Many students have experienced math as just a lot of rules to memorize and follow, a common experience that you might relate to yourself from when you were in school. But that isn’t how math needs to be taught. High-quality math instruction involves active, hands-on inquiry that helps students make sense of patterns, data, and much more. To unlock mathematical learning, students need to question, test, and discover. They need to be engaged.
Engagement is the willingness to invest effort in a task, and it’s especially important when it comes to math instruction, where employing the right materials and using effective teaching strategies can make the subject far less daunting for students. So, a key question to ask in any student-centered approach to math instruction is how can we make math classes dynamic and engaging spaces where students are eager to tackle challenging problems and uncover the math underlying them?
How to engage students in math
Engagement goes beyond listening, completing tasks, and memorizing steps. Engagement occurs when students are emotionally and intellectually invested. It means they care about learning and are willing to apply effort and deep thinking. Research has shown that engaged students have higher levels of achievement in math. Before we get into specific math engagement strategies, let’s look at some core conditions that make this kind of investment possible.
- Safe learning environment: To take on challenges and risk making mistakes in front of their peers, students first have to feel safe. They need to know their efforts will be met with support and kindness. A safe learning environment makes space for positive relationships, active participation, and collaboration—all important ingredients for engagement. A safe environment in math class also means that the process of solving problems is the focus of instruction, not simply getting quick answers.
- Clear expectations: Establishing routines and procedures helps students know what to do and when. This reduces distractions, frees up cognitive space for the tasks at hand, and helps students stay focused. Clear expectations, along with the guidance to meet them, support students’ autonomy and self-efficacy.
- Meaningful work: Learners of any age are willing to invest more effort when they have clear personal reasons for pursuing the work. We’ve all heard the common refrain in math classrooms: Why do I need to learn this? Making connections between content and everyday life, student interests, and career aspirations can motivate students and help them see math as relevant.
- Regular feedback: Engagement is enhanced when students can see concrete evidence of their growth. Regular feedback that highlights progress and addresses misunderstandings helps students connect effort to improvement. Recognition of hard work keeps students motivated to continue investing effort.
8 engagement strategies for math
Many students have negative experiences with math and enter class with limiting beliefs or not seeing how math is relevant to their lives. Incorporating purposeful engagement strategies can address some of these barriers to learning and help students see math as accessible and enjoyable.
1: Frame mistakes as learning opportunities. Mistakes are inevitable—not just in math, but in life. Making mistakes and then working through them is all part of the process of solving complex problems and understanding big ideas. Help students see errors as learning opportunities. The result is that instead of students feeling dejected by failure, ideally, they feel engaged by problems and are willing to persist through them.
It may feel counterintuitive, but it can strengthen a classroom to make calling out errors a normal part of instruction and a way to keep students invested in their learning. The key is to treat mistakes as normal. It goes both ways, too. If you make a mistake as a teacher, call it out and work through it as a class.
In an article on embracing making mistakes in math, former NWEA professional learning team member Nick Joe writes “The reality is that learning math is challenging. Teach [students] that mistakes are just a sign that they’re learning and growing and everyone they make is a chance to rethink the math in from of them and work on understanding it fully.”
2: Foster student discussion. Math talk refers to using language to express mathematical thinking, and it is a researched-based approach to deepening student engagement and understanding. When students articulate the process they used to solve a problem, they gain a firmer grasp of the underlying mathematical reasoning and can more easily identify errors.
3: Pose interesting problems. One way to help make math engaging: present problems that students want to solve. Students come to class naturally curious about the world and wanting to learn, and math class can be a place to tap into that curiosity. Connecting math to the real world and students’ lives outside school is one way to keep students interested. If students love a particular food, for instance, plenty of math lessons can connect to topics like weighing ingredients, doubling or halving quantities, or analyzing nutritional labels. Older students can be shown explicit and more advanced connections to virtually any potential career:
- Financial analysts use exponential growth to calculate compound interest and evaluate investments.
- Architects rely on geometry and measurement to design buildings that are safe, functional, and aesthetically pleasing.
- Pharmacists use ratios and proportions to dispense medications and prepare prescriptions.
- Data scientists apply statistics and probability to identify trends and make predictions.
Math problems don’t necessarily need to connect to the real world to be interesting. Building Thinking Classrooms (BTC) is an educational approach from mathematics education professor Dr. Peter Liljedahl that has gained popularity in recent years. Resources available on the BTC website include tasks, videos, and other materials that can get students of all ages interested and thinking about math, often because of intrigue and challenge purely inherent to different math problems.
4: Set up math centers. Math centers are designated areas of the classroom for students to work on selected tasks individually or in small groups. They provide opportunities for targeted support and hands-on practice. Small-group math centers are especially valuable for engagement as they allow students to work with their peers on tasks that are designed to that group’s specific skills and interests.
5: Use anchor charts. Students are more likely to invest in their learning when they are involved in directing it and provided with supports along the way. Anchor charts help with both goals; students can help make them, and then they can use the charts as they work through different problems. The anchor charts below, for example, although not made by students, provide questions tied to different standards for mathematical practice that students and teachers can reference during instruction. For optimal engagement, create the anchor charts along with the students, so they better understand its content.
6: Use choice boards. A feeling of ownership over learning increases interest, effort, and perseverance. One way to facilitate student autonomy in learning is with choice boards. On a grid similar to a bingo card (though not necessarily 5×5), list different activities all related to the same learning outcome, giving students options for how they will practice a skill. When students choose their own tasks, they become collaborators in their learning process.
7: Build conceptual understanding. There are many ways to engage students in math by focusing on conceptual understanding, but the general idea is to ensure math class doesn’t turn into memorizing steps—a common way that students perceive math. Conceptual understanding in math means understanding why certain steps work and working through the abstract thinking involved in math.
Making concepts concrete and giving students multiple pathways of understanding can help them understand the why behind the what. One approach is known as CPA, standing for concrete-pictorial-abstract. This refers to having students start by physically engaging with concrete objects (C), transition to pictorial representations (P) of the objects, and ultimately use abstract reasoning (A) to identify patterns that apply across multiple contexts. Whenever possible, incorporate visual representations like number lines, bar models, and fraction strips, as well as concrete manipulatives like number blocks or tiles, to help students connect symbols and ideas to things they can see and/or touch.
8: Use research-based digital tools. There are many options out there, and it can be hard to find one that’s grounded in evidence and will work for you and your students. Look for apps and other digital tools that promote student engagement and have the research to back it up. For example, Waggle includes many skill-based games that make math practice fun as well as deliberate. Personalized Path is another digital solution that uses assessment data to identify students’ learning needs and place them at the right level of support and challenge.
Keeping students engaged
Engaging students in math is an ongoing and worthwhile practice. It is the daily work of making skills and knowledge relevant and interesting to young learners. The best strategies will vary based on the specific needs of students, but engagement always comes down to activating learners’ desire to put effort and energy into a task.
Finding the right teaching approach for a specific classroom will always be a moving target, but the effort pays off. When math isn’t presented in an engaging way, some students will find the subject dry and abstract. But when math teaching gets students talking, connects the subject to their lives, and makes use of high-quality materials, it draws students in and they’ll want to learn more. When students are engaged, they are able to truly learn concepts and skills that can last a lifetime.
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