Turkish Journal of Computer and Mathematics Education

366-379

Authors: Reinhard Oldenburg

Two different interpretations of algebra that differ in the ontological status assigned to variables are distinguished. Variables may either be viewed as meta-mathematical tools to express generality or as objects similar to numbers and other members of the mathematical ontology. Both interpretations are detailed and linked with the literature and the use of variables in computer programming. Furthermore, it is analyzed how these two conceptualizations lead to two different understandings of the process of change of values. Some evidence from algebra assessment on the understanding of change by students is given that that illustrate that the theory is useful in analyzing students work.

399-417

Authors: Gökhan Dağhan, Pınar Nuhoğlu Kibar, Buket Akkoyunlu, Gülsün Atanur Baskan

The aim of the study is to determine approaches of administrators and teachers related to the use of interactive whiteboards and tablet PCs which are distributed in schools within FATİH project. Research was carried out with 32 administrator and 36 teachers who works at FATİH project implementation schools. Seperate forms consisting of different open-ended questions were posed to teachers and administrators. Data was analyzed with content analysis. Administrators indicate that the courses supported by this technology will provide effective learning; courses will be more efficient in a shorter time; motivation, interest and involvement will be affected in a positive direction. Teachers states that technology supported courses will increase the interest of students and develop various skills. According to the statements the most important problem related to the use of these technologies seems to be caused by lack of sufficient educational e-content. Organizing “practical” trainings which aims at gaining ability to create educational e-content for teachers could be solution to sufficient e-content problem.

446-462

Authors: Gürsel Güler, Ahmet Temizyürek

This study aims to look into secondary education prospective mathematics teachers’ model creation skills regarding proof of the rule providing the sum of successive odd numbers. The study takes case study method, a qualitative research approach, as the basis to reflect the current situation, and focus group discussions were held in classroom environment to collect data. The study was conducted on twenty prospective math teachers studying pedagogical formation. Focus group discussions held with twenty prospective teachers selected on voluntary basis voluntarily were recorded, put on paper and analyzed descriptively. According to the results derived from the study, it is observed that the prospective teachers used verbal, algebraic and formal models as three model types during the proof of the rule providing the sum of successive odd numbers and created six different proofs along with these models.

483-505

Authors: Serdal Baltacı, Avni Yıldız, Temel Kösa

The potential of GeoGebra in teaching analytic geometry concepts was investigated in this paper. The study carried out with case study methodology and the participants were 6 pre-service mathematics teachers at 3rd grade of elementary mathematics education. All of the participants had the skill of well self-expression and they were volunteers for interview. Two participants were at high achievement levels, two participants were at medium achievement levels and two participants were low achievement levels. While carrying out each lesson, participants used worksheets which were prepared by the researchers. The data were obtained by semi-structured interviews which were carried out at the end of the courses and the data were analyzed with content analysis method. Research results showed that using dynamic mathematics software while studying on analytic geometry provides convenience for the participants and they felt more active while they were using software in the learning environment.

532-552

Authors: Taliha Keleş, Mihriban Hacısalihoğlu Karadeniz

This study aims to classify the Mathematics and Geometry questions which had been asked university entrance examinations carried out between 2006 and 2012 in OSS/MAT1, OSS/MAT2, YGS/MAT, LYS/MAT and LYS/GEO according to the revised Bloom taxonomy in the dimensions of cognitive process. In the study, document analysis method was used. The data gathered for the purpose of the research was analyzed according to the frequency and percentage of the SPSS 20.0 software package. The study findings revealed that, the Mathematics and Geometry questions asked in the university exams are mostly at the level of apply and analyze of the cognitive process dimension in the revised Bloom Taxonomy. It has been determined that there is no remember of the cognitive process. The comparative statistical analyses showed that there wasn’t a significant difference between the years according to the dimensions of cognitive process of Mathematics and Geometry questions asked in the university entrance exams. To reveal the reflection of the curriculum changes made in 2013 on the exam questions, similar studies can be conducted in the future and the results can compared.

163-178

Authors: Çiğdem Kılıç

The aim of this study was to identify the problem posing tendency of preservice teachers (primary and mathematics) in structured problem posing situations. Participants were selected using a two-step sampling process in order to prevent bias. In the first sampling process, a total of 109 pre-service teachers participated in the study. Of these participants, 48 were pre-service primary school mathematics teachers and 61 were pre-service primary teachers who were in their sixth term of school. In the second sampling process, 10 volunteer participants were selected using purposeful sampling. It was found that participants had a tendency to pose result-centered problems (contextually inappropriate and irrelevant result-focused problems) and context-centered problems (standard and non-standard word problems). In some cases, participants did not pose any word problems.

209-229

Authors: Müjgan Baki, Selahattin Arslan

This article reflects a special part of a research conducted to examine the effect of lesson study on prospective classroom teachers’ mathematical pedagogical content knowledge (MPCK). In this article, the special part consists of prospective teachers’ knowledge of lesson planning including a mastery of planning an affective lesson taking into account student’s current knowledge, understanding and difficulties within mathematics. Therefore, the research question is how lesson study practices affect prospective classroom teachers’ knowledge of lesson planning as a sub component of MPCK. The research is conducted with 12 prospective classroom teachers, six of them have already assisted to lesson study and the others have not. Data collection tools consist of video records, class observations, field notes, interviews and lesson plans prepared and used by prospective teachers participated in lesson study. Findings indicated that the prospective classroom teachers who participated in lesson study improved their knowledge in terms of planning an affective lesson taking student’s current knowledge and understanding into consideration. They appeared to be aware of selecting and ordering appropriate activities related to the actual objectives of the mathematical topics. They also appeared to be better in lesson organization and lesson presentation comparing to the other group of prospective teachers who did not participated in lesson study.

