The development of proportional reasoning has long been recognised as a central but problematic aspect of mathematics learning. In a Year 6 teaching intervention the part/whole notion of fractions was distinguished from the part: part notion of ratio, and the "between" and "within" relationships in ratio were emphasised.…

There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing,…

This report explores first year undergraduate mechanical engineering and mathematics students' conceptions of the derivative and the contribution that membership of different departments may have on these conceptions. Quantitative results suggest that mechanical engineering students develop a proclivity for rate of change aspects of the derivative…

This is a study of how urban elementary grades students develop and express functions. Data were analyzed according to the forms of representations students used, the progression in students' mathematical language and the operations they employed, and how they attended to one or more varying quantities. Findings indicate that students are capable…

Three hundred and twenty-four middle school students considered a group of three graphs in a newspaper article about boating deaths. The graphs contained discrepancies and the students were asked to "comment on unusual features." This form of questioning produced a distribution of responses surprising to the authors and perhaps…

In a previous study, we posited a link between Chinese sixth grade students' problem solving and problem posing based on a pattern-formation strategy (Cai & Hwang, 2002). A similar parallel structure between problem solving and problem posing did not obtain for the U.S. sixth graders in the study. The present study attempts to locate this type of…

Assessment practices influence and are influenced by a number of educational as well as social factors. The present study looks at these practices of five primary teachers displayed in the mathematics classroom and in a relevant pedagogical discourse developed in the context of an interview. The results show that, on the whole, their practices…

According to the Third International Mathematics and Science Study (TIMSS) which compared student performance in mathematics and science in 41 countries in 1995, fourth grade students in the United States perform only slightly above the international average in mathematics. The study showed that most U.S. students are mastering basic arithmetic;…

What should constitute a preschool mathematics program for children ages 3 and a half to 5 years? What mathematical ideas could youngsters explore? This paper discusses six broad mathematical concepts for investigation by preschoolers: number, space and location, shape, patterns, measurement, and permutations. For each big idea, activities are…

It is well known that math phobia is a common problem among young school children. It becomes a challenge to educational practitioners and academic researchers to figure out ways to overcome the problem. Collaborative team learning has been proposed as one of the alternatives. This study was part of a large and ongoing research project designed to…

Two South Australian studies--an initial and a follow-up study--explored the extent to which students are able to retain knowledge or skill learned in one context and reproduce this knowledge or skill in a different context. Study 1 was conducted with 121 Year 10 students in a country secondary school; study 2 was conducted with 72 Year 10…

Data from the National Adult Literacy Study (NALS) are used to analyze the prose, document, and quantitative literacy of U.S. teachers and compare them to the literacy of other adults. More than 26,000 people were interviewed for the NALS. As a group, teachers score relatively high in prose, document, and quantitative literacy, and there are no…

This report is one in a series of reference documents designed especially to assist educators who are directly involved in the revision and improvement of content standards. It presumes a basic understanding of the purposes for standards and the process of standards review and evaluation. This document is intended to be a desktop reference volume…

Instructional resources that employ multiple representations have become commonplace in mathematics classrooms. This study will present computer software, LaborScale which was designed to improve seventh grade students' word problem-solving skills through computer-based multiple representations including graphic, symbolic, and audio…

Criticizes the use of new biological theories of human behavior to inform educational policy. Discusses a study by Benbow and Stanley on differential math performance by boys and girls, to illustrate problems inherent in attempts to link a biological substrate with human achievement. (Author/GC)