Eye Movement Patterns Characteristic of Cognitive Style

Various tools have been designed to classify the wholistic/analytic cognitive style, based mostly on behavioral data that reveals little about how these processes function. The main goal of this study is to characterize patterns of eye movements (EM) that are typical of learners with tendencies toward wholistic/analytic styles. Forty students completed the E-CSA-W/A test, while their EM were simultaneously monitored. The results revealed that the overall response time of the wholist group was lower in both tasks. The differences in response time between the groups are interpreted as being influenced by impulsive/reflective styles. While the behavioral data provide us with the end result and quantitative differences between the groups, EM provide us with the qualitative information about the process that led to the response. The study showed that the wholist group is characterized by less fixations and transitions than the analytic group, which is interpreted as reflecting use of whole/partial strategy.

Generic Versus Context-Specific Prompts for Supporting Self-Regulation in Mathematical Problem Solving Among Students With Low or High Prior Knowledge

We compared how 61 seventh graders, with low or high prior knowledge in mathematics, capitalized on two self-regulated learning approaches—generic versus context specific—to (a) enhance self-regulated learning, (b) foster procedural knowledge of routine algebraic tasks, and (c) transfer knowledge to novel mathematical problem solving. The generic approach was based on “IMPROVE” question prompts for comprehension, connection, strategy, and reflection modeled in a free context. The context-specific approach was based on what, when, why, and how (WWWH) question prompts directed explicitly to specific examples in a particular mathematical content area. Findings indicated no difference between the two approaches regarding short-term effects on algebraic procedural tasks; however, differential effects emerged between the two approaches on the self-regulation measure and on long-term transfer to novel tasks (near and far) among students with low or high prior knowledge. The practical and scientific significance of this study are discussed.

Investigating Preschool Children’s Mathematical Engagement in a Multimedia Collaborative Environment

The purpose of this study was twofold: (a) to investigate the effects of preschool children’s mathematical engagement in multimedia collaborative learning (MCL) on various skills of mathematical knowledge; and (b) to examine the differential effects of MCL on mathematical knowledge of younger (M = 4.5) vs. older (M = 5.5) preschoolers. Participants were 76 preschoolers from four kindergartens who were assigned randomly to two learning conditions. One group was exposed to a multimedia environment with collaborative learning (MCL), and the second group was exposed to collaborative learning without multimedia (CL). Findings indicated that the MCL preschoolers improved significantly on various skills of procedural and conceptual knowledge regarding numbers and operations over the CL preschoolers. Positive effects of the MCL condition were found on both the younger and older preschoolers. However, the younger MCL preschoolers improved their mathematical knowledge more than the older ones. The theoretical and practical implications of collaborative and multimedia learning are discussed.

The effects of metacognitive training versus worked-out examples on students' mathematical reasoning

BACKGROUND

The present study is rooted in a cognitive-metacognitive approach. The study examines two ways to structure group interaction: one is based on worked-out examples (WE) and the other on metacognitive training (MT). Both methods were implemented in cooperative settings, and both guided students to focus on the problem's essential parts and on appropriate problem-solving strategies.

AIMS

The aim of the present study is twofold: (a) to investigate the effects of metacognitive training versus worked-out examples on students' mathematical reasoning and mathematical communication; and (b) to compare the long-term effects of the two methods on students' mathematical achievement.

SAMPLE

The study was conducted in two academic years. Participants for the first year of the study were 122 eighth-grade Israeli students who studied algebra in five heterogeneous classrooms with no tracking. In addition, problem-solving behaviours of eight groups (N = 32) were videotaped and analysed. A year later, when these participants were ninth graders, they were re-examined using the same test as the one administered in eighth grade.

METHOD

Three measures were used to assess students' mathematical achievement: a pretest, an immediate post-test, and a delayed post-test. ANOVA was carried out on the post-test scores with respect to the following criteria: verbal explanations, algebraic representations and algebraic solution. In addition, chi-square and Mann-Whitney procedures were used to analyse cooperative, cognitive, and metacognitive behaviours.

RESULTS

Within cooperative settings, students who were exposed to metacognitive training outperformed students who were exposed to worked-out examples on both the immediate and delayed post-tests. In particular, the differences between the two conditions were observed on students' ability to explain their mathematical reasoning during the discourse and in writing. Lower achievers gained more under the MT than under WE condition.

CONCLUSIONS

The findings indicate that the kind of task and the way group interaction is structured are two important variables in implementing cooperative learning, each of which is likely to have different effects on mathematical communication and achievement outcomes.

Vygotsky and Papert: social-cognitive interactions within Logo environments

The purpose of this study was to examine the effects of co-operative and individualised Logo environments on creativity and interpersonal relationships regarding academic recognition and social acceptance. Participants were 83 students who studied in three eighth grade classrooms: one was exposed to a co-operative Logo environment (N = 30), the other to an individualised Logo environment (N = 24), and the third served as a non-treatment control group (N = 29). Results showed that students in the cooperative Logo environment outperformed their counterparts in the other two groups on certain measures of creativity (figurative-originality, verbal-flexibility, and verbal-originality). In addition, the co-operative Logo group developed more positive interpersonal relationships than the students in the other two settings. The results are discussed from three perspectives: the social-cognitive approach emphasising the roles of co-operation and metacognition in developing advanced thinking skills; the educational-technology viewpoint demonstrating the potential use of computers; and the pedagogical view pointing out the implications of the study to school situations and heterogeneous classrooms.