After years of implementing Interactive Math, many California school districts have bowed to parental pressure and returned to a traditional mathematics curriculum. Reforms are catching on in Texas, Ohio, Arkansas, South Carolina, and New Jersey. The white/minority SAT score gap remains wide. The National Council of Teachers of Mathematics 1990…

Describes how a mathematical model can be constructed and used to better understand human impact on natural resources. Uses the source of many current discussions in northern Idaho to present algebraic concepts and show an application of exponential functions. Contains 13 references. (ASK)

Describes a hands-on, guided-learning activity that forges vertical connections among grade levels and relies on physical models in the investigation of algebraic concepts. This lesson helps students discover that a given value can have multiple representations. Includes a sample student activity log. (AIM)

Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as…

Describes how various projects helped middle school students build mathematical conclusions through algebraic thinking as they used number patterns and verbal rules to explore the interrelationships of representations. Suggests some topics for projects. (AIM)

Describes an activity using M&M's in an algebra class after instruction in solving equations that actively involves students in identifying the variable, formulating an equation, then solving the equation. (AIM)

Examines possibilities for learning offered by a piece of software, Fonctuse, likely to encourage the linking of algebraic and graphical representations of functions. Studied the influence of prior algebraic knowledge on the cognitive processes and constructions of knowledge at play in this environment. (Author/MKR)

Four human judges agreed highly among themselves about the presence of errors committed by 60 adults solving algebra word problems, but were in less agreement about categorizing faults. An expert system agreed with judges about correctness of answers, but was in even less agreement about categorizing the faults. (SLD)

Reports on a case study of one student's pattern of engagement in an 8th grade algebra class. Argues both empirically and theoretically that none of the current theories of engagement and motivation serve to characterize the core of this student's decision about engagement: his affective assessment of mathematics. (Author/MM)

The expertise reversal effect occurs when a learning procedure that is effective for novices becomes ineffective for more knowledgeable learners. The authors consider how to match instructional presentations to levels of learner knowledge. Experiments 1-2 were designed to develop a schema-based rapid method of measuring learners' knowledge in a…

The purpose of this study was to examine how various opportunity to learn (OTL) variables impact student outcomes and whether these effects are consistent across different subject areas. In this study, we examined the impact of OTL variables on student performance on English and algebra assessments. Despite the differences in the subject areas, 3…

This article describes ways in which students develop schemas as they generalize and formalize patterns when solving related algebraic problems that involve size, shape, growth, and change. (Contains 7 figures and 3 tables.)

Working from Carolyn Kieran's categorization of "arithmetic" and "algebraic" thinkers, the article describes one eighth-grade "arithmetic" thinker's progress as she attempts to solve one- and two-step equations.

Algebraic thinking in the middle grades involves constructing generalizations, moving beyond the focus of specific calculations in elementary school. This creates exciting opportunities to examine the validity of general arguments. Creating rich mathematical tasks and asking questions related to justification encourages students to examine what…

Many students have traditionally found the processes of algebraic manipulation, especially factorisation, difficult to learn. This study investigated the value of introducing students to a Vedic method of multiplication of arithmetic numbers to algebra that is very visual in its application. This research considered a possible role of the…