The everyday mathematics processes of structural engineers were studied and analyzed in terms of abstraction. A main purpose of the study was to explore the degree to which the notion of a gap between school and everyday mathematics holds when the scope of practices considered "everyday" is extended. J. Lave (1988) promoted a methodology…

This book is about teaching computation in a way that accommodates children who do not learn best with traditional math teaching methods. The teaching approach draws on visual and kinesthetic learning strategies to help all students be math whizzes and provides a comprehensive program for elementary math skills. The book begins with counting and…

Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)

Explores self-regulated learning (SRL) theory in light of the reform vision of mathematics education depicted with "Principles and Standards for School Mathematics," asserting that implementation of mathematics reform makes possible the development of self-regulated learners while also necessitating developing self-regulated learners.…

Suggests that strategy choice is a misleading characterization of efficient mental calculation and that teaching mental calculation methods as a whole is not conducive to flexibility. Proposes an alternative in which calculation is thought of as an interaction between noticing and knowledge. Presents an associated teaching approach to promote…

Analysis of (n=92) university students' construction of visual representations (Venn diagrams) of eight set expressions found competent and error-prone students constructed and used procedures to complete set translation tasks, and two-thirds of observed errors arose from consistent implementation of ill-formed procedures. (Author/MKR)

Postulates a form of mathematical reasoning that learners engage in spontaneously that is not inherently inductive or deductive. This transformational reasoning is generated through the learner's inquiry into how a mathematical system works. (Author/MKR)

Investigated (n=61) undergraduates' ability to unpack informally written mathematical statements into the language of predicate calculus in an introduction to proofs and mathematical reasoning. Found that students were unable to construct proofs or validate them. Appendices are "A Sample Validation" and "Building a Statement Image." (MKR)

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)

Explored relationship of four sources of self-efficacy information to high school students' (n=50) mathematics self-efficacy. Found prior performance to be most efficient predictor of self-efficacy. Global academic self-concept did not explain unique self-efficacy variation beyond prior performance. Effect of self-efficacy on perceived utility of…

Describes four easy-to-construct board games and puzzles that teachers can use to strengthen their students' mathematical problem-solving skills in both the classroom and the real world. (MDM)

Examines the mathematical process used by students when solving physics tasks that require proportional reasoning. Investigates students' understandings and explanations of their mathematical processes. (Author/CCM)

Outlines research that details the mathematical difficulties of physics students. Discusses various methods to overcome these difficulties. Results show the encouraging successes of these projects and a way forward for A-level physics teaching. (Author/CCM)

Suggests that no matter how much algebraic thinking is introduced in the early grades, and no matter how worthwhile this might be, the failure rate in algebra will continue unless the teaching of fractions and decimals is radically revamped. The proper study of fractions provides a ramp that leads students gently from whole number arithmetic up to…

Used Wynn's (1992) procedure in 3 experiments to test 5-month-olds' looking-time reactions to correct and incorrect results of simple addition and subtraction transformations. Found non-systematic evidence of either imprecise or precise adding and subtracting in young infants. Results suggest that infants' reactions to displays of adding and…