When first learning how to write mathematical proofs, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. In this article we explore three specific statements from abstract algebra that involve the number…

Community college developmental math students (N = 657) from three math levels were asked to place five whole numbers on a line that had only endpoints 0 and 20 marked. How the students placed the numbers revealed the same three stages of behavior that Steffe and Cobb (1988) documented in determining young children's number sense. 23% of the…

In this paper, the use of guided hyperlearning, unguided hyperlearning, and conventional learning methods in mathematics are compared. The design of the research involved a quasi-experiment with a modified single-factor multiple treatment design comparing the three learning methods, guided hyperlearning, unguided hyperlearning, and conventional…

An approach close to the original Greek geometric point of view regarding the question and proof of the irrationality of the square root of two is given. (MN)

Annotated listing of research summaries, articles, and dissertations in mathematics education reported in 1993. Grade or age levels are indicated for each citation. Articles and dissertations are indexed by mathematics education topic. Includes a list of the journals searched. (427 citations) (MKR)