The Empowerment of Problem-Based Learning Models to Improve Students’ Quantitative Reasoning

Muhammad Muzaini(1), Muhammad Hasbi(2*), Ernawati Ernawati(3), Kristiawati Kristiawati(4)

(1) Universitas Muhammadiyah Makassar, Indonesia
(2) Institut Agama Islam As'Adiyah Sengkang, Indonesia
(3) Universitas Muhammadiyah Makassar, Indonesia
(4) Universitas Muhammadiyah Makassar, Indonesia
(*) Corresponding Author

Abstract


Quantitative reasoning has been highlighted as essential for middle-school student learning, particularly for themes that require students to make sense of relationships between quantities, according to a growing body of evidence. As a result, the current study adds to the body of literature that explores the growth of students' quantitative reasoning through teaching models. This study uses measuring tools such as a quantitative reasoning test and an observation sheet. The randomized pre-test–post-test control group design has been used in this investigation. The study included 95 second-year middle school students from Pangkep, Makassar, South Sulawesi, who were split into two groups: experimental and control. The N-gain index, which has high, medium, and low categories, was used to calculate the improvement of students' quantitative reasoning exam results. The finding of the data, 86.0 % of students in the experimental class increased their quantitative reasoning exam scores in the high category, while only 46.6% of students in the control class improved their quantitative reasoning exam scores. Students' quantitative reasoning improves substantially more when they utilize the problem-based learning models to learn about the linear program than when they use direct learning. As a result, students' quantitative reasoning can be improved by using problem-based learning models.

Keywords


Problem-Based Learning; Quantitative Reasoning; Linear Program

Full Text:

PDF

References


Abdullah, N. I., Tarmizi, R. A., & Abu, R. (2010). The Effects of Problem Based Learning on Mathematics Performance and Affective Attributes in Learning Statistics at Form Four Secondary Level. Procedia - Social and Behavioral Sciences, 8, 370–376. https://doi.org/10.1016/j.sbspro.2010.12.052

Ackerman, R., & Thompson, V. A. (2017). Meta-reasoning: Monitoring and control of thinking and reasoning. Trends in Cognitive Sciences, 21(8), 607–617. https://doi.org/10.1016/j.tics.2017.05.004

Ak?no?lu, O., & Tando?an, R. Ö. (2007). The Effects of Problem-Based Active Learning in Science Education on Students’ Academic Achievement, Attitude and Concept Learning. EURASIA Journal of Mathematics, Science and Technology Education, 3(1), 71–81. https://doi.org/10.12973/ejmste/75375

Bendall, R. C. A., Galpin, A., Marrow, L. P., & Cassidy, S. (2016). Cognitive Style: Time to Experiment. Frontiers in Psychology, 7, 1786. https://doi.org/10.3389/fpsyg.2016.01786

Brunner, M., Keller, U., Hornung, C., Reichert, M., & Martin, R. (2009). The cross-cultural generalizability of a new structural model of academic self-concepts. Learning and Individual Differences, 19(4), 387–403. https://doi.org/10.1016/j.lindif.2008.11.008

Carroll, J. B. (1992). Cognitive Abilities: the State of the Art. Psychological Science, 3(5), 266–271. https://doi.org/10.1111/j.1467-9280.1992.tb00669.x

Cassidy, S. (2004). Learning styles: An overview of theories, models, and measures. Educational Psychology, 24(4), 419–444. https://doi.org/10.1080/0144341042000228834

Choon-Eng Gwee, M. (2008). Globalization of Problem-based Learning (PBL): Cross-cultural Implications. The Kaohsiung Journal of Medical Sciences, 24(3), S14–S22. https://doi.org/10.1016/S1607-551X(08)70089-5

Davydov, V. V. (1995). The Influence of L. S. Vygotsky on Education Theory, Research, and Practice. Educational Researcher, 24(3), 12–21. https://doi.org/10.3102/0013189X024003012

