Teachers' Point of View in Teaching Mathematical Problem-Solving

##plugins.themes.bootstrap3.article.main##

András Ambrus
Dániel Katona

Abstract

There is still a deep gap between the theories of the didactics of mathematics and mathematics teaching practice worldwide. In our article, we analyse our trial to reach practicing mathematics teachers and summarize their opinion about some basic issues of teaching mathematics problem-solving from the point of view of cognitive load theory, what is a quite new topic in mathematics didactics society. We asked on the one hand, teachers from a small town in Hungary, and on the other hand, expert teachers and four young teachers from elite schools in the capital. The four young teachers have also started their PhD studies in mathematics education, besides school teaching. The opinions of the two groups of teachers reflect different attitudes towards teaching problem-solving, but in both cases relevant and important perspectives of the Hungarian school reality. The base of our study was a talk and an article of the first author, related to the role of human memory in learning and teaching mathematical problem-solving. We have been interested in how classroom teachers can take into consideration some results of the cognitive load theory, e.g. the split-attention effect and schema automation in their teaching practice, as well as in their attitudes to the use of worked examples and distributed practice. We analyse the results mostly from the perspective of desirable developments in in-service teacher training in Hungary.

Downloads

Download data is not yet available.

##plugins.themes.bootstrap3.article.details##

Section
Articles

References

Ambrus, A. (2014). Teaching mathematical problem-solving with the brain in mind: How can opening a closed problem help? Center for Educational Policy Studies Journal, 4(2), 105-120.

Ambrus, A. (2015). A matematika tanulás-tanítás néhány kognitív pszichológiai kérdése [Some cognitive psychological questions in mathematics education]. Gradus, 2(2), 63-73.

Baddeley, A., Eysenck, M. W., & Anderson, M. C. (2009). Memory. New York: Psychology Press.

Clark, R. E., Sweller, J., & Kirschner, P. (2012). Putting Students on the Path to Learning. The Case for Fully Guided Instruction. American Educator, Spring, 6-11.

Dienes, Z. (1960). Building up mathematics. London: Hutchinson Educational.

Halmos, M., & Varga, T. (1978). Change in mathematics education since the late 1950’s – ideas and realisation: Hungary. Educational Studies in Mathematics, 9(2), 225-244.

Hattie, J., & Yates, G. (2014). Visible Learning and the Science of How We Learn. London: Routledge.

Kalyuga, S. (2007). Expertise reversal effect and its implications for learner-tailored instruction. Educational Psychology Review, 19, 509–539.

Kalyuga, S., Chandler, P., & Sweller, J. (1999). Managing split-attention and redundancy in multimedia instruction. Applied Cognitive Psychology,13, 351–371.

Kirschner, P. A. (2002). Cognitive load theory: Implications of cognitive load theory on the design of learning. Learning and Instruction, 12(1), 1–10.

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem Based, Experimental, and Inquiry-Based Teaching. Educational Psychologist, 41(2), 75-82.

Magyar Tudományos Akadémia. (2016). A Tanítói/tanári kérdőívre beküldött válaszok összesítése [Summary of responses to the primary/ secondary school teachers’ questionnaire]. Retrieved from http://mta.hu/data/dokumentumok/iii_osztaly/2016/tanitoi_tanari_kerdoiv_osszegzes_2016%20%281%29.pdf.

Miller, G.A. (1956). The magical number seven, plus or minus two: some limits on our capacity to process information. Psychological Review, 63(2), 81–97.

Paas, F. (1992). Training strategies for attaining transfer of problem-solving skill in statistics: A Cognitive-load approach. Journal of Educational Psychology, 84, 429-434.

Paas, F., Tuovinen, J. E., Tabbers, H. K., & Van Gerven, P. W. M. (2003). Cognitive load measurement as a means to advance cognitive load theory. Educational Psychologist, 38 (1), 63–71.

Polya, G. (1957). How to solve it: A new aspect of mathematical method. Princeton, N. J: Princeton University Press.

Schoenfeld, A. H. (2007). What is Mathematical Proficiency and How Can It Be Assessed?. In A. H. Schoenfeld (Ed.), Assessing Mathematical Proficiency (pp. 59-76). Cambridge: Cambridge University Press.

Schoenfeld, A. H. (1985). Mathematical Problem Solving. New York: Academic Press.

Stahl, S. M., Davis, R.L., Kim, D.H., Lowe, N.G., Carlson, R.E., Fountain, K., & Grady, M.M. (2010). Play it again: The master psychopharmacology program as an example of interval learning in bite-sized portions. CNS Spectrums, 15(8), 491–504.

Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285.

Sweller, J. (2003). Evolution of human cognitive architecture. In B. Ross (Ed.), The psychology of learning and motivation, 43, 215-266. San Diego: Academic Press.

Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2 (1), 59–89.

Sweller, J., Van Merriënboer, J., & Paas, F. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10 (3), 251–296.

Sweller, J., Clark, R. E., & Kirschner, P. A. (2010). Mathematical ability relies on knowledge, too. American Educator, 34(4), 34-35.

Sweller, J., Clark, R. E., & Kirschner, P. A. (2011). Teaching general problem solving does not lead to mathematical skills or knowledge. EMS Newsletter, March, 41-42.

Varga, T. (1965). The use of a composite method for the mathematical education of young children. Bulletin of the International Study Group for Mathematical Learning, 3(2), 1-9.