The role of indigenous traditional counting systems in children's development of numerical cognition: results from a study in Papua New Guinea
Tóm tắt
Từ khóa
Tài liệu tham khảo
Adler, J. (2002). Teaching mathematics in multilingual classrooms. New York: Kluwer.
Bishop, A. J. (1991). Mathematics enculturation: a cultural perspective on mathematics education. Dordrecht: Kluwer.
Bishop, A. J. (2004, July). Critical issues in researching cultural aspects of mathematics education. Paper presented at the 10th International Congress on Mathematical Education, Copenhagen, Denmark.
Bransford, J. D., & Vye, N. J. (1989). A perspective on cognitive research and its implications for instruction. In L. B. Resnick & L. E. Kloper (Eds.), Towards the thinking curriculum (pp. 174–205). Virginia: ASCD Alexandria.
Bryman, A. (2004). Social research methods (2nd ed.). Oxford: Oxford University Press.
Capell, A. (1969). A survey of New Guinea languages. Sydney: Sydney University Press.
Clarkson, P. C. (1993). Language and mathematics: a comparison of bilingual and monolingual students of mathematics. Educational Studies in Mathematics, 23, 417–429.
D'Ambrosio, U. (2001). What is ethnomathematics, and how can it help children in schools? Teaching Children Mathematics, 7(6), 308–311.
D'Ambrosio, U. (2006). The program ethnomathematics: a theoretical basis of the dynamics of intra-cultural encounters. Journal of Mathematics and Culture, 1(1), 1–7.
Department of Education, PNG. (2002). National curriculum statement: Papua New Guinea. Port Moresby, Papua New Guinea: Department of Education.
Department of Education, PNG. (2003). Cultural mathematics: elementary syllabus 2003. Port Moresby, Papua New Guinea: Department of Education.
Department of Education & Training, NSW. (2002). Count me in too. Sydney: DETNSW.
Dowker, A. (2005). Individual differences in arithmetic: implications for psychology, neuroscience and education. Sussex, UK: Psychology Press.
Dowker, A., & Lloyd, D. (2005). Linguistic influences on numeracy. In D. V. Jones, A. Dowker, & D. Lloyd (Eds.), Mathematics in the primary school (pp. 21–35). Oxford, UK: Bangor School of Education.
Edgeworth, M., & Edgeworth, R. L. (1998). Practical Education. London.
Ericsson, K. A., Chase, W. G., & Faloon, S. (1980). Acquisition of a memory skill. Science, 208, 1181–1182.
Ernest, P. (1991). The philosophy of mathematics education. London: Falmer Press.
Fuson, K. C. (1991). Children's early counting: saying the number-word sequence, counting objects, and understanding cardinality. In K. Durkin & B. Shire (Eds.), Language in mathematical education: research and practice (pp. 27–39). Milton Keynes: Open University Press.
Fuson, K. C., & Kwon, Y. (1992). Korean children's understanding of multidigit addition and subtraction. Child Development, 63, 491–506.
Galligan, L. (2001). Possible effects of English-Chinese language differences on the processing of mathematical text: a review. Mathematics Education Research Journal, 13(2), 112–132.
Greer, B. (1980). A first course in statistics. Gloucester: Stanley Thorns Publishers.
Groen, G. J., & Parkman, J. M. (1972). A chronometric analysis of simple addition. Psychological Review, 79(4), 329–343.
Groen, G. J., & Resnick, L. B. (1977). Can preschool children invent addition algorithms? Journal of Educational Psychology, 69(6), 645–652.
Hasselbring, T. S., Goin, L. I., & Bransford, J. D. (1987). Developing automacy. Teaching Exceptional Children, 19, 30–33.
Hung, D. (2002). Situated cognition and problem-based learning: Implications for learning and instruction with technology. Journal of Interactive Learning Research, 13(4), 393-415. Retrieved from http://web5.infotrac.galegroup.com.ezproxy.scu.edu.au/itw/informark
Kail, R. V. (2007). Longitudinal evidence that increases in processing speed and working memory enhance children's reasoning. Psychological Science, 18(4), 312–313.
