COMPARISON OF THE CLASSICAL SOLUTION TO SUBTRACTION EXERCISES AND THEIR SOLUTION WITH REPRESENTATIONS

Andreas Marinos

Abstract


294 pupils aged 8-9 years were given subtraction problems. Initially the pupils managed to solve the exercises using the usual algorithm (a-b=c). Simultaneously they made a representation of their solutions using 4 shapes which had been pre-agreed by the pupils and their teacher. Not only were the results unsatisfactorily worked out, but they were lower than the (also) unsatisfactory solutions given in the students’ efforts to solve the problems in the classical way. A teaching configuration was then prepared. After this an overall improvement was discerned in the majority of pupils, in subtraction problems.

 

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Keywords


primary school, representations, subtraction exercises, using the usual algorithm

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References


Avgerinos, E. & Marinos, A. (2009). Mathematics teachers and new technologies a case study in Dodecanese Island schools. 6th Mediterranean Conference on Mathematics Education 22-26 April pp. 357-364, Plovdiv, Bulgaria

Carpenter, T., Fennema, E. Franke, M. (1996). Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction, The Elementary School Journal, Volume: 97, 1, 3-20

Chi, M. T. H., Feltovich, P. J. & Glaser, R. (1981). Categorization and Representation of physics problems by experts and novices. Cognitive Science, 5, 121–152.

Chularut, P., & DeBacker, T. K. (2004). The influence of concept mapping on achievement, self-regulation, and self-efficacy in students of English as a second language. Contemporary Educational Psychology, 29, 248–263.

Colin, P., Chauvet, F., & Viennot, L. (2002). Reading images in optics: Students’ difficulties and teachers’ views. International Journal of Science Education, 24(3), 313-332.

Dufour – Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical Considerations Concerning the Problem of Representation. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 109-122). Hillsdale, NJ: Lawrence Erlbaum.

Elia, I., Gagatsis, A., & Demetriou, A. (2007). The effects of different modes of representation on the solution of one-step additive problems. Learning and Instruction, 17, 658-672.

Elia, I., Gagatsis, A., & Gras, R. (2006). La « magie » et le pouvoir de l’image pour les petits enfants: application dans la résolution des problèmes du type additif. Scientia Paedagogica Experimentalis, 43, 89-114.

Friel, S., Curcio, F., & Bright, W. (2001). Making sense of graphs: critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124–158.

Fuson, K. (1992). Research on whole number addition and subtraction, in D. A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 243–275

Gagatsis, A., & Christou, C. (2002). The structure of translations among representations in functions. Scientia Paedagogica Experimentalis, 39(1), 39-58.

Gagatsis, A., & Elia, I. (2004). The effects of different modes of representations on mathematical problem solving. In M. Johnsen-Hoines & A. Berit-Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education: Vol. 2 (pp. 447-454). Bergen, Norway: Bergen University College.

Gagatsis, Α., & Elia, I. (2003). Representations and the Geometric Model in the learning of mathematics. (Volume 1). Nicosia: Intercollege Press.

Gagatsis, A., & Shiakalli, M. (2004). Translation ability from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, An International Journal of Experimental Educational Psychology, 24(5), 645-657.

Gagatsis, A., Agathangelou, S., & Papakosta, V. (2010). Conceptualizing the role of pictures in problem solving by using the implicative statistical analysis. Acta Didactica Universitatis Comenianae – Mathematics, 10, 19-34.

Gagatsis, A., Deliyianni, E., Elia, I. & Panaoura, A. (2011). Explorer la flexibilité : le cas du domaine numerique. Annales de didactique et de sciences cognitives, 16, 21-38.

Gagatsis, A., Demetriou, A., Afantiti, Th., Michaelidou, E., Panaoura, R., Shiakalli, M., & Christoforides, M. (1999). L’influenza delle rappresentazioni “semiotiche” nella risoluzione di problemi additivi. La Matematica e la sua Didattica, 2, 382-403.

Gagatsis, A., Elia, I., & Mougi, A. (2002). The nature of multiple representations in developing mathematical relations. Scientia Paedagogica Experimentalis, 39(1), 9-24.

Greer, B., & Harel, G. (1998). The Role of Isomorphisms in Mathematical Cognition. The Journal of Mathematical Behavior, 17(1), 5-24.

Griffin, S., & Case, R. (1997). Re-thinking the primary school math curriculum: an approach based on cognitive science. Issues in Education, 3(1), 1-49.

Hershkowitz Rina, Schwarz Baruch, Dreyfus Tommy (2001). Abstraction in Context: Epistemic Actions published in Journal for Research in Mathematics education 32 σελ 195-222

Horton, P. B., McConney, A. A., Gallo, M., & Woods, A. L. (1993). An investigation of the effectiveness of concept mapping as an instructional tool. Science Education, 77, 95–111

Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, (pp. 33-40). Hillsdale, N.J.: Lawrence Erlbaum.

Marinos, A. Avgerinos E. (2012a). Comparative Study of Improved Achievement in Algebra with Feedback from Teaching by the Direct and Indirect Methods, Eastwest 2012 International congress and exhibition on innovation and entrepreneurship 1-4 September 2012, Nicosia, Cyprus

Marinos, A. Avgerinos, E. (2012b). Impression by students in a mathematical model of causes of fire in a forest. 14th Cyprus Conference of Mathematical Education and Science pp. 244- 17-19 February Paphos.

Mayer, R. E., & Gallini, R. B. (1990). When is an illustration worth ten thousand words. Journal of Educational Psychology, 82, 715-726.

Panaoura, A., Gagatsis, A., Deliyianni E., & Elia, I. (2009). The structure of students’ beliefs about the use of representations and their performance on the learning of fractions. Educational Psychology, 29(6), 713-728.

Presmeg, N. (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42-46.

Rafferty, C. D., & Fleschner, L. K. (1993). Concept mapping: A viable alternative to objective and essay exams. Reading, Research, and Instruction, 32, 25–33.

Robinson, D. H., & Kiewra, K. A. (1995). Visual argument: Graphic organizers are superior to outlines in improving learning from text. Journal of Educational Psychology, 87, 455–467

Roth, W.-M. and Bowen, G. M. (2001). Professionals read graphs: A semiotic analysis, Journal for Research in Mathematics Education 32, 150–194.

Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children’s success, methods and strategies, Educational Studies in Mathematics 47, 145–173

Vergnaud, G. Durand, C. (1976). Structures additifs et complexite psychogenetigue. Revue Francaise de Pedagogie, vol 36, pp 28-43

Von Glaserfeld, E. (1987). Preliminaries to any theory of representation. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 215-225). Hillsdale, NJ: Lawrence Erlbaum.




DOI: http://dx.doi.org/10.46827/ejes.v8i11.3993

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