Closing the Word-Problem Achievement Gap in First Grade: Schema-Based Word-Problem Intervention with Embedded Language Comprehension Instruction.

The main purpose of this study was to test the effects of word-problem intervention, with versus without embedded language comprehension instruction, on at-risk 1st graders' word-problem performance. We also isolated the need for a structured approach to word-problem intervention and tested the efficacy of schema-based instruction at 1st grade. Children (n=391; mean age = 6.53, SD = 0.32) were randomly assigned to 4 conditions: schema-based word-problem intervention with embedded language instruction, the same word-problem intervention but without language comprehension instruction, structured number knowledge intervention without a structured word-problem component, and a control group. Each intervention included 45 30-min sessions. Multilevel models, accounting for classroom and school effects, revealed the efficacy of schema-based word-problem intervention at 1st grade, with both word-problem conditions outperforming the number knowledge condition and the control group. Yet, word-problem performance was significantly stronger for the schema-based condition with embedded language comprehension instruction compared to the schema-based condition without language comprehension instruction. Number knowledge intervention conveyed no word-problem advantage over the control group, even though all 3 intervention conditions outperformed the control group on arithmetic. Results demonstrate the importance of a structured approach to word-problem intervention; the efficacy of schema-based instruction at 1st grade; and the added value of language comprehension instruction within word-problem intervention. Results also provide causal evidence on the role of language comprehension in word-problem solving.

Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners.

The focus of the present study was enhancing word-problem and calculation achievement in ways that support pre-algebraic thinking among 2nd-grade students at risk for mathematics difficulty. Intervention relied on a multi-tier support system (i.e., responsiveness-to-intervention or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation RTI, word-problem RTI, and business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word-problem outcomes; word-problem RTI enhanced proximal word-problem outcomes as well as performance on some calculation outcomes; and word-problem RTI provided a stronger route than calculation RTI to pre-algebraic knowledge.

Does Calculation or Word-Problem Instruction Provide A Stronger Route to Pre-Algebraic Knowledge?

The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and pre-algebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other domain and whether intervention in either or both domains contributes to pre-algebraic knowledge. Participants were 1102 children in 127 2nd-grade classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation intervention, word-problem intervention, and business-as-usual control. Intervention, which lasted 17 weeks, was designed to provide research-based linkages between arithmetic calculations or arithmetic word problems (depending on condition) to pre-algebraic knowledge. Multilevel modeling suggested calculation intervention improved calculation but not word-problem outcomes; word-problem intervention enhanced word-problem but not calculation outcomes; and word-problem intervention provided a stronger route than calculation intervention to pre-algebraic knowledge.

Effects of First-Grade Number Knowledge Tutoring With Contrasting Forms of Practice.

The purpose of this study was to investigate the effects of 1st-grade number knowledge tutoring with contrasting forms of practice. Tutoring occurred 3 times per week for 16 weeks. In each 30-min session, the major emphasis (25 min) was number knowledge; the other 5 min provided practice in 1 of 2 forms. Nonspeeded practice reinforced relations and principles addressed in number knowledge tutoring. Speeded practice promoted quick responding and use of efficient counting procedures to generate many correct responses. At-risk students were randomly assigned to number knowledge tutoring with speeded practice (n = 195), number knowledge tutoring with nonspeeded practice (n = 190), and control (no tutoring, n = 206). Each tutoring condition produced stronger learning than control on all 4 mathematics outcomes. Speeded practice produced stronger learning than nonspeeded practice on arithmetic and 2-digit calculations, but effects were comparable on number knowledge and word problems. Effects of both practice conditions on arithmetic were partially mediated by increased reliance on retrieval, but only speeded practice helped at-risk children compensate for weak reasoning ability.