Improving Multiplication Strategic Development in Children With Math Difficulties

Abstract

The purpose of the present study was to examine the effectiveness of a strategic training program for improving students’ performance in solving multiplication problems. The participants were 3 third graders with math difficulties. In this teaching experiment, microgenetic analysis was used to analyze improvement in students’ strategic development and problem-solving accuracy. The instructional components included selective task assignment and OFSD (encouraging students to use Own strategy to solve problems, providing Feedback, asking for students’ Self-explanations, and explicit Demonstration of strategies when needed). The results showed that the three participants began the intervention at different strategic developmental levels and consequently were given differentiated tasks to promote their strategic development during the intervention. In response to the intervention, the three participants improved their problem-solving accuracy, use of advanced strategies, and flexibility in choosing backup strategies.

Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

“…The major strategy categories to solve multidigit multiplication and division problems involve (a) repeated addition or subtraction: e.g., solving the multiplication problem 12 × 29 by repeatedly adding (multiples of) 29s or solving the division problem 736 : 23 by repeatedly subtracting (multiples of) 23s, (b) partitioning strategies in which one or both of the operands are decomposed: e.g., solving 12 × 29 via 10 × 29 = 290; 2 × 29 = 58; 290 + 58 = 348, and (c) simplifying (or shortcut) strategies, most notably compensation: e.g., solving 12 × 29 via 12 × 30 − 12 × 1 = 360 − 12 = 348 (Ambrose et al 2003;Buijs 2008;Van Putten et al 2005;Zhang et al 2014).…”

Between Counting and Multiplication: Low-Attaining Students’ Spatial Structuring, Enumeration and Errors in Concretely-Presented 3D Array Tasks

“…Thus more recent research in this tradition (e.g. Broza & Kolikant, 2015;Elia et al, 2014;Zhang et al, 2014) has incorporated elements from practitioner research and intervention studies, such as the inclusion of unique 'prompts' when no observable change is independently occurring, after which a new "cognitive snapshot" may be taken.…”

Multi-digit Addition, Subtraction, Multiplication, and Division Strategies

“…Although the available studies show that at the group level there are differences in children's strategy use that can be related to differences in the instruction they received, at the level of an individual child there are a lot of variety and manifestations of strategy preference and use that do not coincide with the nature of the instruction received. Given this complex relation between strategy instruction and strategy development, we plead for instruction that (a) acknowledges that children develop their own strategies and stimulates children to use them, (b) diagnoses strategic development by ongoing assessment and progress monitoring, (c) assigns tasks based on children's current strategy level, (d) stimulates children to (self-)explain their strategies, and (e) provides explicit strategy instruction for struggling children (Zhang et al, 2014). Evidently, more research has to be done to optimize strategy instruction in the domain of multi-digit arithmetic for children with mathematical difficulties.…”

“…To the best of our knowledge, there is hardly any research addressing multi-digit multiplication and division strategies in children with mathematical difficulties. Only Zhang, Xin, Harris, and Ding (2014) investigated the effectiveness of strategy training interventions for children struggling with multiplication in a small-scale study with three 8-9-year-old children. Their results imply that children may experience difficulties in multiplication because their strategy development lags behind and that targeting (strategy) instruction to the individual child's current level of strategy knowledge may be beneficial.…”