Hatice Akkoç

Pre-service mathematics teachers’ concept images of radian

This study investigates pre-service mathematics teachers’ concept images of radian and possible sources of such images. A multiple-case study was conducted for this study. Forty-two pre-service mathematics teachers completed a questionnaire, which aims to assess their understanding of radian. Six of them were selected for individual interviews on the basis of theoretical sampling. The data indicated that participants’ concept images of radian were dominated by their concept images of degree. As the data in this study suggested, pre-service mathematics teachers were reluctant to accept trigonometric functions with the inputs of real numbers but rather they use value in degrees. More interestingly, they have two distinct images of π : π as an angle in radian and π as an irrational number.

Investigating the development of prospective mathematics teachers' technological pedagogical content knowledge

This study investigates how two prospective mathematics teachers integrate technology into their lessons to address student difficulties. Prospective teachers took part in a teacher preparation program which aims to develop technological pedagogical content knowledge (TPCK). As part of this program, prospective teachers participated in workshops which aimed to develop TPCK of derivative and function concepts. Following these workshops, prospective teachers conducted their own workshops during which they discussed student difficulties with various mathematical concepts such as limit, continuity, definite integral, probability and radian with their peers. They also discussed how these difficulties could be addressed during a lesson using technological tools. This paper particularly focuses on radian concept and investigates the development of two prospective mathematics teachers throughout the course in integrating technology into their lessons to address student difficulties with radian concept.

Formative questioning in computer learning environments: a course for pre-service mathematics teachers

This paper focuses on a specific aspect of formative assessment, namely questioning. Given that computers have gained widespread use in learning and teaching, specific attention should be made when organizing formative assessment in computer learning environments (CLEs). A course including various workshops was designed to develop knowledge and skills of questioning in CLEs. This study investigates how pre-service mathematics teachers used formative questioning with technological tools such as Geogebra and Graphic Calculus software. Participants are 35 pre-service mathematics teachers. To analyse formative questioning, two types of questions are investigated: mathematical questions and technical questions. Data were collected through lesson plans, teaching notes, interviews and observations. Descriptive statistics of the number of questions in the lesson plans before and after the workshops are presented. Examples of two types of questions are discussed using the theoretical framework. One pre-service teacher was selected and a deeper analysis of the way he used questioning during his three lessons was also investigated. The findings indicated an improvement in using technical questions for formative purposes and that the course provided a guideline in planning and using mathematical and technical questions in CLEs.

Use of multiple representations in technology rich environments

In this study we present part of a research project that aims to develop prospective mathematics teachers’ Technological Pedagogical Content Knowledge (TPCK) (Mishra and Koehler 2006). The project considers various TPCK components (see Ozmantar et al. 2010). This report focuses on a particular component, namely the knowledge of using multiple representations (MRs) with technology. A course was designed using the TPCK framework, and forty prospective mathematics teachers took part in the course. They were enrolled in a teacher preparation programme in a state university in Istanbul, Turkey. As part of this course, prospective teachers participated in workshops during which they were introduced to the TPCK framework, which was illustrated using function and derivative concepts. The workshops included examples of MRs, how to make links among them, and the way in which technology could contribute to achieving the intended linkages. Following the introductory workshops, the prospective teachers themselves prepared and carried out similar workshops for their peers with different topics including limit, continuity, probability, radian and integral. They were grouped into fours, assigned one of these topics and asked to prepare the workshops in collaboration. The participants also prepared lesson plans and teaching notes and performed micro-teaching (during which they taught lessons to their peers as if they were in a real classroom environment). Following the completion of the course, we attempted to see the participants’ development with regard to using multiple representations (MRs) with technology. For this purpose, we found the functional taxonomy of MRs proposed by Ainsworth (2006) useful in that it allowed us to see development of the participants through our course activities, as well as to perform comparative analyses of participants’ developmental trajectories. Ainsworth’s (2006) taxonomy differentiates three main functions that MRs serve in learning situations: to complement (different representations involve distinct yet complementary information), to constrain (confine inferences and provide a focus) and to construct (by providing cognitive linking of representations, which might eventually lead students to achieve a deeper understanding). Using this framework, we examined the extent to which two prospective teachers (Gamze and Mutlu) used different functions of MRs during instruction. These two

Dokuzuncu sınıf öğrencilerinin merkezi eğilim ve yayılım ölçüleri konusundaki informel istatistiksel çıkarsamaları üzerine bir inceleme

Istatistiksel cikarsama verilerin yorumlanmasini gerektiren bir surectir. Formel olarak istatistik ogretimi almadan istatistiksel cikarsama yapilabilmenin onemli oldugu goz onune alindiginda, bu durumun nasil oldugunun ortaya konmasi onem arz etmektedir. Buradan hareketle arastirmanin amaci, ortaogretime yeni baslamis dokuzuncu sinif ogrencilerinin merkezi egilim ve yayilim olculeri konusundaki informel istatistiksel cikarsamalarinin nasil oldugunu ortaya koymaktir. Bu amac dogrultusunda arastirmada nicel arastirma yontemlerinden tarama yontemi kullanilmistir. Dokuzuncu sinifa yeni baslamis 34 ogrenciye acik uclu sorulardan olusan Informel Istatistiksel Cikarsama Tespit Testi (IICTT) uygulanmistir. Ogrencilerin informel istatistiksel cikarsamalarinin nasil oldugu belirlenirken Makar ve Rubin’in (2009) ortaya koydugu informel istatistiksel cikarsama teorik cercevesi kullanilmistir. Arastirma bulgulari ogrencilerin cogunlugunun merkezi egilim ve yayilim olculeri konusunda informel istatistiksel cikarsama yapabildiklerini gostermektedir. Ayrica arastirmada ogrencilerin formel kavramlari informel referanslarla kullanabildigi gorulmustur.

Voices and values in shaping the subjectivity of pedagogical content knowledge

Abstract Pedagogical content knowledge involves subjective decisions on the parts of teachers in making the content comprehensible to learners. This paper is concerned with the formation of this subjectivity and asks: how do (pre-service) teachers come to know and decide upon the best approach to making the content instructional for learners? In answering this question, this study draws upon data obtained from one pre-service mathematics teacher’s microteaching and retrospective interviews. The data were examined through the lenses of the Bakhtinian notion of voice. The findings suggest that the pre-service teacher’s understanding of pedagogy is formed and transformed, to an important extent, by the voices of others who are not necessarily physically present within the immediate instructional setting and who might be distant in space and time. Assimilation of those voices enacts particular value judgments, which in turn shapes and hence forms the subjectivity of the pre-service teacher’s pedagogical practices.

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.

Examining Professional Identity through Story Telling

This paper focuses on the notion of identity and how it is formed through stories. Many researchers equate identity with the construction of stories. This exploratory case study examines professional identity by interpreting stories which come out of an interview with a prospective mathematics teacher. A semi-structured interview was conducted during a school placement. The interview data was analysed using Kegan’s (1982; 1994) constructive-developmental theory. Findings will be discussed in the light of usefulness of the theory in exploring identity through story telling.