Abstract
The affective domain of mathematics education, ranging from beliefs and attitudes to emotions, has been a frequent topic of discussion. However, in spite of some decades of research in this field, there are still a number of gaps and open questions, among them the field of adult education. This contribution focuses on one specific finding from a qualitative study describing the mathematical beliefs of eight adult education teachers in Switzerland. Illustrating three dualities identified in the participants’ data confirms the complexity of mathematical beliefs and it is argued that a focus on adult education teachers as well as a reflected use of research methods and instruments would be beneficial for the advancement of mathematical belief research, particularly the change of beliefs.
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- 1.
It is worth noting that while many studies refer to this threefold perspective, Ernest has neither been the first nor the only one to describe it. He himself refers—among others—to Thompson’s work (Thompson, 1984), another author is Dionne who described the traditional, the formalist and the constructivist perspective (Dionne, 1984, cited by Pehkonen & Törner, 2004) and Törner and his colleagues talk about the toolbox, the system and the process aspect (Törner & Grigutsch, 1994; Pehkonen & Törner, 2004). However, “all these different notions correspond more or less with each other” (Liljedahl, 2008).
- 2.
This meta study is also an excellent illustration of how conceptual clarity is not only relevant for beliefs themselves, but how other key terms such as stability respectively change are interpreted differently by different researchers sometimes resulting in contradictory findings.
- 3.
However, it should also be noted that recent technological developments have greatly facilitated the use of different methods and it has become much easier to include film or other visual images in research designs.
- 4.
- 5.
An in-depth discussion of these two terms and how they relate to each other is beyond the scope of this contribution, however, mixed methods is understood as combination of qualitative and quantitative methods whereas triangulation refers to a plurality in perspectives which may include different methods (Burzan, 2016).
- 6.
An interesting example in this context is the study reported by Pehkonen and Törner (2004) who in their discussion conclude: “The original underlying hypothesis of our research question […] namely that our methodical approach is to be understood as a triangulation, had to be revised in part. The collected data is only partly redundant, although it merges into a complete picture that could not have been drawn in such detail through any of the three approaches alone. In other words, the results of the various methods complement each other” (no page). It implies that their initial motivation for the use of triangulation was to increase the data’s validity and use the various sources to confirm each other, however, it seems they then changed to seeing the purpose of triangulation as complementary in the sense that it helped them to get a more complete picture.
- 7.
While the previous discussion implies that methodical issues relate mainly to studies using multiple sources of data, this is not the case. Particularly studies referring to qualitative research methods often merely make superficial references, for example claiming to use a grounded theory approach when working with deductive or open coding, even though other basic premises of grounded theory such as a circular research design are at best partially implemented (see for example Bulmer & Rolka, 2005 or Di Martino & Zan, 2011).
- 8.
Ten days before the first interview they received a letter asking them to create a picture as follows: “Imagine you were an artist and have accepted the following contract work: What is mathematics? A personal view. Present your views in a pictorial, creative manner, working with materials and techniques of your choice (coloured pencils, watercolour, collage, etc.).” Together with this task they received an A3-format piece of paper, which they had to use for the creation and presentation of their picture.
- 9.
They also used text and in some cases interviews as multiple sources with the aim of increasing the “trustworthiness of scientific results” (Rolka & Halverscheid, 2011, p. 527), however the focus of their analyses were pictures and the other material was mainly used in order to facilitate the classification of the picture.
- 10.
Relatively few studies address this differentiation, among them Beswick (2012).
- 11.
The term everyday mathematics is also a literal translation of the German term “Alltagsmathematik” which is widely used in adult basic education in Switzerland and therefore denotes the local context.
- 12.
“Mathe” generally denotes a more colloquial and everyday context, whereas “Mathematik” is understood to have more formal connotations and refer to the discipline as such, see also Kaye (2015) for a discussion of the terms mathematics, maths and numeracy in the English context.
- 13.
This is not only clearly expressed in the new Federal Law on Further Education which has come into effect on January 1, 2017 and which includes basic skills, but it is also reflected in the name of the national umbrella organisation, the Swiss Federation for Adult Learning SVEB which in German, French and Italian is always translated as the Swiss Federation for Further Education (own emphasis).
