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Article

Towards a conceptual framework for understanding and developing mathematical competence: A multi-dual perspective

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References

  • Abrantes, P. (2001). Mathematical competence for all: Options, implications and obstacles. Educational Studies in Mathematics, 47, 125–143.
  • Armstrong, A., Ming, K., & Helf, S. (2018). Content area literacy in the mathematics classroom. The Clearing House, 91, 85–95.
  • Blömeke, S., Gustafsson, J. E., & Shavelson, R. J. (2015). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift Für Psychologie, 223, 3–13.
  • Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J., Palm, T., & Palmberg, B. (2014). Developing mathematical competence: From the intended to the enacted curriculum. The Journal of Mathematical Behavior, 33, 72–87.
  • Borasi, R., Siegel, M., Fonzi, J., & Smith, C. F. (1998). Using transactional reading strategies to support sense-making and discussion in mathematics classrooms: An exploratory study. Journal for Research in Mathematics Education, 29, 275–305.
  • Burton, L. (1995). Moving towards a feminist epistemology of mathematics. Educational Studies in Mathematics, 28, 275–291.
  • Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 10, 113–163.
  • Cobb, P., Yackel, E., & Wood, T. (1992). Interaction and learning in mathematics classroom situations. Educational Studies in Mathematics, 23, 99–122.
  • Crick, R. D. (2007). Learning how to learn: The dynamic assessment of learning power. The Curriculum Journal, 18, 135–153.
  • Crotty, M. (1998). The foundations of social research: Meaning and perspective in the research process. Singapore: SAGE.
  • Dang, H. P. (Ed.). (2009). The wisdom and strategy of mathematics teaching in junior high school. Beijing, China: China Financial & Economic.
  • de Lange, J. (2003). Mathematics for literacy. In B. L. Madison & L. A. Steen (Eds.), Quantitative literacy: Why numeracy matters for schools and colleges (pp. 75–89). Princeton, NJ: National Council on Education and Disciplines.
  • Doerr, H. M., & Lesh, R. (2011). Models and modelling perspectives on teaching and learning mathematics in the twenty-first century. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 247–268). Dordrecht, The Netherlands: Springer.
  • Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Helsinki, Finland: Orienta-Konsultit.
  • Ernest, P. (1991). The philosophy of mathematics education. London, UK: Falmer Press.
  • Ernest, P. (2006). Reflections on theories of learning. ZDM – the International Journal on Mathematics Education, 38, 3–7.
  • Freudenthal, H. (2004). Weeding and sowing: Preface to a science of mathematical education. New York, NY: Kluwer Academic Publishers.
  • Geiger, V., Goos, M., & Forgasz, H. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field. ZDM – the International Journal on Mathematics Education, 47, 531–548.
  • Gravemeijer, K. (2008). RME theory and mathematics teacher education. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education (pp. 283–302). Rotterdam, The Netherlands: Sense.
  • Gravemeijer, K., Stephan, M., Julie, C., Lin, F. L., & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education, 15(Suppl 1), 105–123.
  • Gu, Y. (2012). Learning strategies: Prototypical core and dimensions of variation. Studies in Self-Access Learning Journal, 3, 330–356.
  • Hautamäki, J., Arinen, P., Eronen, S., Hautamäki, A., Kupiainen, S., Lindblom, B., … Scheinin, P. (2002). Assessing learning-to-learn: A framework. Helsinki, Finland: National Board of Education.
  • Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32, 195–222.
  • Hofer, B. K. (2008). Personal epistemology and culture. In M. S. Khine (Ed.), Knowing, knowledge and beliefs: Epistemological studies across diverse cultures (pp. 3–22). New York, NY: Springer.
  • Højaard, T. (2010). Communication: The essential difference between mathematical modeling and problem solving. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 255–264). Boston, MA: Springer.
  • Jablonka, E. (2003). Mathematical literacy. In A. J. Bishop, M. A. Clement, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 75–102). Dordrecht, The Netherlands: Kluwer Academic Publishers.
  • Jarvis, P. (2007). Globalisation, lifelong learning and the learning society. London: Routledge.
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • Lerman, S. (2007). Directions for literacy research in science and mathematics education. International Journal of Science and Mathematics Education, 5, 755–759.
  • McNamara, D. S. (2004). SERT: Self-explanation reading training. Discourse Processes, 38, 1–30.
  • Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. In A. Gagatsis & S. Papastavridis (Eds.), Proceedings of 3rd Mediterranean Conference on Mathematical Education (pp. 115–124). Athens, Greece: Hellenic Mathematical Society and Cyprus Mathematical Society.
  • Organisation for Economic Co-operation and Development. (2013). PISA 2012 results: Ready to learn: Students’ engagement, drive and self-beliefs (Vol. III). Paris, France: Author.
  • Organisation for Economic Co-operation and Development. (2016). PISA 2015 assessment and analytical framework: Science, reading, mathematics, and financial literacy. Paris, France: Author.
  • Pugalee, D. K. (1999). Constructing a model of mathematical literacy. The Clearing House, 73, 19–22.
  • Putnam, R. T., Lampert, M., & Peterson, P. L. (1990). Alternative perspectives on knowing mathematics in elementary schools. Review of Research in Education, 16, 57–150.
  • Radford, L. (1998). On signs and representations: A cultural account. Scientia Paedagogica Experimentalis, 35, 277–302.
  • Radford, L. (2013). Three key concepts of the theory of objectification: Knowledge, knowing, and learning. Journal of Research in Mathematics Education, 2, 7–44.
  • Reid, D. A., & Mgombelo, J. (2015). Survey of key concepts in enactivist theory and methodology. ZDM – the International Journal on Mathematics Education, 47, 171–183.
  • Rezat, S., & Strässer, R. (2012). From the didactical triangle to the socio-didactical tetrahedron: Artifacts as fundamental constituents of the didactical situation. ZDM – the International Journal on Mathematics Education, 44, 641–651.
  • Roll, I., Aleven, V., McLaren, B. M., & Koedinger, K. R. (2011). Improving students’ help-seeking skills using metacognitive feedback in an intelligent tutoring system. Learning and Instruction, 21, 267–280.
  • Schlöglmann, W. (2006). Lifelong mathematics learning – A threat or an opportunity? Some remarks on affective conditions in mathematics courses. Adults Learning Mathematics – An International Journal, 2, 6–17.
  • Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. In A. H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 53–70). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Schunk, D. H. (2012). Learning theories: An educational perspective (6th ed.). Boston, MA: Pearson.
  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36.
  • Sfard, A. (2014). Reflections on mathematical literacy. In M. N. Fried & T. Dreyfus (Eds.), Mathematics & mathematics education: Searching for common ground (pp. 157–174). Dordrecht, The Netherlands: Springer.
  • Shi-Da Institute for Mathematics Education. (2018, June 14). Mathematics grounding activity video - Miss, would you please give us one more chance? [Video file]. Retrieved from http://www.sdime.ntnu.edu.tw/page2/news.php?Sn=164
  • Simonson, S. (2011). Rediscovering mathematics: You do the math. Washington, DC: Mathematics Association of America.
  • Skemp, R. R. (1979). Intelligence, learning, and action: A foundation for theory and practice in education. Chichester, UK: Wiley.
  • Steen, L. (2001). The case for quantitative literacy. In L. Steen (Ed.), Mathematics and democracy: The case for quantitative literacy (pp. 1–22). Princeton, NJ: National Council on Education and the Disciplines.
  • Sung, J., & Freebody, S. (2017). Lifelong learning in Singapore: Where are we?. Asia Pacific Journal of Education, 37, 615–628.
  • Tan, J. P. L., Choo, S. S., Kang, T., & Liem, G. A. D. (2017). Educating for twenty-first century competencies and future-ready learners: Research perspectives from Singapore. Asia Pacific Journal of Education, 37, 425–436.
  • Tso, T. Y. (Ed.). (2015). Mathematics for junior high school (Vol. 4, 2nd ed.). Tainan, Taiwan: Nani.
  • Vågan, A. (2011). Towards a sociocultural perspective on identity formation in education. Mind, Culture, and Activity, 18, 43–57.
  • Varela, F., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge, MA: MIT Press.
  • Weinberg, A., & Wiesner, E. (2011). Understanding mathematics textbooks through reader-oriented theory. Educational Studies in Mathematics, 76, 49–63.
  • Westera, W. (2001). Competences in education: A confusion of tongues. Journal of Curriculum Studies, 33, 75–88.
  • Wong, K. Y. (1987). Aspects of mathematical understanding. Singapore Journal of Education, 8, 45–55.
  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.
  • Yang, K. L., & Lin, F. L. (2012). Effects of reading-oriented tasks on students’ reading comprehension of geometry proof. Mathematics Education Research Journal, 24, 215–238.
  • Yore, L. D., Pimm, D., & Tuan, H.-L. (2007). The literacy component of mathematical and scientific literacy. International Journal of Science and Mathematics Education, 5, 559–589.
  • Zawojewski, J. (2010). Problem solving versus modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 237–243). Boston, MA: Springer.

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