PRE-SERVICE TEACHERS’ MODELLING PROCESSES THROUGH ENGAGEMENT WITH MODEL ELICITING ACTIVITIES WITH A TECHNOLOGICAL TOOL

Abstract

Engaging mathematics students with modelling activities helps them learn mathematics meaningfully. This engagement, in the case of model eliciting activities, helps the students elicit mathematical models by interpreting real-world situation in mathematical ways. This is especially true when the students utilize technology to build the models. Researchers have been interested in the phases of modelling processes that students go through when engaging with modelling activities, where looking at these phases from a cognitive aspect gives us insight regarding students’ processes of mathematizing real situation. This was the goal of this research, specifically when middle school pre-service teachers use technology in model eliciting activities. Six groups of pre-service teachers participated in the research engaging in modelling the “summer reading activity.” Three different cycles of modelling processes were identified, differing in the phase of technology use and in its role in building the models. This variability in pre-service teachers’ utilization of technology, in our case the spreadsheets, imply that the technology which is appropriate for a specific modelling activity could be a flexible tool used by the learners to mathematize the real-life situation expressed in the activity.

Appendices

Appendix (1). The “Summer Reading Activity,” as in English & Fox (2005)

Information: The Brisbane City Council Library and St. Peters School are sponsoring a summer reading program. Students in grades 6–9 will read books and prepare written reports about each book to collect points and win prizes. The winner in each class will be the student who has earned the most reading points. The overall winner will be the student who earns the most points. A collection of approved books has already been selected and put on reserve. See the previous page for a sample of this collection. Students who enroll in the program often read between ten and twenty books over the summer. The contest committee is trying to figure out a fair way to assign points to each student. Margaret Scott, the program director, said, “Whatever procedure is used, we want to take into account: (a) the number of books, (b) the variety of the books, (c) the difficulty of the books, (d) the lengths of the books, and (e) the quality of the written reports.”

Note: The students are given grades of A+, A, A−, B+, B, B−, C+, C, C−, D, or F for the quality of their written reports.

Your mission: Write a letter to Margaret Scott explaining how to assign points to each student for all of the books that the student reads and writes about during the summer reading program.

Appendix (2). Analysis of the “summer reading activity” in terms of mathematical ideas, cognitive processes and meta-cognitive processes

The cognitive processes involved reading the activity text, interpreting it in real-world terms, interpreting it in mathematical terms, comparing between the components of evaluation (which component should have more points), discussing a mathematical idea and constructing mathematical/ spreadsheet representations, etc.

The meta-cognitive processes involved deciding how to grade each component of the evaluation, deciding how to use the spreadsheets to build a model, discussing/planning how to proceed with the activity, deciding on the next step of building a model, etc.

The mathematical concepts/ideas involved ratio, correspondence, sum, range and function.