Cultural Symbols Didactize Concreteness Fading in Basic Multiplication

Authors

  • Clement Ayarebilla Ali University of Education Winneba

DOI:

https://doi.org/10.37640/jim.v5i1.1954

Keywords:

Adinkra, Concreteness Fading, Multiplication, Quasi-Experimental Design

Abstract

The purpose of this study is to use cultural Adinkra artifacts to present “Concreteness Fading” in the basic multiplication of one-digit and one-digit numbers. Employing a quantitative approach, the researcher adopted a one-group pretest-posttest quasi-experimental design, and randomly selected 51 participants from 300 student teachers. Data collection involved two sets of tests, analyzed in two stages through task-based transcripts and paired-sample t-tests. The first stage analyzed the tasks the student teachers solved using “Concreteness Fading”. The results revealed smooth and joyful navigations of the stages of Concreteness Fading using the Adinkra symbols. The second stage analyzed the performance of the student teachers with t-test statistics to show significant differences between the control and experimental groups. The results of one sample t-test and paired samples t-test showed that student teachers solved more problems correctly using Concreteness Fading than the conventional concrete manipulatives. Following the findings, we concluded that heavy use of only concrete objects and examples without abstracting can be detrimental to teaching mathematics. We, therefore, recommended that student teachers should always avoid rushing to symbols and symbolic manipulations of mathematics but rather align their methods, techniques, and strategies in the transition through the three stages of Concreteness Fading.

References

Aduko, E. A., & Armah, R. B. (2022). Adapting Bruner’s 3-Tier Theory to Improve Teacher Trainees’ Conceptual Knowledge for Teaching Integers at the Basic School. European Journal of Mathematics and Science Education, 3(2), 61–77. https://doi.org/10.12973/ejmse.3.2.61

Ali, C. A., & Davis, E. K. (2016). Harnessing indigenous basket resources for national development: A long term prospects for mathematics education. In A. Seidu & S. Abazami (Eds.), Proceedings of the Applied Science Conference. University for Development Studies.

Ali, Clement Ayarebilla. (2019). Didactical conceptual structures in extending the triad to the tetrahedron exemplified in the teaching and learning of equations of the circle. University of Cape Coast.

Ali, Clement Ayarebilla. (2021). Ghanaian Indigenous Conception of Real Mathematics Education in Teaching and Learning of Mathematics. Indonesian Journal of Science and Mathematics Education, 4(1), 37–47. https://doi.org/10.24042/ijsme.v4i1.7382

Ali, Clement Ayarebilla. (2022). The didactical phenomenology in learning the circle equation. International Electronic Journal of Mathematics Education, 17(4), em0713. https://doi.org/10.29333/iejme/12472

Ali, Clement Ayarebilla, & Anderson, H. K. (2021). Pre-Service Teachers’ Pedagogical Content Knowledge In Transferring From Basic Musical Notations To Basic Fractions. Journal of STEM Education: Innovations and Research, 22(3), 27–32.

Ali, Clement Ayarebilla, & Davis, E. K. (2018). Harnessing Indigenous Basketry Resources for Prenumber and Early Number Work. Journal of Education and Learning, 7(2), 210–220.

Babbitt, W., Lachney, M., Bulley, E., & Eglash, R. (2015). Adinkra Mathematics: A study of Ethnocomputing in Ghana. Multidisciplinary Journal of Educational Research, 5(2), 110. https://doi.org/10.17583/remie.2015.1399

Bartolomei-Torres, P. (2022). Logical-Mathematical Intelligence: Definition, Characteristics, and Activities for its Development. Learningbp; Learningbp. https://www.learningbp.com/logical-mathematical-intelligence-definition-characteristics-activities-development/

Bhandari, P. (2020, May 1). Internal validity in research | definition, threats & examples. Scribbr. https://www.scribbr.com/methodology/internal-validity/

Bhattacherjee, A. (2023). Improving Internal and External Validity. In A. Bhattacherjee (Ed.), Social Science Research - Principles, Methods, and Practices. Global Text Project. https://socialsci.libretexts.org/Bookshelves/Social_Work_and_Human_Services/Social_Science_Research_-_Principles_Methods_and_Practices_(Bhattacherjee)/05%3A_Research_Design/5.02%3A_Improving_Internal_and_External_Validity

Boddy-Evans, A. (2020). The Origin and Meaning of Adinkra Symbols. ThoughtCo, 22. https://www.thoughtco.com/origin-and-meaning-of-adinkra-symbols-4058700

Bowen, J. (2021, June 17). Ask the Expert: How Can Teaching Math From a Strengths-based Perspective Help Students Succeed? College of Education News. https://ced.ncsu.edu/news/2021/06/17/ask-the-expert-how-can-teaching-math-from-a-strengths-based-perspective-help-students-succeed-when-teachers-utilize-a-students-strengths-they-position-them-as-already-possessing-a/

Brown, N. S. (2019, February 20). 4 ways to add up a love for math. ESchool News. https://www.eschoolnews.com/featured/2019/02/20/love-math/

Bruner, J. (1974). Toward a theory of instruction. Harvard University Press.

