Reality in mathematics assessment – an analysis of task-reality concordance in Finnish and Swedish national assessments
DOI:
https://doi.org/10.7146/nomad.v9i3.147127Abstract
There are a number of possible purposes that can be served by the inclusion of applied tasks in school mathematics. However, the attainment of several of these purposes is likely to be dependent on the applied tasks closely emulating real life task situations. The study reported in this paper is an analysis of this relation between school tasks and problems encountered in real life beyond school that require the application of mathematics for their solutions. The analysis was made on national assessments in Finland and Sweden. The assessment tasks were analyzed in relation to a number of aspects of real life task situations that are a part of a framework for considerations of the quality of real life simulations in school mathematics. There were a substantial proportion of applied tasks in the assessments. The results of the analysis display a large difference between the aspects, in the proportion of tasks that simulate them with reasonable fidelity. There was also a marked difference between the assessments for the different courses in the two countries, in the proportions of tasks simulating the aspects well.
References
Barnes, M., Clarke, D., & Stephens, M. (2000). Assessment: the engine of systemic curricular reform? Journal of Curriculum Studies, 32(5), 623-650. https://doi.org/10.1080/00220270050116923
Björk, L.-E., Brolin, H., & Ekstig, K. (1994a). Matematik 2000, Kurs B. Stockholm: Bokförlaget Natur och Kultur.
Björk, L.-E., Brolin, H., & Ekstig K. (1994b). Matematik 2000, Kurs C. Stockholm: Bokförlaget Natur och Kultur.
Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics more "real"? For the Learning of Mathematics, 13(2), 12-17.
Boaler, J. (1994). When do girls prefer football to fashion? An analysis of female underachievement in relation to "realistic" mathematics contexts. British Educational Research Journal, 20(5), 551-664. https://doi.org/10.1080/0141192940200504
Clarke, D. J., & Helme, S. (1998). Context as construction. In O. Björkqvist (Ed.), Mathematics teaching from a constructivist point of view (pp. 129-147). Vasa, Finland: Faculty of Education, Åbo Akademi University.
Cooper, B. (1992). Testing national curriculum mathematics: Some critical comments on the treatment of 'real' contexts for mathematics. Curriculum Journal, 3(3), 231-244. https://doi.org/10.1080/0958517920030303
Cooper, B., & Dunne, M. (2000). Social class, sex and problem-solving. Buckingham, Philadelphia: Open University Press.
Danielsson, R., Gabrielsson, G., & Löfstrand, B. (1995). Räkna till max: Grundbok och övningsbok kurs E. Malmö, Sweden: Gleerups Forlag.
Fitzpatrick, R., & Morrison, E. J. (1971). Performance and product evaluation. In R. L. Thorndike (Ed.), Educational measurement (2nd ed., pp. 237-270). Washington, DC: American Council on Education.
Gerofsky, S. (1996). A linguistic and narrative view of word problems in mathematics education. For the Learning of Mathematics, 16(2), 36-45.
Greer, B. (1992). Multiplication and division as models of situations. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 276-295). New York: McMillan.
Greer, B. (1993). The modeling perspective on wor(l)d problems. Journal of Mathematical Behavior, 12, 239-250.
Nesher, P. (1980). The stereotyped nature of school word problems. For the Learning of Mathematics, 1, 41-48.
Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge University Press.
Palm, T. (2001a). School mathematics and reality: An analysis of the relation between national assessment tasks and task situations in life beyond school (Research reports, No 2, in Mathematics Education). Department of Mathematics, Umeå university, Sweden.
Palm, T. (2001b). Word problems as simulations of real world task situations: A proposed framework (Research reports, No 3, in Mathematics Education). Department of Mathematics, Umeå university, Sweden.
Palm, T. (2002). Impact of authenticity on sense making in word problem solving (Research reports, No 2, in Mathematics Education). Department of Mathematics, Umeå university, Sweden.
Reusser, K. (1988). Problem solving beyond the logic of things: Contextual effects on understanding and solving word problems. Instructional Science, 17, 309-338. https://doi.org/10.1007/BF00056219
Reusser, K., & Stebler, R. (1997). Every word problem has a solution - The social rationality of mathematical modeling in schools. Learning and Instruction, 7(4), 309-327. https://doi.org/10.1016/S0959-4752(97)00014-5
Silver, E. A., Shapiro, L. J., & Deutsch, A. (1993). Sense making and the solution of division problems involving remainders: An examination of middle school students' solution processes and their interpretations of solutions. Journal for Research in Mathematics Education, 24(2), 117-135. https://doi.org/10.2307/749216
Sowder, L. (1989). Searching for affect in the solution of story problems in mathematics. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective. New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-3614-6_8
Swedish Ministry of Education and Science. (1994). 1994 Curriculum for the non-compulsory school system. Stockholm: Swedish Ministry of Education and Science.
Swedish National Agency for Education. (1996). Study programme: Information for upper secondary schools and upper secondary adult education programme: Natural sciences programme. Stockholm: Swedish National Agency for Education.
Toom, A. (1999). Word problems: Applications or mental manipulatives. For the Learning of Mathematics, 19(1), 36-38. https://doi.org/10.5642/hmnj.199901.20.19
Utbildningsstyrelsen. (1994). Grunderna för gymnasiets läroplan. Helsingfors: Utbildningsstyrelsen.
Verschaffel, L., & De Corte, E. (1997). Word problems: A vehicle for promoting authentic mathematical understanding and problem solving in the primary school. In P. Bryant & T. Nunes (Eds.), Learning and teaching mathematics: An international perspective (pp. 69-97). Howe: Psychology Press.
Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 22(4), 273-294. https://doi.org/10.1016/0959-4752(94)90002-7
Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties? Learning and Instruction, 7(4), 329-338. https://doi.org/10.1016/S0959-4752(97)00007-8
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