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 firstname.lastname@example.org; email@example.com; firstname.lastname@example.org 2 Rhodes University
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. Mathematical Literacy is a subject driven by life-related applications of mathematics. It enables learners to develop the ability and confidence to think numerically and spatially in order to interpret and critically analyse everyday situations and to solve problems. (DOE, 2003, p. 9) This definition alongside the broader description of the new subject’s aims in this document places emphasis on the need to develop life-oriented competences for a range of everyday situations in which mathematical reasoning and mathematical tools can be brought to bear productively to aid informed decision making and problem solving. Situational reasoning relating to the identification and selection of salient features of the context is therefore required alongside and integrated with mathematical reasoning.
Pythagoras, 70, 43-56 (December 2009)
Critiquing the Mathematical Literacy assessment taxonomy
Within this definition, we highlight two features that the broader literature suggests are central to the notion of mathematical literacy1 that is promoted in the South African rhetoric: firstly, the need for the reasoning that is implicated within the need to “think numerically and spatially” and to “interpret” and “critically analyse everyday situations”; and secondly, the need for “problem solving”. Both of these aspects have significant bodies of literature associated with them in the field of mathematics education – some focused on the teaching and learning of mathematics, and some specific to discussions of mathematical literacy. Olkin and Schoenfeld (1994), focusing on mathematics, describe problem solving in terms of “confronting a novel situation and trying to make sense of it” (p. 43). Steen, a leading advocate of what he terms “quantitative literacy” comments that centrally what quantitatively literate citizenship requires is “a predisposition to look at the world through mathematical eyes … and to approach complex problems with confidence in the value of careful...
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.
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.
Please join StudyMode to read the full document