This article provides four mathematical activities for grades 6-8 with situations involving proportional and nonproportional reasoning. For each problem, students construct a table based on the particular situation, generalize a rule to describe those data, and then plot the data on coordinate axes. (YP)

Given are several examples of seemingly unrelated problems that nevertheless can be solved with a single mathematical idea--the proportion. It is hoped that as students see how a variety of problem contexts can be modeled by a proportion, they will use proportions more frequently in problem solving. (MNS)

Describes an inquiry activity in which students explore the variables that influence the amount of time it takes a ball to roll down an inclined plane. Relates features of the activity to recommendations in the NCTM Standards. (MKR)

Analyzes instructional actions designed to help a student understand distance, time, and speed. Focuses on the mathematical knowledge that guided instructional decisions and actions and discusses implications for content preparation of teachers. Contains 48 references. (Author/MKR)

Presents six articles dealing with math and science education: "Sneaker Geometry" (Jack George), "Fairs with a Flair" (Diane McCarty), "Generating Excitement with Math Projects" (Jeffrey Kostecky and Louis Roe), "Playing with Numbers" (Diana Smith), "When Student Teachers Want to Do Hands-On Science" (Betsy Feldkamp-Price), and "Science ala Carte"…

Two experiments examined fifth-grade students' reasoning about data modeling: one involved development of hypermedia documents, the other, use of a simple randomization distribution to test students' hypotheses. Found that data construction and analysis provide an opportunity to involve students in the important enterprise of mathematical…

Describes one teacher's use of traditional wooden blocks in fifth-grade curriculum. Notes that use of blocks can teach communication, teamwork, precision, and arithmetic concepts. Also describes four easy classroom block projects. (TM)

Describes principles for constructing mathematics exercises that challenge students. Presents examples of good problems in differential equations. (MKR)

Presents a dialogue about ethnomathematics that includes discussions of: quipus (knotted cords) as a form of language, difficulty in defining mathematics, culturally embedded mathematical ideas, philosophy and mathematics, quantification without giving meaning to numbers, and evolution in mathematical thinking. (MKR)

Content analysis of 7 mathematics textbook series, grades 1-8, found that textbooks published after 1989 (when NCTM Standards were published) showed shifts of emphasis among content areas; changes in amount of content development, drill, word problems, and problem solving; and increased use of estimation and calculators. (13 references) (MKR)

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…