Ali Delice

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.

Investigation of primary mathematics student teachers’ concept images: cylinder and cone

The aim of the present study is to determine the influence of concept definitions of cylinder and cone on primary mathematics student teachers’ construction of relevant concept images. The study had a relational survey design and the participants were 238 primary mathematics student teachers. Statistical analyses implied the following: mathematics student teachers did not have sufficient level of knowledge about the concepts of cylinder and cone; concept definitions were insufficient in constructing concept images; providing student teachers with formal definitions of the concepts increased performance in choosing the right models of cylinder and cone from a given set of models but decreased performance in constructing a new cylinder; formal definitions did not affect the selection of models which were not cylinder and cone and the construction of a new cone model.

Day conference abstracts

It is recognised that an increasing number of students (in the USA) who are qualified intellectually are deciding not to study mathematics beyond minimum secondary school requirements and that many more girls than boys make this decision. A set of variables explaining individual differences in the learning of mathematics not only affects the amount of effort one is willing to employ to learn mathematics, but also influences the election of additional mathematics courses beyond the basic requirements in secondary schools. This paper reports on pilot study data gained from a Bangla translated version of the Fennema-Sherman Mathematics Attitude Scales (FSMAS). The main purpose of the survey was to check the reliability of using the Bangla translated version of FSMAS in the rural Bangladeshi context and to observe any patterns of differences in attitudes to mathematics among different groups.

An analysis of history of mathematics research literature in Turkey: the mathematics education perspective1

Research in history of mathematics gained momentum in the past two decades in Turkey. The present paper aims to describe the patterns in the history of mathematics research in Turkey and to analyse the research in Turkey using a mathematics education framework. The qualitative paradigm and a case study design are used in the study. The obtained data were analysed by using the document analysis technique with the help of a content analysis. The study group which is comprised of twenty-two postgraduate theses at masters or doctoral level were purposefully selected from the higher education council postgraduate theses database. Findings indicate a dearth of research in the area and that most of the theses are done in the area of mathematics education. Moreover, the focus, in general, was on attitudinal variables, and cognitive aspects seemed to be ignored.

Investigation of Drawings and Rotation Skills In Integral Volume Problems Solving Process Within Communities of Practices / Uygulama Topluluğu Bağlamında İntegral Hacim Problemleri Çözüm Sürecindeki Çizimlerin Ve Döndürme Becerilerinin İncelenmesi

In consequence of the studies on learning and teaching that can be stated as the basis of education and instruction process, new theories have been brought up and the concepts like communities of practices were generated via interaction of them. Communities of practices that one may encounter in daily life as well as education and instruction process can be stated as the learning environment where individual’s problems, matters or interests are shared and that provides expertise by sharing information on a subject or an area. Using visualization skills as well as individual’s algebraic skills in learning environment affect problem solving process. In this research that was conducted with non-positivist interpretive paradigm, drawing and rotation skills within the solution process of integral volume problems were scrutinized in terms of communities of practices. Integral Volume Test, which was tested in terms of reliability and validity, was applied to 101 students who were from the faculty of engineering, mathematics department of faculty of science and letters, primary mathematics teaching department of faculty of education in a state university in Istanbul chosen by using non-purposive sampling technique of nonprobability sample. In this study that benefits from semi-structured interview form and document analysis, data were analyzed with descriptive analysis in two different categories. As a result of the research, it has been revealed that student performances are low, that students having algebraic and spatial skills are successful in problem solving process and that institutional differences such as learning environment and academic members as well as personal differences such as knowledge, skill and motivation affect learning process. Considering that there are little research related to communities of practices, this research is thought to contribute to the literature

An analysis of pre-service mathematics teachers' performance in modelling tasks in terms of spatial visualisation ability

This study aims to identify pre-service teachers’ spatial abilities and to explore the effects of these abilities on performance in mathematical modelling tasks. Following a case study research approach, mixed methods were used for data collection. Participants were 75 pre-service teachers studying an MA degree without dissertation at a state university in Turkey. In order to identify pre-service teachers’ spatial abilities, data was collected using a Mental Rotation and Spatial Visualisation Test. In order to investigate the effects of spatial abilities on performance during the solution process and on the visualisation process, pre-service teachers participated in modelling activities. Descriptive statistics were used to analyse the qualitative data. Results indicated that almost half of the preservice teachers had high level spatial abilities. It was also found that preservice teachers’ mathematical modelling abilities were not sufficiently developed, and that their spatial visualisation abilities were weaker than their mental rotation abilities. Moreover, the result that pre-service teachers who had higher spatial ability also had better performance in modelling tasks than the other pre-service teachers implied a direct relationship.

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