ERG SES D 11, Mathematics and Education
The mathematical concepts with symbols and procedures have their origins in history (Bagni, 2008). Introducing history of mathematics as a new discipline at the beginning of the twentieth century, researchers have begun to use history for teaching mathematics (Furinghetti & Radford, 2002). The knowledge of history of mathematics can also be seen essential knowledge for the teachers who teach mathematics. In this sense, teacher education is an appropriate place to explain potential use of history of mathematics. There are considerable number of studies examined the effects of specially designed practices of using history within prospective teacher education (e.g. Furinghetti, 2007). In general, the studies examining the effectiveness of incorporating the history of mathematics in prospective teacher preparation programs largely showed positive results. This integration could also contribute to students’ understanding of mathematics (Furinghetti, 2004). Studies indicate that history can be used as both a cognitive and motivational tool to support and increase the learning of mathematics and affective dispositions for both prospective teachers and students (Philippou & Christou, 1998). Students’ difficulties and misconceptions about mathematical concepts are similar to the epistemological obstacles in history of mathematics. In order to understand the reasons why students have difficulties when learning some mathematical concepts; teachers should know the evolution of mathematics. For this reason, teachers should initially master the essential historical knowledge behind the mathematical concepts taught in middle school for the use of history, effectively (Fried, 2001). In particular, the reasons for using history of mathematics were grouped into two categories such as history as a tool and history as a goal (Jankvist, 2009). While history as a tool refers to using history in terms of didactic aspect of mathematics the reasons of history as a goal includes issues in evolution of mathematics as a discipline (Tzanakis & Arcavi 2000).
However, there is limited number of studies that focused on the contribution of history of mathematics to prospective teachers’ attitudes and beliefs (Alpaslan et al., 2014). In related literature, studies reported that prospective teachers have inadequate insights about the nature of mathematics in many countries. For example, in the US, prospective teachers believe that mathematics involve many unrelated formulas, rules, symbols, and computations of problems (Ball, 1990). Likewise, Haser (2006) reached the conclusion that Turkish prospective middle school mathematics teachers see mathematics as the collection of rules and calculations of problems. However, related literature reveals a necessity for a more general picture of prospective teachers’ perceptions about history of mathematics. In this regard, this study provides a more general picture by combining qualitative and quantitative methods within an exploratory design. In line with this purpose, this study examines the nature and the changes of prospective middle school mathematics teachers’ perceptions regarding history of mathematics in terms of different dimensions. Perception is used in this study as prospective teachers’ thoughts about their knowledge, attitude toward history of mathematics and the integration it of mathematics education. Through this aim, the following four research questions are framed:
Before and after history of mathematics course, what are prospective middle school mathematics teachers’ perceptions regarding
- their own knowledge of history of mathematics?
- whether mathematics teachers should have knowledge history of mathematics or not?
- the integration ways of history of mathematics to the lessons?
- the possible contributions of the integration of the history of mathematics to the students’ learning?
On the whole, we can offer the perspective that we would analyse other prospective teachers’ perceptions of European countries to get a whole picture and also a framework for designing history of mathematics courses in teacher education programs for future studies.
In this study, a mixed method research, particularly exploratory design, was used as the aim of the study was to analyze prospective teachers’ perceptions about use of history in mathematics education. Exploratory design which based on qualitative design mostly and used quantitative design to validate the qualitative findings (Fraenkel, Wallen, & Hyun, 2012). To do this, qualitative method was conducted first to explore the components of their perceptions and then quantitative method was conducted to understand how their answers supported their perceptions. Participants were 32 prospective middle school mathematics teachers at fourth grade of their teacher training in a public university. Since they were in the last grade, they took many courses related mathematics education (e.g. methods of teaching mathematics, developing materials). In the context of this training program, data were collected before and after they took “History of Mathematics” course. In data collection process, first, six open-ended questions related to perceptions about history of mathematics were asked to participants in the qualitative aspect. In this questionnaire, there were such questions “How would you define your knowledge of history of mathematics? Should the history of mathematics be integrated to mathematics teaching, and if you think so how can it be integrated? etc.”. Then, Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education (ABHME) scale developed by Alpaslan (2011) was used in the quantitative aspect. This scale consists of attitude and beliefs items related using history in mathematics. The beliefs items also have self-efficacy items (e.g. I do not know how to integrate history in mathematics teaching process). Fraenkel et al. (2012) stated that data analysis is separate as qualitative data first and then quantitative data analysis in order to define themes. At this point, the themes and sub-themes were extracted from the answers for open-ended question by using content analysis. In content analysis, an explanation, namely a sentence or a paragraph, that is thought to be meaningful in itself, related to the investigated phenomenon are transformed into codes (Strauss & Corbin, 1990). The codes were drawn up using the answers of the open-ended questions for each question in this study. Then, the scores that the participants took from the scales (pre and post scores) were compared by using paired samples t-test in a statistical program.
