Developing purposeful mathematical thinking: a curious tale of apple trees

Referencias

Ainley, J. (1991). Is there any mathematics in measurement? In D. Pimm & E. Love (Eds.), Teaching and learning school mathematics (pp. 69-76). London, United Kingdom: Hodder and Stoughton. Ainley, J. (1997). Constructing purpose in mathematical activity. In E. Pehkonen (Ed.), Proceedings of the 21th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 17-24). Lahti, Finland: PME. Ainley, J. (2001). Transparency in graphs and graphing tasks: an iterative design process. Journal of Mathematical Behavior, 19(3), 365-384. Ainley, J., Bills, L., & Wilson, K. (2005). Designing spreadsheet-based tasks for purposeful algebra. International Journal of Computers for Mathematical Learning, 10(3), 191-215. Ainley, J., Jarvis, T., & McKeon, F. (forthcoming). Designing pedagogic oppor- tunities for statistical thinking within inquiry-based science. Proceedings of the Seventh Conference of the European Society for Research in Mathematics Education. Rzeszów, Poland: ERME. Ainley, J., Nardi, E., & Pratt, D. (1998). Graphing as a computer mediated tool. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 243- 258). Stellenbosch, South Africa: PME. Ainley, J., Nardi, E., & Pratt, D. (2000). The construction of meanings for trend in active graphing. International Journal of Computers for Mathematical Learning, 5(2), 85-114. Ainley, J., & Pratt, D. (2002). Purpose and utility in pedagogic task design. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th International Confer- ence for the Psychology of Mathematics Education (Vol. 2, pp. 17-24). Nor- wich, United Kingdom: PME. Ainley, J., & Pratt, D. (2010, July). It’s not what you know, it’s recognising the power of what you know: assessing understanding of utility. Paper presented at the 8th International Conference on the Teaching of Statistics. Ljubljana, Solvenia. Ainley, J., Pratt, D., & Nardi, E. (2001). Normalising: children’s activity to con- struct meanings for trend. Education Studies in Mathematics, 45(1), 131-146. Ainley J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23-38. Ben-Zvi, D., & Garfield, J. (Eds.). (2004). The challenge of developing statistical literacy, reasoning, and thinking. Dordrecht, The Netherlands: Kluwer Aca- demic Publishers. Brenner, M. (1998). Meaning and money. Educational Studies in Mathematics, 36(2), 123-155. Cooper, C., & Dunne, M. (2000). Assessing children’s mathematical knowledge. Buckingham, United Kingdom: Open University Press. Department of Education (2002). Revised national curriculum statement grades R-9 (schools) mathematics. Retrieved January 7, 2009, from http://www.education.gov.za. Gerofsky, S. (1996). A linguistic and narrative view of word problems in math- ematics education. For the Learning of Mathematics, 16(2), 36-45. Lave, J., & Wenger, E. (1991). Situated learning: legitimate peripheral partici- pation. Cambridge, United Kingdom: Cambridge University Press. Ministry of Education (2006). Mathematics syllabus primary. Retrieved January 7, 2009, from http://is.gd/kdWZWu. Ministry of Education (2008). The New Zealand curriculum. Retrieved January 7, 2009, from http://nzcurriculum.tki.org.nz/Curriculum-documents/The- New-Zealand-Curriculum. Meira, L. (1998). Making sense of instructional devices: the emergence of trans- parency in mathematical activity. Journal for Research in Mathematics Edu- cation, 29(2), 121-142. Monteiro, C., & Ainley, J. (2004). Critical sense in interpretations of media graphs. In M. Johnsen Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathemat- ics Education (Vol. 3, pp. 361-368). Bergen, Norway: PME. National Council for Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author. Organization for Economic Co-operation and Development. (2003). The PISA 2003 assessment framework. Mathematics, reading, science and problem solving knowledge and skills. Paris, France: Author. Organization for Economic Co-operation and Development. (2006). PISA re- leased items - mathematics. Paris, France: Author. Pratt, D., & Ainley, J. (1997). The construction of meanings for geometric con- struction: two contrasting cases. International Journal of Computers for Mathematical Learning, 1(3), 293-322. Qualifications and Curriculum Agency (2008). The national curriculum. Retrie- ved January 7, 2009, from http://curriculum.qcda.gov.uk. Schliemann, A. (1995). Some concerns about bringing everyday mathematics to mathematics education. In L. Meira & D. Carraher (Eds.), Proceedings of the 19th Conference of the International Group for the Psychology of Mathemat- ics Education (Vol. 1, pp. 45-60). Recife, Brazil: PME. Sierpinska, A. (2011, February). Research into elementary mathematics methods courses in preservice teacher education. Plenary lecture in Seventh Congress of the European Society for Research in Mathematics Education (CERME 7), Rzeszów, Poland. Star, S. L., & Griesemer, J. R. (1989). Institutional ecology, ‘translations’ and boundary objects: amateurs and professionals in Berkeley’s museum of verte- brate zoology, 1907-39. Social Studies of Science, 19(3), 387-420. Van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment prob- lems in mathematics. For the Learning of Mathematics, 25(2), 2-9. Verschaffel, L., Greer, B., & Torbeyns, J. (2006). Numerical thinking. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 51-82). Rotterdam, The Netherlands: Sense Pub- lishers. Wiliam, D. (1992, March). What makes an investigation difficult? Paper present- ed at the Secondary Mathematics Independent Learning Experience Confer- ence, University of Nottingham.