Kail, R. V., & Ferrer, E. (2007). Processing speed in childhood and adolescene: longitudinal models for examining developmental change. Child Development, 78(6), 1760–1770.
Kaleva, W. T. (1995). Ethnomathematics and its implication for mathematics education in Papua New Guinea. In O. P. Ahuja, J. C. Renaud, & R. M. Sekkappan (Eds.), Quality mathematics education in developing countries. Proceedings of the South Pacific conference on mathematics and mathematics education. UPNG, Port Moresby: New Delhi: UBS Publishers.
Lean, G. A. (1992). Counting systems of Papua New Guinea and Oceania. Unpublished PhD Thesis, Lae, PNG: Papua New Guinea University of Technology.
Lynch, J., Ross, M., & Crowley, T. (2002). The Oceanic languages. Richmond, Surrey: Curzon Press.
Masingila, J. O. (1993). Learning from mathematics practice in out-of-school situations. For the Learning of Mathematics, 13(2), 18–22.
Matang, R. A. (1996). Towards an ethnomathematical approach to mathematics education in Papua New Guinea: An alternative proposal. Unpublished QUT M.Ed. dissertation, Brisbane: Queensland University of Technology.
Matang, R. A. (2002). The role of ethnomathematics in mathematics education in Papua New Guinea: implications for mathematics curriculum. Directions: Journal of Educational Studies, USP, 24(1), 27–37.
Matang, R. A. (2003). The cultural context of mathematics learning and thinking in Papua New Guinea. In A. C. Maha & T. A. Flaherty (Eds.), Education for 21st century in Papua New Guinea and the South Pacific (pp. 161–168). Goroka, PNG: University of Goroka.
Matang, R. A. (2005). Formalising the role of indigenous counting systems in teaching the formal English arithmetic strategies through local vernaculars: an example from Papua New Guinea. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: research, theory and practice (proceedings of the 28th annual conference of the mathematics education research group of Australasia) (pp. 505–512). Melbourne: MERGA.
Matang, R. A. (2006). Enhancing the learning of formal English arithmetic strategies by elementary school children through indigenous counting systems of Papua New Guinea: the case of Kâte counting system of Morobe province. In P. M. Pena (Ed.), Sustainable curriculum development: the PNG curriculum reform experience (pp. 96–103). Port Moresby, PNG: PNG Department of Education.
Matang, R. A. (2008). Enhancing children's formal learning of early number knowledge through Indigenous languages and ethnomathematics: The case of Papua New Guinea mathematics curriculum reform experience. Paper presented at the 11th International Congress on Mathematics Education, Monterray, Mexico. http://dg.icme11.org/document/get/322
Matang, R. A. & Owens, K. (2004). Rich Transitions from Indigenous counting systems to English arithmetic strategies: Implications for mathematics education in Papua New Guinea. In F. Favilli (Ed.) Ethnomathematics and mathematics education. Proceedings of the 10th International Congress of Mathematics Education Discussion Group 15 Ethnomathematics (pp. 107-118). Pisa, Italy: Tiporafia Editrice Pisana.
McMurchy-Pilkington, C., Trinick, T., Dale, H., & Tuwhagai, R. (2009). Mahi tahi: collaborating partnerships. In T. Trinick (Ed.), Quality teaching research and development project: Māori medium and Kura Kaupapa Māori research project (pp. 63–75). Auckland, NZ: The University of Auckland.
Meaney, T., Trinick, T., & Fairhall, U. (2012). Collaborating to meet language challenges in indigenous mathematics classrooms. Dordrecht, The Netherlands: Springer.
Miura, I. T., Kim, C. C., Chang, C., & Okamoto, Y. (1988). Effects of language characteristics on children's cognitive representation of number: cross-national comparisons. Child Development, 59(6), 1445–1450.
