ABSTRACT
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.
ABSTRACT
Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting 3(rd) graders' development of mathematics problem solving. In the fall, 122 3(rd)-grade students were assessed on language, nonverbal reasoning, attentive behavior, calculations, word-problem skill, and DA. On the basis of random assignment, students received 16 weeks of validated instruction on word problems or received 16 weeks of conventional instruction on word problems. Then, students were assessed on word-problem measures proximal and distal to instruction. Structural equation measurement models showed that DA measured a distinct dimension of pretreatment ability and that proximal and distal word-problem measures were needed to account for outcome. Structural equation modeling showed that instruction (conventional vs. validated) was sufficient to account for math word-problem outcome proximal to instruction; by contrast, language, pretreatment math skill, and DA were needed to forecast learning on word-problem outcomes more distal to instruction. Findings are discussed in terms of responsiveness-to-intervention models for preventing and identifying learning disabilities.
