Kathy Karns

Enhancing Kindergartners' Mathematical Development: Effects of Peer-Assisted Learning Strategies.

The purpose of this study was to examine the effects of a dyadic peer-mediated treatment on kindergarten childrens mathematics development. Within schools, 20 classrooms were assigned randomly to experimental or control groups. Experimental teachers implemented the peer-mediated treatment twice weekly for 15 weeks. We measured the fidelity of treatment implementation, and teachers completed questionnaires about treatment effectiveness and feasibility. Within classrooms, we pre- and post-tested 168 students (84 per condition) who had been classified into achievement groups based on pretest scores; effects were separated for students identified for or referred to special education and for nondisabled low-, middle-, and high-achieving classmates. Results indicated that treatment implementation was strong for most, but not all, teachers; teachers judged the treatment to be effective and feasible for implementation on their own; and students with and without disabilities, at all points along the achievement continuum, benefited from the treatment. Implications for research and practice are discussed.

High-Achieving Students’ Interactions and Performance on Complex Mathematical Tasks as a Function of Homogeneous and Heterogeneous Pairings

The purpose of this study was to examine high-achieving students’ interactions and performances on complex mathematics tasks as a function of homogeneous versus heterogeneous pairings. Participants were third and fourth graders who had been trained in, and had routinely practiced, constructive peer-tutoring interactions and had experience working individually on performance assessments. We videotaped 10 high achievers working with a high-achieving and with a low-achieving classmate on performance assessments. Results indicated that homogeneous dyads operated more collaboratively, generated greater cognitive conflict and resolution, and produced better quality work. Implications are discussed in terms of optimizing grouping arrangements during collaborative learning activities and preparing students to work productively together on complex tasks.

Effects of Task-Focused Goals on Low-Achieving Students With and Without Learning Disabilities

We examined effects of a task-focused goals treatment (TFG) in mathematics on low-achieving students with and without disabilities. We randomly assigned 40 classrooms to (a) TFG (which incorporated self-referenced assessment feedback, SRAF), (b) SRAF, and (c) contrast (neither TFG nor SRAF). We measured student perceptions of TFG, the difficulty and variety of learning topics, mathematics learning, effort, and intrinsic motivation. TFG students reported enjoying and benefiting from TFG, chose more challenging and a greater variety of learning topics, and increased their effort differentially. Increased effort, however, was associated with greater learning only for low achievers in TFG without learning disabilities, and we found no effects on intrinsic motivation.

The Relation Between Student Ability and the Quality and Effectiveness of Explanations

The purpose of this study was to examine the quality and effectiveness of students’ mathematical explanations as a function of the ability of the tutor. We videotaped dyads from 20 classrooms in which all students had been trained in constructive peer-tutoring interactions and had practiced those methods twice weekly for 23 weeks. From each classroom, one dyad incorporated a high-achieving tutor; the other, a medium-achieving tutor; both tutored the same classmate with a learning disability in the area of mathematics. Results indicated that high-achieving tutors’ explanations were rated higher on conceptual, procedural, and overall quality; incorporated a greater variety of explanatory strategies; earned higher conceptual orientation scores; and resulted in better performances among tutees. Implications are discussed in terms of optimizing grouping arrangements during collaborative learning activities and related concerns about mainstreaming students with learning disabilities for academic instruction.

Comparisons among Individual and Cooperative Performance Assessments and Other Measures of Mathematics Competence

The purposes of this study were to examine how well 3 measures, representing 3 points on a traditional-alternative mathematics assessment continuum, interrelated and discriminated students achieving above, at, and below grade level and to explore effects of cooperative testing for the most innovative measure (performance assessment). Fourth graders (n = 131) with prior training and experience in cooperative mathematics activities individually completed 2 more traditional assessments; half completed performance assessments individually, the other half in dyads. The 2 more traditional measures, but not the performance assessments, demonstrated strong discriminative validity. Among individually administered measures, intercorrelations were moderate and significant; correlations were stronger for performance assessments that were individually rather than cooperatively completed, and exploratory analyses suggested that cooperative performance assessment scores corresponded better with other measures for above-grade-level students than for below-grade-level students. Findings are discussed for statewide assessment programs and instructional decision making with respect to the misalignment between performance assessment forms of mathematical knowledge and typical classroom curricula and the need for preparation in collaborative group processes on problem-solving activities.