Munro, J. (2003). Information processing and mathematics learning difficulties. Australian Journal of Learning Disabilities, 8(4), 19–24.
Nagai, Y. (1999). Developing a community-based vernacular school: a case study of Maiwala elementary school in Papua New Guinea. Language Education, 13(3), 194–206.
Nagai, Y., & Lister, R. (2003). What is our culture? What is our language? Dialogue towards the maintenance of indigenous culture and language in Papua New Guinea. Language Education, 17(2), 87–105.
Owens, K. (2000). Traditional counting systems and their relevance for elementary schools in Papua New Guinea. PNG Journal of Education, 36(1 & 2), 62–72.
Owens, K. (2001). The work of Glendon Lean on the counting systems of Papua New Guinea and Oceania. Mathematics Education Research Journal, 13(1), 47–71.
Park, M. (2000). Linguistic influence on numerical development. The Mathematics Educator, 10(1), 19–24.
Pawley, A., Attenborough, R., Golson, J., & Hide, R. (2005). Papuan pasts: Cultural, linguistic and biological histories of Papuan-speaking peoples. Canberra: Pacific Linguistics, Research School of Pacific and Asian Studies, The Australian National University.
Rickard, T. (1997). Bending the power law: a MPL theory of strategy shift and the automatization of cognitive skills. Journal of Experimental Psychology. General, 126, 288–311.
Ross, M., Pawley, A., & Osmond, M. (Ed.). (1998). The lexicon of Proto Oceanic: The culture and environment of ancestral Oceanic Society (Vol. 1). Canberra: Research School of Pacific Studies, The Australian National University.
Saxe, G. B. (1982). Culture and the development of numerical cognition: studies among the Oksapmin of Papua New guinea. In C. J. Brainerd (Ed.), Children's logical and mathematical cognition (pp. 157–176). New York: Springer-Verlag.
Saxe, G. (1985). The effects of schooling on arithmetical understandings: studies with Oksapmin children in Papua New Guinea. Journal of Educational Psychology, 77(5), 10.
Saxe, G. B. (1991). Culture and cognitive development: studies in mathematical understanding. Hillsdale, NJ: Lawrence Erlbaum Associates.
Smith, G. P. S. (1980). Morobe counting systems: Some preliminary observations. Paper presented to 14th PNG Linguistic Society Congress, University of Technology, Lae.
Smith, G. P. S. (1986). Counting and culture in North-East New Guinea. In P. Geraghty, L. Carrington, & S. A. Wurm (Eds.), Focal II: papers from 4th International Conference on Austronesian Linguistics C-94 (pp. 343–349). Canberra: Pacific Linguistics.
Song, M., & Ginsburg, H. P. (1987). The development of informal and formal mathematical thinking in Korean and U.S. children. Child Development, 58(5), 1286–1296.
Trinick, T. (1999). The relationship between Māori culture and Māori mathematical language. (Masters), Auckland: University of Auckland.
Wassmann, J., & Dasen, P. (1994). Yupno number system and counting. Journal of Cross-Cultural Psychology, 25, 78–94.
Wheatley, T., & Wegner, D. M. (2001). Psychology of automaticity of action [Electronic Version]. International encyclopaedia of the social and behavioural sciences, (pp. -993). Retrieved 17/03/2008.
Wortham, S. (1998). Language in cognitive development: emergence of the mediated mind. Mind, Culture, and Activity, 5(1), 76–79. doi: 10.1207/s15327884mca0501_8 .
Wright, R. J. (1991). The role of counting in children's numerical development. Australian Journal of Early Childhood, 16(2), 43–48.
Wright, R. J. (2002). Assessing young children's arithmetical strategies and knowledge: providing learning opportunities for teachers. Australian Journal of Early Childhood, 27(3), 31–36.
Zeller, R. A., & Carmines, E. G. (1978). Statistical analysis of social data. Chicago: Rand McNally.