An investigation of Norwegian students’ affective domain in mathematics
DOI:
https://doi.org/10.7146/nomad.v14i4.148214Abstract
After decades of research in the affective domain in mathematics education, and search for ways to enhance students’ positive attitudes towards the discipline, the perception that to be able to do mathematics is innate remains a widespread belief. Already twenty years ago the Fourth NAEP study concluded that students believe mathematics to be important, difficult and based on rules, and theses attributions also characterise the view of mathematics even two decades later. As a relationship exists between the claims ”mathematics is difficult” and ”mathematics is boring” one could assume that students lack interest towards mathematics. The conclusions about the present situation are based on a study carried out in Norway in 2005. This paper documents and analyses the data from the study. Six factors are identified and analysed in relation to students ́ affective domain in mathematics. The six factors are: interest, hard-working, self-confidence, usefulness, insecurity, and MAD (Mathematics as an Absolute Discipline).
References
Aiken, L. R. (1980). Attitude measurement and research. In D. A. Payne (Ed.), Recent developments in affective measurement (pp. 1-24). San Francisco: Jossey-Bass.
Akinsola, M. K. & Tella, A. (2007). Students' conceptions about mathematics teaching in Nigeria and Botswana. In I. Attorps & E. Kellner (Eds.), Proceedings of the conference Conceptions and Beliefs in Mathematics and Science Education including MAVI XIII (pp. 10-15). Gävle, May 30 - June 1, 2007.
Bernstein, J., Reilly, L. & Cote-Bonanno, J. (1992). Barriers to women entering the workforce: math anxiety (Report No. CE 064 012). (ERIC, ED 359381).
Brekke, G., Streitlien, Å. & Wiik, L. (2004). Affects and beliefs in school mathematics: gender differences. Paper presented in Discussion Group 19 in ICME10, 2004, Copenhagen, Denmark. Retrieved January 15, 2006 from http://www.icme-organisers.dk/dg19/
Brekke, G. & Streitlien, Å. (2005). Elevers holdningar til matematikkfaget (Informasjonsserien nr 26/2005). Paper presented in the conference Nasjonale prøver, veivalg og utviklingsmuligheter (pp. 83-91). Lillehammer: Lillehammer University College.
Brew, C., Riley, P., Walta, C. & Itter, D. (2006, November). Fear Factor: What does maths anxiety measure in pre-service primary teachers? Paper presented at the Annual Australian Research in Education Conference, Adelaide. SA.
Brown, C. A., Carpenter, T. P., Kouba, V. L., Lindquist, M. M., Silver, E. A. et al. (1988). Secondary school results for the fourth NAEP mathematics assessment: algebra, geometry, mathematical methods, and attitudes. Mathematics Teacher, 81 (5), 337-347, 397. https://doi.org/10.5951/MT.81.5.0337
Byrne, B. M. (2001). Structural equation modeling with AMOS: basic concepts, applications, and programming. Mahwah: Lawrence Erlbaum Associates.
Campbell, K. & Evans, C. (1997). Gender issues in the classroom: a comparison of mathematics anxiety. Education, 117 (3), 332-339.
Child, D. (1970). The essentials of factor analysis (3rd ed.). New York: Continuum.
Clason, D. L. & Dormody, T. J. (1994). Analyzing data measured by individual Likert-type items. Journal of Agricultural Education, 35 (4), 31-35. https://doi.org/10.5032/jae.1994.04031
Di Martino P. & Zan. R. (2003). What does 'positive' attitude really mean? In N. A. Pateman, B. J. Dougherty & J. Zilliox (Eds.), Proceedings of the 27th conference of the international group for the Psychology of Mathematics Education (Vol. 4, pp. 451-458). University of Hawaii.
Dossey, J. A., Mullis, I. V. S., Lindquist. M. M. & Chambers, D. L. (1988). The mathematics report card: trends and achievement based on the 1986 national assessment. Princeton: Educational Testing Service.
Espeland, H., Goodchild, S. & Grevholm, B. (2008). Challenges faced by those working towards a co-learning agreement. In C. Winsløw (Ed.), Nordic research in mathematics education: proceedings from NORMA08 in Copenhagen, April 21 - April 25, 2008 (pp. 81-88). Rotterdam: Sense Publishers. https://doi.org/10.1163/9789087907839_011
Fan, L. & Yeo, S. M. (2008). Integrating oral presentations into mathematics teaching and learning: an exploratory study with Singapore secondary students. In B. Sriraman (Ed.), Beliefs and mathematics: festschrift in honor of Günter Törner's 60th birthday (pp. 99-122). Charlotte, NY: Information Age Publishing.
Fennema, E. & Sherman, J. (1977). Sex-related differences in mathematics achievement, spatial visualization and affective factors. American Educational Research Journal, 14, 51-71. https://doi.org/10.3102/00028312014001051
Fennema. E. & Sherman, J. (1978). Sex-related differences in mathematics achievement and related factors: a further study. Journal for Research in Mathematics Education, 7, 189-203. https://doi.org/10.2307/748997
Frank, M. L. (1988). Problem solving and mathematical beliefs. Arithmetic Teacher, 35 (5), 32-34. https://doi.org/10.5951/AT.35.5.0032
Furinghetti, F. & Pehkonen, E. (2000). A comparative study of students' beliefs concerning their autonomy of doing mathematics. Nordic Studies in Mathematics Education, 8 (4), 7-26.
Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59-72). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_4
Goldin, G. A. (2004). Characteristics of affect as a system of representation. In. M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the international group for the Psychology of Mathematics Education (pp. 109- 114). Bergen University College.
Göb, R., McCollin, C. & Ramalhoto, M. F. (2007). Ordinal methodology in the analysis of Likert scales. Quality & Quantity, 41, 601-616. https://doi.org/10.1007/s11135-007-9089-z
Hannula, M. S. (2004). RF01: Affect in mathematics education - exploring theoretical frameworks. In. M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the international group for the Psychology of Mathematics Education (pp. 107-109). Bergen University College.
Hannula, M. S. & Malmivuori, M. L. (1996). Feminine structures in mathematical beliefs and performances. In E. Pehkonen (Ed.), Current state of research on mathematical beliefs III: proceedings of the MAVI-3 workshop (pp. 31-38). Helsinki, August 23-26, 1996. Department of Teacher Education, University of Helsinki.
Hart, L. E. (1989). Describing the affective domain: saying what we mean. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving (pp. 37-45). New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-3614-6_3
Hundeland, P. S. (2009). Matematikklærerens kompetanse. En studie om hva lærerne på videregående trinn vektlegger i sin matematikkundervisning (Doctoral thesis). Kristiansand: University of Agder.
Jaworski, B., Fuglestad, A. B., Bjuland, R., Breiteig, T., Goodchild, S. et al. (Eds.) (2007). Læringsfelleskap i matematikk. Learning communities in mathematics. Bergen: Caspar Forlag AS.
Kapetanas, E. & Zachariades, T. (2007). Students' beliefs and attitudes concerning mathematics and their effect on mathematical ability. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 258-267). Retrieved May 3, 2008 from http://ermeweb.free.fr/CERME5b/WG2.pdf
Kim, J. &. Mueller, C. W. (1978). Factor analysis: statistical methods and practical issues. Thousand Oaks, CA: Sage Publications. https://doi.org/10.4135/9781412984256
Kislenko, K., Grevholm, B. & Lepik, M. (2007). "Mathematics is important but boring": students' beliefs and attitudes towards mathematics. In C. Bergsten, B. Måsøval & F. Rønning (Eds.), Relating practices and research in mathematics education. Proceedings of NORMA 05: fourth Nordic Conference on Mathematics Education, Trondheim, 2nd-6th September 2005 (pp.349-360). Trondheim: Tapir Academic Publishers.
Kislenko, K. & Grevholm, B. (2008). The Likert scale used in research on affect - a short discussion of terminology and appropriate analysing methods. Paper presented at the Topic Study Group 30 in ICME11, 2008, Monterrey, Mexico. Retrieved June 10, 2008 from http://tsg.icme11.org/tsg/show/31
Kloosterman, P. (2002). Beliefs about mathematics and mathematics learning in the secondary school: measurement and the implications for motivation. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 247-269). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_15
Kloosterman, P. & Clapp Cougan, M. C. (1994). Students' beliefs about learning school mathematics. The Elementary School Journal, 94 (4), 375-388. https://doi.org/10.1086/461773
Kulm, G. (1980). Research on mathematics attitude. In R. J. Shumway (Ed.), Research in mathematics education (pp. 356-387). Reston: NCTM.
Leatham, K. R. (2006). Viewing mathematics teachers' beliefs as sensible systems. Journal of Mathematics Teacher Education, 9, 91-102. https://doi.org/10.1007/s10857-006-9006-8
Leder, G. C. & Forgasz, H. J. (2002). Measuring mathematical beliefs and their impact on the learning of mathematics. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 95-114). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_6
Lester, F. K., Garofalo, J. & Lambdin Kroll, D. (1989). Self-confidence, interest, beliefs, and metacogition: key influences on problem-solving behavior. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: a new perspective (pp. 75-88). New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-3614-6_6
Likert, R. (1932). A technique for the measurement of attitudes. NY: Archives of Psychology.
Ma, X. (1997). Reciprocal relationships between attitude toward and achievement in mathematics. Journal of Educational Research, 90, 221-229. https://doi.org/10.1080/00220671.1997.10544576
McLeod, D. B. (1989). Beliefs, attitudes, and emotions: new views of affect in mathematics education. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: a new perspective (pp. 245-258). New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-3614-6_17
McLeod, D. B. (1992). Research on affect in mathematics education: a reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575-596). New York: Macmillan.
McLeod, D. B. & McLeod, S. H. (2002). Synthesis - beliefs and mathematics education: implications for learning, teaching and research. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 39-58). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_7
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.
Nardi, E. & Steward, S. (2002). 'I could be the best mathematician in the world if I actually enjoyed it. I'm 14, and I know that! Why can't some adult work it out?' Mathematics Teaching, 180, 41-44.
