Explores the co-shaping of public and private discourse and some of the circumstances under which one occasions the other in the evolution of mathematical thinking by pairs of 13-year-olds. Provides evidence that adolescents within novel problem situations can experience some difficulty in making their emergent thinking available to partners in…

According to historical stories, the Saxons placed a bowl with a hole in its bottom in water and used the time it took the bowl to submerge to limit orations. Describes a science activity in which students find a relationship between the diameter of the hole and the time to submergence. (WRM)

Describes a worksheet used by the author to help business communication students get the most out of a set of quantitative data. Describes how the worksheet walks students through a sequence of four activities (orientation, generalization, explanation, and exploration) that help them present and interpret visual data. Discusses benefits to…

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…

The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…

This paper discusses experience with alternative assessment strategies for an introductory course in dynamical systems, where the use of computer algebra and calculus is fully integrated into the learning process, so that the standard written examination would not be appropriate. Instead, students' competence was assessed by grading three large…

Interpretation and construction of graphs are central to the study of physics and to performance in physics. In this paper, I explore the interpretation and construction processes called upon in questions with a graphical component, in Western Australian Physics Tertiary Entrance Examinations. In addition, I list errors made by students as…

The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…

This article describes a unit of instruction designed to promote algebraic thinking in second graders. Students examined second- and fourth-grade students' ages and heights on a table and graph and described the patterns that they observed in the data.

The description about the changed instruction to encourage student exploration of the graphical and then the algebraic representations of functions is presented, which enables the students to understand how the graph, equation, and table of a function are related. The activity addresses both the Learning Principle and the Connection standard and…

This report is part of a long-term research on the construction of mathematical meanings through the interaction with various technologies. The research involved a set of teaching experiments based on body motion with sensors and calculators at different school levels, from kindergarten to secondary school. Here I refer to the one developed in a…

This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, and…

This paper presents an easy and free online tool that has visually enhanced teachers' writing-response pedagogy and helped their students comprehend their composing. Create a Graph is a free and intuitive online data-graphing program developed by the National Center for Education Statistics. In three clicks a visual depiction of weaknesses or…

This document presents a summary of public library statistics collected from fiscal years 1988 through 1993. Statistical information is included on library circulation and interlibrary loan; collections; income; expenditures; expenditures and collections; staff and volunteers; and hours, attendance, reference, and programs. The tables and graphs…

Many testing programs include a section of optional questions in addition to mandatory parts of a test. These optional parts of a test are not often truly parallel to one another, and groups of examinees selecting each optional test section are not equivalent to one another. This paper provides a general method based on missing-data methods for…