250-284

Authors: Murat Duran, Furkan Özdemir, Abdullah Kaplan

The purpose of this study is to reveal the variation in the perception of middle grade students for problem-based learning components in teaching process of probability topics and determine the attitudes of the students. The study makes use of the explanatory pattern of the mixed method, which enables using qualitative and quantitative data together. The sample of the study was composed of 32 students, selected by simple random sampling method, studying 8th grade of a middle state school in the fall semester of 2013-2014 academic terms in the province of Kars. Quantitave data of the study are tutor evaluation scale and learner’s self-evaluation scale developed by Dokuz Eylul University School of Medicine (2002) and scale of mathematical gains in problem-based learning developed by Biber (2012). Qualitative data of the study are tutor evaluation form, self-evaluation form and the form of evaluation of activity process developed by Eski (2011) and the scenarios developed by researchers. The quantitative data analysis of the study makes use of friedman test, wilcoxon signed rank test, one-way analysis of variance and dependent sample t-test. Qualitative data was analysed using descriptive analysis technique. Quantitative results of the study indicate significant change in learners’ evaluation towards themselves, to the tutor and the learning process. Qualitative results showed that the learners abandoned negative thoughts toward the class and achieved learning goals.

299-322

Authors: Gül Kaleli Yılmaz, Bülent Güven

The aim of this study is to determine teachers candidates’ perceptions on ‘distance education’ via metaphors. The sample consisted of 150 teacher candidates’ drawn from departments of science teacher and primary teacher at Faculty of Education in Bayburt University. 70 of the sample are primary teacher candidates that attended courses via distance education in their undergraduate programme. 80 of them are science teacher candidates that took ‘distance education’ elective course. To collect the data the teacher candidates’ were asked to complete this sentence: ‘Distance education is like......because....’. Data was analysed by using content analysis technique one of the qualitative data analysis methods. The results indicate that the teacher candidates’ metaphors referred to such different issues as need-aimed, variety, arbitrary, requirement. Moreover, when the findings are searched, it was determined that the primary teacher candidates take lesson by means of synchron distance education have more negative perception in contrast with science teacher candidates. It was noticed that some factors such as carrying out the synchron distance lessons as 90 min blocks, no chance to ask any question to the teacher out of the lesson time, occasionally encountering technical problems in the lesson causes the negative perception. To develop positive perception about synchron distance education, it is suggested that some distance education conditions which allows communication between students and teachers out of the lesson time should be designed as minimising the technical problems and informing to the participants about distance education applications.

18-30

Authors: Karmelita Pjanic, Edin Liđan

A wide range of mathematical ideas could be used to develop and justify a formula for calculating the area of trapezoid. Those ideas lead to different strategies for finding out area of trapezoid that we classify in three groups: decomposing, enclosing and transforming strategies. Those strategies should be part of mathematics content knowledge for teaching. In this study we trace a change in structure of mathematics content knowledge of nine pre-service mathematics teachers as a result of using GeoGebra applets that visualize different approaches in finding out the area of trapezoid. We argue that engaging pre-service mathematics teachers to develop and justify formula for calculating the area of trapezoid using GeoGebra applets is a worth task that enhances pre-service mathematics teachers’ content knowledge for teaching. Our experiment confirmed that the use of Geogebra encourage pre-service mathematics teachers to uncover new ideas that lead them towards clearer justifications and easier way of proving formula for area of trapezoid.

47-67

Authors: Selahattin Arslan, Duygu Taşkın, Arzu Kirman Bilgin

One of the theories in didactical research is Guy Brousseau’s (1998) Theory of Didactical Situations in Mathematics (TDSM) that investigates how learning occurs. TDSM, which intends to understand, interpret and improve teaching and learning activities, defines three different learning situations. One of these situations is adidactical situation emphasizing learning of students as a result of their interaction with a Milieu. The aim of this study is to compare student achievement in adidactical situation designed as individual work with those designed as group work. To this end, an adidactical situation was designed to form the area formulas for parallelogram and trapezoid. The study was conducted with 60 students of 7th grade. Data was gathered by academic achievement test, observation and semi-structured interviews. Mixed methods research design was utilized. Descriptive analysis was used for the analysis of the qualitative data, and Mann Whitney U - Test was used for the analysis of the quantitative data. Results of the study shows that the students working individually in adidactical situations are more successful than the students working in group in adidactical situations.

93-116

Authors: Alattin Ural

The aim of this study is to investigate what kind of materials are used in which grades in order to improve psychomotor skills and the use of information technologies by students in the courses taught by mathematics teachers and how these materials are used; and to elicit the perceptions of these teachers on the use of these materials. Twenty two mathematics teachers (out of 25) working in 7 secondary schools were given a questionnaire form containing open ended questions and they were asked to write down the answers to those questions on the same form. The research was designed in the scanning model as a qualitative study. The data obtained from teachers were analyzed descriptively and samples from the data were presented categorically. It was observed that, regarding the psychomotor skills, a pair compass-ruler-protractor, dotted-isometric-graph paper, cutting-folding paper in geometry; fraction slips and algebra squares in algebra were the materials used respectively. The grades where these materials are used were 5, 6, 7, and 8 respectively. Regarding the use of information and communication technologies, it was observed that Morpa and Vitamin, the software developed by Turkish Ministery of Education was used to teach the subjects which contain shapes or animation; PowerPoint presentations to teach solid objects, fractals; and animations and videos on the internet to teach solid materials, triangles, fractals, patterns and decoration, equations and symmetry. These activities are used in the grades 8, 7, 6, 5 respectively. The teachers stated that the fact that information technologies and psychomotor skills are not used to the extent they should be stems from the lack of time, lack of computers, the overpopulated classes and the washback effect of the national exams.