Notes on 'perpetual question' of problem solving: how can learners best be taught problem-solving skills?

Article

Yevdokimov, Oleksiy and Taylor, Peter. 2008. "Notes on 'perpetual question' of problem solving: how can learners best be taught problem-solving skills?" Journal of the Korean Society of Mathematical Education Series D: Research in Mathematical Education. 12 (3), pp. 179-191.
Article Title

Notes on 'perpetual question' of problem solving: how can learners best be taught problem-solving skills?

Article CategoryArticle
AuthorsYevdokimov, Oleksiy (Author) and Taylor, Peter (Author)
Journal TitleJournal of the Korean Society of Mathematical Education Series D: Research in Mathematical Education
Journal Citation12 (3), pp. 179-191
Number of Pages13
Year2008
Place of PublicationSeoul, Korea
Web Address (URL)http://ksme.info/
Abstract

Although problem solving was a major focus of mathematics education research in many countries throughout the 1990s, not enough is known about how people best acquire problem-solving skills. This paper is an attempt to advance further development of problem-solving skills of talented school students through combination of some methods accessible from curriculum knowledge and more special techniques that are beyond curriculum. Analysis of various problems is provided in detail. Educational aspects of challenging problems in mathematical contests up to IMO level are, also, taken into account and discussed in the paper.

Keywordsproblem solving; thinking strategies; non-routine tasks; conceptual understanding; mathematical contests
ANZSRC Field of Research 2020390109. Mathematics and numeracy curriculum and pedagogy
520401. Cognition
390409. Learning sciences
Byline AffiliationsDepartment of Mathematics and Computing
University of Canberra
Permalink -

https://research.usq.edu.au/item/9z04x/notes-on-perpetual-question-of-problem-solving-how-can-learners-best-be-taught-problem-solving-skills

Log in to edit

Download files

Published Version
Yevdokimov_Taylor_PV.pdf
File access level: Anyone

  • 1936
    total views
  • 548
    total downloads
  • 2
    views this month
  • 0
    downloads this month

