Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

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…

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)…

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…

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 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…

Considers variables which affect the acquisition of the kinetic theory of heat by children who hold alternative viewpoints. Suggests that the articulation of different viewpoints in no way hinders the acquisition of the desired conceptual framework. Emphasizes the benefit to low-reasoning students in particular. (CW)

Discussed is the philosophy of the educational purpose of science education, the science involved, and the relationships of students and learning and students and content. A list of 14 references is included. (CW)

Reports on the assessment of student thinking in the area of commitment to the laws of conservation of matter and energy during a study of conceptual change among introductory chemistry students. States four conditions upon which strategies for conceptual change are based. (RT)

The importance of instructing gifted students in correlational reasoning is emphasized, with attention to what the skill involves and why it is difficult to learn; effective teaching strategies; and successful programs in whole-class, cooperative-learning, and computer formats. Implications in programming for gifted students are discussed. (SW)

The degree to which today's college students overcome tomorrow's challenge of knowledge obsolescence depends in part on higher education's teaching them how they learn what they learn. The Analysis of Learning Project, used in both undergraduate and graduate business administration courses, is designed to help students understand how they learn.…

The contrast between the teaching of reading and mathematics is drawn. A new set of learning conditions for mathematics is presented based on a model of reading instruction. Immersion, demonstration, engagement, expectations, responsibility, use approximation, response, refinement, and outcomes are discussed. (CW)