American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: https://www.sciepub.com/journal/education Editor-in-chief: Ratko Pavlović
Open Access
Journal Browser
Go
American Journal of Educational Research. 2024, 12(9), 376-390
DOI: 10.12691/education-12-9-6
Open AccessArticle

Investigating the Effects of Active Learning and Problem-based Learning Strategies on Students’ Poor Reasoning Skills in Understanding Mathematics Concepts across Four Different Schools’ Mathematics Classrooms in Kingston & St. Andrew, Jamaica

Conley Morris1, Dickisha Facey1, Jahmela Ogeare1, Selena Morris1 and Shaneille Samuels1,

1Mathematics Department, Shortwood Teachers’ College & University of Technology, St. Andrew, Jamaica

Pub. Date: September 29, 2024

Cite this paper:
Conley Morris, Dickisha Facey, Jahmela Ogeare, Selena Morris and Shaneille Samuels. Investigating the Effects of Active Learning and Problem-based Learning Strategies on Students’ Poor Reasoning Skills in Understanding Mathematics Concepts across Four Different Schools’ Mathematics Classrooms in Kingston & St. Andrew, Jamaica. American Journal of Educational Research. 2024; 12(9):376-390. doi: 10.12691/education-12-9-6

Abstract

This study investigated the effects of active learning (AL) and problem-based learning (PBL) strategies on students’ reasoning skills in understanding mathematics concepts across four different schools in Kingston & St. Andrew, Jamaica. The research was conducted as an action research using mixed methods in response to observed deficiencies in students’ reasoning abilities in mathematics classrooms, a critical component for success in the subject. The data were collected through focus group discussions, interviews, observational notes, and student questionnaires. The findings revealed that while AL and PBL strategies positively impacted students’ reasoning abilities and conceptual understanding, their effectiveness varied significantly across different school contexts. Key factors influencing these outcomes included the alignment of teaching methods with students’ prior knowledge, the flexibility of the curriculum, and the level of teacher preparedness. The study underscored the need for tailored implementation of these strategies, enhanced teacher training, and continuous curriculum revision to maximize the benefits of AL and PBL in mathematics education. The results contribute to a deeper understanding of how innovative teaching strategies can be adapted to improve students’ critical thinking and problem-solving skills in mathematics.

Keywords:
reasoning skills active learning problem-based learning mathematics education conceptual understanding

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Ministry of Education and Youth. "National Standards Curriculum: Pathways to Secondary Education." Government of Jamaica, 2017.
 
[2]  Zabit, M. N. "Problem-based learning on students’ critical thinking skills in teaching business education in Malaysia: A literature review". American Journal of Business Education, vol 3. No. 6, pp. 19-32, 2010.
 
[3]  Kanmani, S., and Nagarathinam, R. "Enhancing critical thinking skills through mathematical reasoning." International Journal of Pure and Applied Mathematics, 2018, vol. 119, no. 15, pp.1441-1450.
 
[4]  Zaini, S., Hassanah, N., and Ayca, C. "The Role of Comprehension in Mathematical Reasoning." International Journal of Mathematics Education, 2019.
 
[5]  Ali, R. "The impact of problem-based learning on students’ problem-solving skills in mathematics education." Journal of Educational Research and Practice, vol. 9, no. 3, 2019, pp. 234-245.
 
[6]  Tawfik, A. A., Reeves, T. D., Stitch, A. E., Gill, A., Hong, C., and Pfeiffer, V. “The role of problem-based learning in developing students’ problem-solving skills in higher education.” Interdisciplinary Journal of Problem-Based Learning, vol. 15, no. 1, 2021, pp. 1-20.
 
[7]  Generalao, B. L. “Developing mathematical reasoning and problem-solving skills among high school students. Journal of Mathematics Education, vol. 5, no. 2, pp. 45-48.
 
[8]  Alliance for Education Solution. "How to measure student engagement: What is the meaning of student engagement? Why is student engagement important?" Alliance for Education Solution (AES), 2024.
 
[9]  Drew, C. "The impact of active learning on student engagement and achievement in the classroom." Journal of Educational Innovation, vol. 18, no. 1, 2022, pp. 35-48.
 
[10]  Praveena, S. "Constructivist teaching and active learning: Enhancing student engagement in modern classrooms." International Journal of Educational Research, vol. 12, no. 4, 2020, pp. 112-125.
 
[11]  Wulandari, M., Amin, S. M., Irawan, E. B., and Masykuri, M. "Enhancing students’ reasoning skills through problem-solving-based mathematics learning." Journal of Educational Research and Practice, vol. 9, no. 2, 2019, pp. 77-85.
 
[12]  Brame, C. J. “Active learning.” Vanderbilt University Center for Teaching. 2016.
 
[13]  Berkeley Center for Teaching & Learning. “Active learning: Overview.” University of California, Berkeley. n.d.
 
[14]  McLeod, S. "'Piaget’s stages: 4 stages of cognitive development theory." Simple Psychology, 3 Nov. 2022, retrieved August 25, 2024, from https:// www. simplypsychology. org/ piaget.html#:~: text = The%20formal%20operational%20period% 20begins,capacity%20for% 20higher%2Dorder%20reasoning.
 
