Prospective middle school mathematics teachers’ conceptualizations of slope

In this study, the conceptualizations used by prospective middle school mathematics teachers when defining, representing, and exemplifying the slope concept and relating it with other mathematical situations were examined. Participants’ conceptualizations were identified by Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. [(2013). Calculus students’ and instructors’ conceptualizations of slope: A comparison across academic levels. International Journal of Science and Mathematics Education, 11(6), 1491–1515. https://doi.org/10.1007/s10763-013-9411-2] framework. The findings showed the prospective teachers mostly used trigonometric and parametric conceptions. Real-world situation, calculus conception, geometric ratio, and determining property were other common conceptualizations used by the participants. On the other hand, algebraic ratio, behaviour indicator, physical property, and functional property conceptualizations were seldom used and linear constant conceptualization was never used by them. The implications for mathematics teacher educators and mathematics education researchers on how to remedy prospective teachers’ possible difficulties and errors about slope are discussed

Reflections of creative drama based instruction for teaching addition of fractions

*Türker Biber, Belma ( Aksaray, Yazar )Çalışmada, alternatif öğretim yöntemlerinden yaratıcı drama yöntemi kullanılarak düzenlenen bir dersin, ortaokul 5. sınıf düzeyinde kesirlerde toplama işlemlerinin öğretiminde nasıl etkili olduğu incelenmiştir. Bu amaçla, 5. sınıf öğretim programında yer alan kesirler alt öğrenme alanı kazanımlarından, “Paydaları eşit olan kesirlerde toplama işlemi yapar” kazanımına yönelik yaratıcı drama yöntemi ile hazırlanan etkinliklerin olduğu bir uygulama yapılmıştır. Çalışma grubu, Samsun ilinde bulunan bir ortaokulun 5. sınıfında öğrenim gören 27 öğrenciden oluşmaktadır. Yaratıcı drama öğretim yöntemi gereği uygulama; ısınma, canlandırma ve değerlendirme aşamalarına ilişkin farklı etkinliklerle gerçekleştirilmiştir. Etkinliklerin uygulanma sürecinin tamamı video kaydına alınmıştır. Veri analizleri sırasında öncelikle grupların video kayıtları izlenmiş ve öğrenci ifadeleri transkript edilmiştir. Ardından öğrenci yanıtlarına ilişkin kağıtlar incelenmiştir. Toplanan veriler içerik analizi yöntemiyle incelenmiştir. Analizler sonrasında kesirlerde toplama işlemine yönelik öğrenci yanıtlarından; doğru yanıt verenler, doğru yanıt verip görsel olarak ifade edemeyenler ve yanlış yanıt verenler şeklinde üç kategoriye ulaşılmıştır. Matematik dersinde yapılan yaratıcı drama uygulaması etkinlikleri sonucunda, öğrencilerin çoğunluğunun matematik yönergelerine doğru yanıt verdikleri tespit edilmiştir. Elde edilen diğer bulgular ışığında, öğrencilerin yaratıcı drama yönteminin kesirlerde toplama işlemi konusunun öğretiminde etkili olduğu, öğrencilerin yeni öğrenmeler elde ettiği sonucuna ulaşılmıştır.Introduction Current teaching approaches, use the teaching methods that develop students in affective and temporal areas instead of giving direct academic information, and support them to cope with the problems they face and make connections between the school and their daily lives (Karaosmanoğlu & Adıgüzel, 2017; San, 1990). By the way, class environments that support students to acquire different skills in order to be able to use the education they receive in their own lives are needed. Therefore, the course designs should include the instructional activities that provide the students with multi-faceted developments with the teaching methods and techniques that taking an active role under the guidance of their teachers. For the mathematical skills, which are tried to be gained by traditional teaching in boring classroom environments, course designs should be made which will enable many students to participate in the class. A learner-centered classroom environment should be created, which is structured in a more engaging way for the student, where students are actively involved, and mathematics teaching is made more enjoyable. Students should be enriched in the learning environments through which they encounter different daily life problems by preventing students from thinking that they have learned to use mathematics only in shopping. Creative drama, which is at the center of learning, provides a variety of educational environments that enable students to think creatively and critically and develop their skills in reading and mathematics through various playful processes (Hendy. & Toon, 2001). In terms of mathematics teaching, it is possible to talk about the benefits of creative drama: For example, creative drama can be asked to stimulate students' problem situations using improvisation and role playing techniques. In this way, students can help to make mathematical problems in their minds by making them meaningful. It increases students' interest in mathematics with dramatic situations involving problems or problems in their environment. In the classrooms that teach mathematics with a creative drama approach, the teacher has the role of a guide that enables students to develop their own mathematical thinking skills. One of the first abstract concepts that students learn in mathematics is the concept of fraction (Pesen, 2007). Studies have been showed (Hasemann, 1981; Behr, Wachsmuth, Post, 1985; Hart, 1993; Kamii and Clark, 1995; Newstead and Murray, 1998) students difficulties arise especially when fractions and fractions are not linking with concrete and understandable examples (Carraher & Schliemann, 1991; Hasemann, 1981; Keijzer & Terwel, 2003). In order to eliminate the difficulties in fraction teaching, lesson plans should be developed in order to relate fractional expressions. At this stage, creative drama method should be included as an effective method. For all reasons in this study, it was examined how a lesson prepared using creative drama method from the alternative teaching methods affects teaching addition of fraction in the 5th grade secondary education. Within the scope of the purpose, an implementation composed of activities prepared by means of creative drama method in terms of the acquisition of “makes an addition in the fractions with equal denominators” from the fractions sub-learning area of acquisitions in the 5th grade curriculum was carried out. Method The research is a case study kind of the qualitative design. We can describe the case study as an empirical process which examines an actual or experienced event in comparison with real life situations (Yin, 2008). In order to determine the effectiveness of the creative drama teaching method, a lesson plan was developed for “makes an addition in the fractions with equal denominators” acquisition. The effectiveness of this plan was addressed and examined as a case. Addressing a case study enabled to see many details in terms of revealing whether the educational activities prepared regarding the use of creative drama method has any effect on teaching fractions or not. The study group consists of 27 students studying in the 5th grade of a secondary school in the province of Samsun. The selection of the students was made randomly, and the students have not had any education regarding creative drama before

