Effectiveness of Abstract – Visual – Concrete Approach in Enhancing Students’ Level of Conceptual Understanding and Mathematical Self-Efficacy
DOI:
https://doi.org/10.55927/ijcs.v1i12.11722Keywords:
Concrete, Abstract, Representations, Self-Efficacy, Conceptual UnderstandingAbstract
This study was designed to transform mathematics instruction into a more engaging and practical learning experience, emphasizing real-world applications. The primary objective was to enhance conceptual understanding and mathematical self-efficacy among Grade 11 senior high school students in Statistics and Probability during the 2021-2022 academic year's second quarter. The findings demonstrated that mathematical self-efficacy positively correlates with conceptual understanding, with high-efficacy students showing greater confidence and positive attitudes toward mathematics. The Abstract-Visual Representation-Concrete (A-V-C) instructional approach proved effective in teaching Pearson product moment correlation and regression analysis. This method progresses from abstract concepts through behavioral modeling to exploratory concrete experiences, enabling students to develop comprehensive understanding through structured, hands-on learning.
Downloads
References
Batanero, C., & Diaz, C. (2011). Training school teachers to teach probability: Reflections and challenges. Chilean Journal of Statistics. Retrieved December 2014 from: http://chjs.deuv.cl/iFirst_art/ChJS010202.pdf
Bennie, K., Hudson, K., & Newstead, K. (1999). Statistics Probability 2 Teachers Document. Mathematics Learning and Teaching Initiative, 1-26. Retrieved last January 9, 2015, from http://academic.sun.ac.za/mathed/MALATI/2Prob2.pdf
Bruner, J. S. (1960). "The growth of representational processes in childhood." In J. M. Anglin (Ed.), Beyond the information given: Studies in the psychology of knowing (pp. 313–324). New York, NY: Norton.
Carr, A., Jonassen, H., Lit Zinger, E., & Marra, M. (1998). Good news to foment educational revolution: The role of systematic change in advancing situated learning, constructivism, and feminist pedagogy. Journal of Educational Technology, 38(1), 5-15.
David, A. G. (2007). The Mathematics Performance of PAC College Freshmen as Influenced by Different Factors. (Master’s Thesis, Pampanga Agricultural College, Magalang, Pampanga.)
Definition of CRA: Retrieved October 15, 2014, from http://www.broward.k12.fl.us/studentsupport/ese/PDF/CRAApproachinMath.pdf
Definition of K to 12: Retrieved October 15, 2014, from http://www.deped.gov.ph/k-to-12/About/features
Definition of Spiral Curriculum: Retrieved October 15, 2014, from http://everydaymath.uchicago.edu/about/why-it-works/spiral/
Dizon, J. C. (2008). Performance of Grade Four Pupils of Arayat East District in the Division Achievement Test. (Master’s Thesis, Pampanga Agricultural College, Magalang, Pampanga.)
Encyclopedia Britannica. Definition of Mathematics. Retrieved January 29, 2015, from www.en.wikipedia.org
Flores, M. M. (2010). "Using the concrete-representational-abstract sequence to teach subtraction with regrouping to students at risk for failure." Remedial and Special Education, 31(3), 195-207. doi:10.1177/0741932508327467
Garfield, J., & Ahlgren, A. (1988). Difficulties in learning basic concepts in probability and statistics: Implications for research. Journal for Research in Mathematics Education, 19, 44-63.
Gomez, B. G. (2010). Predictors of Mathematics Ability of Fourth Year High School Students in Mabalacat, Pampanga. (Master’s Thesis, Pampanga Agricultural College, Magalang, Pampanga.)
Guzman, E. S. (2004). Difficulties Encountered by Freshman Students in College Algebra at Pampanga Agricultural College Magalang. (Master’s Thesis, Pampanga Agricultural College, Magalang, Pampanga.)
Hudson, P., Miller, S. P., & Butler, F. (2006). Adapting and merging explicit instruction within reform-based mathematics classrooms. American Secondary Education, 35(1), 19.
Hughes, E. M. (2011). "The Effects of the Concrete-Representational-Abstract Sequenced Instruction on Struggling Learners' Acquisition, Retention, and Self-efficacy of Fraction." (Dissertation) Graduate School of Clemson University.
Introduction to probability. Retrieved last January 10, 2015, from https://www.youtube.com/watch?v=-8eSOmTPUbk
Johnson, D. M. (1989). "Probability and Statistics." South-Western Publishing Co., Cincinnati, Ohio, 250-357.
Jordan, L., Miller, M., & Mercer, C. D. (1998). The effects of concrete to semi-concrete to abstract instruction in the acquisition and retention of fraction concepts and skills. Learning Disabilities: A Multidisciplinary Journal, 9, 115–122.
Kaput, J. (1992). "Technology and mathematics education." In D. A. Grouws (Ed.), Handbook of research on mathematics and teaching and learning (515-556). New York: Macmillan Publishing Company.
