Two microcomputer-based laboratories, the motion detector and the sound detector, are discussed in terms of their affects upon the facilitation of an understanding of graphs and their ability to aid in the development of conceptual understanding from graphical analysis. The author relates experiences in using these labs with high school students…

Explores the extent to which presentations about multiplication and division involving decimals within three series of mathematics textbooks for grades three through eight help students to counter common learner misconceptions about multiplication and division. Results indicate that theory on conceptual change with its concomitant research have…

Examines infinite sets and cardinality classifications of empty, finite but not empty, and infinite through discussions of numbers that fall into particular categories. Categories discussed include perfect numbers, Mersenne primes, pseudoprimes, and transcendental numbers. Discusses the Null Or Infinite Set Effect (NOISE) and infinitude resulting…

Presented is an activity where students determine the multiplication tables of groups of small order. How this can be used to help develop an understanding of the concept of group isomorphism is explained. (KR)

Mathematical concepts occur spontaneously from many topics and can be developed in the framework of cross-curricular schoolwork. Consequently, students can gain knowledge of where mathematics arises and insight about its purposes. (Included are activities dealing with the reflectional and rotational symmetries of automobile hubcaps evolved from…

Presents number loop pattern activities and games designed to interest elementary students in mathematics and encourage computational skills. The activities work as games and cooperative activities and invite math exploration. (SM)

Presents an intellectual context and critical analysis of specific material from undergraduate mathematics. Although not definitive in any sense of the word, the sample discussions provided for the included "test" questions all contain significant remarks bearing on significant mathematical concepts. (23 references) (Author/JJK)

A former editor of this journal, 1967-69, selects an outstanding article from her tenure for its significance as the beginning of important studies in mathematics learning in young children. The article selected presents a modified technique for assessing a young child's acquisition of length conservation while eliminating or reducing the…

The issue of division by zero is discussed. Activities that cover the topics of measurement division, partition division, relationship to fractions, confusion with dividing into zero, dividing zero by zero, and relation to more formal numbers are presented. (KR)

Investigated the use of the pronoun "it" by a nine-year-old girl as a concept variable conveying the message that she had something in mind that she believed the listener understood. (MDH)

Another way to add and subtract, in which the mental regrouping strategy is applied to an original 10-structure, is presented. Pupils use a visual model, called "little person," to move from counting to visualization. Originally designed for use with pupils with learning disabilities, this method has wider applicability. (KR)

Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

Illustrates the pedagogical implications embodied in Liu Hui's discussion on the ancient Chinese mathematical classic "JIU ZHANG SUAN SHU" (Nine Chapters on the Mathematical Art) with respect to aspects of proof and, more generally, the role of proof in mathematics. Provides examples involving area and volume. (Contains 25 references.)…

This article describes an empirical investigation of the extent to which incorrect arithmetic algorithms persist over time. Results with 30 fourth-year and third-year English students over up to 3 months shed light on "bugs," or students' learning of incorrect concepts, and indicate that they are not very stable in children of this age.…

Arguing that cognitive development involves both conceptual and semiotic achievements, the authors emphasize the distinctness of semiotic issues and develop a differentiated appreciation of semiotic aspects of cognition, particularly in elementary mathematics cognition. Semiotic analyses are provided of differences between counting, adding, and…