Effective teaching in math
Systematic and Explicit InstructionConsistently strong effects were found for systematic, explicit instruction. We define explicit instruction as instruction that involves a teacher demonstrating a specific plan (strategy) for solving the problem types and students using this plan to think their way through a solution. In most studies, the emphasis was placed on providing highly explicit models of steps and procedures or questions to ask in solving problems. The degree of structure and specificity is atypical in conventional mathematics texts.
We divided the explicit instruction studies into two categories: those involving only one problem type, and those involving multiple problem types. In both instances, mean effect sizes were large for both the special education students and the population of low-performing students with no specific learning disability. Although the majority of studies dealt with procedural knowledge, many students with learning disabilities in mathematics struggle with what are considered basic mathematical procedures. This, in turn, limits their ability to solve more-complex problem types in which basic procedures are embedded. |
Student Think- AloudsStudies showed that when faced with multistep problems, students frequently attempted to solve the problems by randomly combining numbers instead of implementing a solution strategy step by step. The process of encouraging students to verbalize their thinking—by talking, writing, or drawing the steps they used in solving a problem— was consistently effective. In part, this procedure may be effective because the impulsive approach to solving problems taken by many students with mathematics difficulties was addressed. Results of these students were quite impressive, with an average effect size of 0.98, which is very large.
In one set of studies, teachers provided numerous explicit models of how to solve a problem or a type of problem. They had students practice verbalizing a solution. A good deal of time went into how to solve, for example, the different types of subtraction problems by using part-whole relationships. This verbalization appeared to help anchor the students both behaviorally and mathematically. |
Peer-Assisted Learning Activities and Formative Assessment DataThe role of peer-assisted learning and ongoing formative assessment data will be discussed in forthcoming NCTM research briefs. Results are quite promising for using peer-assisted learning with low-performing students but much more uncertain for special education students in the general classroom. The use of ongoing formative assessment data invariably improved mathematics achievement of students with mathematics disability.
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