Recent developments in cognitive and educational science highlight the role of the body in learning. Novel digital technologies increasingly facilitate bodily interaction. Aiming for understanding of the body's role in learning mathematics with technology, we reconsider the instrumental approach from a radical embodied cognitive science…

This paper focuses on the emergence of abstraction through the use of a new kind of motion detector--WiiGraph--with 11-year-old children. In the selected episodes, the children used this motion detector to create three simultaneous graphs of position vs. time: two graphs for the motion of each hand and a third one corresponding to their…

Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the general structure of lectures. In this paper, we adapt ideas from narrative analysis and apply them to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture…

It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle,…

A teaching experiment-using Mathematica to investigate the convergence of sequence of functions visually as a sequence of objects (graphs) converging onto a fixed object (the graph of the limit function)-is here used to analyze how the approach can support the dynamic blending of visual and symbolic representations that has the potential to lead…

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…

From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

Using Freudenthal's method of historical phenomenology, the history of statistics was investigated as a source of inspiration for instructional design. Based on systematically selected historical examples, hypotheses were formulated about how students could be supported in learning to reason with particular statistical concepts and graphs. Such a…

The iconographic means of illustrating mathematical facts is discussed along with several examples of graphical solutions to descriptive mathematics problems proposed by pupils. (MN)

We start from the assumption that school mathematics knowledge could be better explained if social practices were considered to be generators of knowledge. This perspective changes the way we look at what school mathematics knowledge is and what it takes to teach and learn it. In this article, we will present a teaching situation about periodic…

Approaches to developing a good mathematics textbook for the junior high student are discussed, with the pitfalls and difficulties reviewed. Examples from new Polish textbooks are presented to illustrate possible solutions. (MP)

Investigates students' abilities to draw inferences. Introduces cognitive conflict in the form of video clips of reasoning expressed by students. Documents change with regard to the levels of observed response for the protocol and the use of displayed variation in the graphs. Analyzes change associated with the presentation of cognitive conflict.…