Systematic Reviews and Meta Analysis
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Mathematics Learning from Concrete to Abstract (1968-2021): A Bibliometric Analysis

Year 2022, Volume: 9 Issue: 4, 445 - 468, 01.07.2022
https://doi.org/10.17275/per.22.99.9.4

Abstract

Mathematics learning is illustrated as a developmental progression in the direction of concrete-to-abstract by educational theorists. Various studies rooted in this notion were conducted in the past. This study aimed to profile the landscape of research rooted in this notion which was published from 1968 to 2021. The bibliographic data of 425 related publications were retrieved from the Scopus database for bibliometric analysis. Descriptive analysis and regression analysis were performed to profile the publication trend. Then, author bibliographic coupling analysis was carried out to identify the domains of research related to mathematics learning from concrete to abstract. The findings show an increasing trend of publication following the exponential model. The research was clustered into five research domains: (i) ‘manipulatives and arithmetic learning’; (ii) ‘mathematics learning of students with learning disabilities’; (iii) ‘Concrete-Representational-Abstract sequence in elementary mathematics teaching’; (iv) ‘Ideal mathematics teaching’; and (v) ‘mathematics problem-solving and mathematics learning of students with autism spectrum disorder’. The two emergent research domains in this research area are (i) ‘mathematics learning of students with learning disabilities’; and (ii) ‘mathematics problem-solving and mathematics learning of students with autism spectrum disorder’, which have the highest proportion of publications since 2015. The findings of this study can help researchers to understand the current landscape of research with the notion of mathematics learning from concrete to abstract, and hence propose pathways for future research.

Supporting Institution

Ministry of Higher Education Malaysia

Project Number

Fundamental Research Grant Scheme with Project Code: FRGS/1/2019/SS109/USM/02/13

Thanks

Acknowledgement to “Ministry of Higher Education for Fundamental Research Grant Scheme with Project Code: FRGS/1/2019/SS109/USM/02/13”.

References

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Year 2022, Volume: 9 Issue: 4, 445 - 468, 01.07.2022
https://doi.org/10.17275/per.22.99.9.4

