Middle school math holds significant importance for students as it introduces key concepts, such as fractions and computational skills, which provide the foundation for advanced math. Effective engagement strategies can help middle school students connect to math content in meaningful ways and build the skills needed for success in more advanced math in high school and college.1,2
A new REL Midwest documentary, produced in collaboration with the Teaching Fractions Toolkit partnership and WTTW (PBS station) in Chicago, presents strategies to increase students' math engagement, learning, and performance in middle school. The program features educators and students using the strategies at Jonathan Burr Elementary School (grades K–8) in Chicago, as well as research experts who speak to the importance and impact of engaging middle school students in math learning to develop their math skills.
The documentary highlights five themes,supported by examples from Jonathan Burr Elementary School, which illustrate evidence-based instructional practices for fostering math engagement, the benefits of engaging math instruction for students, and how school leaders can support the use of these practices.
Students can benefit from exploring math concepts through the use of visual representations, such as number lines, diagrams, and percent bars.3 For example, based on moderate evidence, the What Works Clearinghouse (WWC) practice guide Developing Effective Fractions Instruction for Kindergarten Through Grade 8 recommends that teachers help students understand why procedures for computations with fractions make sense. Teachers can use visual representations, such as number lines, manipulatives, and area models, to help students understand core concepts about computational procedures related to fractions and why they work.
Combining visual representations with concrete representations, such as hands-on manipulatives, also can help students transition to more abstract representations of math concepts.4 Another WWC practice guide, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades, notes strong evidence for the use of concrete and semi-concrete representations to help students conceptualize connections between representations and math concepts. For instance, teachers may use three-dimensional objects that can be touched and manipulated (i.e., base 10 blocks, fraction tiles) to make the underlying math concepts more visible.
At Jonathan Burr Elementary School, middle school teachers use visual aids and hands-on manipulatives to help students grasp math concepts. Teachers note that students who struggle with math tend to thrive when they are able to depict a problem through a diagram or drawing, or use physical objects to represent math concepts. For example, math teachers draw stick figures and other illustrations on the board to help students understand complex math problems. Students featured in the documentary explain that they engage more in discussions in math class when they can visualize a problem.
Another strategy educators can use to build math engagement is to connect the content to students' real-life situations.5 This strategy can help students understand abstract math processes, such as fractions and other rational number concepts.
Connecting instruction to everyday experiences is a strategy to help students master more complex math concepts, such as fractions. Teachers can engage students by presenting math problems with real-world contexts that are familiar and meaningful to them, such as through the use of a measuring tape or by dividing a set of snacks among students. For example, the Developing Effective Fractions Instruction practice guide recommends that teachers build on students' informal understanding of proportionality in the context of sharing items, such as a candy bar with friends, to help teach fractions.
The teachers at Jonathan Burr Elementary School make a point to relate math to students' everyday experiences and emphasize the importance of applying basic problem-solving skills to real-life situations. For example, one teacher took her students on a field trip to a local grocery store to calculate discounts. This experience gave students a contextual understanding of how to apply math outside of the classroom—and it was a lot of fun!
Discussion also can be a powerful tool to build student engagement and understanding. The WWC practice guide Improving Mathematical Problem Solving in Grades 4 Through 8 recommends, based on moderate evidence, that teachers help students recognize and articulate math concepts.6 The practice guide suggests that small-group activities can allow students to articulate the process they used to solve a problem and the reasoning for each step.
The WWC practice guide, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades, finds strong evidence that encouraging students to use clear and concise mathematical language in verbal and written explanations can help students build deeper understandings of math concepts and gives teachers an opportunity to check for understanding.7 There also is strong evidence for the practice of creating space for students to reflect on their problem-solving process. By engaging with peers to share, compare, and discuss their approaches to solving problems, students build skills in communicating their thinking and learn new approaches to solving problems.8
In the documentary, math teachers at Jonathan Burr Elementary School provide students with opportunities to work with their peers or in groups to support math processing, problem solving, and engagement. The goal is for students to have the chance to talk about math every day and become comfortable with describing and reflecting on their problem-solving approaches.
Computational thinking refers to problem-solving strategies that help students approach unfamiliar problems.9 These strategies encourage student inquiry and emphasize understanding concepts instead of memorizing formulas to deepen mathematical learning.10 By providing middle school students with concrete strategies for approaching math problems, teachers can help build students' confidence in and increase their engagement with math.
The documentary illustrates the key elements of computational thinking, which include decomposition, abstraction, pattern recognition, algorithms, and debugging. For more information on computational thinking, see REL Midwest's blog post introducing the ENgagement and Achievement through Computational Thinking partnership and a related infographic.
The documentary also highlights other efforts underway in Illinois to support math achievement. In partnership with the Illinois State Board of Education and Illinois school districts, REL Midwest is working to close gaps in students' math achievement through the development, testing, and refinement of a Teaching Fractions Toolkit. This toolkit draws on the recommendations and implementation steps outlined in the Developing Effective Fractions Instruction practice guide.
In line with these recommendations, the toolkit will provide supports for grade 6 math teachers and leaders to address both teacher understanding of fraction computation, rates, and ratios as well as implications for classroom practice. Supports for grade 6 teachers will include six professional development modules as well as diagnostic and monitoring tools for instruction. In addition, to develop the knowledge of the leaders who support these teachers, the toolkit will provide institutional supports, such as informational videos, infographics, and checklists, for monitoring conditions for the toolkit's successful use.
For more information on the Teaching Fractions Toolkit partnership, see these related resources:
REL Midwest resources:
What Works Clearinghouse practice guides:
1 Birgin, O., Mazman-Akar, S. G., Uzun, K., Göksu, B., Peker, E. S., & Gümüs, B. (2017). Investigation of factors affected to math engagement of middle school students. International Online Journal of Educational Sciences, 9(4). https://iojes.net/?mod=makale_tr_ozet&makale_id=40674
2 Collie, R. J., Martin, A. J., Bobis, J., Way, J., & Anderson, J. (2019). How students switch on and switch off in mathematics: Exploring patterns and predictors of (dis)engagement across middle school and high school. Educational Psychology, 39(4), 489–509. https://doi.org/10.1080/01443410.2018.1537480
3 Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010). Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE 2010-4039). U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance. https://ies.ed.gov/ncee/wwc/practiceguide/15
4 Fuchs, L. S., Newman-Gonchar, R., Schumacher, R., Dougherty, B., Bucka, N., Karp, K. S.,… Morgan, S. (2021). Assisting students struggling with mathematics: Intervention in the elementary grades (WWC 2021006). U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance. https://ies.ed.gov/ncee/wwc/PracticeGuide/26
5 Siegler et al., 2010.
6 Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance. https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/MPS_PG_043012.pdf
7 Fuchs et al., 2021.
8 Woodward et al., 2012.
9 Gadanidis, G. (2017). Five affordances of computational thinking to support elementary mathematics education. Journal of Computers in Mathematics and Science Teaching, 36(2), 143–151.
10 Pei, C. (Y.), Weintrop, D., & Wilensky, U. (2018). Cultivating computational thinking practices and mathematical habits of mind in lattice land. Mathematical Thinking and Learning, 20(1), 75–89. https://doi.org/10.1080/10986065.2018.1403543