Much important research on the learning of mathematics with technology-supported inquiry has been devoted to learning with multiple-linked representations (MLR) as a mode of feedback. Like a mirror, MLR feedback helps students see their actions in one representation "reflected" in another. Yet, research has followed learning episodes…

In light of the recent growing interest in conceptual learning and teaching of calculus, and especially with the focus on using technological environments, our study was designed to explore the learning processes and the role played by multiple-linked representations and by interactive technological environment in objectifying the accumulation…

The present study focuses on the accumulation process involved in the integration of a single-variable function. Observing the work of two high-school calculus students who had not yet learned any other integral-related ideas, we analyze the emergence of the semiotic relationship between personal and mathematical meanings, as expressed through the…

This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpreting graphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of…

Used software environment to examine algebra students' attempts to reformulate narratives using verbal and iconic lexical sets. Described how natural language text turns into a script of events and processes, how the qualitative graphic description of the script is sketched using iconic notations, and how the graph turns into a subject for…

This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, and…

Describes an algebra course organized around the concept of function and based on intensive use of technology. Includes an explanation of the assessment sequence used to explore students' use of familiar representations and procedures to reason logically and to solve and communicate about unfamiliar tasks. (DDR)

Effects of graphic representations of algebraic functions on performance of tasks involving expression transformations were studied for 28 teachers debugging transformed expressions through syntactic manipulations (SYMs) or semantic interpretation (SEI). Those using SEI improved performance using graphs. Some positive effects of graphic feedback…