In mathematics education, representations are used in place of mathematical structures, ideas, or relationships to concretize, transform, and represent them. When students interact with these representations, they engage in various cognitive activities such as thinking, reasoning, understanding, remembering, problem-solving, attention, and…

This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures…

In this paper, Simon describes contemporary information processing approaches to the study of learning and thinking, and discusses the relevance of these studies to the distinction between rote and meaningful learning. Before defining the basic terminology of information processing research, he provides a brief literature review, describing some…

This study investigated five ability tests related to the water-jug problem. Previous analyses identified two processes used during solution: means-ends analysis and memory of visited states. Subjects were 240 undergraduate psychology students. A real-time computer system presented the problem and recorded responses. Ability tests were paper and…

This report contains four papers describing research based on the view of mathematical knowledge as a hierarchy of "rules." The first paper: "The Role of Rules in Behavior" was abstracted in ED 040 036 (October 1970). The second paper: "A Theory of Mathematical Knowledge" defends the thesis that rules are the basic building blocks of mathematical…

The conditions under which explicit instruction in checking, combined with worked examples, may be beneficial in learning how to translate sentences into algebraic equations was examined from the perspective of cognitive load theory. In two experiments it was shown that Grade 8 and 9 students were initially disadvantaged by the inclusion of a…

This paper reports an experiment designed to test theoretical relations among fast problem solving, more complex and slower problem solving, and research concerning fundamental memory processes. Using a cathode ray tube, subjects were presented with propositions of the form "Y is in list X" which they memorized. In later testing they were asked to…

In order to study children's strategies for solving geometric matrices similar to those in the Raven's Progressive Matrices, ninety 7-, 10-, and 13-year-old boys and girls were administered tests of auditory and visual memory, the Raven's, and geometric matrices. The matrices varied in number of elements (1 to 3) and number of transformations (0…

Cognitive development during each of the major stages identified by Piaget is characterized by abilities to solve progressively more complex tasks (e.g., changes in the object concept during the sensori-motor stage, and in conservation of amount, weight, and volume during the concrete operational stage). Several theorists have suggested that these…

The BrainLink project offers educational materials focusing on current neuroscience issues with the goal of promoting a deeper understanding of how the nervous system works and why the brain makes each individual special while conveying the excitement of "doing science" among upper elementary and middle school students. Project materials engage…

An interview protocol was devised to determine whether demands on working memory are reduced by the use of drawn or telegraphic formats. Students were chosen because some aspect of their group testing on presentation formats was provocative (e.g. high spatial score, but low reading comprehension score; high drawn score and low verbal score, etc.).…

The purpose of this study was to determine whether students from different academic settings differ in their usage of metacognitive strategies in mathematical problem solving, and if they do, what the differences are. A questionnaire was administered to students at various levels from academic tracks and academic streams requiring them to…

Predictors of retrieval times produced by students having difficulty developing a reliance on retrieval for simple addition were discovered. The findings support the notion that separate limitations operate in working memory when retrieval occurs and call into question the use of the term "retrieval deficit" to explain difficulties…

Presents two teaching ideas for mathematics instruction. The first employs "mind maps" as a method to help students learn, record, and recall mathematical information. Provides examples for solving quadratic equations and complex numbers. The second discusses two ways to find the average speed during a trip employing differing constant…

Investigated the effects of student working-memory capacity, preference for amount of instruction, spatial problem-solving ability, and school mathematics grades on eighth graders' recall of factual information and conceptual understanding. Pairs of students worked through 16 activities using a dynamic, computer-based geometry program. Presents…