Editor’s note: The Thomas B. Fordham Institute recently launched “The Acceleration Imperative,” a crowd-sourced, evidence-based resource designed to aid instructional leaders’ efforts to address the enormous challenges faced by their students, families, teachers, and staff over the past year. It comprises four chapters split into nineteen individual topics. We're publishing each as a stand-alone blog post.
What little data we have indicates that remote learning has been particularly challenging for students in mathematics. Schools will need to ensure that their recovery strategies allow ample opportunities for students to complete unfinished learning before moving on to new concepts.
Adopting and faithfully implementing a high-quality elementary mathematics curriculum that is aligned to college and career-ready standards—the same curriculum across all grade levels—is one essential step. Such a curriculum does the following:
- Concentrates heavily on arithmetic. Students analyze and solve word problems, practice calculating fluently with mental math and written algorithms, and use the four basic operations on whole numbers, fractions, and decimals.
- Provides sufficient practice with procedures and basic math facts—all developed on a basis of concepts and understanding.
- Enables teachers to orchestrate effective forms of mathematical discourse during lessons, such as eliciting connections between different representations of a problem, or connections between different student strategies.
- Includes effective supports for English learners.
- Enables teachers to involve parents in their children’s mathematical education.
- Adopt and implement a single, high-quality elementary mathematics curriculum across all grades and schools that is aligned to college and career-ready standards. EdReports has given strong favorable reviews to several products, including two we consider exemplars: Eureka Math and Zearn. Their materials are free or low-cost, and both have been adopted widely by some of the best-performing elementary schools in the country.
- Use the same curriculum for interventions and supports—including high-dosage tutoring—that is used for regular classroom instruction.
- Dedicate training and planning time to help teachers develop expertise in the curriculum, including building on what students already know to connect them to grade-level work. In math professional-learning sessions, as in other areas of the curriculum, staff developers should explicitly link what teachers are learning to the curriculum they are using.
The research base identifying what works in mathematics education is substantial—probably more so than any other subject. There are, for example, four different Institute for Educational Sciences Practice Guides that contain a total of twenty-eight recommendations, all of which are backed by an extensive body of high-quality research. These three are particularly important and instructive:
- Studies show that students become more efficient and flexible in selecting appropriate ways to solve problems when they have been regularly exposed to questions that require different strategies to answer. For example, in Eureka Math and Zearn, teachers facilitate classroom discussions about the strategies selected, with questions such as “Which strategy do you prefer and why?” or “Which strategy is the most efficient?”
- Research also underscores the importance of teaching students how to use visual representations. Students who learn to visually represent the mathematical information in problems prior to writing an equation are more effective at problem solving. High-quality curricula build this progression into the development of all concepts.
- How fractions are treated, beginning in the earliest grades, is another hallmark of high-quality programs. IES reviews the research and concludes that “a high percentage of U.S. students lack conceptual understanding of fractions, even after studying fractions for several years.” This conclusion supports using a curriculum that places a high premium on building a conceptual understanding of fractions and the ability to use them to think mathematically.
Achieve the Core. (2013). K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics.
- The basis for the quality indicators used by EdReports in its curriculum reviews. Describes necessary instructional shifts and establishes criteria for how those should show up in curriculum.
Atkinson, R., Derry, S., Renkl, A., and Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181–214.
- Curricula that include multiple worked examples for math problems are effective at promoting conceptual understanding.
Cooper, G., and Sweller, J. (1987). The effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347–362.
- When lessons teach students the concepts (schema) under certain math rules, students’ conceptual understanding and fluency are improved.
Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., and McDowell, J. (2013). “Teaching math to young children: A practice guide.” Washington, D.C.: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.
Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., and Witzel, B. (2009). “Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools.” Washington, D.C.: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
Halpern, D., Aronson, J., Reimer, N., Simpkins, S., Star, J., and Wentzel, K. (2007). “Encouraging Girls in Math and Science.” Washington, D.C.: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education.
Jacobs, V., Franke, M., Carpenter, T., Levi, L., and Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258–288.
- Professional development on bringing in algebraic reasoning to elementary math lessons improved students’ grasp of mathematical content. Speaks to potential benefits of using a curriculum that builds in the teaching of algebraic thinking at the elementary level.
Ng, S.F., and Lee, K. (2009). The model method: Singapore children’s tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282–313.
- The method of model drawing used in Singapore’s national math curriculum for nearly all word problems has had a positive impact on student achievement.
Rittle-Johnson, B., Star, J. R., and Durkin, K. (2009). The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836–852.
- Students’ prior conceptual and procedural knowledge is essential at the elementary school level and even more important in middle-school Algebra classes.
Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., and Wray, J. (2010). “Developing effective fractions instruction for kindergarten through 8th grade: A practice guide.” Washington, D.C.: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
Tajika, H., Nakatsu, N., Nozaki, H., Neumann, E., and Maruno, S. (2007). Effects of self-explanation as a metacognitive strategy for solving mathematical word problems. Japanese Psychological Research, 49(3), 222–233.
- Promoting students’ ability to explain their thinking has a positive impact on their ability to solve math word problems.
Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., and Ogbuehi, P. (2012). “Improving mathematical problem solving in grades 4 through 8: A practice guide.” Washington, D.C.: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.