In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

This project seeks to understand the emergence of mathematical meanings mediated by learners' interactions with multiple artifacts. Extending our prior work which took an enactivist approach and revealed the dynamics of embodied interactions fundamental to understanding fraction division, we now employ a semiotic lens to illuminate how learners…

The author of this paper submits the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Probability and Mathematical Statistics (PAMS) course sequence to teach students PAMS. Furthermore, the author of this paper opines that set theory…

The author of this paper submits that a mathematics student needs to learn to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method (MMM) across the…

This paper describes a framework for making sense of the relationship between emotions, cognition, mathematical activity, and mathematical beliefs. Subjects were participants in a special mathematics anxiety program. Beliefs are classified as instrumental and relational approaches to a situation. Emotion is also distinguished as a two-faceted…

Investigated with 26 gifted seventh-grade girls was the influence of an experimental summer mathematics acceleration program on later mathematics course-taking behavior. Classes were designed to provide social stimulation through such methods as using a woman teacher and assistants for role models, informal structure, organization for small group…

In 1982, the Alfred P. Sloan Foundation recognized that many of the graduates of the colleges and universities in this country were technologically and mathematically illiterate, and an attempt to begin to remedy this serious shortcoming was launched in their New Liberal Arts Program. Lafayette College in Pennsylvania was one of the 30 liberal…

At puberty differences in ability and interest in mathematics between the sexes appear, and they increase with age. This paper describes a special algebra workshop for gifted seventh-grade girls which was designed to improve their competence and accelerate their progress in mathematics, and to increase their awareness of career opportunities in…

Although it takes only 2 years to attain conversational competence in a second language, it takes up to 7 years to realize sufficient language competence to achieve academically at the level of native speakers. Specific adaptations in instructional methods in mathematics for language minority students should include techniques from English as a…

The International Mathematics Tournament of the Towns is a mathematics competition for junior and senior high school students all over the world. The tournament began in 1980 in the former Soviet Union. Participants write contest papers locally, with emphasis on solving within a very generous time allowance a small number of interesting problems.…

Reducing math anxiety and building basic mathematical skills should not be treated as separate processes, but can and should be undertaken simultaneously. To do so requires a positive attitude on the part of the instructor; the establishment of an atmosphere in the classroom that encourages learning; and the instructor's awareness of different…

In this document, available literature is identified and reviewed in order to determine whether there are substantiated cognitive effects associated with the use of games in the mathematics classroom. Three criteria were used for selection of the literature: the treatment was identified as a game; cognitive measures were obtained; and the…

This collection of teaching materials contains information and activities which connect language arts and mathematics. Materials in the collection include: a statement of fundamental assumptions about language, literacy, and learning; objectives for mathematics as communication and mathematical connections; a discussion of a new approach to…

Mathematics and science instruction in schools often poses a challenge for limited-English-proficient (LEP) students. This paper discusses how the various curriculum development and assessment projects sponsored by the California Academic Partnership Program (CAPP) implement techniques for learning and teaching mathematics and science for LEP…

This paper describes in detail the paper-and-pencil POE (Pelham Odd 'R Even) game, in which units of space are the allocated resources. The game is designed to provide an introduction to the rule structure common to the games of EQUATIONS, WFF 'N PROOF, and ON-SENTS & NON-SENTS. Techniques of playing POE, including goals, solutions, moves, scoring…