- 14.
Unfortunately, the recently redesigned SVEB homepage no longer contains any information in English, however, the site http://swisseducation.educa.ch/en contains comprehensive information in English on the Swiss education system in general. (accessed 12 July 2018).
- 15.
The “Netzwerk Alltagsmathematik” as it is called in German brings together some 125 individuals interested in everyday mathematics/numeracy in an informal manner. Many of them work as course leaders, in further education institutions or in academia. As the network provides no personal information apart from their names, it is not possible to describe the network members more systematically. More information on the network (in German) can be found at: http://www.netzwerk-alltagsmathematik.ch (accessed 3 March 2016).
- 16.
Verbal indicators of possibly dualities are contained in phrases like “at the same time”, “it is also”, “on one hand … on the other” or adjectives such as “ambivalent”, to name a few.
- 17.
This statement is also an interesting indicator of how other aspects such as personality traits may shape mathematical beliefs.
- 18.
Switzerland’s armed forces are largely militia based which means that its members work in other professions such as that of a teacher for the most time of their lives.
- 19.
Grades in Switzerland are awarded from 1 to 6 with 4 being a pass and 6 being excellent.
- 20.
In order to reduce the number of mice in the fields, many villages issued a small fee as reward for each caught animal. In rural areas of Switzerland catching mice was therefore a possibility for children to earn pocket money. They could bring a part of the mouse (tail or specific paw) to their village administration and got a little money for each animal they caught.
References
Aguirre, J., & Speer, N. M. (1999). Examining the relationship between beliefs and goals in teacher practice. Journal of Mathematical Behavior, 18(3), 327–356.
Barkatsas, A., & Malone, J. (2005). A typology of mathematics teachers’ beliefs about teaching and learning mathematics and instructional practices. Mathematics Education Research Journal. https://doi.org/10.1007/BF03217416.
Beeli-Zimmermann, S. (2014). Beyond questionnaires—Exploring adult education teachers’ mathematical beliefs with pictures and interviews. ALM International Journal, 9(2), 35–53.
Beeli-Zimmermann, S. (2015). From teaching literacy to teaching numeracy: How numeracy teacher’s previous experiences shape their teaching beliefs. Literacy and Numeracy Studies, 23(1), 20–49.
Beswick, K. (2004). The impact of teachers’ perceptions of student characteristics on the enactment of their beliefs. In M. Johnsen Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 111–118). Bergen: Bergen University College.
Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational Studies in Mathematics, 79(1), 127–147.
Brosnan, P., Edwards, T., & Erickson, D. (1996). An exploration of change in teachers’ beliefs and practices during implementation of mathematics standards. Focus on Learning Problems in Mathematics, 18(4), 35–53.
Bulmer, M., & Rolka, K. (2005). The “A4-Project”—Statistical world views expressed through pictures. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 93–200). Melbourne: PME.
Burzan, N. (2016). Methodenplurale Forschung: Chancen und Probleme von Mixed Methods. Weinheim: Beltz Juventa.
Calderhead, J. (1996). Teachers: Beliefs and knowledge. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 709–725). New York: Macmillan Library Reference.
Condelli, L. (2006). A review of the literature in adult numeracy: Research and conceptual issues. Washington, DC: American Institutes for Research.
Cross, D. I. (2009). Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices. Journal of Mathematics Teacher Education, 12(5), 325–346.
Cross Francis, D., Rapacki, L., & Eker, A. (2014). The individual, the context and practice: A review of the research on teachers’ beliefs related to mathematics. In H. Fives & M. G. Gill (Eds.), Educational psychology handbook. International Handbook of Research on Teachers’ Beliefs (pp. 336–352). New York: Routledge.
Di Martino, P., & Zan, R. (2011). Attitude towards mathematics: A bridge between beliefs and emotions. ZDM Mathematics Education. https://doi.org/10.1007/s11858-011-0309-6.
Dirkx, J. M., & Spurgin, M. E. (1992). Implicit theories of adult basic education teachers: How their beliefs about students shape classroom practice. Adult Basic Education, 2(1), 20–41.
