This research study deals with the modes of representation that ninth-graders choose in order to communicate their problem solving paths and justifications, and the relation between these modes of representations and achievement level. The findings are based on analysis of 350 answers to problems that demanded communication of reasoning,…

The study proves that a didactical model based in a method to solve word problems of increasing complexity which uses a numerical approach was essential to develop the analytical ability and the competent use of the algebraic language with students from three different performance levels in elementary algebra. It is shown that before using the…

We deal with the study of the senses and the meanings generated in the representation of the unknowns in the resolution of word problems involving two unknown quantities. The discussed cases show the difficulties that the students beginning the algebra learning have to deal with when using the equality between "unknown things". For them,…

In this report, we establish benchmarks of readiness for four common first-year college courses: English Composition, College Algebra, Social Science, and Biology. Using grade data from a large sample of colleges, we modeled the probability of success in these courses as a function of ACT test scores. Success was defined as a course grade of B or…

This project focuses on the construction and use of a student-made elementary algebra tutorial World Wide Web page at the University of Memphis (Tennessee), how this helps students further explore the topics studied in elementary algebra, and how students can publish their work on the class Web page for use by other students. Practical,…

This CD-ROM is a teacher resource for standards-based Algebra 1 in the middle and secondary grades. There are three components on the CD including mathematical content, instructional strategies, and assessment. Components include: (1) video clips of Algebra 1 students; (2) commentaries about each video clip; (3) frequently asked questions and…

This collection of activities is intended to enhance the teaching of college algebra through the use of modeling. The problems use real data and involve the representation and interpretation of the data. The concepts addressed include rates of change, linear and quadratic regression, and functions. The collection consists of eight problems, four…

This study explores a program designed to revolutionize developmental mathematics at the college level using the new handheld computer algebra systems and new information about the ways in which students learn mathematics. Students in one class of developmental algebra worked with the new approach to learn algebra by building on their intuitive…

We explore how fourth grade (9 to 10 year olds) students can come to understand and use the syntactic rules of algebra on the basis of their understanding about how quantities are interrelated. Our classroom data comes from a longitudinal study with students who participated in weekly Early Algebra activities from grades 2 through 4. We describe…

During several years of experimentation, we accumulated a large collection of data on the analysis of problems generally encountered in algebra and on the reasoning developed by students at different levels when confronted with these problems. Analysis of this data led us to a new way of looking at differences among word problems, and to the…

This paper reports on the first stage of a research project still in progress aiming at identifying undergraduate students' difficulties and errors in solving linear algebra problems. Some students' difficulties related to very basic notions of vector space theory are shown and discussed with respect to both Balacheff's theory of conceptions and…

In this paper we analyze the meanings of the "equal" sign as generated by sense production of the methods of substitution and comparison for solving problems and systems of equations of two unknowns. These methods are usually introduced through an extension process of the syntax and meanings recently learned by students in order to solve…

This proceedings of the annual conference of the North American Chapter of the International Group for the Psychology of Mathematics Education includes the following papers: "Affective Representation and Mathematical Problem Solving" (Goldin); "Cognitive Readiness and Process-Oriented Instruction in Secondary School Mathematics" (Harrison); "An…

The purpose of this study was to investigate the effects of the Casio 9850 and the TI-85 graphing calculators on college students' procedural skills and conceptual understanding in two different developmental mathematics courses. The courses used in this study were Elementary Algebra and Intermediate Algebra. Both the non-graphing calculator group…

"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…