Ortaokul matematik öğretmeni adaylarının alan derslerindeki matematik ile ortaokul matematiğini ilişkilendirme becerilerinin incelenmesi.

This study investigated if and how preservice middle school mathematics teachers related the mathematical knowledge addressed in general mathematics content courses in a four-year teacher education program to their future teaching of middle school mathematics. The study involved two interrelated sections. On one hand, preservice middle school mathematics teachers' views on the issue were gathered through asking open-ended questions via a semi-structured interview protocol. On the other hand, their performance on a structured task-based interview was observed in order to find out how they utilized their mathematical knowledge of number theory concepts developed in the specific course Basic Algebraic Structures in conducting mathematical tasks of teaching. Semi-structured interview protocol and structured task-based interview protocol were prepared by the researcher. Participants of the study were 14 preservice middle school mathematics teachers who were enrolled in 3rd and 4th years of the teacher education program. Findings revealed that preservice teachers had conflicting views about the content courses. They considered the mathematics learned in general content courses as higher level, irrelevant to middle school mathematics and not applicable to teaching of middle school mathematics, but also as constituting the base for middle school mathematics. Participants' work on the four mathematical tasks of teaching provided several perspectives on the extent to which they were able to use their knowledge from Basic Algebraic Structures course in the teaching of middle school mathematics. Although the participants were selected from among the most competent ones in the Basic Algebraic Structures course and also in teaching related courses, many of them had difficulties with relating their mathematical knowledge from the course to given teaching tasks.M.S. - Master of Scienc

A sixth-grade student's growth in understanding written proof texts: Pre-and post-interview analyses of a teaching experiment study

International audienceThis study aims to describe a 6 th-grade student's progress in understanding written proof texts through participating in an individual teaching experiment. The same task was administered to the student twice in an interview setting, before and a year after the teaching experiment. The student was asked to evaluate four arguments aimed to prove a given conjecture. While in the pre-interview, the student accepted all four arguments based on her Naïve Experience; in the post-interview, she rejected empirical arguments and looked for General Procedures (or Abstract Structures) that necessarily apply to the whole set of numbers under investigation. In the post-interview, spontaneous changes occurred in the student's understanding of the given arguments after she constructed her own proof for the same conjecture. Instructional design elements used in the teaching experiment might have facilitated her understanding of the structure of deductive proof texts

What do prospective mathematics teachers mean by “definitions can be proved”?

International audienceThe research reported here is part of an ongoing study in which prospective middle school mathematics teachers’ conceptions of definition are investigated through their responses to semi-structured interview questions about defining quadrilaterals. Here we present findings from their responses to a subset of the interview questions, with the purpose of understanding what they mean by the expression “definitions can be proved”- an expression commonly referenced, and considered as erroneous in the research literature. Analysis of the responses, through using thematic coding and Toulmin’s (1958) scheme, revealed that participants attributed two different meanings to the phrase: (1) proving the claim that a written definition accurately designates an intended concept and (2) proving the concept being defined (erroneous). Based on our findings, we point to a reconsideration of the phenomenon by the research community

Ortaokul Matematik Öğretmen Adaylarının Matematiksel Tanım Ve Tanımın Matematik Eğitimindeki Önemine Yönelik Algılarının İncelenmesi

Bu çalışmanın amacı dördüncü sınıf ortaokul matematik öğretmeni adaylarının matematiksel tanım algılarını birbirini tamamlayan iki farklı şekilde incelemektir. Öncelikle öğretmen adaylarına matematiksel tanım anlayışlarını yansıtabilecekleri bir görev iki farklı şekilde verilecektir. Bu görevde öğretmen adaylarından kendilerine alfabetik sırada verilen dörtgenleri (deltoid, dikdörtgen, eşkenar dörtgen, kare, paralelkenar, yamuk) herhangi bir öğretim programına bağlı kalmadan tercih ettikleri sıra içerisinde tanımlayarak ikinci bir kişiye tanıtmak üzere bir dizilim oluşturmaları istenecektir. Bu süreç ilk kez uygulandığında katılımcılara sadece dörtgenlerin isimleri verilecek, ve onlardan kendi tanımlarını yapmaları istenecektir. Süreç ikinci kez uygulanırken ise adaylara her bir dörtgen için birden fazla birbirine eş tanım ifadesi verilecektir, katılımcılar istedikleri tanımları seçip kullanabileceklerdir. Ardından, öğretmen adaylarının tanımın matematik disiplinindeki yeri ve önemine dair görüşleri açık uçlu sorulara verdikleri yazılı yanıtlar doğrultusunuda incelenecektir. Öğretmen adaylarının matematik eğitiminde tanımın yeri ve önemi hakkındaki görüşleri ise ayrıca incelenecektir. Çalışmadan elde edilen bulgular bütüncül bir şekilde yorumlanacaktır

