Pre-service elementary teachers' conceptions of proof and counterexamples and their influence on their instructional decisions
Başlık çevirisi mevcut değil.
- Tez No: 401616
- Danışmanlar: DR. ENRIQUE GALINDO
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2014
- Dil: İngilizce
- Üniversite: Indiana University
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 401
Özet
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Özet (Çeviri)
This study examined elementary pre-service teachers' (PSTs) conceptions of proof and counterexamples and whether their conceptions influence their instructional decisions. In particular, the study not only documented PSTs' ability to construct a proof or counterexample, to evaluate or verify a proof, but it also documented how those conceptions or misconceptions impacted their instructional decisions. Participants were a sample of pre-service teachers who enrolled in one section of geometry and measurement courses and one section of mathematics methods courses with its field experience component in a teacher preparation program. The participants were selected based on their responses to a questionnaire, which was administered to all students in those two courses at the beginning of the semester. Data were collected in two phases. Two types of interviews—task-based and scenario-based interviews—which were conducted at the beginning and near the end of the semester, served as the main data. Secondary data sources including classroom observations and class work were also collected. Data were analyzed qualitatively using grounded theory (Glaser & Strauss, 1967) and content analysis. The results of this study exhibited mixed pictures of what constitute proof in the eyes of the PSTs who participated in this study. It was clear that the pre-service teachers had previous experience with constructing and learning proofs when asked to prove or evaluate arguments and they were using those experiences to inform their judgments about what constituted a proof. However despite their experience with proofs, it was also clear that the majority of the pre-service elementary teachers who participated in this study had a naive understanding of what constitutes proof in mathematics classrooms. Furthermore, this study also showed that PSTs' conceptions and/or misconceptions of proof and counterexamples played an important role in their instructional decisions.
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