The Effects of Schema-Broadening Instruction on Second Graders' Word-Problem Performance and Their Ability to Represent Word Problems with Algebraic Equations: A Randomized Control Study

Abstract

The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders' word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which taught students to represent the structural, defining features of word problems with overarching equations. Intervention lasted 16 weeks. We pretested and posttested 270 students on measures of word-problem skill; analyses that accounted for the nested structure of the data indicated superior word-problem learning for SBI students. Descriptive analyses of students' word-problem work indicated that SBI helped students represent the structure of word problems with algebraic equations, suggesting that SBI promoted this aspect of students' emerging algebraic reasoning.When solving word problems, students are faced with novel problems that require transfer. This can be difficult to effect in the primary grades (Durnin, Perrone, & MacKay, 1997; Foxman, Ruddock, McCallum, & Schagen, 1991, cited in Boaler, 1993Larkin, 1989). Some psychologists view such transfer in terms of the development of schemas, by which students conceptualize word problems within categories or problem types that share structural, defining features and require similar solution methods (Chi, Feltovich, & Glaser, 1981; Gick & Holyoake, 1983;Mayer, 1992;Quilici & Mayer, 1996). The broader the schema or problem type, the greater the probability students will recognize connections between novel problems and those used for instruction and will understand when to apply the solution methods they have learned.In a series of studies, we have relied on this conceptualization of transfer to design instruction for helping students build schemas for word-problem types and for broadening those schemas. Prior work (e.g., Fuchs et al., 2003;Fuchs, Fuchs, Prentice, et al., 2004) illustrates the efficacy of this approach, which we refer to as schema-broadening instruction (SBI), for third-grade students on problem types relevant to the third-grade curriculum. More recently, Fuchs, Powell et al. (2009) demonstrated the efficacy of SBI tutoring for a subset of third graders who experience severe mathematics difficulty. With this population, we taught simpler word-problem types, while introducing algebraic equations to represent the defining, structural features of those problem types.Inquiries should be sent to Lynn S. Fuchs, Box 328 Peabody, Vanderbilt University, Nashville,; lynn.fuchs@vanderbilt.edu). NIH Public Access Author ManuscriptElem Sch J. Author manuscript; available in PMC 2010 June 9. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptWe extend this line of work in the present study, applying SBI to problem types appropriate to the second-grade curriculum. We focused on typically developing second-grade students while relying on a whole-class format to deliver instruction, again ...

An exploratory study contrasting high- and low-achieving students' percent word problem solving

“…Within the mathematics education and special education research communities, there is growing evidence about the effectiveness of SBI in supporting students' learning of word problem solving, particularly in arithmetic (e.g., Fuchs et al, 2009;Fuchs, Seethaler, et al, 2008, Fuchs et al, 2010Fuson & Willis, 1989;Jitendra et al, 2007;Lewis, 1989;Willis & Fuson, 1988) and ratio/proportion word problem solving (e.g., Jitendra et al, 2009;Xin, 2008;Xin et al, 2005;Xin, Wiles, & Lin, 2008;Xin & Zhang, 2009). However, other studies have indicated…”

“…An emphasis on deep understanding of problem structure and flexibility in strategy use is central to one instructional intervention, schema-based instruction (SBI), which has shown great promise in helping students become better word problem solvers in elementary and middle school (e.g., Fuchs, Seethaler, Powell, Fuchs, Hamlett, Fletcher, 2008;Fuchs, Zumeta, Powell, Schumacher, Hamlett, & Fuchs, 2010;Jitendra, Griffin, Haria, Leh, Adams, & Kaduvetoor, 2007;Jitendra et al, 2009;Xin, Jitendra, & Deatline-Buchman, 2005;Xin, 2008). In particular, SBI appears to be instrumental in improving students' learning of ratio and proportion problem solving (e.g., Jitendra et al, 2009).…”

Towards efficient measurement of metacognition in mathematical problem solving

“…It is thus advisable to be specific about the context in which metacognition is measured (McNamara 2011). One of the domains in which metacognition is a key variable predicting learning performance is the domain of mathematical problem solving (Desoete and Veenman 2006;Desoete 2009;Fuchs et al 2010;Harskamp and Suhre 2007). In this domain, metacognition is used to monitor solution processes and to regulate the problem solving episodes of analyzing and exploring a task, making a solution plan, implementing the plan and verifying the answer (Schoenfeld 1992).…”

Procedural versus content‐related hints for word problem solving: an exploratory study

“…In combination with the episodes, the computer programmes provide cues and hints to help the students in developing a structured approach. The aim of the episode Read/Analyse is to help students visualize the problem situation (Boonen et al, 2014;Swanson et al, 2014), while the episodes Explore and Plan are focussed on assistance in finding a solution that fits the problem situation (Fuchs et al, 2010;Hegarty & Kozhevnikov, 1999;Mayer, 1992).…”