Exploring, Writing, Presenting, And Defending Mathematical Concepts: A Project For Elementary Teachers

 

Debasree Raychaudhuri

California State University at Los Angeles

 

Introduction: The content courses for elementary teachers seek to instill a deeper understanding of the crucial mathematical concepts surface-learned at earlier stages, typically during the learner’s own elementary / middle school-years. Yet many a times prospective teachers depart with the similar capacities they entered the course with, i.e., possession of surface knowledge (Simon & Blume, ’97; Zazkis & Campbell, ’96; Even, 93) and little confidence to present and defend mathematical concepts (Borko, Eisenhart, Brown, Jones & Agart, ’93,’92).

In this proposal we will describe a group project that attempts to strengthen the tie between the subject mathematics and its future teachers, by demanding that the students explore mathematical concepts from different angles, write a report on their findings, present it to their peers and defend their point of views.

The additional social aspects crucial to this project are student interaction (through collaborative work), peer involvement in assessment of the projects (through written feedback on presentations), and role reversals (every student has the dual role of researcher / presenter of knowledge as well as that of receiver / assessor).

 

Project description: The project is introduced at the beginning of the 10-week course. Following that students meet in their groups (maximum 3 members) and discuss assigned concepts. The concepts assigned can be general (e.g., Whole numbers) to specific (e.g., The number ‘0’) to one where the focus is on comparison (e.g., Theoretical probability versus Empirical probability).

 They then write a report on the concept including an introduction as well as the purpose of the topic, its connection with other mathematical concepts, real-life applications, place in the current K-8 curriculum, origin and evolution (history) of concept, the misconceptions students might form while learning this concept. While the first three components expose the writers to researching the concept beyond examples and procedures thus expanding the subject matter knowledge, the latter three serve as a platform for introducing pedagogical content knowledge.

Based on the written report experience the group members choose the focus for their in-class presentation, which has a duration of 15 minutes. The presentations begin in the fifth week of classes. The preparation begins with a written lesson plan, more meetings, and culminates with the actual presentation. Following the presentation, the audience (peers) provides written feedback on the lesson segment (7-10 minutes) while members complete individual project experience surveys. 

 

Results: In this proposal we report a few of our findings (e.g., i) changes in student outlook of mathematics following their participation in the project, a new realization on their part of ii) the depth of subject matter knowledge actually needed to present and defend a mathematical concept, and of iii) the level of their own preparedness as teachers of mathematics), and hope to elaborate further in our presentation.

 

Summary: This project offers pre-service elementary teachers a rare opportunity, where they explore the concepts of mathematics from different angles, write research reports, talk mathematics in a safe and encouraging setting, receive constructive critique from peers and instructor, and in doing so gain valuable insight about mathematics as well as their own strengths and weaknesses as teachers of the subject.

 

 

References:

 

  1. Borko, H., Eisenhart, M., Brown, C. A., Underhill R. G., Jones, D. & Agard P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily?, Journal for Research in Mathematics Education, 24(1), 23(3), 194-222.
  2. Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D. & Agard, P. (1993). Conceptual knowledge falls through the cracks: Complexities of learning to teach mathematics for understanding, Journal for Research in Mathematics Education, 24(1), 8-40.
  3. Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept, Journal for Research in Mathematics Education, 24(2), 94-116.
  4. Simon, M. A. & Blume, G. W. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers, Journal for Research in Mathematics Education, 25(5), 472-494.
  5. Zazkis, R. & Campbell, S. (1996). Prime decomposition: Understanding uniqueness, The Journal of Mathematical Behavior, 15(2), 207-218.*