Preservice middle school mathematics teachers conceptions of proof

Developing students’ understanding of proof has become an important task of mathematics educators (Hanna & de Villiers, 2008). Teachers’ competence in creating opportunities for their students and enhancing their experiences with proof is considerably affected by their own conceptions of proof (Knuth, 1999). Therefore, this study investigated junior preservice middle school mathematics teachers’ (PST) conceptions of proof through their responses on a written task where conceptions of proof referred to conceptions of what made an argument a mathematical proof (Knuth, 1999). Data were collected from 32 PSTs enrolled in Elementary Mathematics Education program at a Turkish public university. PSTs took algebra and geometry courses, however, geometry courses did not include proof practices. Two mathematical statements (one algebra and one geometry) and three mathematical arguments which were trying to prove these statements were presented for each statement. PST’s were asked to determine whether given arguments were valid proofs for the statements or not and explain their reasoning. Their responses were deductively coded according to Cobb’s (1986) sources of conviction as authoritarian or intuitive, where the former addressed an outside authority (such as a book) as the source and the latter an individual’s “uncritical belief” (Almeida, 2001, p.56) for “a proposition [which] makes intuitive sense, sounds right, rings true” (Cobb, 1986, p.3). Participants’ emphasis on the distinction between empirical and general arguments was validated by the literature, as generality was considered as an important criterion of proof (Balacheff, 1988). Findings showed that PSTs mainly relied on intuitive and authoritarian reasons and general terms in the argument while explaining their reasoning for accepting an algebraic argument as a proof. Some participants stressed that mathematical proofs should not be exemplifying specific cases. PSTs employed intuitive reasons and idea of generality in geometry task. However, they did not mention authoritarian reasons. PSTs relied on similar reasons for evaluating both algebraic and geometric arguments. They were able to transfer their understanding of proof formed in algebra courses to the case of geometry. Not relying on authoritarian sources of conviction in geometry task might be due to the lack of experience of a geometry content course in which they would learn about authorities’ practices and preferences. Mathematics content courses could be enhanced to have more influence on PSTs’ conceptions of proof

Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education

The research reported here is part of an ongoing study in which prospective middle school mathematics teachers’ conceptions of definition are investigated through their responses to semi-structured interview questions about defining quadrilaterals. Here we present findings from their responses to a subset of the interview questions, with the purpose of understanding what they mean by the expression “definitions can be proved”- an expression commonly referenced, and considered as erroneous in the research literature. Analysis of the responses, through using thematic coding and Toulmin’s (1958) scheme, revealed that participants attributed two different meanings to the phrase: (1) proving the claim that a written definition accurately designates an intended concept and (2) proving the concept being defined (erroneous). Based on our findings, we point to a reconsideration of the phenomenon by the research community.                    </p

Au cœur de l'État At the heart of the State

La conférence internationale « Au Cœur de l’État. Comment les institutions traitent leur public » se déroule à l’École des Hautes Études en Sciences Sociales les 11 et 12 juin. Soutenu par l’Advanced Grant du Conseil européen de la recherche dont Didier Fassin est lauréat, ce colloque, dont l’Institute for Advanced Study de Princeton est partenaire, présente et discute des travaux conduits au sein de l’Iris, Institut de recherche interdisciplinaire sur les enjeux sociaux (CNRS-Inserm-EHESS-UP13)

Ortaokul Matematik Öğretmen Adaylarının İspat ve Doğrulama Becerilerinin İncelenmesi

Bu çalışmada, 3. ve 4. sınıf ortaokul matematik öğretmeni adaylarının cebir ve geometri alanlarında matematiksel ispat yapma ve verilen bir argümanın doğru ve tam bir matematiksel ispat olup olmadığını değerlendirme becerileri incelenecektir. Ayrıca öğretmen adaylarının matematiksel ispat ve doğrulama algıları araştırılacak ve karşılaştırılacaktır. Elde edilen sonuçların ilköğretim matematik eğitimi alanında yetiştirilen öğretmen adaylarının matematik alan bilgisi ve matematik eğitimi pedagojik alan bilgisi derslerindeki uygulamalar için değerlendirilmesi beklenmektedir