Portfolio for Models: an Instructional Tool


Models as an Instructional Tool

A professional development course for instructors on creating and implementing models in the classroom as an effective instructional tool to teach abstract and complex concepts.

This course will focus on the use of models in the mathematics classroom. As several students have commented on during class discussions, students often have a difficult time understanding mathematics and the importance of it; they simply memorize and implement formulas. Throughout my mini-course, I would like to show teachers how effective models are in increasing the understanding of high-school mathematics and the application of various topics students study. For example, a model of a Ferris wheel can be used to show one application of trigonometric graphs.

Topics to be addressed:

  • what models are
  • the benefits of including models in instruction
  • how to properly implement a model
  • examples of effective models


Instructional problem

The need for professional development programs for instructors who may not have the knowledge, information, or skills on how to implement effective models, which is a critical component to ensure students have a deep understanding of all math topics learned and the real-life applications of each.

The nature of what is to be learned

Instructors will learn how to effectively implement models in a mathematics classroom.

About the learners

Workshop participants are future or current teachers of mathematics, mostly in the middle school or high school setting. The participants have voluntarily registered for this professional development lesson. The participants are both intrinsically and externally motivated and will be engaged participants.

Gathering Information

Using Surveymonkey.com, I will survey both future and current mathematics teachers as well as a few teachers from other disciplines to determine what information should be included in the course. I will inquire how often models are used in the classroom, how effective students and teachers feel they are, problems encountered implementing models, and benefits of including models in the curriculum.

Instructional Content

From my survery, I have learned that most teachers currently implement models but wrather infrequently. The reason for this "...lack of time and expertise in the production of models." Furthermore, I was pleased to discover 4/5 of the participants indicated that they would be interested in professional development on models. Based on the information I have gathered from my survey (see results here), the mini lesson will include six units.

  1. Activating prior knowledge
  2. Models as a teaching/instructional tool
  3. The benefits of implementing models
  4. Techniques to implement a model effectively
  5. Examples of effective models
  6. Closure

I will begin each unit with specific goals. Next information will be presented to reinforce the topic at hand. After students have explored the new information, they will be asked to reflect on the learning’s. Upon completion of all units, participants will complete an online survey for the purposes of collecting data on the quality and effectiveness of this lesson.

Performance Objectives

Upon completion of this course learners will be able to:

  • Explain/characterize by writing a definition and giving examples of models as a teaching/instructional tool
  • Identify the benefits of implementing models
  • Generate and execute an effective instructional model that may be implemented in the particpants classroom

Instructional Problem and Solution

Unit 1: Activating Prior Knowledge

  • What do you know about models?

Unit 2: Models as a teaching/instructional tool

  • What is a Model?
  • Examples of Models
  • Types of Models
  • Parts of a model
  • Research

Unit 3: The benefits of implementing models

  • What the research says

Unit 4: Techniques to implement a model effectively

Unit 5: Examples of effective models

  • Working model hearts: Building artificial hearts to learn about circulatory system physiology
  • Trigonometry with a Ferris Wheel

Unit 6: Closure

  • Self-reflection
  • Comments
  • Thanks You

Please note: After further consideration, I decided to integrate Unit 5: Examples of effective models into all the other units.

Curriculum Map

File:Modeling Curriculum Map.doc

Click to view the instructional curriculum map, which illustrates the prerequisites, including the enabling and supportive objectives, and shows the organization of each unit within the course, Models: an Instructional Tool.

Initial List of Resourses

  • Books
    • Gilbert, S.W., & Ireton, S.W. (2003). Understanding models in earth and space science. Arlington, VA: NSTA press.
    • Harrison, A.G., & Coll, R.K. (2008). Using analogies in middle and secondary science classrooms: The FAR guide – an interesting way to teach with analogies. Thousand Oaks, CA: Corwin Press.
  • Articles:
    • Duit, R., Roth, W.-M., Komorek, M., & Wilbers, J. (2001). Fostering conceptual change by analogies – between Scylla and Carybdis. Learning and Instruction, 11(4), 283-303.
    • Glynn, S.M. (2008) Making science concepts meaningful to students: Teaching with analogies. In S. Mikelskis-Seifert, U. Ringelband, & M. Bruckmann (Eds.), Four decades of research in science education: From curriculum development to quality improvement (pp. 112-125). Munster, Germany: Waxmann.
    • Greca, I.M., & Moreira, M.A. (2001). Mental, physical, and mathematical models in the teaching and learning of physics. Science Education, 86(1), 106-121.
    • Grosslight, L., Unger, C., Jay, E., & Smith, C.L. (1991). Understanding models and their use in science: Conceptions of middle and high school students and experts. Journal of Research in Science Teaching, 28(9), 799-822.
    • Harrison, A.G., & Treagust, D.F. (1993). Teaching with analogies: A case study in grade-10 optics. Journal of Research in Science Teaching, 30(10), 1291-1307.
    • Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2&3), 109-129.
    • Moyer, P.S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics, 47, 175-197.
    • Schwarz, C.V., & White, B.Y. (2005). Metamodeling knowledge: Developing students’ understanding of scientific modeling. Cognition and Instruction, 23(2), 165-205

Examples of Models


Back to ETAP 623 Spring 2010

View the mini-course Models: an Instructional Tool