# Worked Example Instruction of Decomposition Strategies in Two-Digit Multiplication Problem Solving

#### Abstract

The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem solving. In this multiple-baseline single-case design study, eight fourth- and fifth-grade students were individually taught to use associative and distributive decomposition strategies to solve two-digit multiplication problems through worked examples and explicit instruction. Problem-solving speed, accuracy, and solution methods were monitored throughout baseline and instructional phases. Seven participants applied the associative and distributive decomposition strategies independently during the first instructional session and one began doing so in the fifth session. Accuracy on timed probes increased overall in the instructional phase but was unrelated to decomposition use. Three of eight participants applied decomposition strategies to solve problems on the timed probes and only one of those showed an increase in accuracy corresponding to their initial use of those strategies. Similarly, no clear impact of strategy use was found on problem-solving speed. However, high automaticity for multiplication facts appeared to be associated with decomposition strategy use. High automaticity was observed for all three participants that applied decomposition strategies to probe problems, whereas only one of five that did not apply the strategies to the probes demonstrated high automaticity. Moreover, the participants who applied decomposition strategies on the probes demonstrated effective use of the problems’ structures to form multiples of 10 and generate high-automaticity intermediate computations.

#### Subject Area

Educational psychology|Psychology|Mathematics education

#### Recommended Citation

Pellerzi, Laura Ann Weinberg, "Worked Example Instruction of Decomposition Strategies in Two-Digit Multiplication Problem Solving" (2023). *ETD Collection for Fordham University*. AAI30487987.

https://research.library.fordham.edu/dissertations/AAI30487987