This paper compares the way lessons on systems of linear equations unfold in a classroom in the Negev region of Israel with the way they unfold in a Shanghai and Hong Kong classroom. Lessons are viewed as temporal entities describable not only by the nexus of topics they contain but also by how they flow in time. In this light, the lessons in the…

The purpose of this paper is to offer a framework for categorizing and describing the different types of processes that undergraduates use to construct proofs. Based on 176 observations of undergraduates constructing proofs collected over several studies, I describe three qualitatively different ways that undergraduates use to construct proofs. In…

This paper compares a number of different Computer Algebra Systems (CAS) in their solution of one-step and multi-step problems. The CAS programs considered include DERIVE, Maple, Mathematica, and MuPAD while the problems are taken from the final examinations of grades 9 and 12 in Estonian schools. The different outputs to one-step problems with…

The choice of teaching an effective method--one that most students can master--or an efficient method--one that takes the fewest steps--occurs daily in Algebra I classrooms. This decision may not be made in the abstract, however, but rather in a ready-to-hand mode. This study examines how teachers solve linear equations when the purpose is…

The percentage of high school students passing the first semester Algebra 1A final exam in January 2000 dropped precipitously from the passing rate one year earlier. That decline in final exam passing rates was due largely to the adoption among all schools of a uniform algebra exam combined with a system-wide uniform grading scale. High school…

This book contains volume 1 of the proceedings of the 23rd annual meeting of the International Group for the Psychology of Mathematics Education (PME) held October, 2001 in Snowbird, Utah. Papers include: (1) "Opening the Dimensions of Mathematical Capability: The Development of Knowledge, Practice and Identity in Mathematics Classrooms"…

This two volume collection of proceedings contains working group reports, research reports, oral reports, poster session reports and discussion group reports presented at PME-NA 21. Only the plenary and research reports are full reports; the others are brief abstracts. Full reports include: (1) "Representation, Vision and Visualization:…

The effect of calculator type on student performance on a mathematics examination was studied. Differential item functioning (DIF) methodology was applied to examine group differences (calculator use) on item performance while conditioning on the relevant ability. Other survey questions were developed to ask students the extent to which they used…

By measuring the performance of 62 students enrolled in a community college introductory algebra course, this study challenges the generally accepted assumption among mathematics instructors that mastery of arithmetic is necessary for the learning of algebra. Study subjects were 35% male, 74% Hispanic, 16% Black, 8% white, and 2% other. A pretest,…

Methods of effectively teaching algebraic thinking in elementary schools as well as secondary schools is the topic of the following 19 papers. Papers include: (1) "Transforming Algebra from an Engine of Inequity to an Engine of Mathematical Power by 'Algebrafying' the K-12 Curriculum" (J. Kaput); (2) "Developing a Coherent and…

The ability to use algebra in describing and analyzing real-world situations is becoming a basic skill for all students. The main focus of this book is on patterns, functions, and relationships. Information and ideas on how algebraic thinking can be developed in the years leading to a formal algebra course are included. K-8 teachers are offered a…

This book features a set of problems assembled to reflect the criteria of the mathematics portion of the North Carolina High School Comprehensive Test. The problems are not necessarily suited to timed situations but rather are intended for classroom use by teachers to review high school mathematics and build upon concepts and skills developed in…

As a learning theory, constructivism describes knowledge as being in flux--where an individual internally constructs knowledge through social and cultural mediation. Constructivist learning theorists contend that social activity and discourse must play important roles in order for understanding to occur. This paper describes how the social…

Constructivism is considered a driving force in mathematics education. The purpose of this paper is to describe how the social constructivist view of learning can be useful in the teaching of high school algebra and in the preparation of mathematics teachers. A brief summary of the social constructivist view as a philosophy of mathematics is…

Students undertaking mathematics courses in their final year of secondary education in Victoria are assessed using a combination of school based coursework assessment and examinations. Over the last decade, students have used technology such as graphics calculators, statistical software, spreadsheets, and computer algebra systems (CAS) extensively…