The Effect of Applying the PDCF Model on the Performance of the General Mathematical Problem-Solving

Subject Areas : International Journal of Mathematical Modelling & Computations

Farshid Mirshahi ¹ , Zahra Shokooh Ghazani ² , Ahmad Shahvorani Semnani ³

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Received: 2025-02-18 Accepted : 2025-05-10 Published : 2025-05-12

Keywords: Mathematics Education, Problem-Solving, Continuous Improvement Process,

Abstract :

Problem-solving is a primary and fundamental aspect of mathematics education and learning. Problem-solving can strengthen the connection between mathematics and other branches of science and has been a fundamental and often controversial topic of research for several decades. The present research aims to introduce the new PDCF model and examine its impact on improving the performance of general mathematics problem-solving among university students. The present research method is quasi-experimental. The target group for this purpose was the University students, who were randomly selected into two groups, including the experimental and the control groups. The proposed four-stage PDCF model was applied to the experimental group, but the control group was examined for general mathematics problem-solving performance without any educational intervention. The tools used included a researcher-made general mathematics test in three stages of the proposed model. Additionally, a researcher-made feedback form was provided after each test.The findings of the present research indicate that in the second cycle of the new PDCF model in the experimental group the average scores in the experimental group significantly increased compared to the control group, which did not undergo the model. Levene's test showed that at the beginning of the study and before any intervention, the two groups had equal variance. The results of the Shapiro-Wilk test indicated that the data had good normality. 

References:

[1] Alam El-Hadaei, Seyed Hassan, New Strategies in Mathematics Education, Shive Publishing House, 1st edition, (2013). [Persian]
[2] Alamian, Vahid and Mohseni, Gurban Ali. the effect of the control factor from Schoenfeld's point of view in reducing students' errors based on Newman's error analysis model in the subject of trigonometric ratios, Educational Innovations Quarterly, (2019), No. 79, p. 116– 97. [Persian]
[3] Saif, Ali Akbar 395. Modern Educational Psychology (Psychology of Learning and Education). Tehran: Duran Publications.
[4] Masaki Imai, Mohammad Hossein SalimiNemin, Kaizen: The Key to Japan's Competitive Success, Amirkabir University of Technology Publications, (2015). [Persian]
[5] Deming, W. E. Out of the Crisis (Massachusetts Institute of Technology, Center for Advanced Engineering Study, Cambridge, MA 02139, USA). (1986).
[6] Samadi, Masouma. Investigating the effect of teacher's written feedback in the classroom on self-efficacy and math problem solving of middle school girl students, New Educational Ideas, Al-Zahra Faculty of Educational Sciences, (2007) pp. 137-153. [Persian]
[7] Ions, A. enhancing learning through formative assessment and feedback.london:routldge. (2008).
[8] Epstein &Brosvic, Immediate feedback assessment Technique: multiple- choice test that behaves like an essay examination, Psychological reports, 90(1), (2004), 226.
[9]Skryzpek. Using Plan-Do-Study-Act Cycles and Interdisciplinary Conversations to Transform Introductory Mathematics Courses. (2009).
[10] Hassan, Z., & Hossain, M. S. Improvement of effectiveness by applying pdca cycle or kaizen: an experimental study on engineering students. Journal of Scientific Research, 10(2), (2018): 159-173.
[11] Roy Andersson. Continuous Quality Improvement in Higher Education A case study in Engineering School of Boras University,(2011).
[12]Logothetis, N. Towards a quality management of education. Total Quality Management, 6(5),(1995): 479-486.
[13] Darash, Nasreen;Shahi, Sakineh;Razavi, Seyyed Abbas. The effect of George Polya's method of math education on students' problem solving skills and math academic progress, Journal of Psychological Achievements (Educational Sciences and Psychology), ShahidChamran University, Ahvaz, 4th period, year 25, number 2, (2017): pp. 181-200.Persian.
[14] Johari, S. NorHasniza, I., &Mahani, M. Conceptual and Procedural Knowledge in Problem Solving. Procedia - Social and Behavioral Sciences, 56, (2012): 416 – 425.
[15]Caprioara, D. Problem solving - purpose and means of learning mathematics in school. Procedia - Social and Behavioral Sciences, 191, (2014):1859- 1864
[16]Ersoy, E., Guner, P. The place of problem solving and mathematical thinking the mathematical teaching. The Online Journal of New Horizons in Education, 5, (2015): 120- 130.
[17]Marchis, J. Z.Changing pre-service primary-school teachers’ attitude towards Mathematics by collaborative problem solving. Procedia- Social and Behavioral Sciences, 186, (2015): 174 – 182.
[18]Phonapichat, P., Wongwanich, S., &Sujiva, S. An analysis of elementary school students’ difficulties in mathematical problem solving.Procedia Social and Behavioral Science, 116, (2014): 3169 – 3174.
[19] Page, E.B. Teacher comments and student performances.jurnal of Educational Psychology, 49, (1958): 173-181.
[20]Mitrovica, A., Ohlsson, S., and Barrowa, K. D. The effect of positive feedback in constraint-based intelligent tutoring system. Computers & Education, 60, (2013): 246-272.
[21]Manouchehri,A&Goodman,T, Mathematical curriculum reform and teachers: Understanding the connections, Journal of educationalresearch,92(1), (1998): 27-41.
[22]Caprioara, D. Problem solving - purpose and means of learningmathematics in school. Procedia - Social and Behavioral Sciences, 191, (2014): 1859- 1864.
[23]Stamovlasis,D., &Tsaparlis, G. Cognitive variables in problemsolving: A nonlinear approach. International Journal of Science andMathematics Education, 3, (2005): 7–32.
[24]Phonapichat, P., Wongwanich, S., &Sujiva, S. An analysis of elementary school students’ difficulties in mathematical problem solving.Procedia Social and Behavioral Science, 116, (2014): 3169 – 3174.
[25]Ashmore, A., Frazer, M., &Cassey, R. Problem- solving andproblem-solving networks in chemistry. Journal of Chemical Education,56, (2007): 377– 379.
[26]Guasch, T., Espasa, A., &Kirschner, P. A. E-feedback focused on students discussion to guide collaborative writing in online learning environments. In Preparing Teachers to Teach Writing Using Technology, (2013):195-208
[27]Hattie, J & Timperley, H. The power of feedback, Review of education research, 77, (2007): 81-112.
[28] Carless, D. Salter, D., Yang, M., & Lam, J. Developing sustainable feedback practices. Journal of Studies in Higher Education,press.(2011).
[29]Butler, R., & Nisan, M. Effects of no feedback, task_related comments, and grades on intrinsik motivation and performane. Journal of Educational Psychology. 78 (3), (1986): 210-216.
[30]Montague, M. Solve It! A practical approach to teaching mathematicalproblem-solving skills, Reston, VA: Exceptional Innovations. (2003).