Students Use Interactive Web-Based Materials?

Lawrence C. Moore, and David A. Smith

**Background: Web-Based Interactive Materials. **In recent years there has been a growing consensus among policy boards regarding the essential steps in reforming mathematics and science education. Chambers and Bailey (1996) summarized several reform reports [National Council of Teachers of Mathematics (1991); National Research Council (1991); National Science Foundation (1996)] and concluded that there are six overarching recommendations:

- Integrate the teaching of science and math.
- Emphasize cooperative learning.
- Focus on application and relevant problem solving.
- Teach primarily through discovery learning as opposed to lecture.
- Attend to the motivation of learners.
- Use technology in meaningful ways.

The interactive materials used in this study are those of the Connected Curriculum Project, which addresses each of these six recommendations in the context of lower division college mathematics (see Coyle, et al., 1998, and Colvin, et al., 1999). CCP provides web pages for labs and projects that contain text, hyperlinks, graphics, Java applets, and problems, plus downloadable CAS files in which students respond to challenges, control the interaction, and write a report that may be submitted for a grade. Authors LCM and DAS are the co-directors of CCP, and authors JB and DM are studying how students learn with the CCP materials.

Our work is based on a constructivist perspective in which the learning process is described as "a self-regulated process of resolving inner cognitive conflicts that often become apparent through concrete experience, collaborative discourse, and reflection" (Fosnot, 1993). Portela (1999) notes that "... constructivism has more relevance in education today because the dawn of the Information Age has rapidly increased the amount of, and accessibility to, information." At the same time, he notes the scarcity of studies of how students learn in an information-rich environment. The purpose of the current study is to develop, based on observations of students' work, a set of research questions that will help us understand how students learn in the CCP environment.

**Experimental Setup and Methodology.** Since little research has been done in this area, this phase of the research is necessarily exploratory in nature. In our view, the most appropriate methodology for this type of research is Glaser’s notion of *grounded theory*, which he described as "the discovery of theory from data systematically obtained from social research," and which he contrasted with "theory generated by logical deduction from *a priori* assumptions" (Glaser and Strauss, 1967). Our data gathering methods can be described using Romberg’s method of clinical observations in which "the details of what one observes shift from predetermined categories to new categories, depending upon initial observations" (Romberg, 1992).

The subjects studied were students taking a mathematics course (at a level beyond calculus) in a major research university. These students had been using CCP materials for at least several weeks and were somewhat familiar with *Maple* and with the format of the modules. Students working together were videotaped, and their computer output was collected on a separate, simultaneous videotape. Clips from these simultaneous videotapes were shown as part of our presentation.

**Research Questions. **From the data we identified five categories of research questions:

- What is the role of the instructor in this environment?
- What is the role of the curriculum developer in preparing materials for this environment?
- What types of behavior and thinking processes are students engaged in as they work together in front of the computer?
- What is the importance of student self-monitoring and metacognition in computer based instruction?
- What opportunities and obstacles are raised by the technology itself?

Research in each of these areas has important implications for curriculum developers, mathematics instructors, and students. Here we list in outline form some of the questions prompted by our observations. For more details, see the longer paper (Bookman and Malone, submitted).

Among the questions about the role of the instructor are these:

- When and how should the instructor intervene, support, and guide students in their work?
- Should the instructor assign roles (e.g., hypothesizer, verifier, and recorder) to students within their teams?
- Should roles be structured to minimize the problem of one student taking over the learning situation?
- How can the instructor encourage students to discriminate between difficulties with the tools (e.g., hardware or software) and difficulties with mathematical concepts?
- How can the instructor facilitate productive dialogue among students?

For developers of online curricula, our questions include:

- How can one encourage students to reflect on the quality of their interactions with the materials?
- Can interdependence and shared responsibility, as well as other aspects of cooperative learning, be built into computer modules?
- How can one encourage self-monitoring and metacognition on the part of students?

In the area of student behavior, our data suggest the following questions:

- How, when, and why do students choose among their tools, such as paper and pencil, calculator, and computer algebra system?
- Who (if not the instructor) decides the roles that individuals assume?
- When and why do students use internal and external links provided in the online materials?
- What sorts of online or offline help foster cognition and metacognition?
- Is productive dialogue encouraged more by the environment or by the content of the materials?

Some of the questions with respect to self-monitoring and metacognition:

- How and why do students make time management decisions, for example, dividing their time among reflection, guessing and checking, calculating?
- How do students learn to check answers for reasonableness and for accuracy?
- How do students determine whether the discrepancies they find are due to mathematical or technical errors?

Finally, the technology-specific questions include:

- How long does it take to learn the nuances of the relevant software, and is this time well spent?
- How do students and teachers react to problems with hardware and software when they occur?
- How well does the software enable students to avoid time-consuming calculations, and how is the saved time spent?
- What are the implications of the growing technical sophistication of each new class of college students?

References

Bookman, J. & Malone, D. (submitted). The Nature of Learning in Interactive Technological Environments: A Proposal for a Research Agenda Based on Grounded Theory.

Chambers, Jack & Bailey, Clare. (1996). Interactive Learning and Technology in the US Science and Mathematics Reform Movement. *British Journal of Educational Technology*__ __(27), 123-133.

Colvin, M.R., Moore, L., Mueller, W., Smith, D. & Wattenberg, F. (1999). Design, Development, and Use of Web-based Interactive Instructional Materials. In G. Goodell (Ed.), *Proceedings of the Tenth Annual International Conference on Technology in Collegiate Mathematics*. Reading: Addison-Wesley.

Coyle, L., Moore, L., Mueller, W., & Smith, D. (1998). Web-Based Learning Materials: Design, Usage, and Resources, *Proceedings of the International Conference on the Teaching of Mathematics*, pp.71-73. Somerset, NJ: Wiley.

Fosnot, C. T. (1993). Rethinking Science Education: A Defense
of Piagetian Constructivism. *Journal for Research in Science Education*.

Glaser, B. G. & Strauss, A. L. (1967). *The Discovery of Grounded Theory*. Chicago: Aldine Publishing.

National Council of Teachers of Mathematics (NCTM) (1991). *Professional Standards for Teaching Mathematics.* Reston, VA: NCTM.

National Research Council (1991__)__. *Moving Beyond Myths: Revitalizing Undergraduate Mathematics.* Washington, DC: National Academy Press.

National Science Foundation (NSF) (1996). *Shaping the Future: New Expectations for Undergraduates for Undergraduate Education in Science, Mathematics, Engineering, and Technology.* Washington, DC: NSF.

Portela, J. (1999). Communicating Mathematics through the Internet – A Case Study. *Educational Media International, 36 *(1), 48-67.

Romberg, Thomas A. (1992). Perspectives on Scholarship and Research Methods. In D. A. Grouws (Ed.), *Handbook of Research on Mathematics Teaching and Learning*,* *pp.49-64. New York: Macmillan.