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Abstract

Implementing problem-solving is one of the core objectives of Hong Kong’s Learning to Learn project. Hong Kong recognizes the fundamental importance of problem-solving in math and science education.

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References

  • American College Testing [ACT], Inc. (2007). Rigor at risk: Reaffirming quality in the high school core curriculum. Iowa City, IA: Author.

    Google Scholar 

  • Anderson, J. R., Boyle, C. B., & Reiser, B. J. (1985). Intelligent tutoring systems. Science, 228, 456–462.

    Article  Google Scholar 

  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., … & Tsai, Y. M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180.

    Google Scholar 

  • Bhaskar, R., & Simon, H. (1977). Problem solving in semantically rich domains: An example from engineering thermodynamics. Cognitive Science, 1(2), 193–215.

    Article  Google Scholar 

  • Boaler, J. (2016). Mathematical mindset: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. New York, NY: Jossey-Bass.

    Google Scholar 

  • Buffon, G. (1777). Essai d’arithmĂ©tique morale. Histoire naturelle, gĂ©nĂ©rale er particulière, SupplĂ©ment, 4, 46–123.

    Google Scholar 

  • Camillia, G., & Dossey, J. (2019). Multidimensional national profiles for TIMSS 2007 and 2011 mathematics. Journal of Mathematical Behavior [Online First]. https://doi.org/10.1016/j.jmathb.2019.02.001.

  • Chaitin, G. J. (1998). The limits of mathematics: A course on information theory and the limits of formal reasoning. Singapore: Springer.

    Google Scholar 

  • Chase, W. G., & Simon, H. A. (1973). Perception in chess. Cognitive Psychology, 4, 55–81.

    Article  Google Scholar 

  • Cheung, Q. P. (2017). Break the convention: A question in the interview. School Mathematics Newsletter, 21, 64–76.

    Google Scholar 

  • Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121–152.

    Article  Google Scholar 

  • Cisco Systems. (2019). Expert certification. Retrieved from https://www.cisco.com/c/en/us/training-events/training-certifications/certifications/expert.html.

  • Common Core State Standards Initiative. (2016). Mathematical standards. Retrieved from http://www.corestandards.org/wp-content/uploads/Math_Standards1.pdf.

  • CsapĂł, B., & Funke, J. (Eds.). (2017). The nature of problem solving: Using research to inspire 21st century learning, educational research and innovation. Paris: OECD Publishing. https://doi.org/10.1787/9789264273955-en.

    Book  Google Scholar 

  • Davis, G. A. (1973). Psychology of problem solving: Theory and practice. New York, NY: Basic Books.

    Google Scholar 

  • Dossey, J., Mullis, I., Lindquist, M., & Chambers, D. (1988). The mathematics report card: Are we measuring up? Trends and achievements based on the 1986 national assessment. Princeton, NJ: Educational Testing Service.

    Google Scholar 

  • Fischer, A., Greiff, S., & Funke, J. (2012). The process of solving complex problems. Journal of Problem Solving, 4(1), Article 3. http://dx.doi.org/10.7771/1932-6246.1118.

  • Fortunato, I., Hecht, D., Tittle, C. K., & Alvarez, L. (1991). Metacognition and problem solving. The Arithmetic Teacher, 39(4), 38–40.

    Google Scholar 

  • Frensch, P. A., & Funke, J. (1995). Complex problem solving: The European perspective. New York, NY: Erlbaum.

    Google Scholar 

  • Friedman, T. (2013, October 22). The Shanghai secret. New York Times. Retrieved from http://www.nytimes.com/2013/10/23/opinion/friedman-the-shanghai-secret.html?_r=0.

  • Fung, C. Y. (2014). Mathematical knowledge is “autocratic”. School Mathematics Newsletter, 18, 19–34.

    Google Scholar 

  • Funke, J., & Frensch, P. A. (2007). Complex problem solving: The European perspective - 10 years after. In D. H. Jonassen (Ed.), Learning to solve complex scientific problems (pp. 25–47). New York, NY: Erlbaum.

    Google Scholar 

  • Gadidov, B. (2017, April). Predicting highly qualified math teachers in secondary schools in the United States. Paper presented at SAS Global Forum, Orlando, FL.

