This study compared how selected mathematics textbooks from Mainland China and the United States at the lower secondary grade level represent various types of problems for classroom teaching and learning. The examination of problems was carried out based on the classifications of problem types established in the study, including routine problems…

Arithmetic algorithms include two types of rules: conventional rules that may be changed by authority, and may legitimately vary from one classroom or country to another (e.g. putting the sum below, rather than above, the numbers added) and logical rules that involve the logic of the algorithm. Changes in the logical rules produce incorrect…

The purpose of this paper is to contribute to the debate about how to tackle the issue of "the teacher in the teaching/learning process", and to propose a methodology for analysing the teacher's activity in the classroom, based on concepts used in the fields of the didactics of mathematics as well as in cognitive ergonomics. This…

The inspiration for this article was not conceived over lunch, but more specifically over the box in which the lunches were packaged. Five colleagues brainstormed ideas for teaching a unit on trees for the third grade that would fit in our boxes. The disciplines involved were art, children's literature, science, social studies, and technology.…

We investigated how size and depth are perceived in a plane or convex mirror. In Experiment 1, using a plane or convex mirror, 20 observers viewed a separation between two objects that were presented at a constant distance and reproduced it by a separation between other two objects in a natural viewing situation. The mean matches generally…

Many mathematics educators share a view of mathematics as a social and cultural phenomenon and believe that the learning of mathematics concepts is developed and enhanced through the use of learning communities. Electronic discussion boards provide one avenue for supporting such social learning. This paper discusses the use of a Question and…

How can it be explained that, aside from inter-individual differences, pupils in certain classes are more responsive than others to the formal aspects of a problem that has been set? The author puts forward the hypothesis that teachers differ in their ability to operate relevant variations in the conception of problems. The differences in…

This study involved an investigation of the relationship between the kinds of solution representations Chinese and U.S. students use and the sorts of pedagogical representations Chinese and U.S. teachers use during instruction. The findings suggest that the representations teachers use influence the representations their students use and, hence,…

This article extends a framework for the study of culture-cognition relations to problems of historical research and diachronic analysis. As an illustrative case, we focus on mathematics in Oksapmin communities located in a remote highland area in central New Guinea. The Oksapmin, like their neighboring Mountain-Ok groups to the West,…

To help students understand the real-world applications of calculus, our calculus students all take part in a lab. This is not another "computer lab" but a lab where the students perform experiments and then collect and analyze the data. The students are able to verify for themselves many of physical claims that are left as theory in…

The continuous technological progress of the past few decades affords a different orientation to the teaching-learning process, which is useful and advantageous when mathematical concepts are transmitted. This article pursues two different aims. The first one is to examine the present state of the traditional process in relation to the concepts of…

Statistics education is under review at all educational levels. Statistical concepts, as well as the use of statistical methods and techniques, can be taught in at least two contrasting ways. Specifically, (1) teaching can be theoretically and mathematically oriented, or (2) it can be less mathematically oriented being focused, instead, on…

Children's literature can enhance mathematics lessons by providing a meaningful context, demonstrating that mathematics develops from human experiences and contributes an aesthetic dimension to learning mathematics. Written as a series of real life inspired snapshots of mathematical thinking, "Counting on Frank" (Rod Clement, 1990)…

The compensatory-encoding theory (C-ET) of reading specifies how the efficiency of performance subcomponents affects comprehension under diverse task conditions. It maintains that readers can overcome weak skills through compensatory processes. To test whether C-ET captures more general principles underlying scholastic performance, the authors…

Since 1990, the January issue of "Teaching Pre K-8" has highlighted a school visit by the president of the National Council of Teachers of Mathematics. This article discusses Cathy Seeley's visit to a 6th grade classroom at the J. E. Pearce Middle School in Austin, Texas, where she participated in a math activity from the Connected…