Dwyer, C. A., Gallagher, A., Levin, J., & Morley, M. E. (2003). What is quantitative reasoning? Defining the construct for assessment purposes. ETS Research Report Series, 2003(2), i–48. https://doi.org/10.1002/j.2333-8504.2003.tb01922.x

Ellis, A., Özgür, Z., & Reiten, L. (2019). Teacher moves for supporting student reasoning. Mathematics Education Research Journal, 31(2), 107–132. https://doi.org/10.1007/s13394-018-0246-6

English, M. C., & Kitsantas, A. (2013). Supporting Student Self-Regulated Learning in Problem- and Project-Based Learning. Interdisciplinary Journal of Problem-Based Learning, 7(2), 127–150. https://doi.org/10.7771/1541-5015.1339

Eun, B. (2008). Making connections: Grounding professional development in the developmental theories of vygotsky. Teacher Educator, 43(2), 134–155. https://doi.org/10.1080/08878730701838934

Faradillah, A. (2018). Analysis of Mathematical Reasoning Ability of Pre-Service Mathematics Teachers in Solving Algebra Problem Based on Reflective and Impulsive Cognitive Style. Formatif: Jurnal Ilmiah Pendidikan MIPA, 8(2), 119–128.

https://doi.org/10.30998/formatif.v8i2.2333

Firman, H. (2016). Diagnosing weaknesses of indonesian students’ learning. In What Can PISA 2012 Data Tell Us? (pp. 63–80). Brill. https://brill.com/view/book/edcoll/9789463004688/BP000006.xml

Gaze, E. (2018). Quantitative Reasoning: A Guided Pathway from Two- to Four-Year Colleges. Numeracy, 11(1). https://doi.org/10.5038/1936-4660.11.1.1

Gredler, M. E. (2012). Understanding Vygotsky for the Classroom: Is It Too Late? Educational Psychology Review, 24(1), 113–131. https://doi.org/10.1007/s10648-011-9183-6

Hafiza, N., Usman, & Anwar. (2020). The quantitative reasoning ability of high school students. Journal of Physics: Conference Series, 1460(1), 012033. https://doi.org/10.1088/1742-6596/1460/1/012033

Hasanah, S. I., Tafrilyanto, C. F., & Aini, Y. (2019). Mathematical Reasoning: The characteristics of students’ mathematical abilities in problem solving. Journal of Physics: Conference Series, 1188(1), 012057. https://doi.org/10.1088/1742-6596/1188/1/012057

Hasbi, M., Lukito, A., & Sulaiman, R. (2019). Mathematical Connection Middle-School Students 8 th in Realistic Mathematics Education. Journal of Physics: Conference Series, 1417(1), 012047. https://doi.org/10.1088/1742-6596/1417/1/012047

Hasbi, Muhammad, Lukito, A., Sulaiman, R., & Muzaini, M. (2019). Improving the Mathematical Connection Ability of Middle-School Students through Realistic Mathematics Approach. Journal of Mathematical Pedagogy, 1(1), 37–46. https://journal.unesa.ac.id/index.php/JOMP/article/view/7147

Hmelo-Silver, C. E. (2004). Problem-Based Learning: What and How Do Students Learn? Educational Psychology Review, 16(3), 235–266. https://doi.org/10.1023/B:EDPR.0000034022.16470.f3

Hung, W. (2006). The 3C3R Model: A Conceptual Framework for Designing Problems in PBL. Interdisciplinary Journal of Problem-Based Learning, 1(1), 5–22. https://doi.org/10.7771/1541-5015.1006

Hung, W. (2011). Theory to reality: a few issues in implementing problem-based learning. Educational Technology Research and Development, 59(4), 529–552. https://doi.org/10.1007/s11423-011-9198-1

Jack, J. P., & Thompson, P. W. (2017). 4 Quantitative Reasoning and the Development of Algebraic Reasoning. In Algebra In The Early Grades (pp. 95–132). Routledge. https://doi.org/10.4324/9781315097435-5

Kabael, T., & Akin, A. (2018). Prospective middle-school mathematics teachers’ quantitative reasoning and their support for students’ quantitative reasoning. International Journal of Research in Education and Science, 4(1), 178–197. https://doi.org/10.21890/ijres.383126

Karim, N. (2007). Quantitative Reasoning Applications and Modelling in The Real World at Zayed University. Proceedings of the Ninth International Conference-The Mathematics Education into the 21st Century Project, 348–352.