Export as

Related outputs

Minimising mathematical anxiety in teaching mathematics and assessing student’s work
Yevdokimov, Oleksiy. 2021. "Minimising mathematical anxiety in teaching mathematics and assessing student’s work." Kollosche, David (ed.) 11th International Mathematics Education and Society Conference: Exploring new ways to connect (2021). Virtual Germany.
Links between problems and their role in students' preparation for mathematical contests
Yevdokimov, Oleksiy. 2010. "Links between problems and their role in students' preparation for mathematical contests." Avotina, Maruta, Bonca, Dace, Falk de Losada, Maria, Ramana, Liga and Soifer, Alexander (ed.) WFNMC6: 6th Congress of the World Federation of National Mathematics Competitions. Riga, Latvia 25 - 31 Jul 2010 Australia.
Problem set 12
Yevdokimov, Oleksiy. 2013. "Problem set 12." Australian Senior Mathematics Journal. 27 (2), pp. 63-63.
Problem set 11
Yevdokimov, Oleksiy. 2013. "Problem set 11." Australian Senior Mathematics Journal. 27 (1), pp. 64-64.
On the analysis of indirect proofs: contradiction and contraposition
Jourdan, Nicolas and Yevdokimov, Oleksiy. 2016. "On the analysis of indirect proofs: contradiction and contraposition." Australian Senior Mathematics Journal. 30 (1), pp. 55-64.
Problem set 8
Yevdokimov, Oleksiy. 2011. "Problem set 8." Australian Senior Mathematics Journal. 25 (2), pp. 63-63.
Problem set 7
Yevdokimov, Oleksiy. 2011. "Problem set 7." Australian Senior Mathematics Journal. 25 (1), pp. 64-64.
Problem set 6
Yevdokimov, Oleksiy. 2010. "Problem set 6." Australian Senior Mathematics Journal. 24 (2), pp. 64-64.
Problem set 5
Yevdokimov, Oleksiy. 2010. "Problem set 5." Australian Senior Mathematics Journal. 24 (1), pp. 64-64.
Problem set 9
Yevdokimov, Oleksiy. 2012. "Problem set 9 ." Australian Senior Mathematics Journal. 26 (1), pp. 64-64.
Problem set 10
Yevdokimov, Oleksiy. 2012. "Problem set 10." Australian Senior Mathematics Journal. 26 (2), pp. 63-63.
Notes about teaching mathematics as relationships between structures: a short journey from early childhood to higher mathematics
Yevdokimov, Oleksiy. 2012. "Notes about teaching mathematics as relationships between structures: a short journey from early childhood to higher mathematics." The De Morgan Journal. 2 (1), pp. 69-83.
Cognitive development of proof
Tall, David, Yevdokimov, Oleksiy, Koichu, Boris, Whiteley, Walter, Kondratieva, Margo and Cheng, Ying-Hao. 2012. "Cognitive development of proof." Hanna, Gila and de Villiers, Michael (ed.) Proof and proving in mathematics education. Dordrecht, Germany. Springer. pp. 13-49
On creating a 'free of anxiety' assessment environment for students with special needs
Yevdokimov, Oleksiy. 2011. "On creating a 'free of anxiety' assessment environment for students with special needs ." NORSMA6: New Trends in Special Needs Education in Mathematics: Problems and Possibilities. Kristiansand, Norway 02 - 04 Nov 2011 Kristiansand, Norway.
Problem set 4
Yevdokimov, Oleksiy. 2009. "Problem set 4." Australian Senior Mathematics Journal. 23 (2), pp. 63-63.
Problem set 3
Yevdokimov, Oleksiy. 2009. "Problem set 3." Australian Senior Mathematics Journal. 23 (1), pp. 63-63.
On the nature of mathematical education of engineers: identifying hidden obstacles and potential for improvement
Yevdokimov, Oleksiy. 2008. "On the nature of mathematical education of engineers: identifying hidden obstacles and potential for improvement." Alpers, Burkhard, Hibberd, Stephen, Lawson, Duncan, Mustoe, Leslie and Robinson, Carol (ed.) 2008 Mathematical Education of Engineers Conference . Loughborough, United Kingdom 06 - 09 Apr 2008 Loughborough, UK.
Higher order reasoning produced in proof construction: how well do secondary school students explain and write mathematical proofs?
Yevdokimov, Oleksiy. 2009. "Higher order reasoning produced in proof construction: how well do secondary school students explain and write mathematical proofs?" Lin, Fou-Lai, Hsieh, Feng-Jui, Hanna, Gila and de Villiers, Michael (ed.) ICMI Study 19 Working Conference: Proof and Proving in Mathematics Education. Taipei, Taiwan 10 - 15 May 2009 Taipei.
Theoretical perspectives of the process of making conjectures [in Spanish]
Canadas, Maria, Deulofeu, Jordi, Figueiras, Lourdes, Reid, David A. and Yevdokimov, Oleksiy. 2008. "Theoretical perspectives of the process of making conjectures [in Spanish]." Ensenanza de las Ciencias. 26 (3), pp. 431-444.
Making generalisations in geometry: students' views on the process: a case study