    Google Scholar 

  • Grobler, G. C. (2016a). Interdisciplinary Forensic Science Programme. Hong Kong Science Teachers’ Journal, 31, 14–18.

    Google Scholar 

  • Grobler, G. C. (2016b). Let our students teach! Teaching as a way of mastering knowledge. Hong Kong Teacher’s Journal, 32, 79–83.

    Google Scholar 

  • Heppner, P. P., & Krauskopf, C. J. (1987). An information-processing approach to personal problem solving. Counseling Psychologist, 15, 371–447.

    Article  Google Scholar 

  • Hewitt, D. (2002). Arbitrary and Necessary: A way of viewing the mathematics curriculum. In L. Haggarty (Ed.), Teaching mathematics in secondary schools: A reader (pp. 47–63). London: Routledge.

    Google Scholar 

  • Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., … & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12–21.

    Google Scholar 

  • Hong Kong Education Bureau. (2018). HK Mathematics Creative Problem-Solving Competition. Retrieved from https://www.edb.gov.hk/en/curriculum-development/major-level-of-edu/gifted/resources_and_support/competitions/local/cps.html.

  • Hong Kong Examinations and Assessment Authority. (2016). Category A: Senior secondary subjects. Retrieved from http://www.hkeaa.edu.hk/en/hkdse/assessment/subject_information/category_a_subjects/hkdse_subj.html?A1&1&4.

  • Jonassen, D. H. (2010). Learning to solve problems: A handbook for designing problem-solving learning environments. New York, NY: Routledge.

    Book  Google Scholar 

  • Josephson, J. R., & Josephson, S. G. (Eds.). (1996). Abductive inference: Computation, philosophy, technology. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Klein, D. (2003). A brief history of American K-12 mathematics education in the 20th Century. In J. M. Royer (Ed.), Mathematical Cognition (pp. 175–259). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Klieme, E. (2004). Assessment of cross-curricular problem-solving competencies. In J. H. Moskowitz & M. Stephens (Eds.), Comparing learning outcomes: International assessments and education policy (pp. 81–107). London: Routledge.

    Google Scholar 

  • Laxman, K. (2013). Epistemology of well and ill structured problem solving. In Sebatien Helie (Ed.), The psychology of problem solving (pp. 3–13). New York, NY: Nova Science Publishers Inc.

    Google Scholar 

  • Lee, C. M. (2015). Geometrical probability and Bertrand’s Paradox. School Mathematics Newsletter, 19, 14–27.

    Google Scholar 

  • Leung, K. S. (2015). You will never get a zero in this exam no matter what your answer is. School Mathematics Newsletter, 19, 5–13.

    Google Scholar 

  • Lloyd, C. (2018, June 21). Why our smartest students are failing math. Retrieved from https://www.greatschools.org/gk/articles/why-americas-smartest-students-fail-math/.

  • Lockhart, P. (2009). A mathematician’s lament: How school cheats us out of our most fascinating and imaginative art. New York, NY: Bellevue Literary Press.

    Google Scholar 

  • Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. New York, NY: Routledge.

    Book  Google Scholar 

  • Mangels, J. A., Butterfield, B., Lamb, J., Good, C., & Dweck, C. S. (2006). Why do beliefs about intelligence influence learning success? A social cognitive neuroscience model. Social Cognitive and Affective Neuroscience, 1(2), 75–86.

    Article  Google Scholar 

  • Marinoff, L. (1994). A Resolution of Bertrand’s Paradox. Philosophy of Science, 61(1), 1–24.

    Article  Google Scholar 

  • Mayer, R. E. (1992). Thinking, problem solving, cognition (2nd ed.). New York, NY: W. H. Freeman.

    Google Scholar 

  • Mayer, R. E., & Wittrock, M. C. (2006). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (pp. 287–303). Mahwah, NJ, US: Lawrence Erlbaum Associates Publishers.