Kelly, S., Rice, C., Wyatt, B., Ducking, J., & Denton, Z. (2015). Teacher Immediacy and Decreased Student Quantitative Reasoning Anxiety: The Mediating Effect of Perception. Communication Education, 64(2), 171–186. https://doi.org/10.1080/03634523.2015.1014383

Kim, K.-J., & Kee, C. (2013). Evaluation of an e-PBL model to promote individual reasoning. Medical Teacher, 35(3), e978–e983. https://doi.org/10.3109/0142159X.2012.717185

Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem Solving in Mathematics Education. Springer International Publishing. https://doi.org/10.1007/978-3-319-40730-2

Mann, L., Chang, R., Chandrasekaran, S., Coddington, A., Daniel, S., Cook, E., Crossin, E., Cosson, B., Turner, J., Mazzurco, A., Dohaney, J., O’Hanlon, T., Pickering, J., Walker, S., Maclean, F., & Smith, T. D. (2021). From problem-based learning to practice-based education: a framework for shaping future engineers. European Journal of Engineering Education, 46(1), 27–47. https://doi.org/10.1080/03043797.2019.1708867

McInerney, D. M. (2005). Educational psychology - Theory, research, and teaching: A 25-year retrospective. Educational Psychology, 25(6), 585–599. https://doi.org/10.1080/01443410500344670

McNeil, N. M., & Uttal, D. H. (2009). Rethinking the Use of Concrete Materials in Learning: Perspectives From Development and Education. Child Development Perspectives, 3(3), 137–139. https://doi.org/10.1111/j.1750-8606.2009.00093.x

Midgett, C. W., & Eddins, S. K. (2001). NCTM’s Principles and Standards for School Mathematics: Implications for Administrators. NASSP Bulletin, 85(623), 35–42. https://doi.org/10.1177/019263650108562305

Mkhatshwa, T. P. (2020). Calculus students’ quantitative reasoning in the context of solving related rates of change problems. Mathematical Thinking and Learning, 22(2), 139–161. https://doi.org/10.1080/10986065.2019.1658055

Moore, K. C. (2014). Quantitative Reasoning and the Sine Function: The Case of Zac. Journal for Research in Mathematics Education, 45(1), 102–138. https://doi.org/10.5951/jresematheduc.45.1.0102

Muzaini, M., Juniati, D., & Siswono, T. Y. E. (2019). Exploration of student’s quantitative reasoning in solving mathematical problem: case study of field-dependent cognitive style. Journal of Physics: Conference Series, 1157(3), 032093. IOP Publishing. https://doi.org/10.1088/1742-6596/1157/3/032093

NCTM. (2000). Principles and Standards for School Mathematics.

Nunes, T., Bryant, P., Evans, D., & Barros, R. (2015). Assessing Quantitative Reasoning in Young Children. Mathematical Thinking and Learning, 17(2–3), 178–196. https://doi.org/10.1080/10986065.2015.1016815

Ojose, B. (2008). Applying Piaget’s Theory of Cognitive Development to Mathematics Instruction. Mathematics Educator, 18(1), 26–30. https://tme.journals.libs.uga.edu/tme/article/view/1923

Pedersen, S., & Liu, M. (2002). The Transfer of Problem-Solving Skills from a Problem-Based Learning Environment. Journal of Research on Technology in Education, 35(2), 303–320. https://doi.org/10.1080/15391523.2002.10782388

