The empirical data in this study are from a series of two lessons on measurement implemented in seven classes with 119 six-year-old students in Sweden. Both problem solving and problem posing were shown to be important in early mathematics when students in this study worked on one problem-solving task and one problem-posing task on measurement. As…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

This collection of 58 articles from the recently-published third edition of the International Encyclopedia of Education focuses on learning, memory, attention, problem solving, concept formation, and language. Learning and cognition is the foundation of cognitive psychology and encompasses many topics including attention, memory, categorization,…

The strength of intuitive knowledge is illustrated by the difficulty that individuals have in trying to restructure student misconceptions. In order to harness this power, intuition must be developed within the context of each new concept to be taught. An experiment with one possible approach to this instructional problem is described and…

Because previous research by Bayman and Mayer (1983) suggests that individuals who attempt to learn their first computer language develop a variety of misconceptions of the meanings of individual programming statements, this study investigated whether it is possible to enhance beginning programmers' understanding of the programming statements…

In general, people seem to be poor at noticing analogies, especially when they are required to apply an analogy to a domain that is new. It was suspected that schemas influence the noticing and applying of analogies. Schemas are hypothesized to be abstract propositional structures that emphasize relationships among categories of objects rather…

Research has not clearly determined whether memory development in childhood and adulthood can be accounted for by the age variation of cognitive processes other than memory. To examine this issue, a study was conducted based on a model of structures and processes in complex information processing. Subjects (N=162) were presented with two lists of…

Gifted secondary students not only solved problems better, faster, and with less assistance than average pupils, but also processed information in a different fashion. (MNS)

College students (N=135) were presented with novel, ill-defined problems and asked to select concepts they thought would help solve the problems. The use of concepts organized around long-term goals was positively related to indices of solution quality and originality. (DB)

The research described in this paper leads to an instructional design approach which is an alternative to the consideration of such issues as mathematical skills or level of cognitive development. The approach uses an analysis of traditional instructional tasks to specify the underlying cognitive processes and structures necessary for the…

This paper is a preliminary inquiry by a non-mathematician into graphic methods of sequential planning and ways in which hierarchical analysis and tree structures can be helpful in developing interest in the use of mathematical modeling in the search for creative solutions to real-life problems. Highlights include a discussion of hierarchical…

Explores how a set of possible student misconceptions about solving a complex problem can be used in computer-based intelligent tutoring systems and in computer-based exercise and test generation. Topics discussed include expert systems, misconception covers, discrimination trees, methods of acquiring the set of misconceptions, and protocol…

A study investigated the effectiveness of using a small-group discussion as the main vehicle for the construction of an initial representation of a problem that activates previously acquired knowledge. College students (N=39) were randomly assigned to either an experimental condition or a control condition and asked to brainstorm about a presented…

The focus of this document is on students' understanding of symbolization processes in algebra, and specifically their understanding of semantically laden letters. In the first four sections, four inappropriate ways in which many college students use semantically laden letters are described. Evidence from clinical interview protocols demonstrate…

Seventy-one college general biology students were taught a unit in Mendelian genetics by the traditional lecture method. Emphasis was placed on meiotic formation of gametes, dominance, segregation, and independent assortment. The Punnett square model was used for all practice problems. While using this model, students were asked to: (1) identify…