Eyüp Sevimli

The influence of teacher candidates' spatial visualization ability on the use of multiple representations in problem solving of definite integrals: A qualitative analysis

This study aims to investigate the influence of spatial visualization ability in representations used in definite integral subject. In this sense, a case study has been carried out on 45 mathematics teacher candidates. Multi- method approach was adopted by using more than one research techniques. Tests, Document analysis and semi-structured interviews are the research instruments and inferential & descriptive statistics are used for the data analysis. Findings showed that spatial visualization ability of the teacher candidates is low. In parallel to these findings, it was determined that the candidates, who have low spatial visualization ability, used predominantly algebraic representation. The development of spatial visualization ability, which may influence the relationship between graphical representations and the other representations, increases the performance of solving definite integral problems. Moreover, the candidates are advised to develop their spatial visualization abilities to improve their abilities of interpretation of visual information.

Do calculus students demand technology integration into learning environment? case of instructional differences

This study evaluated how calculus students’ attitudes towards usage of technology changes according to their learning environment and thinking types at the undergraduate level. Thus, the study attempted to determine the place and importance of technological support in the process of attaining the aimed and obtained acquisitions by students. Participants of the study consist of forty-three calculus students who are studying in traditional or CAS-supported teaching environments, and have different thinking types. Pre-and post-assessment tools were used in the data gathering process, and the data were evaluated with descriptive statistics. The results of the study showed that students in the traditional group place more importance on procedural skills, while students in the CAS group attach more importance to conceptual skills in terms of instructional objects. It also determined that acquisitions, which students think developed differ according to learning environment and thinking types. The main implications of the study were discussed in terms of the related literature and teaching practice.

A comparison of mathematics questions in Turkish and Canadian school textbooks in terms of synthesized taxonomy

Bu calismanin amaci, Turkiye ve Kanada’da kullanimda olan ortaokul matematik ders kitaplarindaki sorulari bilissel ogrenme duzeylerine ve soru turlerine gore inceleyip karsilastirmaktir. Bu baglamda Turkiye’de kullanimda olan ortaokul matematik ders kitaplari ile Kanada’da kullanimda olan “Math Makes Sense” adli ders kitaplari icerik analizine tabi tutularak karsilastirilmistir. Arastirmanin amacina uygun olarak veriler toplanip dokuman analizi yapilmistir. Her iki ulke ders kitaplarinda yer alan matematik sorulari, Sentezlenmis Bloom Taksonomisi uzerinden bilissel surec ve bilgi boyutlarina gore kodlanmis ve sorularin bilissel ogrenme duzeylerine gore benzerlik ve farkliliklari karsilastirmali olarak incelenmistir. Turkiye ve Kanada ders kitaplarinda yer alan sorularin bilissel surec ve bilgi boyutu acisindan benzer ozellikler gosterdigi tespit edilmistir. Ancak Kanada ders kitabinda bilissel beceri gerektiren acik uclu soru turlerine daha cok yer verildigi belirlenmistir. Ders kitaplarinin icerigi olusturulurken uluslararasi sinavlarla uyumlu ust bilissel beceri gerektiren sorulara daha fazla yer verilmesi onerilmektedir.

Undergraduates’ propositional knowledge and proof schemes regarding differentiability and integrability concepts

ABSTRACT The purpose of this study was to determine how undergraduates comprehend the theoretical relations between differentiability and integrability concepts within the frame of proof schemes in analysis courses. The study participants were 172 freshmen from three different mathematics departments in Turkey. A questionnaire was used to evaluate the general picture on propositional knowledge about the concepts of continuity, differentiability, and integrability. Afterwards, participants’ written answers on the concepts of differentiability and integrability were analysed, particularly in terms of proof schemes usage. The data collected during the study were analysed and interpreted using a classification method and descriptive statistics. Results indicated that many students who answered the propositions correctly could not use valid arguments for their answers. Most of the arguments used by undergraduates in the external proof scheme based on procedural knowledge and described with reference to authority did not have the content to be evaluated as proof. Although analytical proofs were rarely used by undergraduates, more valid arguments were constructed in such proof approaches. The role of definition and propositional knowledge, and also awareness of counterexample, were discussed in order to construct successful theoretical relations in a teaching environment.

