The Use of Representation in Content Designed for Online Mathematics Instruction

The opportunity to learn mathematics through an online course grows with the expansion of distance education in higher education and in K-12 virtual schools. Instructors may develop course content, but this is time and labor intensive. Content may also be obtained through free Internet sources (freeware) or by purchase from a vendor (purchaseware). How these two sources of content compare has been largely unexplored in the literature.

When learning mathematics online the instructional content is accessed through a computer interface. External representations are used in the content to communicate mathematical ideas. Systems of multiple external representations may be used to provide multiple perspectives on the knowledge domain or multiple entry points for diverse learners. Representations available in online mathematics instruction can include static forms such as verbal text, mathematical text, graphics, and tables. Additionally, there are technologically supported dynamic representations such as animations, audio clips, video clips, and interactive components that respond to user input.

This study was conducted to compare free Internet content and vendor produced content for the use of representation in communicating mathematical ideas. Two research questions were posed. First, how do the types of representations used in Web-based instructional content for mathematics originating from different sources compare? Second, how does representational function, as described by the Ainsworth (1999b) taxonomy, compare within content originating from different sources? These questions were answered through a mixed-method content analysis study.

Content was included in this study if it was available and accessible for research purposes. In addition to this, the content was chosen based on the criteria that it had been developed to teach how to solve, derive, or graph quadratic equation problems. Ten units of purchaseware and 156 units of freeware were selected for analysis.

Results from the study indicated that purchaseware content was denser than freeware and had larger means, minimum frequencies, and maximum frequencies for all categories of representation. Similarities appeared in the correlations between static representation categories of verbal text, mathematical text, graphics, and tables, for both purchaseware and freeware. Similarities in the function of representations were also similar in the static representations. Differences appeared in the technological representation categories of animation, audio clip, video clip, and interactive components.

The conclusions of this research are that differences do exist between freeware and purchaseware. These differences involve the amount of content per unit and the extent of technological representation usage in communicating mathematical concepts. Experimental research is the next step in determining how students respond to combinations of representations when learning mathematics online.