Given its important role in mathematics as well as its role as a gatekeeper to future educational and employment opportunities, algebra has become a focal point of both reform and research efforts in mathematics education. Understanding and using algebra is dependent on understanding a number of fundamental concepts, one of which is the concept of…

T-algebra is a project for creating an interactive learning environment for expression manipulation tasks of elementary algebra. Our main didactical principle has been that all the necessary decisions and calculations at each solution step should be made by the student, and the program should be able to understand the mistakes. This paper…

The adequacy of several approaches to estimation of proficiency distributions for the Trial State Assessment (TSA) in eighth grade mathematics of the National Assessment of Educational Progress was examined. These approaches are more restrictive than the estimation procedures originally used, with the same kind of plausible-values approach that…

Studies were conducted to identify critical barriers which could impede the progress of Hispanic undergraduates enrolled in science and engineering programs. The underlying theme in most studies was the interplay of language in various problem-solving tasks. Studies examined: (1) predictors of academic achievement (as measured by grade point…

In this article, the authors seek to re-conceptualize the perspective regarding students' difficulties with algebra. While acknowledging that students "do" have difficulties when learning algebra, they also argue that the generally espoused criteria for algebra as the ability to work with the syntactical rules for solving equations is…

The shortcomings of the conventional way of using and interpreting multiple-choice tests are summarized. Some theories and methodologies that can be applied for better use multiple-choice test items are described. Empirical facts are introduced to support the theoretical observations. New strategies are proposed that will reduce "noise"…

This issue of the journal contains abstracts and critical comments for 10 published reports on research in mathematics education. The reports concern children's school mobility and achievement, preservice teachers' sources of decisions, spatial visualization in boys and girls, rote versus conceptual emphases in teaching probability, using drawings…

Over the past 15 years a body of research has investigated organizational transitions in adolescent development. Researchers studying school transitions exclusively ask whether significant transition affects students' social and psychological development. To test the presence of transition effects, researchers have typically observed mean…

Describes one teacher's reflection concerning the quest to develop an understanding of school mathematics that promotes and sustains students' opportunities for exploration and conjecture. Recounts that a particular student's exploration of the features of parabolas eventually led to an understanding of the quadratic formula precisely because of…

Integrates mathematics and science by investigating the scientific application of the Polynomial Difference Theorem using data points from an experiment. Utilizes the different capabilities of the graphing calculator to investigate a problem whose solution is a second degree equation and makes connections between the mathematical concepts involved…

Demonstrates how to construct rational, exponential, and sinusoidal functions that appear normal on one scale but exhibit interesting hidden behavior when viewed on another scale. By exploring these examples, students learn the importance of scale, window size, and resolution effects in computer and calculator graphing. (MAZ)

Stresses using the features of graphing calculators to teach parametric equations much earlier in the curriculum than is presently done. Examples using parametric equations to teach slopes and lines in beginning algebra, inverse functions in advanced algebra, the wrapping function, and simulations of physical phenomena are presented. (MAZ)

This study (N = 48) examined the relationship between preservice secondary teachers' subject-matter expertise in mathematics and their judgments of students' algebra problem-solving difficulty. As predicted by the "expert blind spot" hypothesis, participants with more advanced mathematics education, regardless of their program affiliation or…

If labor market phenomena are interpreted from an allocational point of view, where individuals differing in levels of various capabilities have to be matched with jobs differing in job requirements, education can be seen as an intermediary institution affecting the capability endowment of individuals upon entering the labor market. Vertical…

A nationally standardized dropout definition will be of little practical value unless it can be related to the structure, practices, and processes of a given school. A proposed measure of school completion and school leaving called the High School Holding Power Index is described. The index is built on these assumptions: (1) there is a…