hong kong mathematics creative problem solving competition

2023/24香港數學創意解難比賽(初賽) Hong Kong Mathematics Creative Problem Solving Competition for Secondary (Heat)

Problem-Solving

• First Online: 24 March 2020

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• Chong Ho Yu 3 &
• Hyun Seo Lee 4  

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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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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.

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

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

Buffon, G. (1777). Essai d’arithmétique morale. Histoire naturelle, générale er particulière, Supplément , 4, 46–123.

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.

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

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

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.

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 .

Csapó, 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.

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.

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.

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

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.

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.

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

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

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

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

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.

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.

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.

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

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

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.

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.

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

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.

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.

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

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.

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

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

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.

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.

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

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

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.

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

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

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

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 .

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.

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

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

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

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.

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

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.

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

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

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).

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 , 2 3(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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Members of the Training Team are actively involved in many large-scale mathematics competitions such as the International Mathematical Olympiad, Pui Ching Invitational Mathematics Competition, the Hong Kong Youth Mathematical High Achievers Selection Contest and the Hong Kong Mathematics Creative Problem Solving Competition for Secondary Schools. Not only have they won numerous awards, but they have also benefited a lot from the competitions.

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Wordplay | u.s. team wins first place at international math olympiad.

U.S. Team Wins First Place at International Math Olympiad

The United States has won the 57th International Mathematical Olympiad, the world’s most prestigious problem-solving competition for high school students.

The competition, held July 6-16 in Hong Kong, included teams from over 100 countries. The winning U.S. team score was 214 out of a possible 252, ahead of the Republic of Korea (207) and China (204). Rounding out the top ten were Singapore (196), Taiwan (175), North Korea (168), Russian Federation (165), United Kingdom (165), Hong Kong (161) and Japan (156).

Congratulations to the U.S. team: students Ankan Bhattacharya, Michael Kural, Allen Liu, Junyao Peng, Ashwin Sah, and Yuan Yao, head coach Po-Shen Loh, and deputy coach Razvan Gelca.

This week we’ll be featuring two of the problems from this year’s six-problem test, with our discussion moderated by Po-Shen Loh himself.

Here are the two problems — our challenges for this week.

The first challenge is IMO 2016 Problem 2 :

Find all positive integers n for which each cell of an n × n table can be filled with one of the letters I , M and O in such a way that:

• in each row and each column, one third of the entries are I , one third are M and one third are O ; and • in any diagonal, if the number of entries on the diagonal is a multiple of three, then one third are I , one third are M , and one third are O .

Our second challenge is a bit more difficult. Here’s an introduction by Dr. Loh:

This year’s IMO featured an unusually large number of non-standard problems which combined multiple areas of mathematics into the same investigation. The most challenging problem turned out to be #3, which was a fusion of algebra, geometry, and number theory. On that question, the USA achieved the highest total score among all countries, ultimately contributing to its overall victory — a historic repeat #1 finish (2015 + 2016), definitively breaking the 21-year drought since the last #1 finish in 1994, and the first consecutive #1 finish in the USA’s record.

Let’s give it a try. Here’s IMO 2016 Problem 3 :

Let P = A 1  A 2 …   A k  be a convex polygon on the plane. The vertices A 1,  A 2, …,   A k have integral coordinates and lie on a circle. Let S be the area of P . An odd positive integer n is given such that the squares of the side lengths of P are integers divisible by n . Prove that 2 S is an integer divisible by n .

That concludes this week’s challenges. If you’d like to try your hand at the remaining four problems in this year’s IMO exam, you’ll find the complete test here . To obtain a perfect score for the test, you must successfully provide the correct answer for each problem, and also prove that each answer is correct.

A Short Conversation with U.S. Team Coach Po-Shen Loh

I had the good fortune to be in Hong Kong last week for the IMO, and caught up with U.S. coach Po-Shen Loh after the event. Following are excerpts from our conversation:

Gary Antonick : Congratulations on your victory. Were you surprised to win?

Po-Shen Loh : The win was a surprise, and now it means the future will be stronger for the US. Something interesting happened this year: the US training program students were estimating the chance that this year’s US team would win the IMO. Their estimate was 40%. To me, that number is huge. If you did that kind of odds three years ago, you wouldn’t have had that high a percent. There are a lot of very good teams out there. What it means is that last year’s victory has given a big confidence boost.

How you perform on something is not just a function of what you know, but how intensely you engage during the activity. This year, the US team went in with a very contagious We Can Do It attitude. The United States has won before, so winning is possible.

This year was actually a rebuilding year for the USA — four of the team members are not in their final year of school — but they were able to still win.

