Students attitudes towards mathematics: an introduction of the study that includes two countries Estonia and Norway

Transcription

1 Students attitudes towards mathematics: an introduction of the study that includes two countries Estonia and Norway Kirsti Kislenko, Agder University College and Tallinn University, Keywords Affective domain, students beliefs, mathematics education, multi-cultural study Introduction Affect plays an important role in mathematics education. Mathematics has been a highly respected discipline in school for centuries and its high status makes students success in mathematics very important. This has implied the situation where affect has become an interest of researchers in mathematics education as it has been pointed out that students beliefs about mathematics are strongly related to their learning outcomes in mathematics. Some studies about students and teachers attitudes have been carried out in Estonia during the last 10 years [e. g. 1, 2, 3, 4, 5]. In the light of these studies researchers from Norway and Estonia carried out a study to investigate Norwegian and Estonian students views towards mathematics. Data collection in Norway was finished in spring 2005 and the main data collection in Estonia took place in spring The study in Norway was a part of the LCM-project within the Norwegian Research Council s KUL 1 program and it investigated the answer to the question: what kind of beliefs and attitudes towards mathematics teaching and learning do students from one urban area in Norway hold. The main study in Estonia went further and used not only a quantitative strategy (questionnaire, like in Norway) but qualitative (interviews and lesson observations) as well. The questionnaire was used to investigate students beliefs and attitudes towards mathematics teaching and learning. Interviews and lesson observations were planned to enlighten the perspectives of students and teachers. This aims for a general picture of the mathematics classrooms and possible relations between attitudes and the practical situation and to have ideas how teaching and learning can be improved based on the gathered information. Some theoretical underpinnings 1 KUL - Kunnskap, utdanning og læring, translated as Knowledge, education and learning.

2 Researchers have pointed out clearly that there is a lack of well-developed well-defined theoretical framework in the study of affect [e. g. 6, 7]. This problem might be hidden in the meanings of the conceptions belief and attitude. These two notions that are crucial in the study of persons affective domain are hardly definable as they are not directly observable and their meanings overlap [8]. In this study, the definitions for the notions attitude and belief are adopted from Harry C. Triandis [9] and Erkki Pehkonen [10]. Triandis [9] notes that the notion attitude comprises at least three verbs: to think, to feel, and to behave. Even more, from his point of view behaviour is not only determined by what one would like to do but also what one thinks one should do which means that social norms, habits and expected consequences of behaviour are included in the concept of attitude [9]. Pehkonen [10] situates beliefs somewhere between humans affective and cognitive domain, in what he calls the twilight zone and argues that beliefs have a component in both domains (p. 1). He explains beliefs, where the feelings are included, as an individual s subjective knowledge [10] but at the same time suggests distinguishing between affective beliefs and cognitive beliefs [11]. Methods Research participants Six schools from one urban area in Norway that were partners in the KUL- LCM project took part, and 279 students from the grades 7 (34 students), 9 (85 students) and 11 (first year in upper secondary school; 160 students) completed the web-based questionnaire. Seven schools from one urban area in Estonia participated in the Estonian study. The number of the students who completed the web-based questionnaire was 580 whereas there were 232 seventh grade students, 232 students from the ninth grade and 116 students from the grade 11. The semi-structured interviews with the students (N=24) in Estonia were mainly individual. Nine teachers were interviewed in the end of the study in groups or individually, and all the interviews were tape-recorded. Eleven Estonian teachers lessons were observed during two months and finally field notes based on the observations of 55 mathematics lessons were made. Data sources and data collection In the study virtually the same questionnaire was used that was developed for the KIM study in Norway in The KIM project collected data on students understandings of key concepts in the national mathematics curriculum and used a Likert-scale questionnaire that contained 125 items designed to expose students beliefs about mathematics, and mathematics

3 teaching and learning [12]. Based on the data from our pilot study (see more in [13]) and in response to our research questions some changes were carried out within the questionnaire statements. Finally, our questionnaire contained 98 statements divided into 11 groups which were beliefs about: mathematics as a subject; learning mathematics; own mathematical abilities; own experiences (security) during mathematics lesson; teaching of mathematics; learning a new topic in mathematics; environment in class; teaching tools in mathematics lessons; own evaluation for importance of mathematics; evaluation of the teacher; mathematics and the future. For example, the statements in the class your thoughts about mathematics were: mathematics is important ; mathematics is exciting and interesting ; mathematics is difficult ; mathematics is useful for me in my life, etc. Some open-ended questions were included in the questionnaire, mostly in form like something else you want to mention or why/why not. The statements used Likert-scale type responses where 5 represented a highly positive stance (totally agree) and 1 a highly negative stance (totally disagree) and 3 a neutral value. Several statements used the choices from never (4) to very often (1) i.e. they used a 4-point Likert scale. In addition to changing some statements and groups in the KIMquestionnaire for our study, we changed the answering procedure of the questionnaire as well. Our questionnaire was web-based, and was made available for the students on an Internet webpage. Each student was given a unique code that he/she used to log into the questionnaire page. In Norway the students answered the questionnaire mainly during their spare. In Estonia majority of the students completed the questionnaire in their mathematics or computers lessons and they had the possibility to get explanations of the completing procedure from their teacher or from the researcher. As pointed out earlier the interviews and lesson observations were only carried out in Estonia. The interviews with the students considered the following issues: mathematics in general (What is mathematics? How should mathematics be taught? How can mathematics be useful?); the structure of a usual mathematics lesson and the activities of the teacher (What are the usual activities in lessons? What is the most pleasant/unpleasant activity in mathematics lesson? How is the talkingtime in lesson divided by the teacher and the students?); parents and friends attitudes towards mathematics. Six students from the grade 7, 11 students from the grade 9, and 7 students from the grade 11 were interviewed. All, except one double interview, were individual interviews

