In this paper we report the results of an experiment designed to test the hypothesis that when faced with a question involving the inverse direction of a reversible mathematical process, students solve a multiple-choice version by verifying the answers presented to them by the direct method, not by undertaking the actual inverse calculation.…

Although refuted many times, the commonly accepted story about Indigenous communities in Australia is that they had few counting words and thus were lacking in ways to quantify amounts. In this paper, we use the case of quantifying to discuss how Indigenous mathematics can be used, not just to help Indigenous students transition into the classroom…

The purpose of this paper is to explore middle school in-service mathematics teachers' ability (1) to identify and explain students' actions in pattern generalization and (2) to account for the variation in teachers' explanations of students' actions in terms of task and teachers' factors. Two questionnaires were developed: (1) a questionnaire to…

Based on insights into the nature of vocational mathematical knowledge, we designed a computer tool with which students in laboratory schools at senior secondary vocational school level could develop a better proficiency in the proportional reasoning involved in dilution. We did so because we had identified computations of concentrations of…

In order to give insights into cross-national differences in schooling, this study analyzed the development of multiplication and division of fractions in two curricula: "Everyday Mathematics" (EM) from the USA and the 7th Korean mathematics curriculum (KM). Analyses of both the content and problems in the textbooks indicate that…

As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

Study of the performance of nearly 2,000 students in grades 2 through 9 on a variety of mental computation tasks using visual and oral presentation found a wide variation in performance within the sample of each country at each grade level. (33 references) (MKR)

Interviews 53 sixth grade students individually in an attempt to discover whether wrong interpretations of the algebraic structure found in an algebraic context occurs in a purely numerical context. Concludes that students' difficulties with the algebraic structure were also found in purely numerical contexts. (Contains 27 references.) (Author/ASK)

Examines the computational strategies of 10 young street vendors in Beirut by describing, comparing, and analyzing computational strategies used in solving three types of problems: (1) transactions in the workplace; (2) word problems; and (3) computation exercises in a school-like setting. Indicates that vendors' use of semantically-based mental…

Trainee teachers, new and non-specialist teachers of elementary mathematics have a tendency to avoid thought about reasons in mathematics. Instead, they tend to favour the development of computational skill through the rote application of procedures, routines and algorithms. Could elementary mathematics textbooks serve as models of practice and…

Presented is a comparison of two major surveys of the teaching and learning of mathematics conducted by the International Association for the Evaluation of Educational Achievement. Surveys indicate that performance levels have declined in computational skills and increased in algebra. (Author/CW)

A series of 13 survey questions based on a 50-50 spinner is used to explore school students' understanding of statistical variation in a chance setting. Five questions set the context by assessing the understanding of theoretical expectation and representation of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to…

Reanalyzes data obtained in 1987 on mental calculation strategies used by 11-year-olds in England, Wales, and Northern Ireland. Classifies mental strategies developed in the past decade in international research. Compares frequency and effectiveness of the strategies used by pupils of different levels of attainment. Discusses basic arithmetic…

In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules.…

A class of 32 fourth graders, who studied inverse operations in grades 1-3, was given 3 written tests, each followed by an interview, to see how well they could simplify computations using inverse operations. Most could not evaluate 28 + 75 - 75, for example, without performing all operations. (GW)