Research has shown that the tools provided by dynamic geometry systems (DGSs) impact students' approach to investigating open problems in Euclidean geometry. We particularly focus on cognitive processes that might be induced by certain ways of dragging in Cabri. Building on the work of Arzarello, Olivero and other researchers, we have conceived a…

This paper describes the experience of a group of 17 prospective mathematics teachers who were engaged in a series of activities aimed at developing their awareness of creativity in mathematics. This experience was initiated on the basis of ideas proposed by the participants regarding ways creativity of school students might be developed. Over a…

We propose to mine temporal patterns in Intelligent Tutoring Systems (ITSs) to uncover useful knowledge that can enhance their ability to provide assistance. To discover patterns, we suggest using a custom, sequential pattern-mining algorithm. Two ways of applying the algorithm to enhance an ITS's capabilities are addressed. The first is to…

Can middle-grades students determine which of two rectangular prisms has a larger volume? Can they do so without using a formula? Geometry, and particularly the concept of volume, is important in many subjects, such as physics and chemistry. Students greatly enhance their mathematics knowledge when they make generalizations and construct arguments…

"Help! I'm stuck!" How many times have you heard a student make a similar plea? What do you consider when deciding how to respond? What reasoning is most productive? As part of a large research project, the authors explored these questions with 131 prospective and practicing teachers and found patterns in their reasoning. They began their project…

This paper reports on the experiences of a group of teachers engaged in an action research project to develop critical numeracy classrooms. The teachers initially explored how contexts in the media could be used as bases for activities to encourage student discernment and critical thinking about the appropriate use of the underlying mathematical…

This report provides evidence of the influence of a tutorial "communication game" on fifth graders' generative understanding of the integer number line. Students matched for classroom and pretest score were randomly assigned to a tutorial (n = 19) and control group (n = 19). The tutorial group students played a 13-problem game in which…

A common textbook problem asks students to calculate the total distance traveled by a bouncing ball, from its initial release until it comes to rest, under the assumption that the height of each bounce is some fixed proportion "r" of the height of the previous bounce. The solution is found by inserting information about "r" and the height from…

Graphing bivariate data in a scatter plot and drawing an approximate line of best fit for the data have become commonly recommended activities for middle school and high school students. The graphing calculator has provided a mechanism for students both to approximate a best-fit line and to calculate the best-fit line using a built-in option. Two…

Introduction: This study aimed to investigate the errors made by 265 Form 2 male students in simplifying algebraic expressions. Method: A total of 265 Form 2 (Grade 7) male students were selected for this study. 10 high, medium and low ability students in each group were selected for the interviews. 40 items were administered to the respondents to…

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

In this article I report on a study of the cognitive tools that research mathematicians employ when developing deep understandings of abstract mathematical definitions. I arrived at several conclusions about this process: Examples play a predominant role in understanding definitions. Equivalent reformulations of definitions enrich understanding.…

The purpose of this study was to assess 81 kindergarten teachers' pedagogical content knowledge of mathematics on six subcategory areas such as number sense, pattern, ordering, shapes, spatial sense, and comparison. The data showed participants possessed a higher level of pedagogical content knowledge of "number sense" (M = 89.12) compared to…

Numeracy is as essential to becoming an active and thoughtful citizen as literacy. Although the concept of numeracy is complex and robust, there are four areas in which teachers can fairly easily begin to incorporate it into social studies curriculum and instruction. The areas include the students' ability to understand raw numeric data in…

This study examines how students in the early stages of learning about the concept of functions, describe a curve and, in particular, evaluate the appropriateness of their argument about the representation of a function. Students are offered a message game which is related to a curve drawn on a coordinate system, representing an "imaginary…