Educa.ch. (Ed.). (2016). The Swiss education system. https://swisseducation.educa.ch/en/swiss-education-system-3. Accessed December 22, 2016.
Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33.
Evans, J. (2000). Adults’ mathematical thinking and EMOTIONS: A study of numerate practises: Vol. 16. Studies in Mathematics Education Series. London: Routledge/Falmer.
FitzSimons, G. E., Coben, D., & O’Donoghue, J. (2003). Lifelong mathematics education. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 103–142). Dordrecht, The Netherlands: Springer.
Fives, H., & Buehl, M. M. (2012). Spring cleaning for the “messy” construct of teachers’ beliefs: What are they? Which have been examined? What can they tell us? In K. R. Harris, S. Graham, & T. Urdan (Eds.), Educational Psychology Handbook: Vol. 2. Individual differences and cultural and contextual factors (pp. 471–499). Washington, DC: American Psychological Association.
Fives, H., & Gill, M. G. (Eds.). (2014). Educational psychology handbook: International handbook of research on teachers’ beliefs. New York: Routledge.
Forgasz, H., & Leder, G. C. (2008). Beliefs about mathematics and mathematics teaching. In P. Sullivan & T. Wood (Eds.), The International Handbook of Mathematics Teacher Education: Vol. 1. Knowledge and beliefs in mathematics teaching and teaching development (pp. 173–192). Rotterdam: Sense Publishers.
Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterization of beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs. A hidden variable in mathematics education? (pp. 39–57). Dordrecht: Kluwer Academic Publishers.
Gales, M. J., & Yan, W. (2001). Relationship between constructivist teacher beliefs and instructional practices to students’ mathematical achievement: Evidence from TIMMS, Seattle. http://files.eric.ed.gov/fulltext/ED456133.pdf. Accessed February 24, 2017.
Gläser, J., & Laudel, G. (2013). Life with and without coding: Two methods for early-stage data analysis in qualitative research aiming at causal explanations. Forum Qualitative Sozialforschung/Forum: Qualitative Social Research, 14(2), Art. 5.
Goldin, G. A., Rösken, B., & Törner, G. (2009). Beliefs—No longer a hidden variable in mathematical teaching and learning processes. In J. Maasz & W. Schlöglmann (Eds.), Beliefs and attitudes in mathematics education: New research results (pp. 1–18). Rotterdam: Sense Publishers.
Grigutsch, S., & Törner, G. (1998). World views of mathematics held by university teachers of mathematics science. https://duepublico.uni-duisburg-essen.de/servlets/DerivateServlet/Derivate-5249/mathe121998.pdf. Accessed July 5, 2018.
Handal, B. (2003). Teachers’ mathematical beliefs: A review. The Mathematics Educator, 13(2), 47–57.
Henningsen, I., & Wedege, T. (2003). Values and mathematics: Attitudes among teachers in adult education. In J. Maasz & W. Schlöglmann (Eds.), Learning mathematics to live and work in our world. Proceedings of the 10th International Conference on Adults Learning Mathematics in Strobl (Austria) 29th June to 2nd July 2003 (pp. 110–118). Linz: Universitätsverlag Trauner.
Kaasila, R. (2007). Mathematical biography and key rhetoric. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-007-9085-1.
Kaye, D. (2015). What do I teach? Mathematics, numeracy, or maths? In A. Hector-Mason & S. Beeli-Zimmermann (Eds.), Adults learning mathematics—Inside and outside the classroom. Proceedings of the 21st International Conference of Adults Learning Mathematics—A Research Forum (ALM) (pp. 141–149). Bern: University of Bern.
Kelle, U. (2001). Sociological explanations between micro and macro and the integration of qualitative and quantitative methods. Forum Qualitative Sozialforschung/Forum: Qualitative Social Research, 2(1), Art. 5.
Kohlbacher, F. (2005). The use of qualitative content analysis in case study research. Forum Qualitative Sozialforschung/Forum: Qualitative Social Research, 7(1), Art. 21.
Kress, G. R., & van Leeuwen, T. (2006). Reading images: The grammar of visual design. London: Routledge.
Lave, J. (2000). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge: Cambridge University Press.
