Learning to teach mathematics for understanding is not easy. First, practice itself is complex. Second, many teachers' traditional experiences with and orientations to mathematics and its pedagogy are additional hindrances. This paper examines teaching practices and reviews some of what is known about prospective and experienced elementary…

Extracts from financial reports broadcast on two British Broadcasting Corporation (BBC) radio channels are analyzed for cognitive structures that affect the conceptual organization of this discourse type. The approach used for the analysis is based on two assumptions in the relationship of communication and cognition. These are: (1) financial…

This document contains lessons designed for teaching geography and map skills to intermediate level students, although many may be adapted to other grade levels. The lessons place heavy reliance on children making a series of individual and collective maps. The 16 lessons included are: (1) mental maps; (2) conventional maps; (3) map elements; (4)…

Focusing on variables linking fourth graders' reading comprehension and writing ability, a study investigated the (1) relationship between both free recall and comprehension probe scores in reading and analytical scale scores in writing, (2) effects of reading and writing competence on the production of story grammar categories in writing, (3)…

When in childhood concepts about alcohol and drinking begin to develop has just begun to be investigated. A study was conducted to examine cognitive, maturational, and differential exposure influences on the acquisition of concepts about alcoholic beverages in preschool children. Knowledge about alcoholic beverages and drinking was assessed in 65…

In this paper examples of the role of analogical reasoning in expert problem solving are presented. These are intended to show that using an analogy can change an expert's understanding of a problem situation by changing the conceptual model he or she uses to think about the situation. This suggests that using a good analogy may allow students to…

This paper presents evidence to indicate that spontaneously generated analogies can play a significant role in the problem solving process of scientifically trained individuals. In addition, it is suggested that these individuals exhibit more than one method for generating analogies. Ten scientists (representing physics, mathematics, and computer…

In this study 34 spontaneous analogies produced by 16 college freshmen while solving qualitative physics problems are analyzed. A number of the analogies were invalid in the sense that they led to an incorrect answer from the physicist's point of view. However, many were valid, and a few were powerful in the sense that they seemed not only to help…

A model for developing instructional analogies was used to produce experimental treatments that included text from a high school biology textbook to which was added extended verbal analogies written by the researcher linking each of two biology concepts to analogous familiar concepts. The control treatment was text from the biology textbook…

The mathematical experiences of elementary students often focus on memorizing facts and rules as opposed to making sense of the subject and developing problem solving skills. Students spend large amounts of time processing, memorizing and sorting collections of data which are tasks well performed by computer technology. To correct this situation,…

The concept of probability is not an easy concept for high school and college students to understand. This paper identifies and analyzes the students' alternative frameworks from the viewpoint of constructivism. There are various interpretations of probability through mathematical history: classical, frequentist, and subjectivist interpretation.…

The Education Technology Center (ETC) Fractions Group works to investigate well-documented difficulties that children have in understanding fractions. A central assumption underlying this group's inquiry is that students' difficulties in manipulating fractions arise from their lack of understanding about the nature of fractions. In order to learn…

This paper is based on the idea that designing a knowledge representation for an intelligent physics computer tutoring system depends, in part, on the target behavior anticipated from the student. In addition, the document distinguishes between qualitative and quantitative competence in physics. These competencies are illustrated through questions…

Students (N=49) enrolled in a physics course for elementary teachers were evaluated for their abilities to use: (1) combinatorial logic; (2) separation and control of variables; (3) proportional reasoning; and (4) reciprocal implications. Performance of four Piagetian tasks during interviews was treated as a measure of the degree to which students…

A dominant theme in cognitive psychology is that prior knowledge in long-term memory has a strong influence on an individual's cognitive processing. Citing numerous memory studies with children, knowledge base effects are presented as part of a broader picture of memory development. Using the sort/recall procedure (asking subjects to group sets of…