Algebra teachers should show students both correctly and incorrectly solved problems and have students discuss them, according to a new algebra practice guide published by the U.S. Department of Education’s Institute for Education Sciences.
The guide, prepared by Mathematica Policy Research and released this week as part of the What Works Clearinghouse, includes three specific, evidence-based strategies for teaching algebra. It’s based on a review of studies about algebra instruction that were published between 1993 and 2013.
The recommendations say algebra teachers for students in grades 6-12 should:
1) Use solved problems to illustrate common errors and push students’ algebraic reasoning skills. They should then have students discuss problems, solved both correctly and incorrectly, in large and small groups.
2) Help students see structure in algebraic representations. This encourages them to notice similarities between problems that may initially appear to be different. Discuss how a word problem, equation, diagram, and graph may all contain corresponding information.
3) Have students compare different strategies for solving a problem. The guide states that “the recommendation does not advocate that students be fluent in all possible strategies for solving a given problem type. By learning alternative strategies, students can select from different options when they encounter a familiar or unfamiliar problem.”
This final recommendation is rated as having the strongest evidence base of the three.
The practice guide is not dependent on any particular standards or curriculum, though the six-person expert panel that helped develop the guide includes William McCallum, one of the lead writers of the Common Core State Standards for mathematics, and is chaired by Jon R. Star, a consultant for publishers Scholastic and Pearson, which are developing algebra curricula aligned to the common standards.
A version of this news article first appeared in the Curriculum Matters blog.