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)

Describes three labs designed to help students in a first course on ordinary differential equations with three of the most common numerical difficulties they might encounter when solving initial value problems with a numerical software package. The goal of these labs is to help students advance to independent work on common numerical anomalies.…

Two experiments examined the development of children's understanding of part-whole relations. Found that five- and six-year olds evidenced understanding of part-whole relations, but four-year olds did not. Results support the conclusion that an understanding of the relationship between a superordinate set and the basic-level sets that comprise it…

Discusses how experiments can offer students different points of view on the mathematical concepts presented in class and bring these concepts to life. Presents an experiment that demonstrates the interaction between mathematics and fluid dynamics. (Author/ASK)

A study found that among second-grade children with mathematics difficulties (n=49), children with both mathematics and reading difficulties were distinct from children with only mathematics difficulties, with the former being characterized by pervasive deficiencies in mathematical thinking and the latter by more specific deficits in problem…

Two studies of adolescents in England and Russia examined the effects of prolonged instruction on students' development of abstract deductive reasoning and understanding of logical necessity in algebraic and verbal reasoning. Results indicated that prolonged instruction emphasizing the metalevel of algebraic deduction contributed to enhanced…