Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…

Examined whether preschoolers could recognize numerical equivalence for comparisons involving sequentially presented sets. Found that children recognized numerical equivalence for static sets earlier than for sequential sets. Memory of the number of sequentially presented objects emerged earlier than memory for the number of sequential events.…

Although computer scientists understand the importance of discrete mathematics to the foundations of their field, computer science (CS) students do not always see the relevance. Thus, it is important to find a way to show students its relevance. The concept of program correctness is generally taught as an activity independent of the programming…

Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…

Undergraduate programs across the nation are increasingly offering interdisciplinary study programs as markers of their commitment to educate individuals for the demands of contemporary life. Yet, as students engage in interdisciplinary learning projects, an unaddressed question looms large: how to adequately assess student interdisciplinary work.…

This article presents a series of lessons in which grade 5/6 students use measurement activities to design and construct proportion dolls. This article highlights how measurement can connect learning about percents, decimals, and proportions. (Contains 5 figures.)

This article describes one way of embedding remediation in the context of studying more advanced mathematical concepts. In the process of doing so, ways to foster mathematical argumentation and proof are also introduced.

Although this article is reprinted from a 1978 issue of "Arithmetic Teacher," its content is relevant to today's conversations about the roles of conceptual understanding and procedural fluency in the teaching of mathematics. This article attempts to advance and demonstrate the proposition that moves in teaching mathematics can serve as a basis…

We describe a simple undergraduate exercise involving the titration of a weak acid by a strong base using a pH meter and a micropipette. Students then use their data and carry out graphical analyses with a spreadsheet. The analyses involve using mathematical concepts such as first-derivative and semi-log plots and provide an opportunity for…

Two ideas of mathematics that the students discuss here, demonstrate how sometimes a teacher can learn something new from the students. The examples given use geoboard and show relationships of the two ideas with the Pick's theorem.

For the last three years the author of this paper has been teaching mathematics to a group of students at Year 9 level who have rarely had success in mathematics, particularly in the area of algebra. Most of these students struggle with algebraic concepts and processes and generally have poor retention of any acquired knowledge. For the two years…

After figuring out why many kids hate math, these longtime educators Bob and Ellen Kaplan created an after-school program in which children as young as 5 formulate equations of their own--and actually enjoy doing it. This paper discusses the experiences of the Kaplan couple, Bob and Ellen, on their Math Circle class during after-school sessions…

The history of mathematics is full of rich examples that can help students to see the place of the discipline within our cultural heritage. Valuable as this can be, it also has the unfortunate side-effect of making students think that all the math has already been done and they do not get a sense that the subject is dynamic and growing.…

If one rolls a coin across a chessboard and it comes to rest on the board, what is the probability that it covers some corner of one of the grid squares? The online magazine "Plus" (2004) posed this problem for students to solve. It is a useful problem for several reasons: it introduces the idea of probability in a continuous sample space, it has…

The National Council for Teachers of Mathematics (NCTM; 2000) encourages students to experience mathematics in multiple contexts, including science, history, physical education, business sciences, and agricultural sciences. All educators, including professionals such as orientation and mobility specialists who work with students who are visually…