Shares detailed episodes of children's work in repeatedly partitioning geometric shapes to highlight the process of recursion, which can lead to a deeper understanding of imagination and beauty in children's mathematics. (MKR)

Investigates the effects of an instructional intervention derived from the Garofalo and Lester cognitive-metacognitive framework on the problem-solving performance of year six students with different ability levels. Concludes that there was significant improvement in problem-solving performance for the experimental class compared to the control…

Investigates 55 6th grade students' conceptions of "invention and patent processes". Suggests that students have few or simplistic conceptions of invention and patent processes and prior exposure to invention instruction, or previous experiences with inventing did not appear to have an impact on students' conceptions of invention. (Contains 70…

Investigates 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Describes students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra. (Contains…

This study developed a web-based multimedia whiteboard system to help students learning with mathematical problem solving. The purpose is to promote a new online mathematical learning model that students not only use electronic whiteboard to write down their mathematical problem solving solutions but also use voice recording tool to give oral…

Associations between reciprocal and complementary sibling interactions, sibling relationship quality, and children's socio-emotional problem solving were examined in 40 grade 5-6 children (M age = 11.5 years) from middle class, Caucasian, Canadian families using a multi-method approach (i.e. interviews, self-report questionnaires, daily diary…

The study developed a Big 6 Information Problem-Solving Scale (B61PS), including the subscales of task definition and information-seeking strategies, information access and synthesis, and evaluation. More than 1,500 fifth and sixth graders in Taiwan responded. The study revealed that the scale showed adequate reliability in assessing the…

Open-ended tasks were used to examine gender differences in complex mathematical problem solving. The results of this study suggest that, overall, males perform better than females, but the gender differences vary from task to task. A qualitative analysis of student responses to those tasks with gender differences showed that male and female…

The use of a visual representation in learning about proportional relations was studied, examining students' understandings of the invariance of a multiplicative relation on both sides of a proportion equation and the invariance of the structural relations that exist in different semantic types of proportion problems. Subjects were 49 high-ability…

This paper describes the instructional design activities used to create ThinkAbout, a video series meant to teach fifth and sixth graders skills essential for learning, i.e., inquiring, analyzing, synthesizing, seeking alternatives, and creative problem solving. Two basic tenets or underpinning statements served as guidelines for the development…

Forty fifth and sixth graders, matched on sex and measures of test anxiety, defensiveness, and IQ, were divided into two groups, each of which solved Porteus maze tasks and a marble puzzle, with and without memory support, respectively. An anxiety-by-memory support interaction occurred in the number of errors made prior to solving the marble…

Examines the teacher's role in computer-based problem solving using sixth grade students and a computer program called Rocky's Boots. Ways in which the program could be used in thinking skills programs are discussed, program improvements are suggested, and teacher intervention is identified as a critical element in computer-based training. (LRW)

One of the aims of mathematics instruction is to achieve the understanding of mathematical concepts through the development of rich and well organized cognitive representations (Goldin, 1998; NCTM, 2000; DeWindt-King, & Goldin, 2003). In this study the term representation is interpreted as the tool used for representing mathematical ideas such…

This report investigated to what extent a curriculum designed to actively teach critical thinking skills resulted in students utilizing higher-order thinking skills (e.g., analysis, synthesis and evaluation). An intervention strategy was designed for a sixth grade class located in a diverse suburban community in northern Illinois. The intervention…

Research was viewed as needed to establish a classification scheme for the major areas of difficulties individual students have in solving word problems. The results suggest that inability to read problems is a major obstacle for sixth graders, and mastery of components of problem solving ensures process mastery. (MP)