4 and lasted approximately 20 minutes. With the teachers 7 interviews were carried out from which 5 were individual and 2 group interviews. Teachers interviews included the same matters as students ones (about mathematics; about activities in lesson; etc.) with some extra topics like the teaching style and the goals for teaching and learning, the character of the school, issue related to the Estonian school system in general and in the perspective of mathematics, etc. The number of the teachers whose lessons were observed was 11 and the final number of lessons observed was 55. The main aim for lesson observations was to paint a general picture of the classroom culture. Moreover, different teaching styles were in interest of the study. The researcher noted different activities during the lessons, the teaching methods and tools, teachers and students behaviours, the relationship between the teacher and the students, etc. Further ideas The data analysis of Norwegian study has completed and published (look for more in Kislenko [14], and in Kislenko et al. [15]). The deeper data analysis based on the Estonian study is ongoing and the results are not ready for publishing yet. Nevertheless, the conclusions of the TIMSS study in 2003 point out that Norwegian students tend to have a significantly higher level of self-confidence than students from Estonia [16]. We hope that our studies help to illuminate the reasons for this phenomenon. References [1] Lepmann L. (2000). Eesti ja vene õpilaste arusaamad matemaatikaõpetusest. Koolimatemaatika XXVI (pp ). Tartu: Tartu Ülikooli Kirjastus. [2] Lepmann, L., & Afanasjev, J. (2005). Conceptions of mathematics in different ability and achievement groups among 7th grade students. In C. Bergsten and B. Grevholm (Eds.), Proceedings of NORMA 01, the 3rd Nordic Conference on Mathematics Education (pp ). Linköping: Linköping University. [3] Pehkonen, E. (1994). On differences in pupil s conceptions about mathematics teaching. The Mathematics Educator, 5(1), [4] Pehkonen, E. (1996). Some findings in the international comparison of pupils mathematical views. In E. Pehkonen (Ed.), Current state of research on mathematical beliefs III. Proceedings of the MAVI-3 Workshop. Helsinki, August , [5] Pehkonen, E., & Lepmann, L. (1994). Teachers conceptions about mathematics teaching in comparison (Estonia - Finland). In M. Ahtee and E. Pehkonen (Eds.), Constructivist viewpoints for school teaching and learning in mathematics and science (pp ). Helsinki: University of Helsinki. Department of Teacher Education. Research Report 131. [6] Goldin, A. G. (2004). Characteristics of affect as a system of representation. In. M. J. Høines and A. B. Fuglestad (Eds.), Proceedings of the 28 th conference of the

5 international group for the psychology of mathematics education (pp ). Bergen: Bergen University College. [7] Hannula, M. S. (2004). RF01: Affect in mathematics education exploring theoretical frameworks. In. M. J. Høines and A. B. Fuglestad (Eds.), Proceedings of the 28 th conference of the international group for the psychology of mathematics education (pp ). Bergen: Bergen University College. [8] Leder, G. C., & Forgasz, H. J. (2002). Measuring mathematical beliefs and their impact on the learning of mathematics. In G. C. Leder, E. Pehkonen, and G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp ). Dordrecht: Kluwer Academic Publishers. [9] Triandis, H. C. (1971). Attitude and attitude change. New York: John Wiley & Sons. [10] Pehkonen, E. (2003). Læreres og elevers oppfatninger som en skjult faktor i matematikk -undervisningen. In B. Grevholm (Ed.), Matematikk for skolen (pp ). Bergen: Fagbokforlaget. [11] Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G. C. Leder, E. Pehkonen, and G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp ). Dordrecht: Kluwer Academic Publishers. [12] Streitlien, Å., Wiik, L., & Brekke, G. (2001). Tankar om matematikkfaget hos elever og lærarar. Oslo: Læringssenteret. [13] Kislenko, K., Grevholm, B., & Breiteig, T. (2005). Beliefs and attitudes in mathematics teaching and learning. In I. M. Stedøy (Ed.), Vurdering i matematikk Hvorfor og hvordan? Fra småskole til voksenopplæring. Nordisk konferanse i matematikkdidaktikk ved NTNU 15. og 16. november 2004 (pp ). Trondheim: Nasjonal Senter for Matematikk i Opplæringen. [14] Kislenko, K. (in press). Structuring students' beliefs in mathematics: A Norwegian case. Proceedings of the MAVI12 Workshop. Ivalo, May [15] Kislenko, K., Grevholm, B., & Lepik, M. (in press). Mathematics is important but boring : students beliefs and attitudes towards mathematics. Proceedings of the NORMA05 Conference. Trondheim, September [16] Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). TIMSS 2003 international mathematics report. Findings from IEA s trends in international mathematics and science study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College. Summary To investigate students attitudes towards mathematics and to paint a general picture of the classroom context were the aims for carrying out the research in Estonia and Norway. Some main theoretical concepts in relation to this study are discussed in the present article. Moreover, the paper introduces the research participants and both data collection strategies - quantitative (questionnaire) and qualitative (interviews and lesson observations) - that were used in the study.