Yevdokimov, Oleksiy. 2008. "Making generalisations in geometry: students' views on the process: a case study." Figueras, Olimpia, Cortina, Jose Luis, Alatorre, Silvia, Rojano, Teresa and Sepulveda, Armando (ed.) 2008 Annual Conference for the Psychology of Mathematics Education (PME 32): Mathematical Ideas: History, Education and Cognition. Morelia, Mexico 17 - 21 Jul 2008 Morelia, Mexico.
Problem set 2
Yevdokimov, Oleksiy. 2008. "Problem set 2." Australian Senior Mathematics Journal. 22 (2), pp. 63-64.
Problem set 1
Yevdokimov, Oleksiy. 2008. "Problem set 1." Australian Senior Mathematics Journal. 22 (1), pp. 63-64.
Problem solving activities in a constructivist framework: exploring how students approach difficult problems
Yevdokimov, Oleksiy and Passmore, Tim. 2008. "Problem solving activities in a constructivist framework: exploring how students approach difficult problems." Goos, Merrilyn, Brown, Ray and Makar, Katie (ed.) 31st Annual Conference of the Mathematics Education Research Group of Australasia (MERGA 31). Brisbane, Australia 28 Jun - 01 Jul 2008 Adelaide, Australia.
The conjecturing process: perspectives in theory and implications in practice
Yevdokimov, Oleksiy, Canadas, Maria, Deulofeu, Jordi, Figueiras, Lourdes and Reid, David. 2007. "The conjecturing process: perspectives in theory and implications in practice." Journal of Teaching and Learning. 5 (1), pp. 55-72.
Asymptotically accurate flow completion time distributions under fair queueing
Addie, R. G. and Yevdokimov, Oleksiy. 2008. "Asymptotically accurate flow completion time distributions under fair queueing." Green, Richard (ed.) Australasian Telecommunication Networks and Applications Conference (ATNAC 2007): Next Generation Networks: Enabling Closer International Cooperation. Christchurch, New Zealand 02 - 05 Dec 2007 Piscataway, NJ. United States. https://doi.org/10.1109/ATNAC.2007.4665290
Using the history of mathematics for mentoring gifted students: Notes for teachers
Yevdokimov, Oleksiy. 2007. "Using the history of mathematics for mentoring gifted students: Notes for teachers." Milton, Ken, Reeves, Howard and Spencer, Toby (ed.) The 21st Biennial Conference of the Australian Association of Mathematics Teachers Inc.. Hobart, Australia 06 - 09 Jul 2007 Adelaide, Australia.
Inquiry activities in a classroom: extra-logical processes of illumination vs logical process of deductive and inductive reasoning. A case study
Yevdokimov, Oleksiy. 2006. "Inquiry activities in a classroom: extra-logical processes of illumination vs logical process of deductive and inductive reasoning. A case study ." Novotna, Jarmila, Stehlikova, Nada, Kratka, Magdalena and Moraova, Hana (ed.) 30th Conference of the International Group for the Psychology of Mathematics Education. Prague, Czech Republic 16 - 21 Jul 2006 Prague, Czech Republic.
Using materials from the history of mathematics in discovery-based learning
Yevdokimov, Oleksiy. 2006. "Using materials from the history of mathematics in discovery-based learning ." Furinghetti, Fulvia, Kaijser, Sten and Tzanakis, Constantinos (ed.) ICME 10 Satellite Meeting of the International Study Group on the Relations between the History and Pedagogy of Mathematics. Uppsala, Sweden 12 - 17 Jul 2004 Heraclion, Greece.
About a constructivist approach for stimulating students' thinking to produce conjectures and their proving in active learning of geometry
Yevdokimov, Oleksiy. 2006. "About a constructivist approach for stimulating students' thinking to produce conjectures and their proving in active learning of geometry." Bosch, Marianna, Perpinan, Marta and Portabella, M. Angels (ed.) 4th Congress of the European Society for Research in Mathematics Education. Sant Feliu de Guixols, Spain 17 - 21 Feb 2005 Barcelona, Spain.
On development of students' abilities in problem posing: a case of plan geometry
Yevdokimov, Oleksiy. 2005. "On development of students' abilities in problem posing: a case of plan geometry ." Gagatsis, Athanasios, Spagnolo, Filippo, Makrides, Gregory and Farmaki, Vassiliki (ed.) 4th Mediterranean Conference on Mathematics Education. Palermo, Italy 28 - 30 Jan 2005 Palermo, Italy.
Protecting small flows from large ones for quality of service
Addie, R. G., Yevdokimov, Oleksiy, Braithwaite, Stephen and Millsom, David. 2007. "Protecting small flows from large ones for quality of service." Bernstein, David, Dini, Petre, Hladka, Eva, Reza, Hassan, Romascanu, Dan and Sankar, Krishna (ed.) 2nd International Conference on Digital Telecommunications (ICDT 2007). San Jose, United States 01 - 06 Jul 2007 Piscataway, NJ. United States. https://doi.org/10.1109/ICDT.2007.68