Nardi, E. & Steward, S. (2003). Is mathematics T.I.R.E.D? A profile of quiet disaffection in the secondary mathematics classroom. British Educational Research Journal, 29 (3), 345-367. https://doi.org/10.1080/01411920301852
National Research Council. (1989). Everybody counts: a report to the nation on the future of mathematics education. Washington, DC: National Academy Press.
Norwegian directorate for education and training (Utdanningsdirektoratet) (1997) 1. The curriculum for the 10-year compulsory school. Retrieved February 02, 2007 from http://www2.udir.no/L97/L97eng
Norwegian directorate for education and training (Utdanningsdirektoratet) (2009). Common core subjects in primary and secondary education - Mathematics subject curriculum. Retrieved March 01, 2009 from http://www.utdanningsdirektoratet.no/Artikler/_Lareplaner/_english/Common-core-subjects-in-primary-and-secondary-education/
Nurmi, A, Hannula, M. S., Maijala, H. & Pehkonen, E. (2003). On pupils' self-confidence in mathematics: gender comparisons. In N. A. Pateman, B. J. Dougherty & J. Zillox (Eds.), Proceedings of the 27th conference of the international group for the Psychology of Mathematics Education (pp. 453-460). University of Hawaii.
Pehkonen, E. (1994). On differences in pupil's conceptions about mathematics teaching. The Mathematics Educator, 5 (1), 3-10.
Pehkonen, E. (1995). Pupils' view of mathematics: initial report for an international comparison project (Research Report 150). Department of Teacher Education, University of Helsinki.
Pehkonen, E. (2003). Læreres og elevers oppfatninger som en skjult faktor i matematikkundervisningen. In B. Grevholm (Ed.), Matematikk for skolen (pp. 154-181). Bergen: Fagbokforlaget.
Pehkonen, E. & Lepmann, L. (1994). Teachers' conceptions about mathematics teaching in comparison (Estonia - Finland). In M. Ahtee & E. Pehkonen (Eds.), Constructivist viewpoints for school teaching and learning in mathematics and science (Research Report 131) (pp. 105-110). Department of Teacher Education, University of Helsinki.
Pehkonen, E. & Törner, G. (2004). Methodological considerations on investigating teachers' beliefs of mathematics teaching and learning. Nordic Studies in Mathematics Education, 9 (1), 21-49.
Pring, R. (2000). Philosophy of educational research. London: Continuum. https://doi.org/10.1111/1467-8527.t01-1-00129
Rokeach, M. (1972). Beliefs, attitudes, and values. San Francisco: Jossey-Bass Inc.
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press.
Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-369). New York: Macmillan.
Silver, E. A. (1985). Research on teaching mathematical problem solving: some underrepresented themes and directions. In. E. A. Silver (Ed.), Teaching and learning mathematical problem solving: multiple research perspectives (pp. 247- 266). Hillsdale: Lawrence Erlbaum.
Sloman, A. (1987). Motives, mechanisms and emotions. Cognition and Emotion, 1 (3), 209-216. https://doi.org/10.1080/02699938708408049
Spearman, C. (1910). Correlation calculated from faulty data. British Journal of Psychology, 3, 271-295. https://doi.org/10.1111/j.2044-8295.1910.tb00206.x
Statt, D. A. (1990). The concise dictionary of psychology. London: Routledge.
Stodolsky, S. S. (1985). Telling math: origins of math aversion and anxiety. Educational Psychologist, 20, 125-133. https://doi.org/10.1207/s15326985ep2003_2
Thompson, A. G. (1989). Learning to teach mathematical problem solving: changes in teachers' conceptions and beliefs. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving. Research agenda for mathematics education (Vol. 3, pp. 232-243). Reston: Lawrence Erlbaum & NCTM.
Thompson, A. G. (1992). Teachers' beliefs and conceptions: a synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.
Tikly, C. & Wolf, A. (2000). The maths we need now: demands, deficits and remedies (Bedford Way Paper 12). London: Institute of Education.
Tooke, D. J. & Lindstrom, L. C. (1998). Effectiveness of a mathematics methods course in reducing math anxiety of preservice elementary teachers. School Science and Mathematics, 98 (3), 136-140. https://doi.org/10.1111/j.1949-8594.1998.tb17406.x
Uebersax, J. S. (2006). Likert scales: dispelling the confusion. Retrieved January 10, 2008 from http://ourworld.compuserve.com/homepages/jsuebersax/likert. htm
Vale, C. M. & Leder, G. C. (2004). Student views of computer-based mathematics in the middle years: does the gender make a difference? Educational Studies in Mathematics, 56, 287-312. https://doi.org/10.1023/B:EDUC.0000040411.94890.56
Woodard, T. (2004). The effects of math anxiety on post-secondary developmental students as related to achievement, gender, and age. Inquiry, 9 (1). Retrieved January 10, 2008 from http://www.vccaedu.org/inquiry/inquiry-spring2004/i-91-woodard.html
Wu, C. H. (2007). An empirical study on the transformation of Likert-scale data to numerical scores. Applied Mathematical Sciences, 1 (58), 2851-2862.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