Leatham, K. R. (2006). Viewing mathematics teachers’ beliefs as sensible systems. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-006-9006-8.
Leder, G. C., & Forgasz, H. (2002). Measuring mathematical beliefs and their impact on the learning of mathematics: A new approach. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs. A hidden variable in mathematics education? (pp. 95–113). Dordrecht: Kluwer Academic Publishers.
Leder, G. C., Pehkonen, E., & Törner, G. (Eds.). (2002). Beliefs: A hidden variable in mathematics education?. Dordrecht: Kluwer Academic Publishers.
Liljedahl, P. (2008). Teachers’ beliefs as teachers’ knowledge: Presentation at the symposium on the occasion of the 100th anniversary of ICMI, Rome. http://www.unige.ch/math/EnsMath/Rome2008/WG2/WG2.html. Accessed February 15, 2012.
Liljedahl, P., Oesterle, S., & Bernèche, C. (2012). Stability of beliefs in mathematics education: A critical analysis. Nordic Studies in Mathematics Education, 17(3–4), 101–118.
Maasz, J., & Schlöglmann, W. (Eds.). (2009). Beliefs and attitudes in mathematics education: New research results. Rotterdam: Sense Publishers.
Mason, J. (2004). Are beliefs believable? Mathematical Thinking and Learning. https://doi.org/10.1207/s15327833mtl0603_4.
Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analysis. Journal for Research in Mathematics Education. https://doi.org/10.2307/749662.
Mayring, P. (2014). Qualitative content analysis. Theoretical foundation, basic procedures and software solution. http://files.qualitative-content-analysis.aau.at/200000075-82241831d6/Mayring(2014)QualitativeContentAnalysis.pdf. Accessed December 2, 2016.
Millsaps, G. M. (2000). Secondary mathematics teachers’ mathematics autobiographies: Definitions of mathematics and beliefs about mathematics instructional practice. Focus on Learning Problems in Mathematics, 22(1), 45–67.
Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19(4), 317–328.
Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Learning in doing. Cambridge: Cambridge University Press.
O’Donoghue, J. (2002). Numeracy and mathematics. Irish Math Society Bulletin, 48, 47–55.
Op’t Eynde, P., de Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics—Related beliefs: A quest for conceptual clarity and a comprehensive categorization. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs. A hidden variable in mathematics education? (pp. 13–37). Dordrecht: Kluwer Academic Publishers.
Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307–332.
Pehkonen, E. (2008). State-of-the-art in mathematical beliefs research. In M. Niss & E. Emborg (Eds.), Proceedings of the 10th International Congress on Mathematical Education. ICME 10 2004, July 4th–11th, 2004 (pp. 1–14). Roskilde: IMFUFA, Department of Science, Systems and Models, Roskilde University.
Pehkonen, E., & Törner, G. (2004). Methodological considerations on investigating teachers’ beliefs of mathematics and its teaching. Nordisk matematikkdidaktikk/Nordic studies in mathematics education, 9(1), 21–49.
Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning. A Project of the National Council of Teachers of Mathematics (pp. 257–315). Charlotte: Information Age Publishing.
Reusser, K., Pauli, C., & Elmer, A. (2011). Berufsbezogene Überzeugungen von Lehrerinnen und Lehrern. In E. Terhart, H. Bennewitz, & M. Rothland (Eds.), Handbuch der Forschung zum Lehrerberuf (pp. 478–495). Münster: Waxmann.
Richardson, V. (1996). The role of attitude and beliefs in learning to teach. In J. P. Sikula, T. J. Buttery, & E. Guyton (Eds.), Handbook of research on teacher education. A Project of the Association of Teacher Educators (2nd ed., pp. 102–119). New York: Macmillan Library Reference.
Rolka, K., & Halverscheid, S. (2011). Researching young students’ mathematical world views. ZDM Mathematics Education. https://doi.org/10.1007/s11858-011-0330-9.
Schlöglmann, W. (2007). Beliefs concerning mathematics held by adult students and their teachers. In K. Hoskonen & M. S. Hannula (Eds.), Current state of research on mathematical beliefs XII. Proceedings of the MAVI-7 Workshop, May 24–28, 2006 (pp. 97–109). Helsinki: Department of Teacher Education, University of Helsinki.