[15]  McLeod, S. "Lev Vygotsky’s sociocultural theory of cognitive development." Simple Psychology, 26 July 2023, retrieved August 25, 2024, from https://www.simplypsychology.org/vygotsky.html.
 
[16]  Boaler, J., Dieckmann, J., Perez-Nunez, G., Sun, K. L., and Williams, C. "Changing students’ minds and achievement in mathematics: The role of mindset and conceptual understanding." Journal of Educational Psychology, vol. 110, no. 5 2018, pp. 624-639.
 
[17]  Pedraza, J.M. “The role of teaching methods in the development of critical thinking in mathematics.” 2015.
 
[18]  Sweller, J. "Cognitive load during problem solving: Effects on learning." Cognitive Science, vol. 12, no. 2 1988, pp. 257-285.
 
[19]  Verywell Mind. "Cognitive development theory: How early education affects reasoning skills." Verywell Mind. 2020.
 
[20]  Miller, G. A. "The magical number seven, plus or minus two: Some limits on our capacity for processing information." Psychological Review, vol. 63, no. 2, 1956, pp. 81-97.
 
[21]  Flavell, J. H. “Metacognition and cognitive monitoring: A new era of cognitive-developmental inquiry.” American Psychologist, vol. 34, no. 510 1979, pp. 906-911.
 
[22]  Kania, R., Ward, E., and Black, J. “Understanding the role of prior knowledge in learning mathematics: Implications for teaching and curriculum design.” Mathematics Education Research Journal, vol. 35, no. 1, 2023, pp. 125-143.
 
[23]  Taylor, P. "Curriculum overload in mathematics education: Balancing content coverage with higher-order thinking." Journal of Curriculum Studies, vol. 53, no. 2, 2021, pp. 151-165.
 
[24]  Samuels, S. "An investigation into the effects of secondary mathematics trainee teachers’ use of mathematical language in reducing mathematical errors: a Jamaican context." International Journal of Science and Research (IJSR), vol. 12, no. 7, 15 July 2023, pp. 634-644.
 
[25]  Collins, A., Mattocks, A., Lewis, A., Samuels, S., Williams, T., King, M., Willis, S. "A Cross-Sectional Study Investigating the Effects of Learning-Based Activities, Algebra Tiles and Problem-Solving Techniques on Students’ Conceptual Understanding and Problem-Solving Skills in the Jamaican Classroom." American Journal of Educational Research, vol. 11, no. 7, 14 July 2023, pp. 440-456.
 
[26]  Hooda, M., Ayal, E., and Jonsson, L. "Pedagogical challenges in mathematical teaching." Educational Research Quarterly, 2018.
 
[27]  Hooda, K., Garg, S., and Singh, R. "The role of pedagogical practices in shaping mathematical reasoning: A review." Journal of Educational Research, vol. 111, no. 6, 2018, pp. 829-844.
 
[28]  Ayal, N., Hertzog, C., and Korkmaz, M. "Developing critical thinking and problem-solving skills through active learning." Journal of Educational Psychology, vol. 108, no. 1, 2016, pp. 145-157.
 
[29]  Jonsson, A. "Fostering mathematical reasoning through inquiry-based learning: A systematic review." Proceedings of the Research in Mathematics Education, vol. 22, no. 3, 2020, pp. 199-211.
 
[30]  Jordan, N. C., Kaplan, D., Nabors Olah, L., and Hanich, L. "The role of socio-economic status and prior knowledge in mathematical reasoning.” Journal of Educational Psychology, vol. 102, no. 4, 2010, pp. 739-752.
 
[31]  Trowler, V. “Student engagement literature review.” Higher Education Academy, 2010.
 
[32]  Gafoor, K. A., and Kurukkan, A. "Student attitudes towards mathematics: An examination of factors affecting student perceptions and engagement." Educational Studies in Mathematics, vol. 89, no. 2, 2015, pp. 191-209.
 
[33]  National Academies of Sciences, Engineering, and Medicine. “Promoting Critical Thinking in STEM Education.” STEM Education Journal, 2016.
 
[34]  National Council of Teachers of Mathematics. "Principles and Standards for School Mathematics." NCTM, 2013.
 
[35]  Keengwe, J., Onchwari, G., and Agamba, J. J. "Promoting active learning through the integration of digital technologies in higher education." Journal of Information Technology Education: Innovations in Practice, vol. 13, 2014, pp. 73-84.
 
[36]  Buddo, C. "Mathematics education: A case for problem solving.” Jamaica Observer. 19 Feb. 2017, https:// www. jamaicaobserver.com/ 2017/02/19/mathematics-education-a-case-for-problem-solving/.
 
[37]  Attard, C., Berger, N., MacKenzie, E. “The positive influence of inquiry-based learning teacher professional learning and industry partnerships on student engagement with STEM.” Frontiers in Education, vol. 6, 2021.
 
[38]  Richards, T., and Samuels, S. “Exploring the efficacy of guided discovery learning in improving algebraic thinking skills.” International of Science and Research (IJSR), vol. 11, no. 7, pp. 1784-1792.