Enhancing Pre-service Teachers’ Procedural Fluency and Adaptive Reasoning in Trigonometry
Louis Robert C. Sison
Discipline: Education
Abstract:
This study examined the effects of Productive Struggle-Driven Creative Problem-Solving (PSD-CPS) instruction on the procedural fluency and adaptive reasoning of pre-service mathematics teachers in a trigonome- try course at a public university in Malolos City, Bulacan. Using an em- bedded mixed-methods design, quantitative data from a quasi-experi- mental approach and qualitative data from reflective logs, observations, and focus group discussions were analyzed. Results showed significant posttest gains in both control and experimental groups. While procedural fluency gains were moderate, PSD-CPS instruction greatly enhanced adaptive reasoning. Participants positively perceived PSD-CPS as effec- tive in improving their trigonometric understanding.
References:
- Aguilar, J. J., & Telese, J. A. (2018). Mathematics understanding of elementary pre-service teachers: The analysis of their procedural-fluency, conceptual-understanding, and problemsolving strategies.Mathematics Teaching Research Journal,10(3-4), 24. https://scholar-works.utrgv.edu/tl_fac/27">https://scholar-works.utrgv.edu/tl_fac/27">https://scholar-works.utrgv.edu/tl_fac/27
- Alferez, M.S. & Duro, M.A. (2018). Statistics and Probability. Philippines: MSA PublishingCompany.
- Almeida, A.B., Gaerlan, A.A., & Manly, N.E. (2016). Research Fundamentals: From Concept to Output. Quezon City: Adriana Publishing Co., Inc.
- Alrwaished, N. (2024). Mathematics pre-ser-vice teachers’ preparation program fordesigning STEM based lesson plan: en-hanced skills and challenges. Cogent Edu-cation, 11(1). https://doi.org/10.1080/2331186x.2024.2320467">https://doi.org/10.1080/2331186x.2024.2320467">https://doi.org/10.1080/2331186x.2024.2320467
- Altarawneh, A. F., & Marei, S. T. (2021). Mathe-matical proficiency and preservice class-room teachers instructional performance. International Journal of Education and Practice, 9(2), 354–364. https://doi.org/10.18488/jour-nal.61.2021.92.354.364">https://doi.org/10.18488/jour-nal.61.2021.92.354.364">https://doi.org/10.18488/jour-nal.61.2021.92.354.364
- Andrade, R. R., & Pasia, A. E. (2020). Mathemat-ical creativity of pre-service teachers in solving non-routine problems in State University in Laguna. Universal Journal of Educational Research, 8(10), 4555–4567. https://doi.org/10.13189/ujer.2020.081024">https://doi.org/10.13189/ujer.2020.081024">https://doi.org/10.13189/ujer.2020.081024
- Annurwanda, P., & Friantini, R. N. (2022). Math-ematical induction proofing: Procedural fluency reviewed from the creative think-ing level of mathematics students. Jurnal Riset Pendidikan Matematika, 9(1), 22-35. https://doi.org/10.21831/jrpm.v9i1.43987">https://doi.org/10.21831/jrpm.v9i1.43987">https://doi.org/10.21831/jrpm.v9i1.43987
- Ansari, B. I., Taufiq, T., & Saminan, S. (2020). The use of creative problem solvingmodel to develop students’ adaptive reasoning ability: Inductive, deductive, and intuitive. International Journal on Teaching and Learning Mathematics, 3(1), 23–36. https://doi.org/10.18860/ijtlm.v3i1.9439">https://doi.org/10.18860/ijtlm.v3i1.9439">https://doi.org/10.18860/ijtlm.v3i1.9439
- Baah-Duodu, S. (2022). Colleges of education students' mathematics proficiency: As-sessing strategic competency and adap-tive reasoning during supported teaching in schools. International Journal of Innova-tive Research & Development, 11(3). https://doi.org/10.24940/ijird/2022/v11/i3/mar22030">https://doi.org/10.24940/ijird/2022/v11/i3/mar22030">https://doi.org/10.24940/ijird/2022/v11/i3/mar22030
- Beach, J., Álvarez, J. a. M., & Jorgensen, T. (2020). Mathematics Teacher Preparation Standards in a Research-Based Mathe-matics Course for Prospective Secondary Mathematics Teachers: Exploring Student Experiences and Curriculum Writers’ Per-spectives. IUMPST the Journal, 1. http://files.eric.ed.gov/fulltext/EJ1257599.pdf
- Conde, R. L. (2014).Mathematics Pedagogical Content Knowledge of Pre-Service Teachers and Didactics in Mathematics Course Pro-totype(Doctoral dissertation). https://api.reposi-tory.upou.edu.ph/api/core/bit-streams/7bc163f5-c87c-4df4-94bf-b9b94a0b212a/content">https://api.reposi-tory.upou.edu.ph/api/core/bit-streams/7bc163f5-c87c-4df4-94bf-b9b94a0b212a/content">https://api.reposi-tory.upou.edu.ph/api/core/bit-streams/7bc163f5-c87c-4df4-94bf-b9b94a0b212a/content
- Creswell, J. W., & Clark, V. L. P. (2017). Design-ing and conducting mixed methods re-search. Sage publications. (pp. 61-94; 143-170)
- Daher, W., & Anabousy, A. (2020). Flexibility Processes of Pre-service Teachers in Problem Solving with Technology. Inter-national Journal of Technology in Educa-tion and Science, 4(3), 247–255. https://doi.org/10.46328/ijtes.v4i3.96">https://doi.org/10.46328/ijtes.v4i3.96">https://doi.org/10.46328/ijtes.v4i3.96
- Department of Education (2024). MATATAG Curriculum Guide.