Matematik Analiz Dersinde Öğretim Elemanlarının Tercih Ettiği ve Ders Kitabının İçerdiği Örneklerin Yapısal İncelenmesi

The aim of this study is to analyse the structural features of examples which textbook located and lecturers’ choosed in teaching of engineering calculus. The study had interpretivist paradigm in qualitative research approach and the data collection process was conducted through content analysis method. The course content of calculus, which are lectured by different instructors in engineering departments, are followed during a semester within the context of the study. Examples in the textbooks and the lecture notes are analyzed with document analysis method based on their structural features of representation, language and knowledge. Besides, data are presented with descriptive statistics method. Semi-structured interviews are conducted to detect any possible components affecting lecturers’ exemplification behavior, and the records are interpreted by using the inferential content analysis. The findings show that the examples of both textbooks and lecture notes have a formal language and procedural knowledge. It is also found that lecturers, unlike the content of textbooks, use more algebric representations than graphical ones. The results of the study indicate that the structural features of examples which were choosed by lecturers and which were located in textbook are similar. Besides epistemological belief, the components of the teaching environment and the type of used sources have a significant role affecting the choices of the lecturers. It has been made some suggestions for authors and researchers, which may contribute to the teaching practice for further studies.

The relationship between students' mathematical thinking types and representation preferences in definite integral problems

Students’ cognitive differences in problem solving have been the focus of much research. One classification of these differences is related to whether visualisation is used. Krutetskii (1976) categorised mathematical thinking into three different types. In addition to the analytic and geometric preferences, he drew attention to the existence of harmonic processes, which use both analytic and geometric reasoning. Presmeg (1985), in her study on the visualisation process and learner difficulties, used Krutetskii’s (1976) classification, and concluded that students struggled more in managing visual processes than in managing analytic ones. Like mathematical thinking differences, multiple representation preferences are important when considering individual differences. Choosing an appropriate representation is an important step to successful problem solving. Sevimli and Delice (2011) claimed that students have difficulties when choosing an appropriate representation. The reason for these difficulties is the differences in the students’ thinking. Therefore, it is necessary to explore the relationship between preferred representation types and differences in mathematical problem-solving processes. The main research question of this study is related to the effect of input representations in the problem statement on students’ choices. This study identifies students’ representation preferences. The participants were 37 first year mathematics education students, who were selected by using a purposeful sampling technique. In this research, two different tests were used for two different purposes. The Mathematical Process Instrument (MPI) developed by Presmeg (1985) was used to determine the type of the participants’ mathematical thinking: visual, analytic or harmonic. The second data collection tool was a Representation Preferences Test (RPT) which was developed by the researchers. The RPT was designed to determine participants’ tendencies to use different representations for the definite integral. The test consisted of nine items, each of which stated a question in one of three representations (numerical, graphical or algebraic). The participants were expected to identify the representation type(s) which they believed would facilitate the process of solving a given definite integral problem. When tests were administered, participants were not allowed to make any calculations. Hence, the RPT provided a measure of students’ representation preferences. Each participant’s representation preferences for each question were

Geometri Problemlerinin Çözüm Süreçlerinde Görselleme Becerilerinin İncelenmesi: Ek Çizimler Investigation of Visualization Ability in Geometry Problem Solving Process: Auxiliary Drawings

Visualization, particularly in last decades, is in the centre of mathematics education researchers since it assists understanding of mathematical concepts and enables intuitional view in mathematics but also in the centre of focus by playing an important role in the geometry problem solving process. Many researches are conducted about attitudes of the students with respect to geometry problems. In this study, secondary school mathematics students’ differences in skills and awareness stage through geometry problem solving process are investigated. This research, in particular, focused on the changes made to the drawing of the given geometric figures. From methodology point of view this research is a case study with interpretive paradigm and multi-method approach, moreover, it is mainly qualitative in terms of data. There are two research tools used in the research. A 24 geometry problem set, which are constructed from National exams and geometry textbooks, was applied to 52 students of year 11 in secondary school. Semi--structured interviews were conducted by 10 students who are selected by non-probabilistic purposeful sampling method to examine students’ solution processes in problem set and visualization skills more deeply. Qualitative data, were analyzed by categorization method, is presented as descriptive. Research findings revealed that the dimension and representation types used in the geometry problems affects students’ auxiliary drawings on the figure. Moreover, results also showed that students are more successful at problem types of two-dimensional compared to three dimensions, visual representations compared to verbal representations and transition between the same dimension compared to the different dimensions. Results also showed that when the changes are not made or misused on the drawings through the geometry problem solving process, in which visualizing the data, auxiliary drawings and transition between dimensions are expected to be done, students cannot complete problem solving process successfully. This research emphasizes that the use of problems to develop visual-spatial skills, activities and material in geometry classes may positively influence students performance. This research is essential in terms of revealing one of the reasons behind the lower performance of Turkish students in international exams. Key words: Visualization, auxiliary drawing, geometry problem