Academic Quarterly

Marvelous Mathematician Spring 2020

The Importance of Student Engagement in Learning Mathematics

Why engagement is important

Research has shown a strong positive correlation between engagement and student achievement (Boykin and Noguera 2011; Marks 2000). Mid-continent Research for Education and Learning (McREL) defines engagement as “a condition of emotional, social, and intellectual readiness to learn characterized by curiosity, participation, and the drive to learn more” (Abla and Fraumeni 2019). A Gallup study of more than 110,000 students in 128 schools “found that student engagement and hope were significantly positively related to student academic achievement progress (growth) in math, reading, and all subjects combined” (Reckmeyer 2019). Put simply, more engagement results in higher achievement.

The Standards for Mathematical Practice were released as part of the Common Core State Standards for Mathematics (2010). These standards remain a part of almost all state standards for both Common Core and non–Common Core states. The Mathematical Practice standards, in particular, emphasize the importance of student engagement and interaction with mathematics. Each of the eight Mathematical Practice standards describes what “mathematically proficient students” do to build and demonstrate math proficiency. Unfortunately, these practices are often still missing from the math learning experiences of many students due to ineffective implementation of problem-based lessons or over reliance on direct instruction, where it may not be appropriate. Common elements of the mathematical practices that are often missing from lessons are the following: critiquing each other’s [students’] work, discussing the mathematics, developing mathematical models, and identifying and describing patterns, connections, justifications, and generalizations.

Many math lessons today are delivered ineffectively through a lecture-style approach that lacks high levels of student engagement. Direct instruction can be an effective approach if key principles of explicit instruction are followed in order to keep students highly engaged, such as a brisk pace, frequent student interactions, and guided practice with corrective feedback (Archer and Hughes 2011). The potential of inquiry-based lessons often also falls short due to a lack of clear directions, a lack of ongoing guidance to maintain engagement, and a lack of explicit connections to prior learning (see CORE Academic Quarterly Spring 2019 on Applying Explicit Instructional Techniques to both Direct Instruction and Inquiry-based Learning).


The key for all math instruction is a high level of student engagement. Below are six recommended approaches and some helpful resources to foster greater student engagement:

  1. Provide multiple opportunities for students to talk and make sense of their learning. Discussion is an excellent way to engage students in thinking and analyzing or defending their ideas. Productive teacher talk moves can be deliberately introduced to students and utilized to increase student discourse. The Institute for Learning’s Accountable Talk Sourcebook is an excellent resource for ideas related to fostering and managing student discourse.
  2. Build in routines for group work to maximize discussion and problem-solving. Established routines for discussion are especially important in classrooms that have English-language learners and students who struggle. Having routines and consistent expectations reduces the need to think about usual teacher expectations and standard processes, which then allows more cognitive energy toward deeper thinking about math. Post anchor charts that explain what you should see and hear from students when they are transitioning to and participating in group work. Anchor charts are one way to provide a consistent reminder and guide to efficient use of discussion and small- group problem-solving time.
  3. Engage in multiple checks for understanding throughout each lesson using frequent questioning with a variety of response modes such as physical responses, white boards, response cards, interactive polling, or quick writes. Teacher questioning, with questions that require explanation (Rosenshine 2012), plays a pivotal role in assessing student understanding (Manouchehri and Lapp 2003). Teachers can also use online applications such as Plickers to quickly engage students in reflecting while providing the teacher with feedback on student understanding.
  4. Use journal writing, foldables, or interactive journals to give students an opportunity to consolidate and organize their thinking throughout a lesson. Journals are a great way to have students reflect on their performance or understanding related to lesson outcomes. Self-reflection on learning is among the teaching techniques with the highest effect sizes in Hattie’s research (Hattie, Fisher, and Frey 2017). Journals are also a great technique to use for reflections and synthesis of learning at the conclusion of online learning sessions for students.
  5. Use the rigorous and relevant content from your curriculum; don’t water it down. Mathematical experiences that are challenging but accessible are far more engaging and do more to increase learning than are experiences consisting of easily learned content (Willen and Snider 2009). Challenging students’ ideas also helps them see the gap between their present understanding and the new learning.
  6. Provide students with choice in how they acquire, solve, and present solutions. Teachers can build in differentiation that also builds student autonomy by allowing students to use a variety of tools in order to solve challenging problems. For more ideas on effective practices with student-centered math, refer to the Nellie Mae Education Foundation (2014).


To achieve mathematical proficiency as described in the Mathematical Practice standards, teachers must shift instructional practices so that students are actively participating and engaged with the mathematics. To do so, school leaders must understand the benefits of active student engagement while building teachers’ skills for increasing student engagement through supportive professional learning. The tips shared in this blog will help shift math classrooms from passive to active learning. However, teachers do not need to do them all at once. Teachers can implement ideas incrementally in order to allow both themselves and their students to learn and practice new routines at a digestible pace, so that the mathematics, not the routines, remain the focus of instruction.

Abla, C., and B. R. Fraumeni. 2019. Student engagement: Evidence-based strategies to boost academic and social-emotional results. McRel International.

Archer, A. L., and C. A. Hughes. 2011. Explicit instruction: Effective and efficient teaching. New York: Guilford.

Boykin, A. W., and P. Noguera. 2011. Creating an opportunity to learn: Moving from research to practice to close the achievement gap. Alexandria, VA: ASCD.

Hattie, J., D. Fisher, and N. Frey. 2017. Visible learning for mathematics. Thousand Oaks, CA: Corwin.

Manouchehri, A., and D. A. Lapp. 2003, November. Unveiling student understanding: The role of questioning in instruction. Mathematics Teacher 96(8), 562–566.

Marks, H. M. 2000, Spring. Student engagement in instructional activity: Patterns in the elementary, middle, and high school years. American Educational Research Journal 37(1), 153–184.

National Governors Association Center for Best Practices and Council of Chief State School Officers. 2010. Common Core State Standards for Mathematics. Washington, DC: NGA Center for Best Practices and CCSSO.

Reckmeyer, M. 2019, October 30. Focus on student engagement for better academic outcomes.  Gallup.

Rosenshine, B. 2012, Spring. Principles of instruction: Research-based strategies that all teachers should know. American Educator 36(1), 12–19, 39.

Walters, K., T. M. Smith, S. Leinwand, A. Stein, and P. Bailey. 2014, November. An up-close look at student-centered math teaching: A study of highly regarded high school teachers and their students. Nellie Mae Education Foundation.

Willan, L., and J. Snider. 2009, June. Understanding the neuroscience of rigorous learning in student engagement: Evidence-based strategies to boost academic and social-emotional results. Hechinger Institute on Education and the Media, 11–13.


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