Describes a method being developed for teaching mathematical physics at the college level without the use of calculus. (SL)

Explores the hypothesis that play can be a useful preliminary experience for the more advanced problem-solving involved in mathematical concept formation. (Author/RK)

Develops a division algorithm in terms of familiar manipulations of concrete objects and presents it with a series of questions for diagnosis of students' understanding of the algorithm in terms of the concrete model utilized. Also offers general guidelines for using concrete illustrations to explain algorithms and other mathematical principles.…

This article was written in part to celebrate the anniversaries of landmark mathematical works by Newton and Descartes. It's other purpose is to dispel some myths about Sir Isaac Newton and to encourage readers to read Newton's works. (PK)

Discussed is the topic of least common multiple (LCM), a rationale for its importance, and suggestions for when and how to teach it. (RH)

Examines the factors influencing the use of a plan by four- and five-year-old children to judge the relative number of two sets by one-to-one correspodence. Results suggest that most children have one-to-one plans in long-term memory by age four. (Author/RWB)

Outlines one teacher's questioning of the understanding of computational processes by her students in mathematics class. Points out the importance of teaching the context of meaning and its application in mathematics. (MD)

The ratio factors approach involves recognizing a given fraction, then multiplying so that units cancel. This approach, which is grounded in concrete operational thinking patterns, provides a standard for science ratio and proportion problems. Examples are included for unit conversions, mole problems, molarity, speed/density problems, and…

Describes three studies in which students (N=515; N=60; N=135) were asked to indicate appropriate operations and numbers used in solving open mathematical sentences. Analysis of data and interviews suggest two error patterns: "finding a solution" and "inverse operation." Indicates that "finding a solution" strategy…

Included are a general introduction to the topic of metacognition, a discussion of how metacognition is involved in mathematical performance, and a short section on metacognition and instruction. (MNS)

Presents placement test results showing a lack of understanding of basic math concepts among entering college students. Explains the application of the learning cycle model in teaching abstract mathematical concepts and offers examples of the model's use. (DMM)

A research study with first-grade pupils considered the effect of conservation and transitivity on learning the concept of measurement, and provided insights into the processes children use to solve measurement problems. The tasks, reactions, and implications for instruction are discussed. (MNS)

Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend to blend conceptual physics with mathematical symbolism in a way that profoundly affects the way equations are…

Fact-filled textbooks that stress memorization and drilling are not very good for teaching students how to think mathematically and solve problems. But this is a book that comes to the rescue with an instructional approach that helps students in every grade level truly understand math concepts so they can apply them on high-stakes assessments,…

This paper suggests that logic consists of a collection of propositions and operations of negation, conjunction, disjunction, implication, and equivalence. It points out that the operations on dispositions depend upon the truth-value of the propositions involved. This raises the questions, How do we know whether a proposition is true or false? and…