This report describes and interprets findings from the 1981-82 national mathematics assessment, the third such assessment conducted by the National Assessment of Educational Progress. The results show a leveling off of the performance of American 17-year-olds, who had shown a decline between 1978 and 1982; 9-year-olds' performance has changed…

Energy is a problem affecting all individuals. To help today's students understand the problem and become realistic decision-makers, materials have been developed by the Sunny Side Up (in Mathematics) program to introduce energy concepts into the mathematics curriculum. Objectives of the program are to: (1) provide highly effective practice in…

Reports on research designed to systematically examine how the use of personalized word problems as practice examples would affect learning and attitudes. A computer program was used to generate the problems. It was concluded that presenting problems in familiar contexts made materials more interesting and understandable for students. (PK)

Offers examples of non-standard mathematical application problems. The applications come from a variety of areas including industry and other cultures. (PK)

Argues that Turtle Geometry has a great deal to offer mathematics teaching and learning. Suggests that it helps develop general problem-solving strategies and encourages new approaches to teaching and learning. (PK)

Describes responses of fifth to eighth grade students to different types of test items requiring estimation. Reports that performance differed by item format, types of numbers and operations in the items, and grade level of students. (Author/YP)

Presents a series of five activities that introduce division of fractions through real-world situations. Discusses problems related to resurfacing a highway, painting dividing stripes on a highway, covering one area A with another area B, looking for patterns, and maximizing the result of a division problem. Includes reproducible worksheets. (MDH)

Proposes three types of supplementary problems to develop students' skill in interpretation of graphically represented data. Eleven examples are presented and solved for the following types of problems: comparison of one quantity to another, comparison of two quantities that each depend on a common parameter, and reasonable data prediction. (MDH)

The relationship between quantitative problem solving and commonsense has provided the basis for an expanding exploration for Colleran and O'Donoghue. For example the authors (Colleran et al., 2002, 2001) discovered the pivotal role commonsense plays in adult quantitative problem solving and suggest commonsense is an important "resource? in…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…

Background: Understanding and solving problems involves different levels of representation. On the one hand, there are logico-mathematical representations, or problem models (PMs), which contain information such as "the size of the flock changed from 31 sheep to 42" while, on the other hand, there are more qualitative representations, or…

This study examined the strategies used by pre-service teachers when responding to number sense related questions. 15 pre-service teachers from one University in Southern Taiwan were interviewed. Results indicated that about one-third of these pre-service teachers were able to use number sense strategies (such as understanding the meaning of…

Students often find their first university linear algebra experience very challenging. While coping with procedural aspects of the subject, solving linear systems and manipulating matrices, they may struggle with crucial conceptual ideas underpinning them, making it very difficult to progress in more advanced courses. This research has sought to…

Last year, the author worked with a group of Key Stage 3 (KS3) consultants at a regional roadshow devoted to the topic of information and communications technology (ICT), "Embedding ICT in mathematics teaching." The roadshow was organized by the Association of Teachers of Mathematics (ATM) and the Mathematical Association (MA), and the…