Generalization is critical to mathematical thought and to learning mathematics. However, students at all levels struggle to generalize. In this paper, I present a theoretical analysis connecting Piaget's assimilation and accommodation constructs to Harel and Tall's (1991) framework for generalization in advanced mathematics. I offer a theoretical…

The body of research examining students' graphing understandings across STEM fields indicates students are not developing productive meanings for graphs. We conjecture such failings may, in part, be explainable by features of students' use of coordinate systems and graphing activity that are under examined. In this theoretical report, we present a…

This paper aims to contribute to discussions on the multimodal nature of cognition through an elaboration of the ways multimodal aspects of thinking are exploited by learners doing mathematics. Moving beyond the fact "that" multimodality occurs, this paper focuses on "how" it occurs, with particular attention drawn to the…

Box plots are frequently used, but are often misinterpreted by students. Especially the area of the box in box plots is often misinterpreted as representing number or proportion of observations, while it actually represents their density. In a first study, reaction time evidence was used to test whether heuristic reasoning underlies this…

The article provides a review of recent research on human performance on the traveling salesman problem (TSP) and related combinatorial optimization problems. We discuss what combinatorial optimization problems are, why they are important, and why they may be of interest to cognitive scientists. We next describe the main characteristics of human…

This study analyzes the interpretive activities of scientists related to familiar and unfamiliar graphs. The analyses show that when scientists were familiar with a graph, they read it transparently and thereby leapt beyond the material basis to the thing the graph is said to be about. In contrast, when scientists were less familiar with the…

In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graph interpretation skills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's…

This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

Uses a brief fictional narrative to discuss how visual media frequently offer a superior alternative to prose for the communication of some kinds of information, specifically, to describe; represent abstract structures; convey spatial relationships; provide a meaningful context for unfamiliar information; assist readers in their attempts to solve…

The eight articles and two commentaries of this theme issue indicate the main lines of thinking represented at a symposium on the comprehension of graphics in text. The common assumption is that graphics per se do not have a direct effect on learning results but are effective only when processed adequately. (SLD)

Describes and compares three approaches to task analysis--behaviorally-based, concept-based, and cognitive process-based--and provides four tentative recommendations for determining which approach is appropriate in a particular situation. Five flowcharts and fourteen references are included. (MBR)

This article presents research on students' understanding of basic concepts in Graph Theory. Students' understanding is analyzed through the lens of the theoretical framework of reducing abstraction (Hazzan, 1999). As it turns out, in spite of the relative simplicity of the concepts that are introduced in the introductory part of a traditional…

Examines research on computers as cognitive enhancers, focusing on applications software that includes spreadsheets, graphing, and databases. Appropriate computer-based problem-solving environments for young children are reviewed, and implications for teachers are suggested. (Contains eight references.) (LRW)

This study examines how task characteristics (the number of visual chunks and the amount of planning time) and test-taker characteristics (graph familiarity) influence the perceptual and cognitive processes involved in graph comprehension, the strategies used in describing graphs, and the scores obtained on the graph description task in a…

The purpose of this study was to assess fourth- and fifth-grade students' (9- and 10-year-olds') affective response and ability to discriminate between melody and improvisation after receiving instruction in singing and/or playing a piece in the blues style. Subjects (N= 102) were assigned to one of three equal-sized groups. Group 1 learned to…