- Ebio, J. B. (2022). Mathematics Content Knowledge of Pre-service Elementary Teachers.International Journal of Ad-vanced Multidisciplinary Studies,2(3), 323-334. https://www.ijams-bbp.net/wp-content/up-loads/2022/04/IJAMS-MARCH-323-334-2.pdf">https://www.ijams-bbp.net/wp-content/up-loads/2022/04/IJAMS-MARCH-323-334-2.pdf">https://www.ijams-bbp.net/wp-content/up-loads/2022/04/IJAMS-MARCH-323-334-2.pdf
- Failing, S. (2024). Facilitating Productive Strug-gle in an Online Secondary Education Mathematics Methods Course: Experi-ences of Pre-Service Teachers. Journal of Teaching and Learning, 18(1), 56–74. https://doi.org/10.22329/jtl.v18i1.7813">https://doi.org/10.22329/jtl.v18i1.7813">https://doi.org/10.22329/jtl.v18i1.7813
- Fi, C. D. (2003). Preservice secondary school mathematics teachers’ knowledge of trigo-nometry. https://doi.org/10.17077/etd.hgi8dv0k">https://doi.org/10.17077/etd.hgi8dv0k">https://doi.org/10.17077/etd.hgi8dv0k
- Findell, B., Swafford, J., & Kilpatrick, J. (Eds.). (2001).Adding it up: Helping children learn mathematics. National Academies Press.
- Fortes, E. C., & Andrade, R. R. (2019). Mathe-matical creativity in solving Non-Routine problems. The Normal Lights, 13(1). https://doi.org/10.56278/tnl.v13i1.1237">https://doi.org/10.56278/tnl.v13i1.1237">https://doi.org/10.56278/tnl.v13i1.1237
- Gurat, M. (2018). Mathematical Problem-Solv-ing Heuristics among Student Teachers. Journal on Efficiency and Responsibility in Education and Science, 11(3), 53–64.https://doi.org/10.7160/eriesj.2018.110302
- Hokor, E. K., & Arhin, J. (2021). Analysis of high school students’ errors in solving trigo-nometry problems. Journal of Mathemat-ics and Science Teacher, 1(1), em003. https://doi.org/10.29333/mathsciteacher/11076">https://doi.org/10.29333/mathsciteacher/11076">https://doi.org/10.29333/mathsciteacher/11076
- Karatas, S. (2022).The Impacts of Supporting Productive Struggle Teaching Practice on Students’ Conceptual Understanding, Pro-cedural Fluency, and Strategic Compe-tence: The Case of Quadratic Func-tions(Doctoral dissertation, The Univer-sity of Texas Rio Grande Valley). https://scholar-works.utrgv.edu/etd/1153
- Khalil, M. K., & Elkhider, I. A. (2016). Applying learning theories and instructional design models for effective instruction. AJP Ad-vances in Physiology Education, 40(2), 147–156. https://doi.org/10.1152/ad-van.00138.2015">https://doi.org/10.1152/ad-van.00138.2015">https://doi.org/10.1152/ad-van.00138.2015
- Klang, N., Karlsson, N., Kilborn, W., Eriksson, P., & Karlberg, M. (2021). Mathematical Problem-Solving Through Cooperative Learning—The importance of peer ac-ceptance and friendships. Frontiers in Ed-ucation, 6. https://doi.org/10.3389/feduc.2021.710296">https://doi.org/10.3389/feduc.2021.710296">https://doi.org/10.3389/feduc.2021.710296
- Komarudin, K., Sukardi, N. N., Yuberti, Y., Afandi, M., & Ramury, F. (2023). An analy-sis of students’ mathematical Adaptive Reasoning: the impact of Creative Prob-lem-Solving (CPS) learning model and en-trepreneurial character. ARITHMETIC Ac-ademic Journal of Math, 5(1), 1. https://doi.org/10.29240/ja.v5i1.5777">https://doi.org/10.29240/ja.v5i1.5777">https://doi.org/10.29240/ja.v5i1.5777
