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Walkoe, Janet; Levin, Mariana – For the Learning of Mathematics, 2020

We hypothesize that one thing that has been holding the field back from recognizing the algebraic potential of young children's early experiences is an emphasis on specific definitions of what counts as algebra-relevant knowledge. In this article, we seek to develop a perspective on algebraic thinking that foregrounds the algebraic potential of…

Descriptors: Algebra, Thinking Skills, Mathematics Education, Definitions

Norton, Anderson – For the Learning of Mathematics, 2019

Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

Descriptors: Mathematics Education, Mathematics Instruction, Instructional Effectiveness, Geometry

Ulrich, Catherine – For the Learning of Mathematics, 2015

This is the first 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. My explanation starts with the formation of arithmetical units, which presage…

Descriptors: Mathematics Education, Secondary School Mathematics, High School Students, Constructivism (Learning)

Chazan, Daniel; Herbst, Patricio – For the Learning of Mathematics, 2011

Video recordings of instruction have been a mainstay for supporting conversations about teaching by representing particularities of instruction and by presenting the viewer with a multitude of details for interpretation. In this essay, we contrast non-fictional videotapes of actual classroom interaction with fictional animations of classroom…

Descriptors: Video Technology, Interaction, Algebra, Essays

Bokhove, Christian; Drijvers, Paul – For the Learning of Mathematics, 2010

The algebraic expertise that mathematics education is aiming for includes both procedural skills and conceptual understanding. To capture the latter, notions such as symbol sense, gestalt view and visual salience have been developed. We wonder if digital activities can be designed that not only require procedural algebraic skills, but also invite…

Descriptors: Mathematics Education, Algebra, Symbols (Mathematics), Student Behavior

Peer reviewed

Menghini, Marta – For the Learning of Mathematics, 1994

Discusses algebra teaching by looking back into the history of algebra and the work of George Peacock, who considered algebra from two points of view: symbolic and instrumental. Claims that, to be meaningful, algebra must be linked to real-world problems. (18 references) (MKR)

Descriptors: Algebra, Mathematics Education, Mathematics History, Mathematics Instruction

Peer reviewed

Shumway, Richard – For the Learning of Mathematics, 1990

Discussed are supercalculator capabilities and possible teaching implications. Included are six examples that use a supercalculator for topics that include volume, graphing, algebra, polynomials, matrices, and elementary calculus. A short review of the research on supercomputers in education and the impact they could have on the curriculum is…

Descriptors: Algebra, Calculators, Calculus, Cognitive Development

Peer reviewed

Watson, Jane M. – For the Learning of Mathematics, 1988

Presents a selection of solutions of the "Three Hungry Men" problem from grade three to college students with three different strategies used: backward, forward, and forward/backward strategies. Provides error patterns in each strategy. Discusses some implications for teaching of problem solving. (YP)

Descriptors: Algebra, College Mathematics, Elementary School Mathematics, Error Patterns

Peer reviewed

Burton, Martha B. – For the Learning of Mathematics, 1988

A major component of student difficulty with algebra is the inability to make sense of the algebra symbol system as a language. Accordingly, remedies should be sought by considering algebra in a linguistic sense. (PK)

Descriptors: Algebra, College Mathematics, Communication Skills, Linguistics

Peer reviewed

Sutherland, Rosamund – For the Learning of Mathematics, 1991

Discusses concerns for mathematics education research on algebra and requestions methods that focus on the Piagetian concept of cognitive obstacles. Suggests the use of computer-based environments to develop the concept of variable and offers research findings indicating that experiences working with variables in LOGO influences student…

Descriptors: Algebra, Cognitive Development, Cognitive Dissonance, Cognitive Processes

Peer reviewed

Burton, Martha B. – For the Learning of Mathematics, 1991

Described are the difficulties in translating word sentences between English and Algebra. Two classic sentences that typically produce student errors are presented with explanations that can be shared with the students on overcoming these translation difficulties. (MDH)

Descriptors: Algebra, Elementary School Mathematics, Elementary Secondary Education, Mathematics Education

Peer reviewed

Sutherland, Rosamund – For the Learning of Mathematics, 1993

Analyzes case study data of 10 low achieving students, ages 14-15, to examine the effects of participation in computer spreadsheet sessions on their understanding of mathematical symbols. Participation improved students' attitudes toward problem solving. (MDH)

Descriptors: Affective Behavior, Algebra, Case Studies, Computer Assisted Instruction

Peer reviewed

Arcavi, Abraham – For the Learning of Mathematics, 1994

Attempts to describe a notion parallel to number sense, called symbol sense, incorporating the following components: making friends with symbols, reading through symbols, engineering symbolic expressions, equivalent expressions for non-equivalent meanings, choice of symbols, flexible manipulation skills, symbols in retrospect, and symbols in…

Descriptors: Algebra, Algorithms, Mathematical Concepts, Mathematics Education

Peer reviewed

Arcavi, Abraham; Bruckheimer, Maxim – For the Learning of Mathematics, 1989

A description of De Morgan's life and work is followed with quotations of his thoughts and insights on the teaching and learning of mathematics. The purpose is to illustrate the sharpness of his ideas, his creative insights, and his wit for the enjoyment of the reader. (DC)

Descriptors: Algebra, Arithmetic, Concept Formation, Geometric Concepts

Peer reviewed

Harel, Guershon – For the Learning of Mathematics, 1987

Reports on the findings of an examination of 32 linear algebra textbooks. The examination, to determine existing approaches to teaching the topics, was in preparation for developing a linear algebra program for high school students. (PK)

Descriptors: Algebra, High Schools, Mathematics Curriculum, Mathematics Education