Model Eliciting Activities and Reflection Tools for Problem Solving
(Summarized by: Dr.
Geetanjali Soni, LITRE assessment coordinator)
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Model Eliciting Activities were developed by mathematics education researchers (Lesh, 1998, 2002) to better understand and encourage problem solving. An MEA is an activity that is “thought-revealing and model-eliciting (Lesh, Hoover et. al, 2000) and have been adapted for other areas such as engineering (Diefes-Dux et al, 2004, 2006; Hjalmarson, 2006) and gifted education (Chamberain and Moon, 2005)
MEA’s are designed to encourage students to build mathematical models in order to solve complex problems, as well as provide a means for educators to better understand student’s thinking,. MEA’s are based on six specific principals (Lesh et. al 2000) and involve careful development and field-testing. For examples of MEA’s see Lesh & Yoon (2004)
The Six principles for designing MEA’s are (Lesh et. al 2000):
1. Model Construction principle: problems must be designed to allow for the creation of a model dealing with elements, relationships and operations between these elements, patterns and rules governing these relationships etc.
2. The Reality Principle: problems must be meaningful and relevant to the students.
3. Self-assessment principle: students must be able to self-assess or measure the usefulness of their solutions.
4. Construct documentation principle: students must be able to reveal and document their thinking processes within their solution.
5. Construct shareability and reusability principle: solutions created by students should be generalizable or easily adapted to other situations.
6. Effective Prototype principle: others should easily be able to interpret solutions.
Researchers have also developed a series of reflection tools that help students think about and record specific strategies they use while problem solving and about group functioning.
Diefes-Dux H., Follman, D., Imbrie, P.K., Zawojewski, J., Capobianco, B. and Hjalmarson M. (2004) Model Eliciting Activities: An In-class Approach to Improving Interest and Persistence of Women in Engineering. Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition. American Society for Engineering
http://www.iwitts.com/html/022diefes-dux.pdf
Lesh, R. (1998). The development of representational abilities in middle school mathematics: The development of student's representations during model eliciting activities. In I.E. Sigel (Ed.), Representations and student learning. Mahwah, NJ: Lawrence Erlbaum.
Lesh, R. (2002). Research design in mathematics education: Focusing on design experiments. In L. English (Ed.), International handbook of research design in mathematics education, 2002. Mahwah, NJ: Lawrence Erlbaum.
Lesh, R., & Doerr, H. M. (2003). Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Mahwah, NJ: Lawrence Erlbaum.
Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education. Mahwah, NJ: Lawrence Erlbaum.
Lesh, R., & Kelly, A. (1997). Teachers' evolving conceptions of one-to-one tutoring: A three-tiered teaching experiment. Journal for Research in Mathematics Education, 28(4), 398–430.