in the standard algorithm work.

‘Encouraging Discourse’

Danielle Ngo is a 3rd grade teacher and Lower School math coordinator at The Windward School . She has been a teacher for 10 years and works primarily with students who have language-based learning disabilities:

Growing up, so many of us were taught that there is one right answer to every math problem, and that there is one efficient way to arrive at that conclusion. The impetus to return to this framework when teaching math is a tempting one and one I’ve found myself having to fight actively against during my own classroom instruction. In my experience, the most effective way to counter this impulse is to mindfully increase the discourse present during my math lessons. Encouraging discourse benefits our students in several ways, all of which solidify crucial math concepts and sharpen higher-order thinking and reasoning skills:

Distributes math authority in the classroom: Allowing discourse between students—not just between the students and their teacher—establishes a classroom environment in which all contributions are respected and valued. Not only does this type of environment encourage students to advocate for themselves, to ask clarifying questions, and to assess their understanding of material, it also incentivizes students to actively engage in lessons by giving them agency and ownership over their knowledge. Learning becomes a collaborative effort, one in which each student can and should participate.

Promotes a deeper understanding of mathematical concepts: While the rote memorization of a process allows many students to pass their tests, this superficial grasp of math skills does not build a solid foundation for more complex concepts. Through the requisite explanation and justification of their thought processes, discourse pushes students to move beyond an understanding of math as a set of procedural tasks. Rather, rich classroom discussion gives students the freedom to explore the “why’s and how’s” of math—to engage with the concepts at hand, think critically about them, and connect new topics to previous knowledge. These connections allow students to develop a meaningful understanding of mathematical concepts and to use prior knowledge to solve unfamiliar problems.

Develops mathematical-language skills: Students internalize vocabulary words—both their definitions and correct usage—through repeated exposures to the words in meaningful contexts. Appropriately facilitated classroom discourse provides the perfect opportunity for students to practice using new vocabulary terms, as well as to restate definitions in their own words. Additionally, since many math concepts build on prior knowledge, classroom discussions allow students to revisit vocabulary words; use them in multiple, varied contexts; and thus keep the terms current.

‘Explore-Before-Explain’

Patrick Brown is the executive director of STEM and CTE for the Fort Zumwalt school district,in Missouri, an experienced educator, and a noted author :

The current COVID-19 pandemic is a sobering reminder that we are educating today’s students for a world that is increasingly complex and unpredictable. The sequence that we use in mathematics education can be pivotal in developing students’ understanding and ability to apply ideas to their lives.

An explore-before-explain mindset to mathematics teaching means situating learning in real-life situations and problems and using those circumstances as a context for learning. Explore-before-explain teaching is all about creating conceptual coherence for learners and students’ experiences must occur before explanations and practice-type activities.

Distance learning reaffirmed these ideas when I was faced with the challenge of teaching area and perimeter for the first-time to a 3 rd grade learner. I quickly realized that rather than viewing area and perimeter as topics to be explained and then practiced, situating learning in problem-solving scenarios and using household items as manipulatives can illustrate ideas and derive the mathematical formulas and relationships.

Using Lego bricks, we quickly transformed equations and word problems into problem-solving situations that could be built. Student Lego constructions were used as evidence for comparing and contrasting physically how area and perimeter are similar and different as well as mathematical ways to calculate these concepts (e.g., students quickly learned by using Legos that perimeter is the distance around a shape while area is the total shape of an object). Thus, situating learning and having students use data as evidence for mathematical understanding have been critical for motivating and engaging students in distance learning environments.

Using an explore-before-explain sequence of mathematics instruction helps transform traditional mathematics lessons into activities that promote the development of deeper conceptual understanding and transfer learning.

A ‘Whiteboard Wall’

Andrea Clark is a grade 5-7 math and language arts teacher in Austin, Texas. She has a master’s in STEM education and has been teaching for over 10 years:

If you want to increase motivation, persistence, and participation in your math classroom, I recommend a whiteboard wall. Or some reusable dry erase flipcharts to hang on the wall. Or some dry erase paint. Anything to get your students standing up and working on math together on a nonpermanent surface.

The idea of using “vertical nonpermanent surfaces” in the math classroom comes from Peter Liljedahl’s work with the best conditions for encouraging and supporting problem-solving in the math classroom. He found that students who worked on whiteboards (nonpermanent surfaces) started writing much sooner than students who worked on paper. He also found that students who worked on whiteboards discussed more, participated more, and persisted for longer than students working on paper. Working on a vertical whiteboard (hung on the wall) increased all of these factors, even compared with working on horizontal whiteboards.