G.A. : This year’s test seemed to emphasize creativity more than previous years. How would you say the problems were creative?

P-S.L : This year’s problems — particularly #3, which we shared above — fused different subjects together in creative ways. Whenever you have fusion, as in cuisine, then there is creativity involved.

G.A. : How was the U.S. team selected and trained?

P-S.L : Students are selected from an original pool of hundreds of thousands of entrants through a series of selection exams run by the Mathematical Association of America, the official organizers for the USA participation in the IMO. The six student team is then brought together prior to the IMO for a three-and-one-half-week training program at Carnegie Mellon University, which is also organized by the MAA.

Participating in the training camp will be the current year’s six-person team, along with fifty-four additional students who might be on the team in future years. This year we also included ten international students — students on IMO teams from other countries. We paid for their airfare, hotel, food and teaching.

G.A. : Wait — you trained some of the team members from other IMO teams?

P-S.L. : Ten of them, including several gold medalists. Two of the four gold medalists on the Singapore team, for example, trained with the US. One of them commented that one of the techniques he used to solve one of the problems in this year’s IMO was from our training program.

This was such a big success that next year, we’re inviting 30 internationals.

G.A. : Do any other countries do this?

P-S.L. : Not at this scale. It’s counter-intuitive. First, bringing in the international students gives the top US students peers. They always tell you — if you’re the smartest guy in the room, you’re in the wrong room. So we bring in these peers, who are actually at the same level as these top six. Of course that increases the level.

Secondly, when the students come to the IMO, there’s no culture shock. You’ve suddenly landed and you look over there — oh my goodness. There’s the South Koreans. There’s the Chinese. There’s the Singaporeans. These guys must be amazingly good.

I remember when I went to the IMO that was exactly the experience I had.

But if you train together you’ve already been in this international experience for the prior three and a half weeks.

G.A. : Who thought of this idea to train so many members of so many different teams?

P-S.L. : My idea. I think of some pretty strange stuff.

G.A. : What does IMO training look like?

P-S.L. : We have math class from 8:30 in the morning until about 3:00 PM, with time for lunch. And then a seminar at 7:30 PM for an hour.

Every other day the day runs until 6:00 because we have a practice test.

There’s a video about this: An Inside Look at the MAA’s Mathematical Olympiad Summer Program .

At this event that we run — it’s a very different atmosphere. You’re not there to beat anyone. You just work together for 3 1/2 weeks.

How does the US IMO training program differ from other training programs?

The US program did not stress that much mechanics. That was actually a worry that some people had — if you come to the US training program, you might not get enough training.

G.A. : What separates the top performers in the IMO from the rest of those at this event?

P-S.L. : I don’t want to say it’s genetic. A lot of people say you must be born with something very special. Maybe once in a while, you may see something like that. But people are basically the same.

Here’s an example. Suppose I tell you to memorize the following:

First of all, what is gravity?

Now — how about the following? Could you memorize and rewrite the same way? Impossible.

প্রথম সব, মাধ্যাকর্ষণ কি ?

But it’s not impossible. All the people in Bangladesh can do it.

What I’m referring to — you have some concepts in your brain called letters and words. When you look at the English version of this question about gravity, your brain is not memorizing where the squiggles are. Your brain has conceptualized it already, and then compresses the information. You have no problem dealing with it.

So — what’s the difference between a top performer and everyone else? If you look at mathematics — if you’ve built the concept structure, when you reason about the problem, you’re reasoning in large concepts. You’re working with large concepts and putting them together.

It’s not a miracle. It’s just about whether your brain has partitioned the concept map, and whether you can deal with entire concepts as primitive arguments as apposed to working with each little letter at a time.

G.A. : Thank you, Po.

For a gentler introduction to some concepts in this year’s International Mathematical Olympiad, National Coach Po-Shen Loh highlights several through his puzzles this week on Expii here .

Want to stay in shape for next year’s Math Olympiad? Each week, Po-Shen Loh posts a set of five questions on Expii, ramping up in difficulty from accessible to intense. In collaboration with the recent film The Man Who Knew Infinity  about the intriguing mathematical genius Srinivasa Ramanujan, who overcame impossible odds to change the future of mathematics, they are scouring the world for undiscovered mathematical ability, in the Spirit of Ramanujan Talent Search .

That’s it for this week. As always, once you’re able to read comments for this post, use Gary Hewitt’s Enhancer to correctly view formulas and graphics. (Click here for an intro.) And send your favorite puzzles to [email protected].

Check reader comments on Friday for solutions and a recap by Po-Shen Loh.

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