Quantitative data and final-qualitative data are still being analyzing in order to reflect a comprehensive picture about the nature and changes of PTs’ perceptions about History of Mathematics (HoM). However, pre-qualitative data findings were presented as in the following. The findings indicated that PTs’ perceptions about their knowledge level of HoM revealed that most of them found their knowledge about HoM is superficial or moderate. PTs (n=15) who believed they have superficial knowledge stated that knew only the name of some famous mathematicians due to some famous formulas. PTs (n=14) who believed they have moderate level stated that they additionally knew mathematical development of some civilizations (e.g. Egypt, The Babylonians) and historical development of some mathematical contents (e.g. numbers). Finally, three PTs who believed they had deep knowledge mentioned about their personal interest on HoM. Another important finding showed that 31 PTs thought knowing HoM was a necessity for all mathematics teachers for the following reasons: (i) gaining cultural knowledge/respect, (ii) strengthening subject matter knowledge, (iii) improving teaching process, and (iv) improving students’ attitudes towards mathematics. Only one PT asserted that teachers do not need to know HoM because there are not any questions in national exams. PTs proposed 80 suggestions about the integration of HoM in mathematics lessons that were categorized into three main groups: (i) out of class activities, (ii) in-class activities, and (iii) others. Out of class activities involved the suggestions with high student-responsibility like poster/research/term paper preparation, reading books about math history. In-class activities involved the suggestions with high teacher-responsibility like giving brief oral information, activity/problem solving, lesson discussions. Others involved the suggestions with other persons’ responsibilities. Finally, in pre-qualitative data, 106 arguments reflecting PTs’ perceptions about contributions of integrating HoM for the students were grouped into three dimensions: personal, cognitive, and physiological.
Alpaslan, M. (2011). Prospective elementary mathematics teachers' knowledge of history of mathematics and their attitudes and beliefs towards the use of history of mathematics in mathematics education. Unpublished Master’s Thesis, Middle East Technical University, Ankara, Turkey. Alpaslan, M., Işıksal, M., & Haser, Ç. (2014). Pre-service mathematics teachers’ knowledge of history of mathematics and their attitudes and beliefs towards using history of mathematics in mathematics education. Science & Education, 23(1), 159-183. Bagni, G. T. (2008). A theorem and its different proofs: History, mathematics education and the semiotic cultural perspective. Canadian Journal of Science, Mathematics, and Technology Education, 8(3), 217–232. Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449–466. Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.). New York, NY: McGraw-Hill. Fried, M. (2001). Can mathematics education and history of mathematics coexist? Science & Education, 10, 391–408. Furinghetti, F. (2004). History and mathematics education: A look around the world with particular reference to Italy. Mediterranean Journal for Research in Mathematics Education, 3(1–2), 1–19. Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics, 66(2), 131–143. Furinghetti, F., & Radford, L. (2002). Historical conceptual developments and the teaching of mathematics: From phylogenesis and ontogenesis theory to classroom practice. In D. L. English (Ed.), Handbook of international research in mathematics education (pp. 631–654). Mahwah, NJ: Lawrence Erlbaum. Haser, C. (2006). Investigation of preservice and inservice teachers’ mathematics related beliefs in Turkey and the perceived effect of middle school mathematics education program and the school contexts on these beliefs. Unpublished Doctoral Dissertation, Michigan State University, East Lansing. Jankvist, U. T. (2009). A categorization of the ‘‘whys’’ and ‘‘hows’’ of using history in mathematics education. Educational Studies in Mathematics, 71(3), 235–261. Philippou, G. N., & Christou, C. (1998). The effects of a preparatory mathematics program in changing prospective teachers’ attitudes towards mathematics. Educational Studies in Mathematics, 35, 189–206. Strauss, A. L. & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newburry Park, CA: Sage. Tzanakis, C., & Arcavi, A. (2000). Integrating history of mathematics in the classroom: An analytic survey. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education—The ICMI Study (pp. 201–240). Dordrecht: Kluwer Academic.
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