Proposes that the learning of mathematics requires that the socially developed mathematical form, as well as the concepts it represents, become the property of the individual student. Indicates that the distinction between the form and content of mathematics, together with interrelationships between the two, is of crucial importance to effective…

Two methods are considered for finding the logarithm of a number using elementary arithmetic. (DT)

Methods of teaching students to solve equations and inequalities containing parameters are suggested. (DT)

A geometric method of solving quadratic equations is described. (DT)

An algebraic-geometric solution technique used by the ancient Chinese is examined. (DT)

Students who learn mathematics with CAS calculators are likely to develop new practices for doing and recording mathematics. Students discussed in this paper were able to use CAS calculators in examinations, making their own decisions about what to document as written records for solutions to problems. A comparison of some features of written…

The paper examines how community was established in a professional development institute that focused on algebra content knowledge for middle school mathematics teachers. This qualitative study was framed within a situative perspective. We analyzed multiple data sources to identify the ways in which community was established. Results indicate…

This paper is part of a dissertation defended in January 2001 as part of the author's Ph.D. requirement. The study investigated the effects of use of Mathematica, a computer algebra system, in learning basic linear algebra concepts, It was done by means of comparing two first year linear algebra classes, one traditional and one Mathematica…

New models of graphing calculators arrive on a regular basis. Texas Instruments alone introduced 8 models in a 10 year period. At many schools it is impractical or impossible to have every student use the same model and often different brands as well as different models are used in the same classroom. This situation brings about both advantages…

This paper explores how college students understand ideas of functions, and which representations are productive for them in promoting their ability to work flexibly across representations. The study used pre- and post-test scores, and triangulations via student self evaluations, to generate a hypothesis related to flexible thinking and success in…

Algebra and calculus students have difficulties to express themselves in a statement of mathematical symbols and to comment on written mathematical statements to end with equivalent mathematical symbols statement. In this study, the reasons behind the meaning students load to the mathematical symbols and written mathematical statements was…

Research indicates that students have great difficulty solving certain algebra word problems. These solutions, moreover, appear to be due to some situational factors characteristic of algebra problems, e.g., presentation and response format. This study investigates students' preconceptions, post facto alternative concepts based on key features of…

The concept of function is considered as foundational in mathematics. Yet, it proves to be elusive and subtle for students. A generic image that can act as a cognitive root for the concept is the function box. This is not a simple pattern-spotting device, but a concept that embodies the salient features of the idea of function, including process…

This paper explores questions about linear relationships through the use of pattern. Participants in the session generated and extended patterns and used calculators to investigate the relationships. Examples from current Texas Instruments (TI) books and U.S. textbook series, plus examples from proposed TI materials are shared. These activities…

This paper suggests a route to deep, long-term algebra reform that begins not with more new approaches but with elementary school teachers and the reform efforts that currently exist. This route involves generalization and expression of that generality using increasingly formal languages, beginning with arithmetic, modeling situations, geometry,…