This book consists of a series of activities aimed at providing a problem solving, hands-on approach so that students can experience concepts in algebra. Topics include ratio and proportion, patterns and formulas, integers, polynomials, linear equations, graphs, and probability. The activities come in the form of reproducible blackline masters…

This book was written as a resource for middle and high school teachers hoping to ease their students' transition to algebra. Drawing on experiences with three professional development programs, key "habits of thinking" that characterize the successful learning and use of algebra are outlined. Strategies teachers can use to cultivate…

This paper presents a developmental model of students' acquisition of competence in quantitative and algebraic problem solving. A key notion underlying the developmental model is a distinction between grounded and abstract representations. Grounded representations, like story problems, are more concrete and familiar, closer to physical objects and…

Recent reports have pointed to the need for teachers to have "deep understanding" of concepts and procedures in school mathematics, particularly those related to functions. However, previous research has demonstrated that many students, including preservice teachers, have limited understanding of functions. This paper describes a set of nonroutine…

Which manual calculation skills are still needed when students use graphic/symbolic calculators or computers with computer algebra systems (CAS)? What should students be able to do manually, i.e. just using paper and pencil? This text is the outcome of a two-day discussion on these questions, held by the four authors. Our answers and proposals are…

The purpose of this study was to determine if the use of Learning Logic, an integrated-learning system, by high school students in Algebra I had a significant effect on the performance of these students when they subsequently enrolled in a traditionally taught Algebra II course. Four high schools were selected in which Learning Logic was used for…

The observations of a five-year-old girl about the mutliplication tables are presented. The results are compared to structures in modern algebra. The incident is suggested as an example of Bruner's hypothesis: Any subject can be taught effectively in some intellectually honest form to any child at any stage of development. (LS)

The purpose of this study was to develop a device for predicting student success in a high school Elementary Algebra course. It was intended to assist guidance counselors in advising students in selecting the most appropriate mathematics course. (Editor)