- Komolthiti, M. (2016). Leadership journeys: A narrative research study exploring women school superintendent’s meaning-making of leadership development experiences(Doctoral Dissertation). Available from ProQuest Dissertations and Theses data-base. https://repository.library.north-east-ern.edu/files/neu:cj82nr11x/fulltext.pdf">https://repository.library.north-east-ern.edu/files/neu:cj82nr11x/fulltext.pdf">https://repository.library.north-east-ern.edu/files/neu:cj82nr11x/fulltext.pdf
- Loc, N. P., Oanh, N. P. P., Thao, N. P., Van De, T., & Triet, L. V. M. (2022). Activity theory as a framework for teaching mathematics: An experimental study. Heliyon, 8(10), e10789. https://doi.org/10.1016/j.heli-yon.2022.e10789">https://doi.org/10.1016/j.heli-yon.2022.e10789">https://doi.org/10.1016/j.heli-yon.2022.e10789
- Lubid, A. (2024). The implementation of trifo-calization in Philippine education and its impact on quality, accessibility, and rele-vance in the province of Marinduque: A strategic analysis.International Journal of Arts, Sciences and Education,5(2), 222–240. https://www.mail.ijase.org/in-dex.php/ijase/article/view/357">https://www.mail.ijase.org/in-dex.php/ijase/article/view/357">https://www.mail.ijase.org/in-dex.php/ijase/article/view/357
- Mattis, N. (2018). Launch-Explore-Summarize in High School Calculus(2018). Honors Theses. 477. https://digitalcom-mons.bucknell.edu/honors_theses/477">https://digitalcom-mons.bucknell.edu/honors_theses/477">https://digitalcom-mons.bucknell.edu/honors_theses/477
- Mishra,L. (2016). Focus group discussion in qualitative research.TechnoLearn: An In-ternational Journal of Educational Tech-nology,6(1). https://ndpublisher.in/ad-min/issues/tlV6N1a.pdf">https://ndpublisher.in/ad-min/issues/tlV6N1a.pdf">https://ndpublisher.in/ad-min/issues/tlV6N1a.pdf
- Mohammed, A. A. (2024). Preservice Teacher’s Attitude toward Problem-Solving in Math-ematics Education. Noumerico Journal of Technology in Mathematics Education, 2(2), 113–126. https://doi.org/10.33367/jtme.v2i2.5335">https://doi.org/10.33367/jtme.v2i2.5335">https://doi.org/10.33367/jtme.v2i2.5335
- Muin, A., Hanifah, S. H., & Diwidian, F. (2018). The effect of creative problem solving on students’ mathematical adaptive reason-ing. Journal of Physics Conference Series, 948, 012001. https://doi.org/10.1088/1742-6596/948/1/012001">https://doi.org/10.1088/1742-6596/948/1/012001">https://doi.org/10.1088/1742-6596/948/1/012001
- Nabie, M. J., Akayuure, P., Ibrahim-Bariham, U. A., & Sofo, S. (2018). Trigonometric Con-cepts: Pre-Service Teachers' Perceptions and Knowledge.Journal on Mathematics Education,9(1), 169-182. https://files.eric.ed.gov/fulltext/EJ1193604.pdf">https://files.eric.ed.gov/fulltext/EJ1193604.pdf">https://files.eric.ed.gov/fulltext/EJ1193604.pdf
- Nilimaa, J. (2023). New examination approach for Real-World Creativity and Problem-Solving Skills in Mathematics. Trends in Higher Education, 2(3), 477–495. https://doi.org/10.3390/high-eredu2030028">https://doi.org/10.3390/high-eredu2030028">https://doi.org/10.3390/high-eredu2030028
- OECD (2023), PISA 2022 Results (Volume I): The State of Learning and Equity in Edu-cation, PISA, OECD Publishing, Paris, https://doi.org/10.1787/53f23881-en">https://doi.org/10.1787/53f23881-en.">https://doi.org/10.1787/53f23881-en.
