The purpose of this investigation was to explore how differences in an elementary mathematics teacher's subject matter knowledge structure impact classroom teaching and student learning. The study included two phases. Phase 1 focused on the selection of a single case. An open-ended questionnaire and interview were used to identify the subject matter knowledge structure for addition, subtraction, multiplication, and division of three elementary teachers. One teacher was selected who demonstrated clearly different levels of knowledge for multiplication and division. An additional interview provided information on the teacher's specific climate for teaching mathematics and details about the unit on multiplication and division to be observed.
Phase 2 included daily classroom observations for approximately one hour each day of a seven-week unit on multiplication and division. Informal interviews were conducted with the teacher throughout the unit to better understand the lessons and allow the teacher an opportunity to clarify statements and actions. A final teacher interview occurred after the last classroom observation. At the conclusion of the observations, the students were assessed to determine their knowledge of multiplication and division based on the teacher's unit objectives. And six students, representing the range of class performance, were interviewed to provide additional insights into the students' learning.
The teacher's subject matter knowledge of multiplication was strong but her knowledge of division was faulty and incomplete on several topics including the different meanings of division, the conceptual underpinnings of division procedures, the relationships between symbolic division and real life problems, and the idea of divisibility. Although the translation of the teacher's subject matter knowledge was complex, it seemed to be directly related to classroom teaching and students' learning. The teacher's narrow understandings were associated with an incomplete developing of the full range of division situations. Although the students had significantly more success on the post assessment problems involving multiplication than on those involving division (understandable since the teacher spent more time teaching multiplication than division), a more worrisome concern was that the students in this study exhibited serious misconceptions associated with the meanings of division, division computation, and notions of divisibility. / Graduation date: 2000
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/33169 |
| Date | 30 August 1999 |
| Creators | Buckreis, William F. |
| Contributors | Niess, Margaret L. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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