Adeneye O. A. Awofala1 & Elizabeth Atinuke Ajao 2
1Department of Science and Technology Education, Faculty of Education, University of Lagos, Nigeria
2Department of Science and Technology Education, Faculty of Education, University of Lagos, Nigeria
Abstract: This study explored trends in problem solving in mathematics research from 2000 to 2020. A total of hundred (100) articles related to mathematical problem solving were examined from the selected journal articles available online. Topical issues as well as methodological trends (research methods, type and size of sample, tools for data collection and techniques for data analysis) were investigated. Content analysis was employed to analyse the sampled data using open codes according to the categories, and themes were generated for some research questions. The results showed that topical issues mainly investigated in mathematical problem solving within the trend period were problem solving ability, teaching, meta-cognition, thinking through, views, process, strategies, creativity, difficulties, efficacy, assessment, performance, representation, and problem-solving curriculum respectively. Methodological trends showed a preference for the qualitative research method. Tests and interviews were the dominant data collection tools utilized while qualitative descriptive analysis was the most preferred data analysis technique. It is therefore concluded that this study can serve as a foundation for further studies and an enhanced study on mathematical problem solving.
Keywords: Trends, Research, Problem Solving, Mathematics
Published: October 4, 2021
AECT (2001). What is descriptive research? Retrieved from http://members.aect.org/edtech/ed1/41/41-01.html
Akyuz, G. (2020). Non-routine problem-solving performances of mathematics teacher candidates. Educational Research and Reviews, 15(5), 214-224.
Allevato, N. S. G., & Onuchic, L. R. (2008). Teaching mathematics in the classroom through problem solving. In 11th International Congress on Mathematical Education, 6-13 July 2008, Monterrey, Mexico (Unpublished). Retrieved from http://www.matedu.cinvestav.mx/~rptec/sitio_web/Documentos_files/tsg19icme11.pdf
Awofala, A. O. A. (2002). Concept mapping and problem solving paradigms and achievement in secondary school Mathematics. Unpublished M.Ed Project. University of Ibadan, Nigeria.
Arum, R. P., Widjajanti, D. B., & Retnawati, H. (2019). Metacognitive awareness: How it affects mathematical problem-solving process. Journal of Physics: Conference Series, 1320, 1-6, doi: 10.1088/1742-6596/1320/1/012054
Berisha, V., Thaqi, X., &Jashari, H. (2014). Problem solving in mathematics textbooks for lower secondary school in Kosovo. ICRAE Conference Proceedings.
Berkeley Math (2020). George Polya’s problem solving techniques. Retrieved from https://math.berkeley.edu/~gmelvin/polya.pdf
Carol, T. (2016, January 19). Why choose qualitative research over quantitative research? [Blog post]. Retrieved from https://medium.com/@thomascarol1988/why-choose-qualitative-research-over-quantitative-research-8cf3141d99a5
Casto, R. (2020). Routine and non-routine problem [Slideshare]. Retrieved from https://www.slideshare.net/mobile/reycastro1/routine-and-non-routine-problems
Clontz, S. (2020, October 15). Puzzle types: Math word, logic and more [Blog post]. Retrieved from https://clontz.org/puzzles/types/
DeFranzo, S. E. (2020). What’s the difference between qualitative and quantitative research? Retrieved from https://www.snapsurveys.com/blog/qualitative-vs-quantitative-research/
Dundar, E., & Merc, A. (2017). A critical review of research on curriculum development and evaluation in ELT. European Journal of Foreign Language Teaching, 2(1), 136-164.
Emerald Publishing (2020). How to use mixed methods research. Retrieved from https://www.emeraldgrouppublishing.com/how-to/research-methods/using-mixed-methods-research
English, L., Lesh, R., &Fennewald, T. (2008). Future directions and perspectives for problem solving research and curriculum development.
In 11th International Congress on Mathematical Education, 6-13 July 2008, Monterrey, Mexico (Unpublished). Retrieved from https://www.researchgate.net/publication/38183931_Future_directions_and_curriculum_development&ved
Ersoy, E., & Guner, P. (2015). The place of problem-s0lving and mathematical thinking in the mathematical teaching. TOJNED- Only Journal of New Horizons in Education, 5(1), 120-130.
Hastuti, I. D., Nusantara, T., & Susanto, H. (2016). Constructive metacognitive activity shift in mathematical problem-solving. Educational Research and Reviews, 11(8), 656-667.
Hoosain, E. (2004). What are mathematical problems? Humanistics Mathematics Network Journal, 27(12), 1-8. Available at http://scholarship.claremont.edu/hmnj/vol1/iss27/12
Inter Ponce (2020). Evaluation of progress in problem solving. Retrieved from http://ponce.inter.edu/cai/tesis/bfeliciano/Cap_2.htm
Izzati, L. R., & Mahmudi, A. (2018). The influence of metacognition in mathematical problem solving. Journal of Physics: Conference Series, 1097, 1-7, doi: 10.1088/1742-6596/1097/1/012107
Jacobs, V. R. Martin, H. A., Ambrose, R. C., & Philipp, R. A. (2014). Polya’s problem solving techniques. Teaching Children Mathematics, 21(2), 107-113.
Jonassen, D. H. (1997). Instructional Design Models for well-structured and ill-structured problem-solving learning outcomes. ETR&D, 45(1), 65-94.
