The effectiveness and efficiency of individual versus collaborative learning was investigated as a function of instructional format among 140 high school students in the domain of biology. The instructional format either emphasized worked examples, which needed to be studied or the equivalent problems, which needed to be solved. Because problem…

Arithmetic word problems are often presented accompanied by illustrations. The present study examined how different types of illustrations influence the speed and accuracy of performance of both good (n = 67) and poor arithmeticians (n = 63). Twenty-four arithmetic word problems were presented with four types of illustrations with increasing…

A series of experiments involving more than 40 mechanical engineers and engineering students with different levels of expertise examined strategies, competence, and style of the designers in problem-solving behavior. A model is proposed that explains differences in designing as an interaction of domain-specific and heuristic competence. (SLD)

Effects of guided (GI) and direct instruction (DI) in solving subtraction problems for mathematically low performers in regular schools were compared. In the GI condition, self-development of solution procedures was encouraged whereas in the DI condition one prescribed strategy was to be used. Forty children (M[subscript age] = 9.3 years) were…

Most mathematical problems can be solved using different methods. We tested the effectiveness of presenting more than one solution method by means of worked-out examples. In Experiment 1, a 2x3-factorial design was implemented ("multiple solutions": multiple/uniform; "instructional support": none/self-explanations/instructional explanations).…

In this study, 100 Italian eighth graders were divided into two groups to compare the effects of two instructional interventions--the first based on problem-solving through discussion, the second on individual problem-solving--on students' learning of two historical topics (World War I and the economic boom), interest and self-perception of…

This study investigated the role of different modes of representation, i.e., verbal description, decorative pictures, informational pictures and number line, in solving additive change problems. Data were collected from 1447 students in Grades 1, 2, and 3. Structural equations modelling affirmed the existence of four first-order…

Implemented and evaluated a classroom-based research project designed to examine the impact of instruction in a question analysis strategy on the development of novice chemistry students' problem solving expertise. Results for students in 18 classrooms provide some indications that strategy instruction accompanied by strategic supports has a…

Two features of a new horizontal conceptualization of expertise are explored. Polycontextuality refers to the multiple ongoing tasks apparent in expert work, and boundary crossing is considered as a cognitive process that characterizes much expertise. Three case studies, one in a Finnish elementary school, illustrate these concepts. (SLD)

Cognitive load theorists have frequently used subjective measures of cognitive load to test the effectiveness of instructional procedures. This study sought to broaden the applications of subjective measures by testing their ability to detect variations in intrinsic cognitive load within tasks. In two experiments students were asked to complete…

Word problems as used within the culture of mathematics education often promote a suspension of sense making by the students. In the papers in this issue, an alternative conceptualization of word problems is proposed that calls for mathematical modelling that takes real world knowledge into account. (SLD)

This paper examines task design that affords deep changes in mathematical thinking in the context of peer interaction. We describe a study in which 60 low-level high-school students solved a proportional reasoning task, the "blocks" task as individuals and/or in dyadic interaction. We show that we could tailor the design of the task in order to…

Two experiments involving 67 elementary school and 439 high school students show that students present solutions to many unsolvable problems without showing realistic reactions. Results are discussed with respect to the quality of word problems in teaching mathematics, the culture of teaching and learning, and the issue of social rationality in…

This paper focuses on the role of evaluation in mathematics in 749 elementary school children. The macroevaluative skills and calibration scores of high versus low mathematical problem solvers were contrasted as measures of metacognition. No relevant calibration differences were found for gender. In addition, the performances of children with…

A cognitive education program applicable across many classroom settings was evaluated with 147 Australian students in grades 4 through 7 who were or were not exposed to the Process-Based Instruction (PBI) approach. Results indicate the positive effects of PBI on student achievement and student and teacher attitudes. (SLD)