Analyzes the nature and growth of students' algebraic knowledge and thinking from an epistemological perspective supported by historical observations. Focuses on two crucial transitions: from the purely operational algebra to the structural algebra of a fixed value of an unknown and then to the functional algebra of a variable. (Contains 58…

Proposes methods to teach the more difficult concepts of linear algebra. Examines features of the Linear Algebra Curriculum Study Group Core Syllabus, and presents problems from the core syllabus that utilize the mathematical process skills of making conjectures, proving the results, and communicating the results to colleagues. Presents five…

Presents a summary report of the Algebra Working Group's discussion subgroup on tertiary algebra at the Seventh International Conference on Mathematical Education held in Quebec City, Canada in August 1992. (MKR)

This booklet presents the high school assessment program for algebra by listing Maryland's Core Learning Goals. The match of content indicators and the skills for successful elaborations in thinking, communication, and technology regarding algebra are discussed. (ASK)

Data from (n=470) students at Owens Technical College in Fall 1991 showed that high school GPA was the best predictor of grades in Basic Algebra, followed by high school rank, college GPA, ACT natural sciences, ASSET numerical skills, and ASSET elementary algebra scores. (11 references) (SW)

This paper brings a teacher's perspective to bear on recent policy initiatives requiring all high school graduates to complete an Algebra One course. The paper is based on the teacher's experience in teaching high school students who have not been successful in mathematics, at Holt High School in Michigan. The teacher is caught between a desire to…

Discusses reasons for using spreadsheets in mathematics education. Presents mathematics activities for beginning algebra classes using spreadsheets. (ASK)

Analyzes student construction of function-based problem solving methods in introductory algebra. Describes longitudinal observation of a pair of students that studied algebra for three years using the function approach including intensive use of graphing technology. Offers terms for describing and explaining what and how do learners appreciate and…

Reviews three geometry textbooks in order to examine both the quantity and content of algebra review. Concludes that although the books incorporate a great deal of algebra, much of it is noncontextual review. (ASK)

Discussed is the use of magic squares as examples in a first year course in linear algebra. Four examples are presented with each including the proposition, the procedure, and a proof. (KR)

Ideas which apply language concepts to the study of algebra are presented. Discussed are algebraic notation, vocabulary, vocalization, and written assignments. The careful use of algebraic language in mathematics classes is emphasized. (CW)

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Describes an interdisciplinary quantitative reasoning course that uses algebra to answer questions from science. Describes the development, philosophy, and structure of the course and demonstrates two of the projects developed for this course. Presents student reactions and attitudes towards the course. (Contains 11 references.) (Author/ASK)

Presents the algorithm to approximate square roots as reproduced from the 1579 edition of an algebra book by Rafael Bombelli. The sequence of activities illustrates that the process of understanding an original source of mathematics, first at the algorithmic level and then with respect to its mathematical validity in modern terms, can be an…

Presents five recommendations of the Linear Algebra Curriculum Study Group: (1) The syllabus must respond to the client disciplines; (2) The first course should be matrix oriented; (3) Faculty should consider the needs and interests of students; (4) Faculty should use technology; and (5) At least one follow-up course should be required. Provides a…