Maintains that findings showing numerical computation abilities in infants are considerably more robust and consistent than Wakeley, Rivera, and Langer suggest. Asserts that all the interim replication attempts have successfully replicated Wynn's original findings. Discusses possible reasons for failure to replicate in Wakeley et al. experiments.…

Explains the concept of Question-Answer Relationships (QAR), and provides an outline for teaching the strategy. Offers examples of learning experiences that integrate the QAR strategy with mathematics content and offers directions on how to create a unit that integrates strategy instruction with content instruction. (SR)

Observed the work at 16 automobile manufacturing sites to study the level and content of mathematics required of workers. identified the mathematical demands of various aspects of production. Results raise questions about how well schools prepare students for the "global competitive workplace." (SLD)

Summarizes and revises the report given to the Committee on the Undergraduate Program in Mathematics of the Mathematical Association of America (MAA) who is developing new guidelines for instruction in mathematics by a group of chemists at Macalester College in order to list specific knowledge and skills in mathematics needed by chemistry…

Summarizes the report given to the Committee on the Undergraduate Program in Mathematics of the Mathematical Association of America (MAA) who is developing new guidelines for instruction in mathematics with a chemical engineering group at Clemson University in order to list specific knowledge and skills in mathematics needed by engineering…

Explores the state of the relationship between science and mathematics as it currently exists. Looks at the problems experienced by science undergraduates in terms of their mathematics skills. Reviews literature of mathematics, science, and primary education in order to explore the relationship as exemplified therein. (Contains 135 references.)…

In this article we propose the following definition for advanced mathematical thinking: Thinking that requires deductive and rigorous reasoning about mathematical notions that are not entirely accessible to us through our five senses. We argue that this definition is not necessarily tied to a particular kind of educational experience; nor is it…

This investigation examined the effect of an extended time testing accommodation on the performance of students with disabilities, students educationally at risk in math, and students without disabilities. Ninety-seven eighth-grade students completed two equivalent forms of a standardized mathematics test, each under different testing conditions…

In a previous article in this series, it was suggested that it is part of our responsibility as teachers to attempt to induce "perturbations" in our students' mathematical thinking. Especially when teaching seniors and capable students at any level, it is important that we unsettle them, shake their perceptions and attempt, wherever…

In this article, the author talks about his experiences when he started a mathematics degree with the Open University. He shares what happened during a course on mathematical models and methods and his major influences in mathematics. He also offers his current pedagogy that is based purely on his experiences and time spent talking to other…

According to this author, the solution to the "phonics versus whole language" debate over the teaching of reading is balance and a focus on the needs of all students. There is similarly a need, in developing numerate young people, to focus on the teaching and learning of mathematics and mathematics skills some of the time, and on…

It is an eye opening experience for students to find out that even a great mathematician like Leibniz made mistakes, forgot to check carefully his calculations, and was temporarily misled by user-friendly but incorrect formulas. From Leibniz's mishap with the derivation of the rules of differentiation students can learn the importance of spending…

The ubiquity of calculators led to many "computational abuses", when numbers substitute for substance. On the other hand, it resulted in decrease in number oriented dexterity of students. The latter led to a disdain for even simple calculations to work about unfamiliar mathematical problems. As a reaction to the former, the reputation of…

Advocates of the ''continuity hypothesis'' have argued that innate non-verbal counting principles guide the acquisition of the verbal count list (Gelman & Gallistel, 1978). Some studies have supported this hypothesis, but others have suggested that the counting principles must be constructed anew by each child. Defenders of the continuity…

In the study reported here, we investigate the skills needed to validate a proof in real analysis, i.e., to determine whether a proof is valid. We first argue that when one is validating a proof, it is not sufficient to make certain that each statement in the argument is true. One must also check that there is good reason to believe that each…