In this paper, I explore two beliefs about learning and teaching that I argue are prevalent among educators. The first is the belief that subject matter expertise is sufficient for success in teaching. The second belief is that to learn a specific content area, one needs to begin with an understanding of the formal structure and abstract…

Predictors of retrieval times produced by students having difficulty developing a reliance on retrieval for simple addition were discovered. The findings support the notion that separate limitations operate in working memory when retrieval occurs and call into question the use of the term "retrieval deficit" to explain difficulties…

Secondary school students' use of multiplicative strategies in an exploratory New Zealand Numeracy Project was examined. This Numeracy Project enabled teachers to interview each of their students concerning their mathematical knowledge and strategies. The percentage of students who used multiplicative strategies increased from initial to final…

To probe beyond declarative knowledge about real numbers in secondary school, the authors interviewed students in Grades 9, 10 and 12. The main question seems to be whether the length of a decimal expansion is "indefinite" or "infinite." It blurs the mental representation of rational numbers as well. (Contains 3 footnotes.) [For complete…

This study investigated the influence of textbooks on teaching strategies, specifically secondary school mathematics textbooks. The study compared the teaching strategies of 14 teachers using University of Chicago School Mathematics Project (UCSMP) textbooks in 13 schools with that of another 14 teachers using traditional textbooks in those…

This paper presents an inquiry into teaching and learning practices in a Year 11 mathematics class at a private college for girls in Western Australia, studying a topic on vectors. The focus is on learning through problem-solving, where students used graphics calculators as a matter of routine. Constructivist and sociocultural theories were…

Specific examples of effective use of multisensory aids are given. All can easily and inexpensively be made by the teacher or the students. Examples are grouped under the following major headings: number patterns, arithmetic skills, geometric concepts, algebraic concepts, and models. (LS)

A description is given of a game simulation course, developed for a full year of general mathematics credit. It traces a rock-and-roll band, with each student acting as manager. Ten activities are outlined. (MNS)

A problem-solving lesson is described, with a worksheet involving the gauges on a car's instrument panel. (MNS)

The activity provides practice plotting points in the Cartesian plane, develops inductive skills in pattern recognition, develops verbal and translation skills, and acquaints students with some properties of linear relations. Three worksheets are included. (MNS)

Differences in attitudes toward algebra and general mathematics among ninth-grade students were measured to determine both individual personality variables and attitudes toward the learning environment. Students in the upper and lower tracks shared many personal attitudes, but differed in their views of classroom adequacy. (Authors/PP)

Twenty-four distinguished mathematics educators responded to a survey conducted at the end of 1981, which asked what are the 10 most important books for a secondary school mathematics teacher to read. Provided here is a compilation of all the books noted by the educators collected under 10 topic areas. (MP)

An approach to teaching multiplication and division with negative numbers that focuses on graphs to illustrate concepts is revealed. The material and problems used are presented with comments on the teaching methods applied with 11-year-olds. (MP)

Four games and documentation in a computer assisted mathematics program (Applesoft Basic) are reviewed. Although the games do not teach mathematical concepts, they do serve to reinforce concepts/skills students already possess. The intended audience is elementary/junior high school students, but the programs could be used for mathematics…