This volume presents different issues and views on research in mathematics education in Australia. Chapters include: (1) "An Introduction to This Review" (Kay Owens); (2) "Recent Research Monographs" (Kay Owens and editors of the monographs); (3) "Language Factors in Mathematics Education" (Nerida Ellerton, Ken…

This study investigated the effects of specific criteria for marking a test on its reliability and validity. Eight algebra word problems were administered to grade 10 students. The objectivity of scoring criteria improved the reliability of the test, but did not affect its validity. (MNS)

Four teaching ideas are discussed: a "giant" math problem designed to motivate students to use library sources, calculators, computers, and textbooks; a different way of finding fractional equivalents; a task-card project designed to encourage mathematics students to use libraries; and journal writing in a mathematics class. (MP)

Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

Proposes activities that promote students' awareness of the structure of the information involved in their everyday activities, and builds the concept of function from students' mental representations of phenomena. Recommends the use of spreadsheets to provide external representations of these functions. (DDR)

Addresses the early stages of children's introduction to the use of variables in formal algebraic notation. Describes a teaching approach that aims to situate the use of formal notation in meaningful contexts. Presents a study of a teaching sequence based on children working with this approach using graphical feedback in problem solutions. (AIM)

Describes a project incorporating movies, literature, games, and other resources into mathematics instruction. Focuses on cultural differences. (Contains 10 references.) (YDS)

Research findings concerning student learning difficulties in algebra are discussed. A teaching approach which takes into consideration these findings is suggested. Encouraging students to see patterns and to develop flexibility in their thinking are stressed. (CW)

Discussed is the use of magic squares as examples in a first year course in linear algebra. Four examples are presented with each including the proposition, the procedure, and a proof. (KR)

Discussed are the idea, examples, problems, and applications of convexity. Topics include historical examples, definitions, the John-Loewner ellipsoid, convex functions, polytopes, the algebraic operation of duality and addition, and topology of convex bodies. (KR)

Described is an approach to teaching algebra in a meaningful context by using problem solving to motivate students and increase their retention. Examples of this approach are given. (CW)

Presents four worksheets designed to introduce middle school students to the use of diagrams to solve real world problems. Describes instructional usage of the worksheets with answers to all worksheets. (YP)

Some appearances of pi in a wide variety of problems are presented. Sections focus on some history, the first analytical expressions for pi, Euler's summation formula, Euler and Bernoulli, approximations to pi, two and three series for the arctangent, more analytical expressions for pi, and arctangent formulas for calculating pi. (MNS)

The Hawaii Algebra Learning Project (HALP) developed a curriculum that intertwines algebraic content, instructional methods, and assessment techniques with a problem-solving focus. (MKR)

For students to develop an understanding of functions, they must have opportunities to solve problems that require them to transfer between algebraic, numeric, and graphic representations (transfer problems). Research has confirmed student difficulties with certain types of transfer problems and has suggested instructional factors as a possible…