Developing a self efficacy scale toward using rubric

Güneş, Perihan (Aksaray, Yazar)Bu araştırmada, öğretmen adaylarının rubriğe ilişkin özyeterliklerini belirlemede kullanılacak geçerli ve güvenilir ölçümler sunan bir ölçme aracının geliştirilmesi amaçlanmıştır. Uzman görüşleri doğrultusunda hazırlanan taslak “Rubrik Kullanma Özyeterliği Ölçeği” üç devlet üniversitesinde beş ayrı bölümde okumakta olan toplam 402 öğretmen adayına uygulanmıştır. Ölçekten elde edilen ölçümlerin yapı geçerliği faktör analizi kullanılarak araştırılmıştır. Araştırmanın ilk aşamasında temel bileşenler ve açımlayıcı faktör analizi, son aşamasında ise doğrulayıcı faktör analizi uygulanmıştır. Toplam 13 maddeden oluşan ölçeğin iç tutarlık güvenirlik katsayısı Cronbach alfa= .91 olarak hesaplanmıştır. Araştırma sonuçları, rubrik kullanma özyeterliği ile ilgili geliştirilen ölçeğin geçerli ve güvenilir ölçümler sağlayan bir araç olarak kullanılabileceği göstermektedir.The aim of this study is to develop a valid and reliable scale that can be used to measure pre-service teachers’ selfbelief in using rubrics. Self-efficacy scale toward using rubric was applied to 402 pre-service teachers from 3 state universities in Turkey. For the structure validity of the scale, firstly, an exploratory factor analysis was performed, and for the uni-dimensional structure that was seen to be meaningful in the first analysis, a principal component analysis was performed. In the last step of the analyses, the model, which was formed according to the basic components and factor analysis results, was tested through a confirmatory factor analysis. The scale is composed of 13 items, and the reliability coefficient was calculated to be Cronbach alpha= .91. As a result, it can be said that the developed scale is a valid and reliable measurement tool to be used in measuring self-efficacy toward using rubric

Rubrik Kullanma Özyeterlik Ölçeği Geliştirme çalışması

Bu araştırmada, öğretmen adaylarının rubriğe ilişkin özyeterliklerini belirlemede kullanılacak geçerli ve güvenilir ölçümler sunan bir ölçme aracının geliştirilmesi amaçlanmıştır. Uzman görüşleri doğrultusunda hazırlanan taslak “Rubrik Kullanma Özyeterliği Ölçeği” üç devlet üniversitesinde beş ayrı bölümde okumakta olan toplam 402 öğretmen adayına uygulanmıştır. Ölçekten elde edilen ölçümlerin yapı geçerliği faktör analizi kullanılarak araştırılmıştır. Araştırmanın ilk aşamasında temel bileşenler ve açımlayıcı faktör analizi, son aşamasında ise doğrulayıcı faktör analizi uygulanmıştır. Toplam 13 maddeden oluşan ölçeğin iç tutarlık güvenirlik katsayısı Cronbach alfa= .91 olarak hesaplanmıştır. Araştırma sonuçları, rubrik kullanma özyeterliği ile ilgiligeliştirilen ölçeğin geçerli ve güvenilir ölçümler sağlayan bir araç olarak kullanılabileceği göstermektedi

Matematiksel modelleme etkinlikleri bağlamında öğrenci düşünmelerine yönelik öğretmen farkındalığı ve fark etme stratejileri

