An Examination of Model-Eliciting Activities Designed by Pre-Service Mathematics Teachers Based on Six Design Principles

Author(s):

Mesture Kayhan Altay(presenting / submitting)Şeyma Şengil Akar Elif Yetkin Özdemir

Conference:

ECER 2012

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 11, Mathematical Concepts and Teacher Education 2

Parallel Paper Session

Time:

2012-09-20

17:15-18:45

Room:

ESI 3 - Aula 2

Chair:

Contribution

Introduction

Models and modeling (M&M) perspective of mathematical thinking and learning gained greater attention with the reform movement began in2005, inTurkey. M&M perspectives focus on the development of knowledge, conceptual tools, and/or models in order to make decisions to solve complex, real-life problems (Lesh & English, 2005). These models and/or conceptual tools are “powerful (for some specific purposes), sharable (with other people) and reusable (beyond the context in which they were developed)” (Lesh & English, 2005, p. 488).

Model-eliciting activities (MEA)s are meaningful and interesting thought-revealing (Lesh, et al., 2000) activities that require students to express and adapt their current ways of thinking in order to interpret and develop useful tools/models to solve the complex, real-life problem situations. Lesh and his colleagues (Lesh, et al., 2000; 2002) described six principles for developing MEAs. These principles are:

1) The model construction principle: The task should require students to construct, describe, explain, manipulate, predict, and control structurally significant systems (i.e. models).

2) The reality principle: The task should involve a problem-situation that could really happen in real-life so that students could make sense of the problem by using their personal knowledge and experiences.

3) The self-assessment principle: The task should involve appropriate criteria for students so that they could assess/judge when their responses are finished or when it needs to be improved.

4) The construct documentation principle: The task should ensure that responding the question (by documenting givens, goals, and solution pathways) reveals students’ thinking (mathematical objects, relations, operations, patterns, and regularities).

5) The construct shareability and reusability principle: The conceptual tools or mathematical models developed as a product of the activity should provide a way of thinking that is shareable, transportable, easily modifiable, and reusable so that it could be applied to other situations.

6) The effective prototype principle: The model developed as the product of the activity should be significant, but also simple so that it could be used for a variety of structurally similar situations.

Activities that satisfy these principles explained above provide students opportunities to develop “sharable, manipulatable, modifiable, and reusable conceptual tools (i.e., models) for constructing, describing, explaining, manipulating, predicting, or controlling mathematically significant systems” (Lesh & Doerr, 2003, p. 1)

Problem Statement and the Purpose of the Study

Research has shown that pre-service and in-service teachers have difficulties in designing, approaching, as well as using MEAs in their mathematics classrooms (Bukova-Güzel, 2011; Yu & Chang, 2009). Currently, many teachers inTurkey are unfamiliar with M&M perspective. However, several faculties of education started offering elective courses for pre-service teachers so that they learn more about modeling perspective, and how to design and use (MEA)s in their future classes. In this study, we aimed to investigate pre-service mathematics teachers’ understanding of M&M perspective. For this purpose we examined MEAs developed by pre-service mathematics teachers who took an elective course related to mathematical modeling. We are particularly focused on to what extend pre-service mathematics teachers took into account the six principles for developing MEAs.

Method

This case study was conducted during the fall semester of 2011-2012 academic year with 30 pre-service mathematics teachers taking Modeling in Teaching Mathematics course. Participants were enrolled in a mathematics teacher education program in one of the large universities in Ankara, Turkey. They were in the second year of their undergraduate program. Data were collected during the Modeling in Teaching Mathematics course that was offered for the first time as an elective course. The course was offered for 14 weeks, two hours per week, by the two researchers. At the beginning of the course, 10 groups of three pre-service mathematics teachers were formed according to their GPA. As a requirement of the course, they were asked to design a MEA with their group by taking into account the six design principles (e.g., construction principle, reality principle, self-assessment principle) and apply to their peers. They were also required to present their MEAs to their classmates and write a report to explain their MEAs. Reports of MEAs and researcher’s detailed notes taken during the class discussions constituted data sources. These data were analyzed based on six principles of designing MEAs.

Expected Outcomes

Preliminary analysis has shown that pre-service teachers had difficulties in designing model-eliciting activities satisfying six design principles. Most of the pre-service mathematics teachers used “the reality principles” effectively on their designs. In particular, they considered sociocultural and local issues when they design their activities. We, however, observed that they struggled with conceptualizing and using other principles in designing MEAs. For instance, pre-service teachers assumed that they satisfied “the model construction principle” if their task required a variety of solutions that make students engage with mathematical concepts. Furthermore, pre-service teachers pointed out that their MEAs satisfied “the model documentation principle” because the task included merely writing activities to explain their thinking. Findings also showed that pre-service teachers confused “the construct shareability and reusability principle” with “the effective prototype principle.” To conclude, it is possible to state that providing opportunities for pre-service teachers to engage them with designing MEAs is crucial to get deeper information about how the pre-service teachers constructed the MEAs based on these six principles. More detailed analysis and findings of the study will be discussed in the paper.

References

Bukova-Güzel, E. (2011). An examination of pre-service mathematics teachers’ approaches to construct and solve mathematical modeling problems. Teaching Mathematics and Its Applications, 30, 19-36. Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly and R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591-645). Mahwah, NJ: Lawrence Erlbaum. Lesh, R., Cramer, K., Doerr, H., Post, T., Zawojewski, J., (2002) Model Development Sequences. In Lesh, R., Doerr, H. (Eds.) Beyond Constructivism. Models and modeling perspectives on mathematics problem-solving, learning, and teaching. Lawrence Erlbaum Associates, Mahwah, New Jersey. Lesh, R. & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H.M. Doerr (Eds.), Beyond Constructivism: Models and modeling perspectives on mathematics problem-solving, learning, and teaching (pp.3-34). Mahwah, NJ: Lawrence Erlbaum Associates. Lesh, R. & English, L.D. (2005). Trends in the evolution of models & modeling perspectives on mathematical learning and problem solving. The International Journal of Mathematics Education (ZDM), 37 (6), 487-489. Yu, S. & Chang, C. (2009). What Did Taiwan Mathematics Teachers Think of Model-Eliciting Activities and Modeling? 14. International Conference on the Teaching of Mathematical Modeling and Applications, ICTMA-14, University of Hamburg, Hamburg.

Author Information

Mesture Kayhan Altay (presenting / submitting)

Hacettepe University

Elementary Mathematics Education

Ankara

Şeyma Şengil Akar

Hacettepe University, Turkey

Elif Yetkin Özdemir