Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

This article presents the authors' response to Asha K. Jitendra's Response to Xin and Zhang ("The Journal of Educational Research," 2009, Vol. 102, No. 6). The claim of "factual errors, including inappropriate quotes, misrepresentation of information, and inadequate scholarship in Xin and Zhang's text" are not justified. In this rejoinder, the…

In this article, the author explores what Assessing Pupils' Progress (APP) is about. He contends that the predilection for testing is a catastrophe as far as the teaching and learning of mathematics is concerned; it is an outcome of the drive for collecting so-called "data" on pupils. What those people, who should know better, either choose to…

Flexible knowledge, knowing multiple approaches for solving problems, is a hallmark of expertise in mathematics. Frequently, the author writes, students memorize only one method of solving a certain kind of problem, without understanding what they are doing, why a given strategy works, and whether there are alternative solution methods. Comparison…

Discusses the creed in symmetry and the omnipresence of symmetrical relationships in mathematics and nature, discusses mathematicians' attraction toward looking for symmetrical relationships as an unstated problem-solving heuristic, and shows how symmetry can be used as a didactical tool. (Author/MKR)

An attempt is made to show that algebra is rarely obvious, and merely expecting children to learn rules is an oversimplification. Sections cover: (1) The Non-visual Nature of Algebra; (2) The Apparently Arbitrary Nature of Algebra; (3) The Relationship Between Symbolism, System and Question; (4) The Complex Nature of Algebra; and (5) Some…

The main aim of this paper is to demonstrate that new and highly effective computer-based learning tools can be designed by adhering to a simple principle: Good learning tools conform to and support the processes and structures that comprise learning. The paper first discusses the processes involved in learning cognitive skills, then describes…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

Deficits common among secondary students with learning disabilities or mathematics deficiencies are considered, along with a strategy to teach upper level mathematics, such as algebra or calculus. The strategy involves use of a mentor to help students to comprehend mathematics vocabulary, develop their own problem-solving strategy, and create a…

This publication contains revised versions of the major papers presented at a research conference on the learning and teaching of algebra. The papers and discussions focused on four major themes: what is algebra and what should it become, in light of continuing technological advances; what has research told us about the teaching and learning of…

Instructional techniques are outlined, as utilized in a remedial algebra course offered at the Community College of Allegheny County. The paper first provides background information concerning the college, the characteristics of its students, the content of the remedial course, and the testing procedures used to place students in the course. The…

Discusses the need to consider the cognitive models of students and their learning processes when designing computer tutorials, and describes a tutorial designed to teach students how to generate algebraic equations for story problems. Testing and revisions of the tutorial, with both college and high school students are described. (14 references)…

Reviews of the courseware "Discovery! Experiences with Scientific Reasoning" and "Guess My Rule" are given. Discusses the accompanying manuals, the relative ease of use, and content of the programs. (PK)

Argues that the use of computer technologies in secondary schools should change the nature of mathematics education. Urges the rethinking of the uses of traditional paper-and-pencil computations. Suggests some computer applications for elementary algebra and for problem solving in arithmetic and calculus. (TW)

Explores the role that symbolic-graphical calculators can play in the current calls for reform in the mathematics curriculum. Discusses symbolic calculators and graphing calculators in relation to problem solving, computational skills, and mathematics instruction. (MDH)