This is the second of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. In Part I, I discussed the formation of arithmetical units and composite…

In recent years computer algebra systems (CAS) have become an integrated part of the upper secondary school mathematics program. Despite the many positive possibilities of CAS, there also seems to be a flip side of the coin in relation to actual difficulties in learning mathematics, not least because a strong dependence on CAS for mathematical…

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

Many mathematics teachers struggle to support their students' developing understanding of proof as an essential element in investigations of mathematics. The area of mathematics where the development of an understanding of proof is most challenging is algebra. In the case of algebraic proof, analysis of student written work on tasks that demand…

This paper examines various cognitive strategies applied while CAS (Computer Algebra System) are used in undergraduate-level engineering mathematics teaching and learning. We posed some questions in relation to such CAS use: What kind of tools can CAS offer to enhance different cognitive strategies of students? How can the use of CAS widen the…

This study investigates algebraic reasoning and self-regulation skills among elementary school teachers who participated in a professional development program either with IMPROVE metacognitive questioning (PD + Meta) or with no metacognitive guidance (PD). Sixty-four Israeli teachers participated in a 3-year program designed to enhance…

Considers various aspects of teaching and learning stemming from the integration of graphing calculator use in a semester-long college algebra course. Argues that technology use has had a positive impact on various dimensions of student learning. (Author/CCM)

This report summarizes findings on strategies chosen by students (n=38) when solving algebra problems related to various functions with the freedom to use a TI-83 graphing calculator, influences on student problem-solving strategy choices, student ability to approach algebra problems with use of multiple representations, and student beliefs on how…

A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…

This research report describes the findings of a study on teachers' ways of interpreting student responses to tasks involving equivalent expressions. The teachers in this study were engaged in model-eliciting activities designed to promote the development of their knowledge and reveal their models (or interpretations) of their students' algebraic…

College students' strategies to discriminate relevant from irrelevant information in algebra story problems were identified and compared to strategies used by younger students in previous studies. College students identified numbers relevant for solution (Experiment 1) or provided verbal reports as they computed answers (Experiment 2). Type of…

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…