This study aims to examine teacher's noticing and noticing strategies towards student's mathematical thinking process. The case study was conducted in the lessons of a mathematics teacher teaching at the seventh grade level of a middle school in Ankara. Data was collected through semi-structured interviews with the teacher, in-class video recordings, student observations, and documents obtained from student studies. Four modeling activities relating statistical subjects were used to observe student's thinking process. The collected data were analyzed by content analysis and descriptive analysis method. There were figured out 3 categories of teacher's noticing about student thinking: (a) conceptual understanding (b) procedural understanding (c) mathematical language use. It has been found that the teacher's noticing about student's thinking is mostly focused on conceptual understandings. Regarding the teacher's noticing strategies, the following categories were reached: a) Identification and description, (b) evaluation and interpretation, and (c) justification. The teacher defined the situations that she noticed in her students during the appropriate model development process as repetition, overhearing, and biased hearing. She interpreted the process or result of the situations she noticed and made various assessments. In justifying her comments, she presented evidence from students' rhetoric/behavior or offered predictions/assumptions based on her knowledge and expectations about their students

Teacher noticing of students’ thinking in the context of mathematical modeling activities related to statistics

In this study, we investigated mathematics teacher’s noticing of students’ thinking in the context of mathematical modeling activities (MEAs) related to statistics. One middle-school mathematics teacher participated in the study, which adopted a case study design. Data were collected through interviews with the teacher based on video recordings of students’ group work, the written works of the students, and the researchers’ observations and field notes. As students evolved from first-draft solutions to more powerful, sharable ways of thinking about the modeling activity, the teacher focused on student thinking related to four distinct aspects of the overall modeling activities: understanding the problem, manipulation, interpretation, and verification. She mostly focused on procedural aspects of students’ thinking during the manipulation step. Her attention and interpretation of the manipulation step focused on the students’ (a) identification of the solution (how students reach the solution), (b) reasons why they selected these solutions (explanations and justifications of the solutions), and (c) features of the solutions they used. The teacher also noticed how the students’ performances depended on the structure of the activity (whether a data set was given). She pointed out that MEAs support students’ engagement, conceptual understanding, skills related to statistics, and ability to use data processing concepts in their daily lives

Matematik Tarihinin Öğretimi İçin Alternatif Bir Öğretim Yöntemi: Yaratıcı Drama

The study was aimed to investigate the influences of pre-service teachers' learnings, thoughts and feelings, and opinions about the approach during the course period by using creative drama as a teaching method. The research group included 22 pre-service teachers who were studying at second class of a state university’s elementary mathematics teacher department. The history of mathematics course activities which were prepared with using creative drama method were implemented in two hours per week for 10 weeks. Qualitative and quantitative approaches were used for collecting data. The constructivist learning environments assessment scale, general assessment form that evaluates the learners feelings, thoughts and gains about course, reflective diaries, video camera records that were recorded during the courses and interviews at the end of the courses have been investigated as data collected instruments. According to the survey; pre-service teachers found creative drama which is teachers faced new method that effective in teaching mathematics and its history. Pre-service teachers indicated that they wanted to use creative drama in their professional working life because of reasons and benefits such as provide attention and motivation for course, learning retention, recovery the course from boredom. Another important result obtained from findings is pre-service teachers’ thinking about course; they don’t define the course such as “very bad, don’t understand” and all pre-service teachers marked “learned” on the general assessment form by supporting positive commentsÇalışmada, yaratıcı drama yöntemi kullanılarak işlenen Matematik Tarihi Dersinin öğretmen adaylarının öğrenmelerine, duygu ve düşüncelerine etkisinin ve öğretmen adaylarının bu yaklaşımla ilgili görüşlerinin araştırılması amaçlanmıştır. Araştırmanın çalışma grubunu, bir devlet üniversitesinin İlköğretim Matematik Öğretmenliği bölümü 2. sınıfında öğrenim gören 22 öğretmen adayı oluşturmaktadır. Öğretmen adaylarına haftada iki saat olmakla birlikte 10 hafta süreyle Yaratıcı Drama yöntemi kullanılarak hazırlanan etkinliklerle matematik tarihi dersi anlatılmıştır. Nitel ve nicel araştırma yöntemlerinin her ikisi de kullanılmıştır. Veri toplama araçları olarak, yapılandırmacı öğrenme ortamlarını değerlendirme ölçeği ile öğrencilerin süreç sonunda duygu, düşünceleri ve edindikleri kazanımları belirlemek için genel değerlendirme formu, yansıtıcı günlükler, video gözlem kayıtları ve görüşmeler kullanılmıştır. Araştırmanın sonuçlarına göre; öğretmen adayları yeni karşılaştıkları yaratıcı drama yöntemini, matematik ve tarihini öğretmekte etkili bulmuşlardır. Yaratıcı drama yöntemini, derse ilgi ve motivasyon sağlaması, öğretilenlerin kalıcılığı, dersi sıkıcılıktan kurtarması gibi nedenlerle kendi meslek yaşantılarında da kullanmak istediklerini belirtmişlerdir. Yaratıcı dramanın etkili bir yöntem olduğunu hem günlüklerinde hem de yapılan tartışmalarda dile getiren öğretmen adaylarının hemen hepsinin değerlendirme formundaki “öğrendim” ifadesini olumlu açıklamalarla destekleyerek işaretledikleri tespit edilmiştir. Öğretmen adaylarının dersle ilgili düşünceleri arasında ders “anlaşılmadı, çok kötü” gibi ifadelere rastlanmaması bulgulardan elde edilen bir diğer önemli sonuçtur.