- Pallant,J. (2020).SPSS survival manual: A step by step guide to data analysis using IBM SPSS. Routledge. https://doi.org/10.4324/9781003117452">https://doi.org/10.4324/9781003117452">https://doi.org/10.4324/9781003117452
- Pepkin, K. L. (2004). Creative problem solving in math.Tersedia. http://hti. math. uh. edu/curriculum/units/2000/02/00.02,4.
- Pulles, S., & Burns, M. (2022). Alignment of K-8 mathematics interventions with strands of mathematical proficiency in meta-ana-lytic research. Psychology in the Schools, 59(6), 1192-1208. https://doi.org/10.1002/pits.22676">https://doi.org/10.1002/pits.22676">https://doi.org/10.1002/pits.22676
- Saldaña, J. (2021). Coding techniques for quan-titative and mixed data.The Routledge re-viewer’s guide to mixed methods analysis, 151-160.
- Sams, N. L. (2021). Praxis Preparation for Pre-service Teachers: Using Online Tools to En-gage in Productive Struggle. University of Pittsburgh. https://www.proquest.com/open-view/aeb5690d73071af6b249540355450d4b/1?pq-origsite=gscholar&cbl=18750&diss=y">https://www.proquest.com/open-view/aeb5690d73071af6b249540355450d4b/1?pq-origsite=gscholar&cbl=18750&diss=y">https://www.proquest.com/open-view/aeb5690d73071af6b249540355450d4b/1?pq-origsite=gscholar&cbl=18750&diss=y
- Stanford, J. (2022). The Development of Adap-tive Reasoning in the Mathematics Class-room. Learning to Teach Language Arts, Mathematics, Science, and Social Studies Through Research and Practice, 11(1). https://openjournals.utoledo.edu/in-dex.php/learningtoteach/arti-cle/view/580">https://openjournals.utoledo.edu/in-dex.php/learningtoteach/arti-cle/view/580">https://openjournals.utoledo.edu/in-dex.php/learningtoteach/arti-cle/view/580
- Tursynkulova, E., Madiyarov, N., Sultanbek, T., & Duysebayeva, P. (2023). The effect of problem-based learning on cognitive skills in solving geometric construction problems: a case study in Kazakhstan. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1284305">https://doi.org/10.3389/feduc.2023.1284305">https://doi.org/10.3389/feduc.2023.1284305
- Usman, A. I. (2020). Mathematical proficiency of pre-service secondary school teachers in triangle trigonometry in Nigeria.Asia Mathematika,4(1), 26-36.
- Warshauer, H. K. (2015). Productive struggle in middle school mathematics class-rooms.Journal of Mathematics Teacher Education,18, 375-400. https://doi.org/10.1007/s10857-014-9286-3">https://doi.org/10.1007/s10857-014-9286-3">https://doi.org/10.1007/s10857-014-9286-3
- White, H., & S. Sabarwal. (2014). Quasi-experi-mental Design and Methods. Methodologi-cal Briefs: Impact Evaluation 8, UNICEF Of-fice of Research, Florence. https://www.betterevalua-tion.org/sites/default/files/Quasi-Exper-imental_Design_and_Methods_ENG.pdf">https://www.betterevalua-tion.org/sites/default/files/Quasi-Exper-imental_Design_and_Methods_ENG.pdf">https://www.betterevalua-tion.org/sites/default/files/Quasi-Exper-imental_Design_and_Methods_ENG.pdf
- Widya, W., Nurpatri, Y., Indrawati, E. S., & Ikhwan, K. (2020). Development and Ap-plication of Creative Problem solving in Mathematics and Science: a literature re-view. Indonesian Journal of Science and Mathematics Education, 3(1), 106–116. https://doi.org/10.24042/ijsme.v3i1.4335">https://doi.org/10.24042/ijsme.v3i1.4335">https://doi.org/10.24042/ijsme.v3i1.4335
- Zebua, S., & Waruwu, E. (2022). Students' Math-ematical Procedural Fluency Based on Self-regulated learning.Journal of Innova-tion and Research in Primary Educa-tion,1(2), 56-62. https://doi.org/10.56916/jirpe.v1i2.179">https://doi.org/10.56916/jirpe.v1i2.179">https://doi.org/10.56916/jirpe.v1i2.179