Khandkar, S. H. (2009). Open coding – University of Calgary. Retrieved from http://pages.cpsc.ucalgary.ca/~saul/wiki/uploads/CPSC681/open-coding.pdf
Kusumadewi, C. A., & Retnawati, H. (2020). Identification of elementaryschool students’ difficulties in mathematical problem solving. Journal of Physics: Conference series, 1511, 1-10, doi: 10.1088/1742-6596/1511/1/012031
Lester, F. K. (2013). Thoughts about research on mathematical problem-solving instruction. The Mathematics Enthusiast, 10(1), 245-278.
Liljedahl P., Santos-Trigo M., Malaspina U., & Brudar R. (2016). Problem solving in Mathematics Education. In Problem solving in Mathematics Education. ICME 13 Topical Surveys. Springer, Cham. Available at https://doi.org/10.1007/978-3-319-40730-2_1
Magno, C. (2011). The use of study strategies on mathematical problem-solving. The International Journal of Research and Review, 6(2), 57-82.
Marchis, J. (2012). Non-routine problems in primary mathematics workbooks from Romania. Acta Didactica Napocensia, 5(3), 49-56.
Medelyan, A. (2019, October 10). Coding qualitative data: How to code qualitative research [Blog post]. Retrieved from https://getthematic.com/insights/coding-qualitative-data/amp
Meutia, C. I., Ikhsan, M., & Saminan. (2020). Mathematical problem solving skills of junior high school students. Journal of Physics: Conference series, 1460(1), 1-6. doi: 10.1088/1742-6596/1460/1/012010
Motter, A. (2012). George Polya. Retrieved from http://www.math.wichita.edu/history/men/polya.html
National Council of Teachers of Mathematics (NCTM) (2020). Problem solving. Retrieved from https://www.nctm.org/Research-and-Advocacy/Research-Brief-and-Clips/Problem-Solving/
Nzmaths (2020). Benefits of problem solving. Retrieved from https://nzmaths.co.nz/benefits-problem-solving
Oldridge, M. (2017, November 23). What do we mean when we say, “Teaching through problem-solving in mathematics classrooms [Blog post]? Retrieved from https://medium.com/@MatthewOldridge/what-do-we-mean-when-we-say-through-problem-solving-in-mathematics-classrooms-ae1893d66be9
Ortiz, E. (2016). The problem-solving process in a mathematics classroom. Transformation, 1(1), 1-13.
Peterson, B., McAuliffe, S., &Vermeulen, C. (2017). Writing and mathematical problem solving in Grade 3. South African Journal of Childhood Education, 7(1), 1-9.
Puzzles9 (2020). What is puzzle? Retrieved November 20, 2020, from https://puzzles9.com/what-is-puzzle/
Rohmah, M. & Sutiarso, S. (2018). Analysis of problem solving in mathematics. Theory Newman, 14(2), 671-681.
Schroeder, T. L. & Lester, F. K. (Jr) (1989). Developing understanding in mathematics via problem solving. In P. Trafton (Ed.), New directions for elementary school mathematics (31-42). Reston, VA: National Council of Teachers of Mathematics.
Serc (2018). Well-structured versus ill structured problems. Retrieved from https://serc.carleton.edu/sp/carl_ltc/quantitative_writing/wellversusill
Seward, K. (2011, July 1). An introduction to problem solving [Tutorial 8]. Retrieved from https://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut8_probsol.htm
Study for success (2017). Information about problem solving. Retrieved from http://tutorials.istudy.psu.edu/problemsolving/problemsolving2.html
Sulak, S. (2010). Effect of problem-solving strategies on problem solving achievement in primary school mathematics. Procedia Social and Behavioral Sciences, 9, 468-472.
The executive Guide (2020). What is problem solving. Retrieved from https://asq.org/quality-resources/problem-solving
Trismani, M. &Winarso, W. (2019). Identification of student metacognition levels in problem solving and mathematical literacy. Cahaya Pendidikan, 5(2), 13-29.
Vasileiou,K., Barnett, J., Thorpe, S. & Young, T. (2018). Characterizing and justifying sample size sufficiency in interview-based studies: Systematic analysis of qualitative health research over 15-year period. BMC Med Res Methodol, 18(148), 1-18.
Wikipedia (2020). Puzzle. Retrieved November 20, 2020, from https://en.m.wikipedia.org/wiki/puzzle
Wiktionary (2020). Problem. Retrieved from https://en.m.wiktionary.org/wiki/problem
Wilson, J. W., Fernandez, M. L. &Hadaway, N. (1993). Mathematical problem-solving. In P. S. Wilson (Ed.), Research ideas for the classroom: High School Mathematics. NewYork: MacMillan.
Xenofontos, C. & Andrews, P. (2014). Defining mathematical problems and problems solving: Prospective primary teachers’ beliefs in Cyprus and England. Mathematics Education Research Journal, 26(2), 279-299.
Yavus, G., Deringol-karatas, Y., Arslan, C. & Erbay, H. N. (2015). Research trends on mathematical problem solving in Turkey: Master thesis and dissertations of 2006-2013 period. Procedia Social and Behavioural Sciences, 177, 114-117.
International Journal of Social Sciences & Educational Studies
ISSN 2520-0968 (Online), ISSN 2409-1294 (Print), September 2021, Vol.8, No.3