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Mathematical
Critiquing the Mathematical Literacy Assessment Taxonomy: Where is the Reasoning and the Problem Solving?

Hamsa Venkat 1 Mellony Graven 2 Erna Lampen 1 Patricia Nalube 1 1 Marang Centre for Mathematics and Science Education, Wits University hamsa.venkatakrishnan@wits.ac.za; christine.lampen@wits.ac.za; patricia.nalube@wits.ac.za
2 Rhodes University

m.graven@ru.ac.za In this paper we consider the ways in which the Mathematical Literacy (ML) assessment taxonomy provides spaces for the problem solving and reasoning identified as critical to mathematical literacy competence. We do this through an analysis of the taxonomy structure within which Mathematical Literacy competences are assessed. We argue that shortcomings in this structure in relation to the support and development of reasoning and problem solving feed through into the kinds of questions that are asked within the assessment of Mathematical Literacy. Some of these shortcomings are exemplified through the questions that appeared in the 2008 Mathematical Literacy examinations. We conclude the paper with a brief discussion of the implications of this taxonomy structure for the development of the reasoning and problem‐solving competences that align with curricular aims. This paper refers to the assessment taxonomy in the Mathematical Literacy Curriculum Statement (Deparment of Education (DOE), 2007).

Mathematical Literacy was introduced as a new subject in the post-compulsory Further Education and Training (FET) curriculum in 2006. Its introduction made a mathematically-oriented subject – either Mathematics or Mathematical Literacy – compulsory for all FET learners. The curriculum statement for Mathematical Literacy defines the subject in the following terms: Mathematical Literacy provides learners with an awareness and understanding of the role that mathematics plays in the modern world.



References: Boaler, J. (1997). Experiencing school mathematics: Teaching styles, sex and setting. Buckingham: Open University Press. Clarke, D. (1996). Assessment. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook on mathematics education (pp. 327-370). Dordrecht: Kluwer Academic Publisher. de Lange, J. (1999). Framework for classroom assessment in mathematics. Utrecht: Freudenthal Institute & the National Center for Improving Student Learning and Achievement in Mathematics and Science. Available from http://www.fi.uu.nl/catch/products/framework/de_lange_frameworkfinal.pdf. Functional Skills Support Programme. (2007). Resources to support the pilot of functional skills: Teaching and learning functional mathematics. London: Crown Copyright. Halmos, P. (1975). The problem of learning to teach. American Mathematical Monthly, 82(5), 466-476. Jablonka, E. (2003). Mathematical Literacy. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 75-102). Dordrecht: Kluwer Academic Publisher. Jansen, J. (2009, January 4). Old school: New system produces the same results. The Sunday Tribune, p. 20. Maguire, T., & O’Donoghue, J. (2003). Numeracy concept sophistication – An organizing framework, a useful thinking tool. In J. Maaß & W. Schlöglmann (Eds.), Proceedings of the 10th International Conference on Adults Learning Mathematics (pp. 154-161). Linz, Austria: ALM and Johannes Kepler Universität. Department of Education. (2003). National curriculum statement Grades 10-12. (General): Mathematical Literacy. Pretoria: Department of Education. Department of Education. (2007). National curriculum statement Grades 10-12 (General): Subject Assessment Guidelines. Mathematical Literacy. Pretoria: Department of Education. Organisation for Economic Cooperation and Development. (2003). The PISA 2003 assessment framework Mathematics, Reading, Science and problem-solving knowledge and skills. Paris: Organisation for Economic Cooperation and Development. Olkin, I., & Schoenfeld, A. H. (1994). A discussion of Bruce Reznick 's chapter. In A. H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 39-51). Hillsdale, NJ: Lawrence Erlbaum Associates. Polya, G. (1962). Mathematical discovery: On understanding, learning and teaching problem-solving. New York: Wiley. Presmeg, N. (1986). Visualisation in high school mathematics. For the Learning of Mathematics, 6(3), 42-46. 55 Critiquing the Mathematical Literacy assessment taxonomy Prince, R., Frith, V., & Burgoyne, N. (2008, August). Mathematical Literacy  Grade 11 and 12 exemplars. Paper presented at the South African Mathematics Society Workshop. Pretoria. Qualifications and Curriculum Development Agency (2007). Functional skills standards. London: Qualifications and Curriculum Development Agency. Available at http://orderline.qcda.gov.uk/gempdf/ 1847215955.pdf. Scribner, S. (1984). Studying working intelligence. In B. Rogoff & J. Lave (Eds.), Everyday cognition: Its development in social context. Cambridge, MA: Harvard University Press. Steen, L. A. (2001). The case for quantitative literacy. In L. A. Steen (Eds.), Mathematics and democracy. The case for quantitative literacy (pp. 1-22). Washington, DC: The Mathematical Association of America. Available from http://www.maa.org/ql/mathanddemocracy.html. Umalusi. (2009). 2008 Maintaining standards report. From NATED 550 to the new national curriculum: Maintaining standards in 2008. Pretoria: Umalusi. Venkat, H., Graven, M., Lampen, E., Nalube, P., & Chitera, N. (2009). Reasoning and reflecting in Mathematical Literacy. Learning and Teaching Mathematics, 7, 47-53. Available from http:/www.sun.ac.za/ mathed/AMESA/amesal_n7_a13.pdf. 56

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