Ching, B. H.-H., & Wu, X. (2019). Concreteness fading fosters children’s understanding of the inversion concept in addition and subtraction. Learning and Instruction, 61, 148–159. https://doi.org/10.1016/j.learninstruc.2018.10.006

Creswell, J. W., & Creswell, J. D. (2018). Research design: Research of qualitative quantitative and mixed (5th ed.). SAGE Publications, Inc.

Dicken, L. (2023, October 22). How to Deal With a Fading Friendship. WikiHow. https://www.wikihow.com/Deal-With-a-Fading-Friendship

Donovan, A. M., & Fyfe, E. R. (2022). Connecting concrete objects and abstract symbols promotes children’s place value knowledge. Educational Psychology, 42(8), 1008–1026. https://doi.org/10.1080/01443410.2022.2077915

Douglas, H., Headley, M. G., Hadden, S., & LeFevre, J.-A. (2020). Knowledge of mathematical symbols goes beyond numbers. Journal of Numerical Cognition, 6(3), 322–354. https://doi.org/10.5964/jnc.v6i3.293

Efiabevi, E. (2013). Adinkra. Freedom Hall. https://freedomhallblog.wordpress.com/2013/04/30/524746_525071414223355_293027976_n-jpg/

Febriana, D. F., Amin, S. M., & Wijayanti, P. (2019). Concreteness fading process of elementary school students based on mathematical ability. Journal of Physics: Conference Series, 1157(4), 042049. https://doi.org/10.1088/1742-6596/1157/4/042049

Fyfe, E. R., McNeil, N. M., & Borjas, S. (2015). Benefits of “concreteness fading” for children’s mathematics understanding. Learning and Instruction, 35, 104–120. https://doi.org/10.1016/j.learninstruc.2014.10.004

Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness Fading in Mathematics and Science Instruction: a Systematic Review. Educational Psychology Review, 26(1), 9–25. https://doi.org/10.1007/s10648-014-9249-3

Fyfe, E. R., & Nathan, M. J. (2019). Making “concreteness fading” more concrete as a theory of instruction for promoting transfer. Educational Review, 71(4), 403–422. https://doi.org/10.1080/00131911.2018.1424116

Horn-Olivito, H., & Martinovic, D. (2017). Eastwood Whole School Inquiry on Concreteness Fading. Mathematics Knowledge Network.

Kim, H. (2020). Concreteness Fading Strategy: A Promising and Sustainable Instructional Model in Mathematics Classrooms. Sustainability, 12(6), 2211. https://doi.org/10.3390/su12062211

Kofi, E., Ayarebilla, C., & Darko, D. (2021). Effectiveness of Semiosis for Solving the Quadratic Equation. European Journal of Mathematics and Science Education, 6(1), 13–21. https://doi.org/10.12973/ejmse.2.1.13

Kokkonen, T., Lichtenberger, A., & Schalk, L. (2022). Concreteness fading in learning secondary school physics concepts. Learning and Instruction, 77, 101524. https://doi.org/10.1016/j.learninstruc.2021.101524

Kokkonen, T., & Schalk, L. (2021). One Instructional Sequence Fits all? A Conceptual Analysis of the Applicability of Concreteness Fading in Mathematics, Physics, Chemistry, and Biology Education. Educational Psychology Review, 33(3), 797–821. https://doi.org/10.1007/s10648-020-09581-7

Kuepper-Tetzel, C. (2018, February 1). Concreteness Fading: A Method To Achieve Transfer. The Learning Scientists. https://www.learningscientists.org/blog/2018/2/1-1

Kuwornu-Adjaottor, J. E. T., George, A., & Melvin, N. (2016). The philosophy behind some Adinkra symbols and their communicative values in Akan. Philosophical Papers and Review, 7(3), 22–33. https://doi.org/10.5897/PPR2015.0117

Logsdon, A. (2022, October 22). Logical-Mathematical Learning Style. Verywell Family. https://www.verywellfamily.com/mathematical-logical-learners-2162782

McNeil, N. M., & Fyfe, E. R. (2012). “Concreteness fading” promotes transfer of mathematical knowledge. Learning and Instruction, 22(6), 440–448. https://doi.org/10.1016/j.learninstruc.2012.05.001

Ministry of Education. (2019). New Curriculum for Upper Primary (Basic 4-6). National Council for Curriculum and Assessment (NaCCA).

Okyere, M. (2021). Culturally Responsive Teaching Through the Adinkra Symbols of Ghana and its Impact on Students’ Mathematics Proficiency [University of Alberta]. https://doi.org/10.7939/r3-a38y-wx79

Pearce, K., & Orr, J. (2018). Make math moments with the concreteness fading model. Make Math Moments. https://makemathmoments.com/concreteness-fading/

Pickering, N. (2022, January 18). Concrete Representational Abstract Sequence. Maneuvering the Middle. https://www.maneuveringthemiddle.com/difficult-math-concepts/

Suh, S., Lee, M., & Law, E. (2020). How do we design for concreteness fading? survey, general framework, and design dimensions. In E. Rubegni, A. Vasalou, N. Parés, & N. Sawhney (Eds.), Proceedings of the Interaction Design and Children Conference (pp. 581–588). Association for Computing Machinery. https://doi.org/10.1145/3392063.3394413

Downloads

Published

2024-05-27