Keeler, C., & Steinhorst, K. (2001). A new approach to learning probability in the first statistics course. Journal of Statistics Education, 9(3).
Luke, J. (2012). "The Impact of Manipulatives on Students’ Performance on Money Word Problems." Georgia State University.
Mahanta, D. (2012). "Achievement in Mathematics: Effect of Gender and Positive/Negative Attitude of Students." Department of Mathematics, Nowgong Girls’ College, Nagaon (Assam).
Mathematics Learner’s Module 8. Department of Education, Bonifacio Building, DepEd Complex, Meralco Avenue, Pasig City, Philippines.
Medina, R. P. (2005). The Mathematics Readiness of Students in Taking General College Physics I at Negros Oriental State University. Retrieved February 25, 2015, from http://physics.msiit.edu.ph/spum/papers/
Misquitta, R. (2011). "Teaching Fractions to Middle-School Students Struggling in Mathematics: An Exploratory Study." (Doctoral Dissertation), University of Texas, USA.
Moore, D. S. (1997). Probability and Statistics in the Core Curriculum. Confronting the Core Curriculum, 93-98. Retrieved February 19, 2015, from http://www.stat.purdue.edu/~dsmoore/articles/StatInCore.pdf
National Council of Teachers of Mathematics. (1989). "Curriculum and Evaluation Standards for School Mathematics." Reston, VA: Author.
Pangan, G. L. (2010). Exploring the Use of the Concrete-Representational-Abstract Approach in Teaching Probability. (Master’s Thesis, Bulacan State University, Bulacan.)
Papaieronymou, I. (2009). Recommended Knowledge of Probability for Secondary Mathematics Teachers. Proceedings of CERME 6, Lyon, France.
Parreno, E., & Jimenez, R. (2006). Basic Statistics Worksheet. C & E Publishing, Inc., Quezon City, Philippines.
Pratt, D. (2011). Re-connecting probability and reasoning about data in secondary school teaching. 58th World Statistics Congress of the International Statistical Institute.
Quismundo, T. (2011). "2/3 of Philippine high schools obtain low NAT scores." Retrieved September 5, 2014, from http://newsinfo.inquirer.net/63039/23-of-philippines-high-schools-obtain-low-nat-scores.
Reston, E., & Bersales, L. G. (2011). Reform Efforts in Training Mathematics Teachers to Teach Statistics: Challenges and Prospects. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching Statistics in School Mathematics: Challenges for Teaching and Teacher Education: A Joint Study ICMI/IwASE Study Book. Heidelberg: Springer.
Reyes, J. D. (2019). Mathematics Anxiety and Self-Efficacy: A Phenomenological Dimension. Journal of Humanities and Education Development (JHED), 1(1), 22–34. Retrieved from https://mail.theshillonga.com/index.php/jhed/article/view/9/4.
Reyes, J. D. C. (2019). Team-Pair-Solo: An Experimental Approach in Teaching Random Variables and Discrete Probability Distributions. Journal of Humanities and Education Development (JHED), 1(1), 35-45. Retrieved from http://www.theshillonga.com/index.php/jhed/article/view/8.
Reyes, J. D. (2020). Effectiveness of Concrete-Representational-Abstract Sequence of Instruction in Probability on Select Groups of Eighth Graders. International Journal of Multidisciplinary Research and Growth Evaluation, 2(1), 438-443.
Reyes, J. D., Insorio, A. O., Ingreso, M. V., Holario, F. F., & Gutierres, C. R. (2019). Conception and Application of Contextualization in Mathematics Education. International Journal of Educational Studies in Mathematics, 6(1), 1-18. Retrieved from https://dergipark.org.tr/en/download/article-file/664590.
Ignacio Jr., A. G., & Reyes, J. D. (2017). Exploring Mathematics Achievement Goals Using Kolb’s Learning Style Model. Asia Pacific Journal of Multidisciplinary Research, 5(1), 19-24.
Shaughnessy, M. (1977). Misconceptions of Probability: An experiment with a small-group, activity-based, model-building approach to introductory probability at the college level. Educational Studies in Mathematics, 8, 295-316.
Special Connections. (2005). From Concrete to Representational to Abstract. Retrieved January 9, 2015, from http://www.specialconnections.ku.edu/cgi-bin/cgiwrap/specconn/main.php?cat=instruction&subsection=math/cra.
Throwing a Die/Dice. Retrieved last January 10, 2015, from https://www.youtube.com/watch?v=8ZsEYKN0ht8.
Tossing a Coin. Retrieved last January 10, 2015, from https://www.youtube.com/watch?v=JzN-GRSk8_4.
University of Kansas. Special Connections. Retrieved October 15, 2014, from http://www.specialconnections.ku.edu
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Joseph D. Reyes

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





















