Representation in science is anything that stands for something else--drawings, pictures, graphs, or other representational forms (Danish et al. 2020). Representations serve as public displays of phenomena that make aspects of those phenomena explicit (Gilbert 2008). They can serve to make the invisible visible, communicate ideas, display…

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…

The learning process for a user becomes seriously restrictive in trying to discover the relationships between concepts and in searching for a part of concept (called an object) such as a solved example illustrating the concept or the application of the concept. This article presents the theory for building a relational graph that depicts how…

In this article, we will describe the results of a study of 6th grade students learning about the mathematics of change. The students in this study worked with software environments for the computer and the graphing calculator that included a simulation of a moving elevator, linked to a graph of its velocity vs. time. We will describe how the…

This paper describes the possible effects of feedback on learning (associations) using a connectionist tool, the delta rule. Feedback in instruction can be described in terms of the interaction of stimulus inputs and response outputs, an associationist perspective. Here the delta rule is applied to each instance that an input and an output likely…

Describes the different effects for four types of activities on students' pronunciation of targeted second-language (L2) vocabulary used in oral presentations. Samples of pronunciation were elicited at three points. The observed effects over time are presented graphically, and the complex learning processes underlying these effects are discussed.…

Statistical data can be represented in a number of qualitatively different ways, the choice depending on the following three conditions: the concepts to be investigated; the nature of the data; and the purpose for which they were collected. This paper begins by setting out frameworks that describe the nature of statistical thinking in schools, and…

Replicates an earlier study that used videotapes to examine the types of errors made by novice economics students in graphic analysis of a simple supply-demand problem. Further explores the issue by improving the framework for analyzing errors and documenting some methods used by novice groups to correct errors. (MJP)