### Australian Mathematics Literacy Perspectives: Assessment

#### Abstract

This is a companion paper and should be read with the earlier one (White, 2017) that focused mainly on Australian governmental policies. In this paper, a more classroom and student focus will be adopted while summarising a few of the salient points of the first paper. A brief listing of five different types of mathematical literacy is provided. The definition used by the Program for International Student Assessment (PISA) is selected and

some brief remarks are provided on this program. PISA items are presented in the form of word problems. If a country such as Australia or Indonesia wants to improve their PISA results then it would demand that some class time is devoted to the development of the abilities of younger students to handle word problems before they turn fifteen and are subjected to PISA. To support classroom teachers, Newman (1977, 1983) defined five specific mathematical literacy levels as crucial to performance on mathematical word

problems: reading, comprehension, transformation, process skills, and encoding. Newman's Error Analysis (NEA) provides a framework for considering the reasons that underlay the difficulties students experience with mathematical word problems and a process that assists teachers to determine where misunderstandings occur. NEA also provides directions for where teachers could target effective teaching strategies to overcome them. There is a brief discussion of strategies to assist students improve their

mathematical literacy.

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Askew, M. (2003), Word problems: Cinderellas or wicked witches? In I. Thompson (Ed.), Enhancing primary mathematics teaching (pp. 78-85). Berkshire, England: Open University Press.

Bautista, D., & Mulligan, J. (2010). Why do disadvantaged Filipino children find word problems in English difficult? In L. Sparrow, B. Kissane, & C. Hurst, Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, pp. 69-76). Fremantle, Western Australia: MERGA Inc.

Bautista, D., Mulligan, J. & Mitchelmore, M. (2009). Young Filipino students making sense of arithmetic word problems in English. Journal of Science and Mathematics Education in Southeast Asia, 32(2), 131-160.

Carpenter, T. P., & Lehrer, R. (1999). Teaching and Learning Mathematics with Understanding. In E. Fennema & T. A. Romberg (Eds). Mathematics Classrooms That Promote Understanding (pp. 19-32). Mahwah, N.J.: Lawrence Erlbaum Associates.

Casey, D.P. (1978). Failing students: a strategy of error analysis. In P. Costello (ed.). Aspects of Motivation (pp. 295-306). Melbourne: Mathematical Association of Victoria.

Clarkson, P.C. (1980). The Newman Error Analysis- some extensions. In B.A. Foster (Ed.), Research in Mathematics Education in Australia 1980 (Vol. I, pp. 11-22). Hobart Mathematics Education Research Group of Australia.

Clarkson, P.C. (1983). Types of errors made by Papua New Guinean students, Report No. 26. Lae: Papua New Guinea University of Technology Mathematics Education Centre.

Clarkson, P.C. (1991). Language comprehension errors: A further investigation. Mathematics Education Research Journal 3(2), 24-33.

Clements, M.A. (1980). Analysing children's errors on written mathematical tasks. Educational Studies in Mathematics, 11 (1), 1-21.

Clements, M.A. (1982). Careless errors made by sixth-grade children on written mathematical tasks. Journal for Research in Mathematics Education, 13(2), 136-144.

Clements, M.A. (1984). Language Factors in School Mathematics. In P. Costello, S. Ferguson, K. Slinn, M. Stephens, D. Trembath, & D. Williams (Eds.), Facets of Australian Mathematics Education (pp. 137-148) , Australian Association of Mathematics Teachers, Adelaide, South Australia.

Clements, M.A. (2004). Analysing Errors Made by Pupils on Written Mathematics Tasks. Sultan Hassanal Bolkiah Institute of Education, Universiti Brunei Darussalam.

Clements, M.A., & Ellerton, N. F. (1992). Overemphasising process skills in school mathematics: Newman analysis data from five countries. In W. Geeslin & K. Graham (Eds.), Proceedings of the Sixteenth International Conference on the Psychology of Mathematics Education (Vol. 1, pp. 145-152). Durham, New Hampshire: International Group for the Psychology of Mathematics Education.

