Discussed is the question of teachers' knowledge about mathematical topics. The building of an analytic framework of subject matter knowledge for teaching the topic of functions in mathematics is demonstrated. Discussed is the construction of mathematics courses prospective mathematics teachers take. (KR)

Reported are the effects of a conceptually oriented unit on decimal fractions. The relationships between short-term changes in solving processes and the stability of these processes over time, performance of students, and entry achievement level and the long-term effects of conceptually based instruction are discussed. (KR)

Defines the mathematical concept of proportionality. Uses graphs of linear relationships to explore and make generalizations about the characteristics of proportional situations to help students critically evaluate problems involving proportions. (MDH)

Discusses a pedagogical approach to calculus based on the question: What kinds of problems should students be able to solve? Includes a discussion of types of problems and curriculum threads for such a course. Describes a projects-based calculus with examples of projects and classroom activities. (Author/MDH)

Described is a theorem which is generally not present in most high school geometry textbooks. Presented are two proofs and two cases which illustrate the use of the SSA theorem. (CW)

Problem-solving strategies which use reflective thinking and inference in mathematics are discussed. Examples are provided with discussions of the learning process. The advantages of this approach are stressed. (CW)

Presents calendars for the months of May, June, July, and August that contain problems and projects to be done for almost every day of the month. Provides instructions on how parents can utilize the calendars. (MDH)

The article discusses the ways that less successful mathematics students used graphing software with capabilities similar to a basic graphing calculator to solve algebra problems in context. The study is based on interviewing students who learned algebra for 3 years in an environment where software tools were always present. We found differences…

We previously conducted a curriculum analysis of third-grade mathematics textbooks aimed at investigating the extent to which teaching the recommended methods for problem solving adhered to the 2000 National Council of Teachers of Mathematics (NCTM) Standards and instructional design criteria. In this article, we extend the previous findings by…

fMRI was used to examine the differential effect of two problem-solving strategies. Participants were trained to use both a pictorial/spatial and a symbolic/algebraic strategy to solve word problems. While these two strategies activated similar cortical regions, a number of differences were noted in the level of activation. These differences…

Purpose: The literature indicates the advantages of decisions formulated through intuition, as well as the limitations, such as lack of consistency in similar situations. The principle of consistency (invariance), requiring that two equivalent versions of choice-problems will produce the same preference, is violated in intuitive judgment. This…

The "Thinking Mathematics" approach to teaching is guided by two ideas: (1) that learning requires knowledge upon which new problems and situations are interpreted and (2) that mathematics skills are applied in context. This paper reports research that examined whether teaching mathematics students in high school remedial classes can be…

This document is designed to assist teachers by providing practical examples of real world applications of high school mathematics. Fifteen problems are presented that individuals in industry and business solve using mathematics. Each problem provides the contributor's name, suggested skills required to solve the problem, background information…

This publication compiles a series of 18 articles originally published in 1989-91 in the Arithmetic Teacher on implementing the National Council of Teachers of Mathematics (NCTM) K-8 curriculum standards. The articles and references in the bibliography are organized into five groupings: (1) "Themes That Cut Across Mathematics," covering…

Although many common problem-solving errors within the realm of school mathematics have been previously identified, a compilation of such errors is not readily available within learning disabilities textbooks, mathematics education texts, or teacher's manuals for school mathematics texts. Using data on error frequencies drawn from both the Fourth…