It is well known that students benefit from opportunities to interpret and create different representations (e.g., diagrams, graphs, tables, symbols) of mathematical ideas. Employing Marton's Variation theory as a lens, I argue for an expansion of the use of multiple representations in task design for graphs: Incorporate two different forms of the…

Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of…

On-demand education enables individual learners to choose their learning pathways according to their own learning needs. They must use self-directed learning (SDL) skills involving self-assessment and task selection to determine appropriate pathways for learning. Learners who lack these skills must develop them because SDL skills are prerequisite…

Over 10 years have passed since the publication of Carr and Burkholder's (1998) technical article on how to construct single-subject graphs using Microsoft Excel. Over the course of the past decade, the Excel program has undergone a series of revisions that make the Carr and Burkholder paper somewhat difficult to follow with newer versions. The…

Creating single-subject (SS) graphs is challenging for many researchers and practitioners because it is a complex task with many steps. Although several authors have introduced guidelines for creating SS graphs, many users continue to experience frustration. The purpose of this article is to minimize these frustrations by providing a field-tested…

Describes and compares three approaches to task analysis--behaviorally-based, concept-based, and cognitive process-based--and provides four tentative recommendations for determining which approach is appropriate in a particular situation. Five flowcharts and fourteen references are included. (MBR)

Discusses rationale for distinguishing between task analysis and instructional analysis, contributions they make to instructional design, and why they are dependent on each other. Major functions in the instructional analysis process are described, examples are provided, and benefits of using this approach to achieve effective and efficient…