An important approach for developing children's algebraic thinking involves introducing them to generalized arithmetic at the time they are learning arithmetic. Our aim in this study was to investigate children's attention to and expression of generality with the subtraction-compensation property, as evidence of a type of algebraic thinking known…

Teachers whose mathematical meanings support understanding across different contexts are likely to convey them in productive ways for coherent student learning. This exploratory study sought to elicit 67 secondary mathematics pre-service teachers' (PSTs) meanings for quadratics with growing pattern creation and multiple translation tasks. A…

We examine teachers' use of resources as they prepare to teach the topic of numerical series of real numbers, in order to identify how their "personal relationship" with mathematical content--and its teaching--interacts with their use of a commonly used textbook. We describe this interplay between textbook and personal relationship, a…

Currently, instruction pays little attention to the development of students' sampling variability reasoning in relation to statistical inference. In this paper, we briefly discuss the especially designed sampling variability learning experiences students aged about 15 engaged in as part of a research project. We examine assessment and…

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…

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students' understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus…

Explores the relationship between learners' actions, visualizations, and the means by which these are articulated. Describes a microworld called Mathsticks which is designed to help students construct mathematical meanings by forging links between the visual and symbolic representations they develop and their actions. Presents a case study of two…