A Sacramento County district successfully combines rigorous standards with civic values and service learning, requires both algebra and geometry, and helps students pass the high school exit exam. The community has been involved in raising standards and developing accelerated learning programs at all 29 elementary schools. (MLH)

In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple[R], which provides the means…

We present the design principles for a new kind of computer system that helps students learn algebra. The fundamental idea is to have a system based on the microworld paradigm that allows students to make their own calculations, as they do with paper and pencil, without being obliged to use commands, and to verify the correctness of these…

This article presents teaching ideas designed to support the belief that students at all levels (preservice teachers, majors, secondary and elementary students) need exposure to non-routine problems that illustrate the effective use of technology in their resolution. Such use provides students with rapid and accurate data collection, leading them…

This study examined practices of teachers in Wake County Public Schools (WCPSS) high school Algebra I classes. Regression analyses of standardized state testing results allowed for identification of the most effective and least effective Algebra I teachers and schools. The study used surveys, observations, and focus group interviews to compare and…

The term "numeracy" is used in the adult education community to include an array of mathematically related proficiencies that are evident in adults' lives and worthy of attention in adult education settings. This occasional paper attempts to describe the complex nature of numeracy as it exists today. All stakeholders--including policymakers,…

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…

Using symbolic algebra to represent and solve linear equations is one of the expectations within the "Algebra" content standard for the 6-8-grade band in the National Council of Teachers of Mathematics (NCTM) "Principles and Standards for School Mathematics" (2000). Students' understanding of these concepts, even before a formal algebra course,…

Although the myth of public education as the "great equalizer" is alive and well in the minds of many, the reality is that the notion of public schools as the savior of the less fortunate is fundamentally compromised when institutional decision making does more to suppress low-income and minority students through low expectations…

This exploratory study applied two new cognitively sensitive measurement models to constructed-response quantitative data. The models, intended to produce qualitative characteristics of examinee performance, were fitted to algebra word problem solutions produced by 285 examinees taking the Graduate Record Examinations (GRE) General Test. The two…

This study evaluated expert system diagnoses of examinees' solutions to complex constructed-response algebra word problems. Problems were presented to three samples (30 college students each), each of which had taken the Graduate Record Examinations General Test. One sample took the problems in paper-and-pencil form and the other two on computer.…

This updated reprint of a classic work presents design analysis of geometric patterns and information helpful to constructing mathematical drawings of industrial and achitectural features. Both simple and complex designs are given. Problems combine both algebra and geometry. The work is divided into six chapters which are further divided into…

There has been concern over the validity of the Algebra Diagnostic Test (ADT) used to determine the actual level of student preparation for the first quarter of calculus as taught at the University of California, Santa Barbara. It has been hypothesized that performance-based questions, along with the more traditional multiple choice questions,…

This study explores seventh- and eighth-grade students' thinking about mathematical patterns. Interviews were conducted in which students solved problems about sequential perimeter and area problems modeled with pattern blocks and tiles, generalized the relationships related to the patterns and represented the relationships symbolically,…