Schraw, G., & Olafson, L. (2014). Assessing teachers’ beliefs: Challenges and solutions. In H. Fives & M. G. Gill (Eds.), Educational Psychology Handbook. International handbook of research on teachers’ beliefs (pp. 87–105). New York: Routledge.
Skott, J. (2001). The emerging practices of a novice teacher: The roles of his school mathematics images. Journal of Mathematics Teacher Education. https://doi.org/10.1023/A:1009978831627.
Skott, J. (2009). Contextualising the notion of ‘belief enactment’. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-008-9093-9.
Skott, J. (2013). Understanding the role of the teacher in emerging classroom practices: Searching for patterns of participation. ZDM Mathematics Education. https://doi.org/10.1007/s11858-013-0500-z.
Skott, J. (2014). The promises, problems and prospects of research on teachers’ beliefs. In H. Fives & M. G. Gill (Eds.), Educational Psychology Handbook. International handbook of research on teachers’ beliefs (pp. 13–30). New York: Routledge.
Speer, N. M. (2005). Issues of methods and theory in the study of mathematics teachers’ professed and attributed beliefs. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-005-2745-0.
Speer, N. M. (2008). Connecting beliefs and practices: A fine-grained analysis of a college mathematics teacher’s collections of beliefs and their relationship to his instructional practices. Cognition and Instruction. https://doi.org/10.1080/07370000801980944.
Staub, F. C., & Stern, E. (2002). The nature of teachers’ pedagogical content beliefs matters for students’ achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology. https://doi.org/10.1037/0022-0663.94.2.344.
Statistics Canada, & OECD (Eds.). (2005). Learning a living. First results of the adult literacy and life skills survey. Paris: OECD.
Steen, L. A. (2001). Mathematics and numeracy: Two literacies, one language. The Mathematics Educator, 6(1), 10–16.
Stone, R. (2009). “I, robot” free will and the role of the maths teacher—Who decides on how we teach? In G. Griffiths & D. Kaye (Eds.), Numeracy works for life. Proceedings of the 16th International Conference of Adults Learning Mathematics, July 6–9, 2009 (pp. 246–253). London: London South Bank University.
Swan, M. (2006). Designing and using research instruments to describe the beliefs and practices of mathematics teachers. Research in Education, 75(1), 58–70.
Swars, S. L., Smith, S. Z., Smith, M. E., & Hart, L. C. (2009). A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-008-9092-x.
Sztajn, P. (2003). Adapting reform ideas in different mathematics classrooms: Beliefs beyond mathematics. Journal of Mathematics Teacher Education, 6, 53–75.
Tashkkori, A., & Teddlie, C. (2008). Quality of inferences in mixed methods research: Calling for an integrative framework. In M. M. Bergman (Ed.), Advances in mixed methods research: Theories and applications (pp. 101–119). Los Angeles: SAGE.
Taylor, E. (2003). The relationship between the prior school lives of adult educators and their beliefs about teaching adults. International Journal of Lifelong Education. https://doi.org/10.1080/02601370304828.
Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15(2), 105–127.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook for research on mathematics teaching and learning. New York: Macmillan.
Törner, G., & Grigutsch, S. (1994). „Mathematische Weltbilder“ bei Studienanfängern - eine Erhebung. Journal für Mathematik-Didaktik, 15(3/4), 211–252.
Wedege, T. (1999). To know or not to know—Mathematics, that is a question of context. Educational Studies in Mathematics, 39, 205–227.
Woolfolk Hoy, A., Davis, H., & Pape, S. J. (2006). Teacher knowledge and beliefs. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 715–737). Mahwah: Erlbaum.
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Beeli-Zimmermann, S. (2018). “I’ve Never Cooked with My Maths Teacher”—Moving Beyond Perceived Dualities in Mathematical Belief Research by Focusing on Adult Education. In: Safford-Ramus, K., Maaß, J., Süss-Stepancik, E. (eds) Contemporary Research in Adult and Lifelong Learning of Mathematics. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-96502-4_11
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