Preservice mathematics teachers' types of mathematical thinking: Use of representations, visual-spatial abilities, and problem solving performances

International audienceThe main purpose of this study was to examine preservice mathematics teachers' types of mathematical thinking and to investigate whether there are any differences between different types of thinkers based on their problem solving performances, use of representations and visual-spatial abilities. The sample of the study consisted of 113 preservice mathematics teachers in a private and four public universities. The results showed that although problem solving performances were similar for each type of mathematical thinking, preservice teachers who adopted harmonic and geometric types of mathematical thinking preferred to use schematic representations more than analytic thinkers in their problem solving processes. The findings provided an insight about preservice teachers' preferences for a visual approach and the implications of these preferences for teacher education programs were discussed

Dönüşüm Geometrisinin Sanal Dinamik Geometri Ortamında Kavramsal Olarak İrdelenmesi Conceptually Studying Transformational Geometry in a Virtual Dynamic GeometryEnvironmen

Teknoloji matematik eğitim ve öğretiminde etkin olarak kullanıldığında öğrencilerin matematiksel akil yürütmelerine, başarılarına ve anlamalarına olumlu katkıda bulunmaktadır (MEB, 2013;NCTM, 2000). Eğitim teknolojisinin aktif olarak kullanıldığı alanların başında geometri gelmektedir. Bu çalıştayda geometri öğretiminde sıklıkla kullanılan araçlardan GeoGebra ve Geometer’s Sketchpad ile dönüşüm geometrisini ele alan etkinlikler yapılacaktır. Öğretmenler, öğrenciler ve öğretmen adayları dönüşüm geometrisi konu alanına giren yansıma, öteleme ve dönmeyi kavramsal olarak tanımlamada ve anlamada zorluklar yaşamaktadır. Bu çalıştayda dinamik geometri araçları ile oluşturulmuş etkinlikler kullanılarak, öğretmenlerin dönüşümleri kavramsal olarak irdelemeleri ve uygulamaları planlanmaktadır. Çalıştay üç asamadan oluşacaktır. Birinci aşamada dönüşümleri içeren bir etkinlik ile öğretmenlerin dönüşüm çeşitlerini sınıflandırmaları ve özelliklerini keşfetmeleri sağlanacaktır. İkinci aşamada dönüşüm çeşitlerinin matematiksel olarak manaları irdelenecek ve dönüşümler tanımlanacaktır. Son aşamada ise GeoGebra’da çeşitli dönüşümler oluşturulacak ve dönüşüme örnek ve örnek olmayan durumlar incelenecektir

Experienced Private Course Teachers Tutors and Their Students Views about PrivateCourses Tutoring

The aim of the study was to explore the views of mathematics and science teachers and their 12th-grade students about private courses. Participants were three experienced teachers, one mathematics and two science, who have worked at a private course in Ankara for at least 10 years, and their three 12th-grade students. Students were attending the same private course and studying for the university entrance exam. This was a qualitative case study in which the interviews were conducted with each teacher and student. The semi structured interviews included open-ended questions. Each interview was voice recorded and lasted approximately 20 minutes for students and 35 minutes for teachers. Data analysis began with open-coding of the transcripts and proceeded to more fine-grained coding. The results showed that experienced teachers preferred to work at private courses. The themes, which the participants described as the differences between private courses and public schools, were time allocation for teaching, the evaluation of the teachers’ performance, teaching for the exam. The categories which were deduced from students’ responses as their reasons for attending private courses were test anxiety, teachers’ quality, overcome to shortcomings and habit. Although all participants pointed out that private courses were a problem in education system they did not agree that just the closure could be a solution for this problem in the conditions of Turkey

The influence of the context of conditional probability problems on probabilistic thinking: A case study with teacher candidates

International audienceThis study investigates the influence of the context of conditional probability problems on probabilistic thinking processes of mathematics teacher candidates. Data were collected from four mathematics teacher candidates through semi-structured clinical interviews. Teacher candidates were expected to solve and explain three conditional probability problems, which were selected based on specific contexts. The findings revealed that, when the context is related to a social issue such as health or justice, that can be a hindrance to probabilistic thinking. In addition, while solving questions, teacher candidates focused on their beliefs regarding the social issue rather than using logical and numerical reasoning given in the questions. On the other hand, the findings highlighted the importance of the instruction on conditional probability, as the candidates represented a high-level of probabilistic thinking in the case of consecutive events that were frequently used in curricula

Preservice teachers’ use of representations and visual-spatial abilities in problem solving

This study aimed to investigate preservice teachers’ use of representations, visual-spatial abilities, and their relationships with word problem solving performances. The sample of the study consisted of 113 preservice mathematics teachers in a private and four public universities. The results showed that there was no significant relationship between problem solving performance and visual-spatial abilities. Preservice teachers’ visual-spatial abilities only had a weak relationship with use of schematic representations among all the variables. While most of the solutions including schematic representations were correct, more than half of the solutions involving pictorial representations were incorrect. The findings suggested that the influence of representations on performance significantly differed in terms of the types of representations and visual-spatial abilities did not have an influence on preferences for problem solving methods. Preservice teachers’ learning experiences and aims for easy and quick solutions could be more decisive in their use of representations