Adding additional whiteboard space for my students to write on the walls has changed my math classroom (I have a few moveable whiteboard walls covered in dry erase paint as well as one wall with large whiteboards from end to end). My students spent less time sitting down, more time collaborating, and more time doing high-quality math. They were more willing to take risks, even willing to erase everything they had done and start over if necessary. They were able to solve problems that were complex and challenging, covering the whiteboards with their thinking and drawing.

And my students loved it. They were excited to work together on the whiteboards. They were excited to come to math and work through difficult problems together. They moved around the room, talking to other groups and sharing ideas. The fact that the boards were on the wall meant that everyone could see what other groups were doing. I could see where every group was just by looking around the room. I could see who needed help and who needed more time to work through something. But my students could see everything, too. They could get ideas from classmates outside of their group, using others’ ideas to get them through a disagreement or a sticking point. It made formally presenting their ideas easier, too; everyone could just turn and look at the board of the students who were sharing.

I loved ending the math class with whiteboards covered in writing. It reminded me of all of the thinking and talking and collaborating that had just happened. And that was a good feeling at the end of the day. Use nonpermanent vertical surfaces and watch your math class come alive.

Thanks to Cindy, Danielle, Patrick, and Andrea for their contributions!

Please feel free to leave a comment with your reactions to the topic or directly to anything that has been said in this post.

Consider contributing a question to be answered in a future post. You can send one to me at [email protected] . When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.

You can also contact me on Twitter at @Larryferlazzo .

Education Week has published a collection of posts from this blog, along with new material, in an e-book form. It’s titled Classroom Management Q&As: Expert Strategies for Teaching .

Just a reminder; you can subscribe and receive updates from this blog via email (The RSS feed for this blog, and for all Ed Week articles, has been changed by the new redesign—new ones are not yet available). And if you missed any of the highlights from the first nine years of this blog, you can see a categorized list below.

• This Year’s Most Popular Q&A Posts
• Race & Racism in Schools
• School Closures & the Coronavirus Crisis
• Classroom-Management Advice
• Best Ways to Begin the School Year
• Best Ways to End the School Year
• Student Motivation & Social-Emotional Learning
• Implementing the Common Core
• Facing Gender Challenges in Education
• Teaching Social Studies
• Cooperative & Collaborative Learning
• Using Tech in the Classroom
• Student Voices
• Parent Engagement in Schools
• Teaching English-Language Learners
• Reading Instruction
• Writing Instruction
• Education Policy Issues
• Differentiating Instruction
• Math Instruction
• Science Instruction
• Advice for New Teachers
• Author Interviews
• Entering the Teaching Profession
• The Inclusive Classroom
• Learning & the Brain
• Administrator Leadership
• Teacher Leadership
• Relationships in Schools
• Professional Development
• Instructional Strategies
• Best of Classroom Q&A
• Professional Collaboration
• Classroom Organization
• Mistakes in Education
• Project-Based Learning

I am also creating a Twitter list including all contributors to this column .

Mini-Course: Teaching Math

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

Sign Up for EdWeek Update

Edweek top school jobs.

Sign Up & Sign In

• Prodigy Math
• Prodigy English
• Is a Premium Membership Worth It?
• Promote a Growth Mindset
• Help Your Child Who's Struggling with Math
• Parent's Guide to Prodigy
• Back to School
• Assessments
• Math Curriculum Coverage
• English Curriculum Coverage
• Teacher Resource Center
• Administrators
• Game Portal
• Case Studies

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

Written by Ashley Crowe

• Teaching Strategies
• Teacher Resources

• Why are effective Math strategies so important for students?
• Getting students excited about Math problems
• Top 9 math strategies for engaging lessons
• How teachers can refine math strategies

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1. Explicit instruction

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

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

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

2. Conceptual understanding

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

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

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

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

3. Using concepts in Math vocabulary

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

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

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

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

4. Cooperative learning strategies

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

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

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

5. Meaningful and frequent homework

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

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

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

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

Ready to make homework fun?

6. Puzzle pieces math instruction

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

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

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

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

7. Verbalize math problems

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

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

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

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

8. Reflection time

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

Group Reflection

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

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

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

Individual Reflection

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

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

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

9. Making Math facts fun

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

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

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

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

How teachers can refine Math strategies

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

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

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

Share this article

Table of Contents

Make learning fun, adaptive and insightful

Kids practice standards-aligned skills in Math and English as they play our fun, adaptive learning games.