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:
- 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.
- 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.
- 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.
- 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.
- Zazkis, R.
& Campbell, S. (1996). Prime decomposition: Understanding uniqueness, The
Journal of Mathematical Behavior, 15(2), 207-218.