    Google Scholar 

  • Moser, J., Schroder, H. S., Heeter, C., Moran, T. P., & Lee, Y. H. (2011). Mind your errors: Evidence for a neural mechanism linking growth mindset to adaptive post error adjustments. Psychological Science, 22, 1484–1489.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics [NCTM] (1989). Curriculum and Evaluation Standards. Reston, VA: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Organization for Economic Cooperation and Development [OECD]. (2013a). Technical report of the survey of adult skills (PIAAC). Retrieved from https://www.oecd.org/skills/piaac/_Technical%20Report_17OCT13.pdf.

  • Organization for Economic Cooperation and Development [OECD]. (2013b). The survey of adult skills: Reader’s companion. Paris: OECD Publishing. Retrieved from: http://dx.doi.org/10.1787/9789264204027-en.

  • Organization for Economic Cooperation and Development [OECD]. (2017). PISA 2015 results (Volume V): Collaborative Problem Solving, PISA. Paris: OECD Publishing. https://doi.org/10.1787/9789264285521-en.

  • Polya, G. (1954a). Mathematic and plausible reasoning—Volume I: Induction and analogy in mathematics. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Polya, G. (1954b). Mathematic and plausible reasoning—Volume II Patterns of plausible inference. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Polya, G. (1957). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Santos, L. (2017). The role of critical thinking in science education. Journal of Education and Practice, 8, 159–173.

    Google Scholar 

  • Simon, H. A., & Newell, A. (1971). Human problem solving: The state of the theory in 1970. American Psychologist, 26(2), 145–159. https://doi.org/10.1037/h0030806.

    Article  Google Scholar 

  • Skinner, B. F. (1966). An operant analysis of problem solving. In B. Kleinmuntz (Ed.), Problem solving: Research, method, and theory (pp. 225–257). New York, NY: Wiley.

    Google Scholar 

  • Soh, K. (2019). PISA and PIRLS: The effects of culture and school environment. Singapore: World Scientific.

    Google Scholar 

  • Tukey, J. W. (1977). Exploratory data analysis. Reading, MA: Addison- Wesley.

    Google Scholar 

  • Wai, M. Y. (2011). Further applications of mathematics: Explore Ptolemy’s theorem and its applications. School Mathematics Newsletter, 17, 43–58.

    Google Scholar 

  • Wenke, D., Frensch, P. A., & Funke, J. (2005). Complex problem solving and intelligence: Empirical relation and causal direction. In R. J. Sternberg & J. E. Pretz (Eds.), Cognition and intelligence: Identifying the mechanisms of the mind (pp. 160–187). New York, NY: Cambridge University Press.

    Google Scholar 

  • Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 25–48.

    Article  Google Scholar 

  • Wong, N. Y., Marton, F., Wong, K. M., & Lam, C. C. (2002). The lived space of mathematics learning. Journal of Mathematical Behavior, 21, 25–47.

    Article  Google Scholar 

  • Wong, P. W. (2018). STEM for parents. Hong Kong: Shing Tao Publisher.

    Google Scholar 

  • Young, A. E., & Worrell, F. C. (2018). Comparing metacognition assessments of mathematics in academically talented students. Gifted Child Quarterly, 62, 259–275.

    Article  Google Scholar 

  • Yu, C. H., Anthony, S, & Behrens, J. T. (1995, April). Identification of misconceptions in learning central limit theorem and evaluation of computer-based instruction as a remedial tool. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA. (ERIC Document Reproduction Service No. ED 395 989).

    Google Scholar 

  • Yu, C. H., DiGangi, S., & Jannasch-Pennell, A. (2008). The role of abductive reasoning in cognitive-based assessment. Elementary Education Online, 7(2), 310–322. Retrieved from http://ilkogretim-online.org.tr/index.php/io/article/view/1804/1640.

  • Yu, C. H., Lee, H. S., Lara, E., & Gan, S. G. (2018). The ensemble and model comparison approaches for big data analytics in social sciences. Practical Assessment, Research, and Evaluation, 23(17). Retrieved from https://pareonline.net/getvn.asp?v=23&n=17.

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Yu, C.H., Lee, H.S. (2020). Problem-Solving. In: Creating Change to Improve Science and Mathematics Education. Springer, Singapore. https://doi.org/10.1007/978-981-15-3156-9_4

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  • DOI: https://doi.org/10.1007/978-981-15-3156-9_4

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