Clements, M. A., & Ellerton, N. F. (1993). The centrality of language factors in mathematics teaching and learning. Paper presented at the International Seminar on the Mathematical Sciences, MARA Institute, Kuching, Sarawak.

Clements, M. A., & Ellerton, N. F. (1995). Short-answer and multiple-choice pencil-andpaper tests: Still useful for school mathematics in the 21st century? Journal of Science and Mathematics Education in Southeast Asia, 18(2), 10-23.

Ellerton, N. F., & Clarkson, P.C. (1996). Language factors in mathematics teaching and learning. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (Part 2, pp. 987-1033). Dordrecht, The Netherlands: Kluwer Academic Publishers.

Ellerton, N.F. & C1ements, M.A. (1991). Mathematics in language: A review of language factors in mathematics learning. Australia: Deakin University Press.

Ellerton, N. F., & Clements, M. A. (1996). Newman error analysis. A comparative study involving Year 7 students in Malaysia and Australia. In P. C. Clarkson (Ed.), Technology and mathematics education (pp. 186-193). Melbourne: Mathematics education Research

Group of Australasia.

Ellerton, N. F., & Clements, M. A. (1997). Pencil and paper tests under the microscope. In F. Biddulph & K. Carr (Eds.), People in mathematics education (pp. 155-162). Waikato, NZ: Mathematics Education Research Group of Australasia.

Faulkner, R. (1992). Research on the number and type of calculation errors made by registered nurses in a major Melbourne teaching hospital. Unpublished M.Ed. research paper, Deakin University, Geelong, Australia.

Ismail Hj Raduan (2010). Error analysis and the corresponding cognitive activities committed by year five primary students in solving mathematical word problems. Procedia Social and Behavioral Sciences 2, 3836–3838.

Jablonka, A. (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, the Netherlands: Kluwer Academic Publishers.

Jiminez, E. C. (1992). A cross-lingual study of Grade 3 and Grade 5 Filipino children's processing of mathematical word problems, SEAMEO-RECSAM, Penang.

Kaur, B. (1995). A window to the problem solvers' difficulties. In A. Richards (Ed.), Forging links and integrating resources (pp. 228-234).Darwin: Australian Association of Mathematics Teachers.

Kaushil, LD., Sajjin Singh, & Clements, M. A. (1985). Language factors influencing the learning of mathematics in an English-medium school in Delhi. Delhi, India: State Institute of Education (Roop Nagar).

Marinas, B., & Clements, M. A. (1990). Understanding the problem: A prerequisite to problem solving in mathematics. Journal of Science and Mathematics Education in South East Asia, 13(1), 14-20.

Mohidin, R. (1991). An investigation into the difficulties faced by the students of Form 4 SMJA Secondary School in transforming short mathematics problems into algebraic form. Penang: SEAMEO-RECSAM.

Murata, A. (2008). Mathematics teaching and learning as a mediating process: the case of tape diagrams. Mathematical Thinking and Learning, 10(4), 374 - 406.

Newman, M. A. (1977). An analysis of sixth-grade pupils' errors on written mathematical tasks. Victorian Institute for Educational Research Bulletin, 39, 31-43.

Newman, M. A. (1983). Strategies for diagnosis and remediation. Sydney: Harcourt, Brace Jovanovich.

Organisation for Economic Co-operation and Development (OECD). (2002). PISA 2000 Technical Report. Paris: OECD.

Organisation for Economic Co-operation and Development (OECD). (2004). Learning for Tomorrow’s World. Paris: OECD.

Organisation for Economic Cooperation and Development. (2006). Assessing scientific, reading and mathematical literacy: A framework for PISA 2006. OECD: Paris. Retrieved 5/01/06, from http://www.pisa.oecd.org/dataoecd/63/35/37464175.pdf

Organisation for Economic Co-operation and Development (OECD). (2016). PISA 2015 assessment and analytical framework: Science, reading, mathematics and financial literacy. Paris: Author.

Piccoli, A. (2018). NAPLAN is on the way out, but national testing is here to stay. The Sydney Morning Herald, News Review, June 23-24,p.33.

