Amy E. Lein

Teaching Mathematical Word Problem Solving The Quality of Evidence for Strategy Instruction Priming the Problem Structure

This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et al. and 10 single case design (SCD) research studies using criteria suggested by Horner et al. and the What Works Clearinghouse. Results indicated that 14 group design studies met the criteria for high-quality or acceptable research, whereas SCD studies did not meet the standards for an evidence-based practice. Based on these findings, strategy instruction priming the mathematics problem structure is considered an evidence-based practice using only group design methodological criteria. Implications for future research and for practice are discussed.

Exploring the Impact of Knowledge of Multiple Strategies on Students’ Learning About Proportions

Proportional reasoning is widely considered to be a major goal of mathematics education in the middle grades. The literature identifies three strategies that are commonly used by students in solving simple proportion problems: cross multiplication, equivalent fractions, and unit rate. In past research, scholars have expressed concern that students rely too heavily on cross multiplication when solving these types of problems and have advocated delaying instruction on cross multiplication in favor of both the unit rate and equivalent fractions strategies. As part of a study evaluating a 6-week curriculum unit on ratio, proportion, and percent problem solving, we assessed students’ strategy repertoire for solving proportion problems and the extent to which students’ prior knowledge of one or more strategies impacted their learning from the curricular intervention. Results indicated that students relied almost exclusively on the equivalent fractions strategy for solving simple proportion problems, and that students who had prior knowledge of more than one strategy learned more from the intervention than those who knew one or no strategies.

Assessing the Relation Between Seventh-Grade Students’ Engagement and Mathematical Problem Solving Performance

In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger intervention study assessing improvement in middle school students’ proportional reasoning was assessed on initial mathematics achievement, on-task behavior, and mathematics problem-solving performance. Results suggested that engagement uniquely predicted mathematics problem-solving performance after controlling for prior mathematics achievement. Furthermore, the authors found differential rates of engagement for the three achievement groups. Based on an analysis of engagement by instructional lesson, the authors offer suggestions for addressing engagement when designing instruction.

The contribution of domain-specific knowledge in predicting students' proportional word problem-solving performance

This study explored the extent to which domain-specific knowledge predicted proportional word problem-solving performance. We tested 411 seventh-grade students on conceptual and procedural fraction knowledge, conceptual and procedural proportion knowledge, and proportional word problem solving. Multiple regression analyses indicated that all four domain-specific knowledge variables (i.e., conceptual and procedural fraction knowledge, conceptual and procedural proportion knowledge) significantly predicted proportional word problem-solving performance. Conceptual fraction and procedural proportion knowledge contributed the most unique variance (10.0 and 6.7%, respectively, of the total variance) to proportional word problem solving. Procedural fraction and conceptual proportion knowledge each also contributed significant unique variance to proportional word problem solving explaining 5.6 and 2.8%, respectively. The results support the notion that both conceptual fraction and proportion knowledge and procedural fraction and proportion knowledge play a major role in understanding individual differences in proportional word problem-solving performance to inform interventions.