Training Can Increase Students’ Choices for Written Solution Strategies and Performance in Solving Multi-Digit Division Problems

Abstract

Making adaptive choices between solution strategies is a central element of contemporary mathematics education. However, previous studies signal that students make suboptimal choices between mental and written strategies to solve division problems. In particular, some students of a lower math ability level appear inclined to use mental strategies that lead to lower performance. The current study uses a pretest-training-posttest design to investigate the extent to which these students’ choices for written strategies and performance may be increased. Sixth graders of below-average mathematics level (n = 147) participated in one of two training conditions: an explicit-scaffolding training designed to promote writing down calculations or a practice-only training where strategy use was not explicitly targeted. Written strategy choices and performance increased considerably from pretest to posttest for students in both training conditions, but not in different amounts. Exploratory results suggest that students’ strategy choices may also be affected by their attitudes and beliefs and the sociocultural context regarding strategy use.

Strategies of Pre-Service Early Childhood Teachers for Solving Multi-Digit Division Problems

“…Educational reforms across countries have promoted the application of flexible strategies, in addition to the traditional algorithm, for solving division problems. Many studies have evaluated the division strategies adopted by primary school students [3,5,6,[8][9][10][11][12][13]47]. Investigations on this topic, however, have not been conducted with future early childhood teachers.…”

“…As shown above, a wide range of studies has identified and evaluated the strategies employed by primary school students on multi-digit division problems [3,5,6,[8][9][10][11][12][13]47]. Investigations with secondary school students and pre-service primary teachers, however, have been rarely conducted, while the strategies employed by future early childhood teachers on multi-digit division problems have remained unexplored.…”

“…Instructed students, however, tend to apply more structured procedures, identifying a progression from mental and informal strategies to written approaches [3,13,14,16,36]. There is evidence that a student's high performance on multi-digit division problems is positively associated with written strategies [3,8,9]. Strategy selection for this type of problem may depend on various factors including the characteristics of the numbers involved in the problem [3,12], the approach used to tackle the problem [3,8], and the instructional setting of the solver [6,10,14,46].…”

“…Most research on this topic has been undertaken with primary school students [3,5,6,[8][9][10][11][12][13] and conducted by Hickendorff and Fagginger-Auer and their colleagues in the Netherlands [3,5,6,[8][9][10]. In that country, the Realistic Mathematics Education (RME) reform has heavily influenced school teaching by promoting the learning of flexible strategies and introducing the traditional division algorithm in the last year of primary school [6].…”

“…We attempt to assess whether teachers have acquired the problem-solving knowledge and skills promoted by official curricula across educational systems and thus whether recent reforms are impacting on our students' division strategies. We also seek to investigate whether or not future early childhood teachers make use of arithmetical strategies, as primary school students do [3,5,6,[8][9][10][11][12][13], or by contrast, they additionally incorporate algebraic strategies as observed with secondary school students [15]. In a general problem-solving context with pre-service primary teachers, research suggests these teachers alternatively apply arithmetical and algebraic strategies, depending on problem characteristics [25,26].…”