Ramful, A., & Ho, S. Y. (2015). Quantitative reasoning in problem solving. Australian Primary Mathematics Classroom, 20(1), 15–19. https://doi.org/10.3316/INFORMIT.059052016332967

Saleh, M., Prahmana, R. C. I., Isa, M., & Murni, M. (2017). Improving the Reasoning Ability of Elementary School Student through the Indonesian Realistic Mathematics Education. Journal on Mathematics Education, 9(1), 41–53. https://doi.org/10.22342/jme.9.1.5049.41-54

Santos-Trigo, M. (2020). Encyclopedia of Mathematics Education (S. Lerman (ed.)). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0

Sari, Y., Sutrisno, S., & Sugiyanti, S. (2020). Experimentation of Problem Based Learning (PBL) Model on Student Learning Motivation and Achievement on Circle Material. Formatif: Jurnal Ilmiah Pendidikan MIPA, 9(4), 315–324. https://doi.org/10.30998/formatif.v9i4.3650

Sidenvall, J., Lithner, J., & Jäder, J. (2015). International Journal of Mathematical Students ’ reasoning in mathematics textbook task-solving. International Journal of Mathematical Education in Science and Technology, 46(4), 533–552. https://doi.org/10.1080/0020739X.2014.992986

Stanton, N. (1995). Human Cognitive Abilities: A Survey of Factor-Analytic Studies, by J. B. Carroll, Cambridge University Press, Cambridge (1993), pp. iv + 819, ISBN 0-521-38712-4. Ergonomics, 38(5), 1074–1074. https://doi.org/10.1080/00140139508925174

Stocker, J. D., Hughes, E. M., Wiesner, A., Woika, S., Parker, M., Cozad, L., & Morris, J. (2021). Investigating the Effects of a Fact Family Fluency Intervention on Math Facts Fluency and Quantitative Reasoning. Journal of Behavioral Education, Naep 2018. https://doi.org/10.1007/s10864-020-09422-1

Sumartini, T. S. (2015). Peningkatan kemampuan penalaran matematis siswa melalui pembelajaran berbasis masalah. Mosharafa: Jurnal Pendidikan Matematika, 4(1), 1–10. https://journal.institutpendidikan.ac.id/index.php/mosharafa/article/view/mv4n1_1/244

Syarifuddin, Nusantara, T., Qohar, A., & Muksar, M. (2019). The Identification Difficulty of Quantitative Reasoning Process toward the Calculus Students’ Covariation Problem. Journal of Physics: Conference Series, 1254(1), 012075. https://doi.org/10.1088/1742-6596/1254/1/012075

Tallman, M. A., & Frank, K. M. (2020). Angle measure, quantitative reasoning, and instructional coherence: an examination of the role of mathematical ways of thinking as a component of teachers’ knowledge base. Journal of Mathematics Teacher Education, 23(1), 69–95. https://doi.org/10.1007/s10857-018-9409-3

van der Vleuten, C. P. M., & Schuwirth, L. W. T. (2019). Assessment in the context of problem-based learning. Advances in Health Sciences Education, 24(5), 903–914. https://doi.org/10.1007/s10459-019-09909-1

Weber, E., Ellis, A., Kulow, T., & Ozgur, Z. (2014). Six principles for quantitative reasoning and modeling. The Mathematics Teacher, 108(1), 24–30. https://doi.org/10.5951/mathteacher.108.1.0024




DOI: http://dx.doi.org/10.30998/formatif.v12i1.8502

Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Formatif: Jurnal Ilmiah Pendidikan MIPA

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Publisher:
Institute for Research and Community Services
(LPPM) Universitas Indraprasta PGRI

Kampus A Building 3, 2nd Floor | Jl. Nangka No. 58 C (TB. Simatupang), Kel. Tanjung Barat, Kec. Jagakarsa, Jakarta Selatan 12530, Jakarta, Indonesia. 


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

View My Stats