No abstract

No abstract

People need the idea of transformation geometry in order to understand the nature and environment they live in. The teachers should provide learning environments towards perceptual understanding in symmetry training and development practice skills of the students. In order to make up such a learning environment, teachers should have information about the mathematical structure of the concept of symmetry, the difficulties the students encounter while learning, misconceptions and the causes. Therefore, the challenges and the common mistakes the 8 th grade middle school students encounter about the transformation geometry was analysed in the study. The study was conducted using mixed method designs with 125 8 th grade students. At the end of the study, it was observed that the students understood that the translation transformation is a movement of replacement, but they had difficulty in the topics such as the direction of the transformation and the position of the shape within the transformation. A misconception was developed for the reflection by confusing the similarity with the congruence property of the shapes. It was detected that the students had difficulty in identifying the equation of the axis of symmetry for the images of the shapes under reflection, confused the rule that the points intersecting with the symmetry of the shape within the reflection should intersect with the image under transformation and they made mistakes since they couldn't explore the relationship between symmetry axis in regular polygons and sides. They had problems in finding and practicing the angle of rotation about rotational transformation and also. In the study, learning environments were recommended towards overcoming these challenges for teachers and coursebook writers and improving conceptual information and the skill to practice these concepts.

No abstract

The purpose of this study is to examine pre-service elementary mathematics teachers' problems posed about algebraic expressions and equations. Data was collected from 96 pre-service elementary mathematics teachers in the spring semester of 2012-2013 who were enrolled in a teacher education program at a public university. Problem Posing Test consists 5 open ended items which were developed by researchers was used as a data collection tool. Pre-service elementary mathematics teachers were asked to pose problems corresponding to the algebraic expressions and equations. Problems were examined and classified. Descriptive statistics were used to determine pre-service elementary mathematics teachers' problem types. Findings of the study indicated that in general problem types were classified as story and solvable problems, they used daily language for posing problems. Keywords:Algebraic expressions and equations, problem posing, pre-service teacher See Extended Abstract GirişEvrensel bir dil olan matematik çeşitli alanlara ayrılmıştır. Bu alanlardan birisi olan cebir, sayı ve sembolleri kullanarak bunlar arasındaki ilişkileri denklemlere dönüştüren bir matematik dalıdır ve matematiksel kavramların öğrenilmesinde çok önemli bir role sahiptir (Baki, 2008;Kieran, 1992;Van Dooren, Verschaffel & Onghena, 2002). National Council of Teachers of Mathematics'e (NCTM, 2000) göre cebir öğrenme alanı, öğrencilerin örüntüleri ilişkilendirerek mantıksal çıkarım (akıl yürütme) yapma, problem çözme gibi üst düzey becerileri kazanmalarını sağlar. Ayrıca bu öğrenme alanında öğrencilerin örüntüleri, fonksiyonları ve bağıntıları kavraması; cebirsel semboller kullanarak matematiksel durumları göstermesi; nicel ilişkileri anlama ve göstermede matematiksel modelleri kullanması ve değişiklikleri analiz etmesi beklenir. Öğrencilerin 1 Bu çalışma Roma'da düzenlenen 2013 INTE kongresinde sunulan sözlü bildirinin genişletilmiş halidir.