Abstract

Project Number

Fundamental Research Grant Scheme with Project Code: FRGS/1/2019/SS109/USM/02/13

References

  • Abdoulaye, F. A. Y. E. (2021). Analysis on Lower Graders' Mathematics Textbooks in Senegal, Japan and Singapore, in Application of Spiral Structure of Its Contents and Concrete, Pictorial and Abstract (CPA) Approach. NUE Journal of International Educational Cooperation, 14, 101-111.
  • Abejón, R., Pérez-Acebo, H., & Clavijo, L. (2018). Alternatives for chemical and biochemical lignin valorization: hot topics from a bibliometric analysis of the research published during the 2000–2016 period. Processes, 6(8), Article 98. https://doi.org/10.3390/pr6080098
  • Bassette, L., Bouck, E., Shurr, J., Park, J., & Cremeans, M. (2019). Comparison of concrete and app-based manipulatives to teach subtraction skills to elementary students with autism. Education and Training in Autism and Developmental Disabilities, 54(4), 391-405.
  • Bone, E. K., Bouck, E. C., & Smith III, J. P. (2021). Using the VA framework to teach algebra to middle school students with high-incidence disabilities. Journal of Special Education Technology, Advance online publication]. https://doi.org/10.1177/01626434211019388
  • Bouck, E. C., & Park, J. (2018). A systematic review of the literature on mathematics manipulatives to support students with disabilities. Education and Treatment of Children, 41(1), 65-106.
  • Bouck, E. C., & Park, J. (2020). App-based manipulatives and the system of least prompts to support acquisition, maintenance, and generalization of adding integers. Education and Training in Autism and Developmental Disabilities, 55(2), 158-172.
  • Bouck, E. C., & Sprick, J. (2019). The virtual-representational-abstract framework to support students with disabilities in mathematics. Intervention in School and Clinic, 54(3), 173-180.
  • Bouck, E. C., Anderson, R. D., Long, H., & Sprick, J. (2021). Manipulative-based instructional sequences in mathematics for students with disabilities. TEACHING Exceptional Children. [Advance online publication]. https://doi.org/10.1177/0040059921994599
  • Bouck, E. C., Bassette, L., Shurr, J., Park, J., Kerr, J., & Whorley, A. (2017a). Teaching equivalent fractions to secondary students with disabilities via the virtual–representational–abstract instructional sequence. Journal of Special Education Technology, 32(4), 220-231.
  • Bouck, E. C., Chamberlain, C., & Park, J. (2017b). Concrete and app-based manipulatives to support students with disabilities with subtraction. Education and Training in autism and Developmental Disabilities, 52(3), 317-331.
  • Bouck, E. C., Maher, C., Park, J., & Whorley, A. (2020a). Learning fractions with a virtual manipulative based graduated instructional sequence. Education and Training in Autism and Developmental Disabilities, 55(1), 45-59.
  • Bouck, E. C., Mathews, L. A., & Peltier, C. (2020b). Virtual manipulatives: A tool to support access and achievement with middle school students with disabilities. Journal of Special Education Technology, 35(1), 51-59.
  • Bouck, E. C., Park, J., Cwiakala, K., & Whorley, A. (2020c). Learning fraction concepts through the virtual-abstract instructional sequence. Journal of Behavioral Education, 29(3), 519-542.
  • Bouck, E. C., Park, J., Levy, K., Cwiakala, K., & Whorley, A. (2020d). App-based manipulatives and explicit instruction to support division with remainders. Exceptionality, 28(1), 45-59.
  • Bouck, E. C., Park, J., Satsangi, R., Cwiakala, K., & Levy, K. (2019). Using the virtual-abstract instructional sequence to support acquisition of algebra. Journal of Special Education Technology, 34(4), 253-268.
  • Bouck, E. C., Satsangi, R., & Park, J. (2018a). The concrete–representational–abstract approach for students with learning disabilities: An evidence-based practice synthesis. Remedial and Special Education, 39(4), 211-228.
  • Bouck, E. C., Shurr, J., Bassette, L., Park, J., & Whorley, A. (2018b). Adding it up: Comparing concrete and app-based manipulatives to support students with disabilities with adding fractions. Journal of Special Education Technology, 33(3), 194-206.
  • Bouck, E. C., Working, C., & Bone, E. (2018c). Manipulative apps to support students with disabilities in mathematics. Intervention in School and Clinic, 53(3), 177-182.
  • Braithwaite, D. W., Goldstone, R. L., van der Maas, H. L., & Landy, D. H. (2016). Non-formal mechanisms in mathematical cognitive development: The case of arithmetic. Cognition, 149, 40-55.
  • Bruner, J. S. (1966). Toward a theory of instruction (Vol. 59). Harvard University Press.
  • Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380-400.
  • Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179-202.
  • Chang, S. H., Lee, N. H., & Koay P. L. (2017). Teaching and learning with concrete-pictorial-abstract sequence: A proposed model. The Mathematics Educator, 17(1), 1-28.
  • Chen, X., Yu, G., Cheng, G., & Hao, T. (2019). Research topics, author profiles, and collaboration networks in the top-ranked journal on educational technology over the past 40 years: A bibliometric analysis. Journal of Computers in Education, 6(4), 563–585
  • 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.
  • Coles, A., & Sinclair, N. (2019). Re-thinking ‘concrete to abstract’in mathematics education: Towards the use of symbolically structured environments. Canadian Journal of Science, Mathematics and Technology Education, 19(4), 465-480.
  • Cramer, K., & Wyberg, T. (2009). Efficacy of different concrete models for teaching the part-whole construct for fractions. Mathematical thinking and learning, 11(4), 226-257.
  • Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H. C. (2015). Word problems: a review of linguistic and numerical factors contributing to their difficulty. Frontiers in psychology, 6, Article 348. https://doi.org/10.3389/fpsyg.2015.00348
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There are 92 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Research Articles
Authors

Huan Chın 0000-0003-0991-7299

Cheng Meng Chew 0000-0001-6533-8406

Menaga Suseelan This is me 0000-0002-9319-8284

Project Number Fundamental Research Grant Scheme with Project Code: FRGS/1/2019/SS109/USM/02/13
Publication Date July 1, 2022
Acceptance Date April 1, 2022
Published in Issue Year 2022 Volume: 9 Issue: 4

Cite

APA Chın, H., Chew, C. M., & Suseelan, M. (2022). Mathematics Learning from Concrete to Abstract (1968-2021): A Bibliometric Analysis. Participatory Educational Research, 9(4), 445-468. https://doi.org/10.17275/per.22.99.9.4