Based on a synthesis of the literature in inductive reasoning, a framework for prescribing and assessing mathematics inductive reasoning of primary school students was formulated and validated. The major constructs incorporated in this framework were students' cognitive abilities of finding similarities and/or dissimilarities among attributes and…

Studied the efficiency of worked examples as a substitute for conventional practice problems in training both elderly (24 older adults in the Netherlands) and young adults (30 Dutch college students). As predicted, results show that for the elderly, the efficiency of studying worked examples is higher than the efficiency of solving conventional…

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…

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)

Assessed the strategic flexibility of students in mental arithmetic up to the number 100. Results from 60 Dutch second graders show that students' preference for certain mathematical procedures depend on the number characteristics of the problems, indicating that the students had a good conceptual understanding of numbers and procedures. Actual…

This study investigated factors promoting the use of self-constructed diagrams by examining students' perceptions and daily class activities, and comparing Japanese (n = 291) and New Zealand (n = 323) students. Algebra word problems and a questionnaire were administered. The results revealed that the New Zealand students used diagrams more often…

Mental arithmetic strategies were studied with 91 Dutch third graders who computed by splitting off 10s and units in both numbers or counting by 10s up or down from the first unsplit number. Results reveal flexibility in changing between and within strategy use. Implications for instruction are discussed. (SLD)

The role played on shallow and deep levels of comprehension by text changes aimed at improving relationships within text ideas or producing better links with the reader's knowledge were studied with 67 Spanish 10th graders. Both textual changes contributed separately to recall, but problem solving increased only when the two were presented…

Two studies involving a total of 66 Australian high school students investigated the effects of training in the use of general strategies on the performance of high- and low-achieving students in trigonometry. The positive effects of management training were identified for both high- and low-achieving students. (SLD)

A study of interactions among Swedish intermediate-grade students as they solved a nonstandard mathematics task confronting the phenomenon of infinity shows that the children can reach a considerable understanding of the problem by contextualizing the problem in different ways. The collective orchestration of problem variations results in enhanced…

Qualitative features of teacher-student interaction during classroom teaching and learning while modern technological thinking and problem-solving skills were mediated were studied for 22 seventh-grade boys in Finland. Reciprocal understanding between teacher and student were necessary in order for the teacher's special instructional assistance to…

An experiment involving 14 small groups of Swedish students (usually 3 per group) aged 10, 11, and 12 years shows that these students acting in groups and creating shared contextualizations were able to solve mathematics word problems calling for real-world knowledge. Research has shown students acting alone to have difficulty with the same types…

Studied the influence of authentic contexts and self-made graphical representations on students' well-documented tendency to apply the linear model improperly in representing and solving nonproportional word problems. Findings for 152 Flemish 8th graders and 161 10th graders do not show the expected effects; in fact, these forms of help had…

Problem-solving models in memories of 11 good and 12 poor novice first-year university students were studied. The students reconstructed physics problems seen briefly, relying on models in memory. Both good and poor students had models of problem situations at their disposal, but good students performed better than poor students. (SLD)

The influence of multiple learning contexts and problem solving guidance on the acquisition of applicable knowledge and subjective learning outcomes in complex learning was studied with 60 economics students from a vocational school. No single learning condition was superior with regard to all learning outcomes. The problem of self-evaluation of…