Alternative paths to improved word-problem performance: An advantage for embedding prealgebraic reasoning instruction within word-problem intervention.

Abstract

The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded prealgebraic reasoning instruction, improved word-problem performance. Students with mathematics difficulty (MD; n ϭ 304) were randomly assigned to a business-as-usual condition or 1 of 2 variants of word-problem intervention. The prealgebraic reasoning component targeted relational understanding of the equal sign as well as standard and nonstandard equation solving. Intervention occurred for 16 weeks, 3 times per week, 30 min per session. Sequential mediation models revealed main effects, in which each intervention condition significantly and substantially outperformed the businessas-usual condition, corroborating prior research on the efficacy of schema word-problem intervention. Yet despite comparable effects on word-problem outcomes between the two word-problem conditions, the process by which effects accrued differed: An indirect path via equal-sign understanding and then equation solving was significant only for the word-problem intervention condition with embedded prealgebraic reasoning instruction. Additionally, the effect of this condition on equal-sign reasoning was strong. Given the link between equal-sign reasoning for success with algebra and the importance of algebra for success with advanced mathematics, results suggest an advantage for embedding prealgebraic reasoning instruction within word-problem intervention. Educational Impact and Implications StatementThis study suggests prealgebraic reasoning is important within math word-problem instruction for third-grade students who experience difficulty with math. Prealgebraic reasoning involves interpreting the equal sign as "the same as" and solving equations (e.g., 3 ϩ __ ϭ 9 or 7 ϭ 13 Ϫ __). As students develop strong prealgebraic reasoning, they are better equipped to solve word problems.

How to Structure and Intensify Mathematics Intervention

“…An educator should use explicit instruction and visual representations to help students learn how to solve mathematics problems (Doabler et al, 2019). The common session structure should also feature a focus on how to set up and solve word problems (Powell et al, 2021). Embed appropriate behavioral support, such as daily report cards (Vannest et al, 2011) or check-in/check-out interventions (Kern & Wehby, 2014), when a student exhibits challenging behaviors.…”

“…We recommend that an educator create a common intervention session structure to help the student anticipate the lesson content and the educator effectively plan the intervention. For example, Powell et al (2021) A common session structure should have a warmup, explicit modeling and practice on a mathematics skill, and a review. While the use of a consistent session structure is critical, the structure can vary depending on the educator and student needs.…”

Strategies to Help Students Solve Addition and Subtraction Word Problems

“…The unique features will be explained for each structure to help students discriminate between them (see Table 1 for description). In Jitendra's (2007) curriculum, students are introduced to the graphic organizer that corresponds with each structure, whereas in Pirate Math Equation Quest (Powell & Berry, n.d.;Powell et al, 2021), students are introduced to the algebraic equation that corresponds with each target schema. Instruction is focused on the reading of word problems and classifying them into their target structure, which is identification knowledge.…”

“…To reach mastery in solving additive word-problem structures, students must demonstrate mastery in the core skills required to solve word problems: (a) identification knowledge (i.e., identifying structure of the word problem), (b) elaboration knowledge (i.e., schematically mapping information presented in the word problem to the core features embedded within the structure), (c) planning knowledge (i.e., identifying the operation and algebraic equation to yield a solution), and (d) execution knowledge (i.e., carrying out the computation). An example of this can be seen in Pirate Math Equation Quest (Powell & Berry, n.d.;Powell et al, 2021). The program focuses on building mastery in core skills required for problem solving through fluency building activities.…”

“…What structure is this? ; Powell & Berry, n.d.;Powell et al, 2021). These quick activities distribute practice across time enabling students to master the core skills required to solve additive word problems.…”