Prakitipong, N. & Nakamura, S. (2006). Analysis of mathematics performance of grade five students in Thailand using Newman procedure. Journal of International Cooperation in Education, 9(1), 111-122.

Sahlberg, P. (2011). Finnish Lessons. New York: Teachers College Press.

Singh, P., Rahman, A. A., & Hoon, T. C. (2010). The Newman Procedure for Analyzing Primary Four Pupils Errors on Written Mathematical Tasks: A Malaysian Perspective. Procedia Social and Behavioral Sciences 8, 264–271.

Singhatat, N. (1991). Analysis of mathematics errors of lower secondary pupils in solving word problems. Penang, Malaysia: SEAMEO-RECSAM.

Sulaiman, S., Remorin, P. R. (Eds.) (1993). Science- and mathematics-related project work Abstracts of SEAMEO-RECSAM participants. Penang, Malaysia: SEAMEO RECSAM.

Thomson, S., & Fleming, N. (2004). Summing it up: Mathematics Achievement in Australian schools in TIMMS 2002 (TIMMS Australia Monograph No 6). Camberwell, Victoria: ACER.

Thomson, S., Hillman, K., & De Bortoli, L. (2013). A teacher’s guide to PISA mathematical literacy. Camberwell, Victoria: ACER Press.

Thomson, S., De Bortoli, L., & Underwood, C. (2016). PISA 2015: a first look at Australia’s results. Camberwell, Victoria: ACER Press

Thomson, S., De Bortoli, L., & Underwood, C. (2017). PISA 2015: Reporting Australia's results. Retrieved on 16th March 2017 from: http://research.acer.edu.au/ozpisa/22

Thongtawat, N. (1992). Comparing the effectiveness of multiple-choice and short-answer paper-and-pencil Tests. Penang, Malaysia: SEAMEO-RECSAM.

Tuck, S. (1983). An investigation of the effectiveness of the Newman Language Mathematics Kit, unpublished M.Ed thesis, Monash University.

Watson, L (1980). Investigating errors of beginning mathematicians. Educational Studies in Mathematics, 11(3), 319-329.

White, A. L. (2008).Counting On: Evaluation of the impact of Counting On 2007 program. Sydney, Australia: Curriculum K-12 Directorate, Department of Education and Training.

White, A. L. (2009). A revaluation of Newman's Error Analysis. In D. Martin, T. Fitzpatrick, R. Hunting, D. Itter, C. Lenard, T. Mills, L. Milne (Eds) Mathematics of prime importance, (pp. 249-257) (Proceedings of 46th Annual Conference of the Mathematics Association of Victoria). Brunswick Melbourne: M.A.V

White, A. L. (2010). Numeracy, literacy and Newman's Error Analysis. Journal of Science and Mathematics Education in Southeast Asia, 33(2), 129-148.

White, A. L. (2011). Diagnostic assessment and problem solving in mathematics. In R.P. Devadason, U.H. Cheah, & K.T. NG. Transforming school science and mathematics education in the 21st century (Proceedings of the Fourth International Conference on Science and Mathematics Education - CoSMEd 2011[CD]). Penang, Malaysia:

SEAMEO RECSAM.

White, A. L. (2013). Literacy and mathematics. In R. Gregson (Ed.), Literacy across the curriculum (pp. 34-51). Illinois, USA: Common Ground Publishing.

White, A. L. (2017). Mathematics Literacy: An Australian Perspective and Experience. Southeast Asian Mathematics Education Journal, 7(1), 33-42.

White, A. L., & Clements, M. A. (2005). Energising upper-primary mathematics classrooms in Brunei Darussalam: The Active Mathematics in Classrooms (AMIC) Project. In H. S. Dhindsa, I. J. Kyeleve, O. Chukwu, & J. S. H. Q. Perera (Eds.). Future directions in

science, mathematics and technical education (pp. 151-160) (Proceedings of the Tenth International Conference). Brunei Darussalam: University Brunei Darussalam.

DOI: https://doi.org/10.46517/seamej.v8i1.65

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