Knowledge assessments in undergraduate mathematics education commonly evaluate response correctness to determine learner proficiency. However, simultaneous evaluation of learner metacognition more accurately assesses the multiple dimensions of knowledge and has been shown to increase assessment validity and reliability. Research into…

Lists five criteria in the acceptance of mathematical theorems, such as understanding, significance, compatibility, reputation, and convincing argument. Concludes that social and language factors are involved in the process of the acceptance. (YP)

This paper uses a book, "Proofs and Refutations: The Logic of Mathematical Discovery," as an example of Lakatos's use of dialogue. The book was originally adapted from his dissertation and influenced by Polya and Popper. His discussion of the Euler conjecture is summarized. Three purposes for choosing the dialogue form for the book were…

This article develops an algorithm to find all solutions to the problem, making all sums of a hexagram's nine lines the same. It shows how to exploit the geometric structure of the hexagram and its group of automorphisms. (YP)

Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

Numerous research studies over the past five years indicate that a high percentage of college students have severe deficiencies in their ability to use mathematics as a language for representing simple quantitative relationships. In the United States these problems are nearly as common among students with strong computational skills in algebra and…

Contrasted are engineering statistics with statistics for students of mathematics and social science. Topics considered are level of abstraction, amount of technical detail, and choice of subject. The nature of exercises suitable for various courses is described. (KR)

College students who were either monolingual speakers of English or bilingual Hispanics participated in two studies dealing with the comprehension of sentences containing negations. Both the influence of different sentence constructions on comprehension, as well as the heuristics and misconceptions exhibited by subjects as they attempted to…

This thesis describes the design, development, implementation, and evaluation of a training module to instruct graduate foreign students to learn the representation of the binary system and the method of decimal-binary conversion. The designer selected programmed instruction as the method of instruction and used the "lean" approach to…

A critical curriculum promoting mathematical literacy can be effective in involving more people of color in mathematics and science fields. A program that conveys the relevance of mathematics and statistical knowledge can be politically and socially empowering. Describes how ethnomathematics challenges the Eurocentric dichotomy between practical…

The role of methods courses to help prospective elementary teachers learn to teach mathematics was investigated. The influence of past experience on preservice teachers, their lack of subject knowledge, and the lack of time set aside for a methods course are discussed. (KR)

Teacher preparation curriculum at Technion--Israel Institute of Technology (Israel) includes courses intended to bridge the gap between the pure mathematics courses and those in psychology. The focus of this paper is an experimental program for one of these courses and data collected while implementing it. This is a second report on a naturalistic…