The development of reasoning skills during compulsory 16 to 18 mathematics education

References

• Argyropoulos, E., Vlamos, P., Katsoulis, G., Markatis, S., & Sideris, P. (2001). Euclidean geometry general lyceum A and B. Athens: Organization Textbook Publishing (OEDB). (Publication Iota 2010).
   Google Scholar
• Attridge, N. (2013). Advanced mathematics and deductive reasoning skills: Testing the theory of formal discipline ( Unpublished doctoral thesis). Loughborough University, UK.
   Google Scholar
• Attridge, N., & Inglis, M. (2013). Advanced mathematical study and the development of conditional reasoning skills. PLoS ONE 8(7): e69399. doi:10.1371/journal.pone.0069399.t004
   PubMed Web of Science ®Google Scholar
• Bruine de Bruin, W., Parker, A. M., & Fischhoff, B. (2007). Individual differences in adult decision-making competence. Journal of Personality and Social Psychology, 92, 938–-956. doi:10.1037/0022-3514.92.5.938
   PubMed Web of Science ®Google Scholar
• Durand-Guerrier, V. (2003). Which notion of implication is the right one? From logical considerations to a didactic perspective. Educational Studies in Mathematics, 53(1), 5–34. doi:10.1023/A:1024661004375
   Google Scholar
• Evans, J. St. B. T., Clibbens, J., & Rood, B. (1995). Bias in conditional inference: Implications for mental models and mental logic. The Quarterly Journal of Experimental Psychology, 48A, 644–670. doi:10.1080/14640749508401409
   Google Scholar
• Evans, J. St. B. T., Handley, S. J., Neilens, H., & Over, D. E. (2007). Thinking about conditionals: A study of indiviual differences. Memory & Cognition, 35, 1772–1784. doi:10.3758/BF03193509
   PubMed Web of Science ®Google Scholar
• Hodgen, J., Marks, R., & Pepper, D. (2013). Towards universal participation in post-16 mathematics: Lessons from high-performing countries. London: Nuffield Foundation.
   Google Scholar
• Hodgen, J., Pepper, D., Sturman, L., & Ruddock, G. (2010). Is the UK an outlier? An international comparison of upper secondary mathematics education. London: Nuffield Foundation.
   Google Scholar
• Houston, K. (2009). How to think like a mathematician. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511808258
   Google Scholar
• Hoyles, C., & Küchemann, D. (2002). Students’ understanding of logical implication. Educational Studies in Mathematics, 51, 193–223. doi:10.1023/A:1023629608614
   Google Scholar
• Inglis, M., & Simpson, A. (2009a). Conditional inference and advanced mathematical study: Further evidence. Educational Studies in Mathematics, 72, 185–198. doi:10.1007/s10649-009-9187-z
   Web of Science ®Google Scholar
• Inglis, M., & Simpson, A. (2009b). The defective and material conditionals in mathematics: Does it matter? In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd conference of the international group for the psychology of mathematics education (Vol. 3, pp. 225–232). Thessaloniki: Greece.
   Google Scholar
• Lehman, D. R., & Nisbett, R. E. (1990). A longitudinal study of the effects of undergraduate training on reasoning. Developmental Psychology, 26, 952–960. doi:10.1037/0012-1649.26.6.952
   Web of Science ®Google Scholar
• Leptou, E., & Loizou, N. (1991). Geometry lessons lyceum A and B. Nicosia: The Curriculum Development Unit.
   Google Scholar
• Locke, J. (1706/1971). Conduct of the understanding. New York, NY: Burt Franklin.
   Google Scholar
• Mouzakitis, A. (2006). A comparative analysis of Italian and Greek Euclidean geometry textbooks: A case study. Philosophy of Mathematics Education Journal, 19. Retrieved from http://people.exeter.ac.uk/PErnest/pome19/index.htm.
   Google Scholar
• Oakley, C. O. (1949). Mathematics. The American Mathematical Monthly, 56(1), 19. doi:10.2307/2305812
   Google Scholar
• Reid, D., & Inglis, M. (2005). Talking about logic. For the Learning of Mathematics, 25(2), 24–25.
   Google Scholar
• Sá, W. C., West, R. F., & Stanovich, K. E. (1999). The domain specificity and generality of belief bias: Searching for a generalisable critical thinking skill. Journal of Educational Psychology, 91, 497–510. doi:10.1037/0022-0663.91.3.497
   Web of Science ®Google Scholar
• Smith, A. (2004). Making mathematics count: The report of Professor Adrian Smith’s inquiry into post-14 mathematics education. London: The Stationery Office.
   Google Scholar
• Stanic, G. M. A. (1986). The growing crisis in mathematics education in the early twentieth century. Journal for Research in Mathematics Education, 17, 190–205. doi:10.2307/749301
   Web of Science ®Google Scholar
• Stanic, G. M. A., & Kilpatrick, J. (1992). Mathematics curriculum reform in the United States: A historical perspective. International Journal of Educational Research, 17, 407–417. doi:10.1016/S0883-0355(05)80002-3
   Google Scholar
• Stanovich, K. (2004). The robot’s rebellion. Chicago: The University of Chicago Press.
   Google Scholar
• Toplak, M. E., West, R. F., & Stanovich, K. E. (2011). The Cognitive Reflection Test as a predictor of performance on heuristics-and-biases tasks. Memory & Cognition, 39, 1275–1289. doi:10.3758/s13421-011-0104-1
   PubMed Web of Science ®Google Scholar
• Vorderman, C. (2011). A world-class mathematics education for all our young people. Retrieved from http://www.tsm-resources.com/pdf/VordermanMathsReport.pdf
   Google Scholar
• Walport, M. (2010). Science and mathematics secondary education for the 21st century: Report of the science and learning expert group. London: Crown.
   Google Scholar