Starting from a situated cognition perspective, this paper reports on the activity of 9th grade students who are interpreting the shape of a graph arising from the motion of a bouncing ball. In an unfamiliar context, informed by previous knowledge of similar experiments, the obstacle of understanding why the graph does not start from the origin is…

The teaching and learning of early algebra draw heavily on arithmetic and the relationship between these two forms of activity is much debated. Drawing on interviews with 12 year old pupils we consider the ways in which some pupils used substitution of numbers for letters to extend their ability to manipulate algebraic expressions. We argue that…

Increasing numbers of mathematics educators, policy makers, and researchers believe that algebra should become part of the elementary education curriculum. Such endorsements require careful research. This paper presents the general results of a longitudinal classroom investigation of children's thinking and representations over two and a half…

A series of 13 survey questions based on a 50-50 spinner is used to explore school students' understanding of statistical variation in a chance setting. Five questions set the context by assessing understanding of theoretical expectation and representation of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to…

This paper reports on research conducted to understand undergraduate students' ways of reasoning about systems of differential equations (SDEs). As part of a semester long classroom teaching experiment in a first course in differential equations, we conducted task-based interviews with six students after their study of first order differential…

A conception of discussing mathematical material in the domain of calculus is outlined. Applications include that university students work at their knowledge and prepare for their oral examinations by utilizing the dialog system. The conception is based upon three pillars. One central pillar is a knowledge base containing the collections of…

A Year 3 angles unit using the Teaching for Abstraction paradigm was developed on the basis of earlier empirical research and trailed by 12 New South Wales (NSW) teachers. Analysis of data submitted by the teachers showed that the unit was generally successful but a number of minor areas for improvement were identified. An analysis of independent…

To set goals and make informed choices, students need an array of thinking and problem-solving skills. Fundamental to this is an understanding of mathematical techniques and processes that will enable them to apply the basic skills necessary to address everyday mathematical situations, as well as acquire higher order skills in logical analysis and…

This paper explores the mathematical education of electronic engineering students through an analysis of how mathematics is constituted for the purpose of learning in a university setting. The nature and role of mathematics, offered to students via implicit and explicit messages within mathematics and engineering discourse, is described.…

This study attempted to show that students that are classified as visual learners will score higher on standardized tests than those students that are classified as non-visual learners because visual learners possess the traits needed to do well on standardized tests. The study used (33) visual and (33) non-visual adult learners in the adult basic…

This study attempted to determine which teaching method, mainly manipulatives or the standard curriculum, best allowed the students to learn first grade math concepts. The manipulatives consisted of objects such as unifix cubes, personal chalkboards, work mats, and various other articles, which allowed the students to see the math that they were…

This Middle School Course of Study document is designed to be user friendly. Units can be used sequentially and each unit may need a different amount of time to complete. When using this document, consider the students' prior knowledge and their understanding of the concepts. The Idaho Mathematics Achievement Standards are consistently referenced…

Mathematical practices and knowledge are often in dispute for those race and class identities at the margins of social power. This talk will describe both the ways in which mathematics can be complicit with social domination, and the ways in which it can aid in resistance and reconfiguration. It will end with a presentation of Culturally…