The Spirograph, a device used for artwork and designs, is utilized to explore the mathematical topics of symmetry, ratio, divisibility, and modular arithmetic. A worksheet for each topic is included along with pedagogic information and extensions and also the answer key. (JJK)

Described are ways that specific concepts from abstract algebra can be programed using the software package features of the Ada Programming Language, which is the primary language of the Department of Defense. Included are typical programs with their respective outputs. (JJK)

Discussed are the geometric patterns formed when two geometric patterns are superimposed. General moire fringes, circular and line gratings, physical applications, and projects for students are described. (CW)

Outlines an epistemological conception that relates formal aspects of mathematical proof to its pragmatic dimensions. In addition to applications, makes use of several concepts from analytical philosophy to present a view of proof best categorized as dialectical. Implications for teaching are discussed. (Contains 30 references.) (Author/MDH)

The author shows some causes of failure in the creation of mathematical concepts. One is the stiffening of concept cores, which prevents identification of atypical exemplars and solution of atypical problems and causes a bifurcation between the natural system of everyday concepts and the formal system of school concepts. (Author/MDH)

Discusses how different meanings can be given to the proof at different levels and branches of mathematics education. (ASK)

Illustrates the addition, subtraction, and representation of fractions using an area model and a measurement model. Also demonstrates multiplication and division of fractions by employing the area model. (ASK)

A study contrasted two instructional approaches for teaching decimals to 44 junior high school remedial students and students with learning disabilities. Findings indicate significant effects on conceptual tasks for students who were taught decimals with an emphasis on conceptual understanding; however, low-achieving students required considerable…

Investigated differences in oral-language development, emergent literacy skills, mathematical reasoning and concepts, and behavior for full-day versus half-day kindergarten students in the Irving (Texas) Independent School District. Found statistically significant advantages for the full-day program, particularly for English-speaking students.…

Two studies pursued theory that knowledge of addition combinations facilitates learning of subtraction combinations. Study 1 involved 25 kindergartners and 15 first graders in a gifted program; study 2 involved 21 first graders in a regular program. Participants responded to two pairs of problems. Findings revealed that the complementary…

Presents a study in which postgraduate elementary school preservice teachers (n=44) were given four tasks, two to assess their understanding of perimeter and two to assess their understanding of area. Concludes that teachers have a procedural understanding of perimeter and area rather than a conceptual and relational understanding. Contains 15…

Traces three major stages in the development of algebraic notation: (1) rhetorical or prose; (2) syncopated; and (3) symbolic. Illustrates the development of a standardized, efficient symbol system by tracing the evolution of some common symbols, including the symbols for equals, addition, subtraction, multiplication, and division. (Author/WRM)

Discusses the development of multiplicative and divisional schemes within a constructivist framework. Illustrates child thinking and child methods relative to the meanings of these operations using interviews with children. Compares the constructivist perspective on the development of meanings of multiplication and division to what is found in…

Provides an activity to investigate and construct an inductive proof. Claims that this particular example helps students better understand the nature of inductive reasoning and inductive proofs since the expression can be investigated by spreadsheets or calculators, hypothesized, tested, and modeled, both physically and pictorially, to at least…

Presents a problem for students in grades 4-6 on Venn diagrams with or without manipulatives. Lists questions for teachers to reflect upon during the problem-solving process concerning student understanding of problems, problem-solving strategies, assessment, and reasoning skills. (ASK)