Sistematik Derlemeler ve Meta Analiz
BibTex RIS Kaynak Göster

Mathematics Learning from Concrete to Abstract (1968-2021): A Bibliometric Analysis

Yıl 2022, Cilt: 9 Sayı: 4, 445 - 468, 01.07.2022
https://doi.org/10.17275/per.22.99.9.4

Öz

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.

Destekleyen Kurum

Ministry of Higher Education Malaysia

Proje Numarası

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

Teşekkür

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

Kaynakça

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  • 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
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  • 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.
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  • 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.
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  • 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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Yıl 2022, Cilt: 9 Sayı: 4, 445 - 468, 01.07.2022
https://doi.org/10.17275/per.22.99.9.4

Öz

Proje Numarası

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

Kaynakça

  • 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
  • Ding, M., & Li, X. (2014). Transition from concrete to abstract representations: The distributive property in a Chinese textbook series. Educational Studies in Mathematics, 87(1), 103-121.
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  • Gibbs, A. S., Hinton, V. M., & Flores, M. M. (2018). A case study using CRA to teach students with disabilities to count using flexible numbers: Applying skip counting to multiplication. Preventing School Failure: Alternative Education for Children and Youth, 62(1), 49-57.
  • Gökçe, S., & Guner, P. (2021). Forty years of mathematics education: 1980-2019. International Journal of Education in Mathematics, Science and Technology, 9(3), 514-539.
  • Gomez-Jauregui, V., Gomez-Jauregui, C., Manchado, C., & Otero, C. (2014). Information management and improvement of citation indices. International Journal of Information Management, 34(2), 257-271. http://doi.org/10.1016/j.ijinfomgt.2014.01.002 Greenes, C. (1995). Mathematics learning and knowing: A cognitive process. Journal of Education, 177(1), 85-106.
  • Gulkilik, H., Moyer-Packenham, P. S., Ugurlu, H. H., & Yuruk, N. (2020). Characterizing the growth of one student’s mathematical understanding in a multi-representational learning environment. The Journal of Mathematical Behavior, 58, Article 100756. https://doi.org/10.1016/j.jmathb.2020.100756
  • Gümüş, S., Gök, E., & Esen, M. (2020). A review of research on international student mobility: Science mapping the existing knowledge base. Journal of Studies in International Education, 24(5), 495-517. http://doi.org/10.1177/1028315319893651
  • Hinton, V. M., & Flores, M. M. (2019). The Effects of the Concrete-Representational-Abstract Sequence for Students at Risk for Mathematics Failure. Journal of Behavioral Education, 28(4), 493-516.
  • Hsieh, F. J., Wang, T. Y., & Chen, Q. (2018). Exploring profiles of ideal high school mathematical teaching behaviours: perceptions of in-service and pre-service teachers in Taiwan. Educational Studies, 44(4), 468-487.
  • Hsieh, F. J., Wang, T. Y., & Chen, Q. (2020). Ideal Mathematics Teaching Behaviors: A Comparison between the Perspectives of Senior High School Students and Their Teachers in Taiwan and Mainland China. Eurasia Journal of Mathematics, Science and Technology Education, 16(1), Article em1808. https://doi.org/10.29333/ejmste/110491
  • Kushairi, N., & Ahmi, A. (2021). Flipped classroom in the second decade of the Millenia: A bibliometrics analysis with Lotka’s law. Education and Information Technologies, 1–31.
  • Lafay, A., Osana, H. P., & Valat, M. (2019). Effects of interventions with manipulatives on immediate learning, maintenance, and transfer in children with mathematics learning disabilities: A systematic review. Education Research International, 2019, Article 2142948. https://doi.org/10.1155/2019/2142948
  • Leong, Y. H., Ho, W. K., & Cheng, L. P. (2015). Concrete-Pictorial-Abstract: Surveying its origins and charting its future. The Mathematics Educator, 16(1), 1-18.
  • Li, Y., & Schoenfeld, A. H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. International Journal of STEM Education, 6, Article 44. https://doi.org/10.1186/s40594-019-0197-9
  • Litster, K., Moyer-Packenham, P. S., & Reeder, R. (2019). Base-10 blocks: A study of iPad virtual manipulative affordances across primary-grade levels. Mathematics Education Research Journal, 31(3), 349-365.
  • Lommatsch, C. W., & Moyer-Packenham, P. S. (2020). Learning Logic: examining the effects of context ordering on reasoning about conditionals. International Journal of Mathematical Education in Science and Technology, 51(5), 730-753.
  • Long, H., Bouck, E., & Domka, A. (2021). Manipulating Algebra: Comparing Concrete and Virtual Algebra Tiles for Students with Intellectual and Developmental Disabilities. Exceptionality, 29(3), 197-214.
  • Mancl, D. B., Miller, S. P., & Kennedy, M. (2012). Using the concrete‐representational‐abstract sequence with integrated strategy instruction to teach subtraction with regrouping to students with learning disabilities. Learning Disabilities Research & Practice, 27(4), 152-166.
  • McNeil, N., & Jarvin, L. (2007). When theories don't add up: disentangling he manipulatives debate. Theory into practice, 46(4), 309-316.
  • Milton, J. H., Flores, M. M., Moore, A. J., Taylor, J. L. J., & Burton, M. E. (2019). Using the concrete–representational–abstract sequence to teach conceptual understanding of basic multiplication and division. Learning Disability Quarterly, 42(1), 32-45.
  • Moher, D., Liberati, A., Tetzlaff, J., Altman, D. G., & Prisma Group. (2009). Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement. PLoS medicine, 6(7), Article e1000097.
  • Mongeon, P., & Paul-Hus, A. (2016). The journal coverage of web of science and scopus: A comparative analysis. Scientometrics, 106(1), 213–228.
  • Moyer-Packenham, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in mathematics, 47(2), 175-197.
  • Moyer-Packenham, P. S., & Westenskow, A. (2013). Effects of virtual manipulatives on student achievement and mathematics learning. International Journal of Virtual and Personal Learning Environments, 4(3), 35-50.
  • Moyer-Packenham, P. S., & Westenskow, A. (2016). Revisiting the effects and affordances of virtual manipulatives for mathematics learning. In Utilizing virtual and personal learning environments for optimal learning (pp. 186-215). IGI Global.
  • Moyer-Packenham, P. S., Ulmer, L. A., & Anderson, K. L. (2012). Examining Pictorial Models and Virtual Manipulatives for Third-Grade Fraction Instruction. Journal of Interactive Online Learning, 11(3), 103-120.
  • O’Meara, N., Johnson, P., & Leavy, A. (2020). A comparative study investigating the use of manipulatives at the transition from primary to post-primary education. International Journal of Mathematical Education in Science and Technology, 51(6), 835-857.
  • Park, J., Bouck, E. C., & Fisher, M. H. (2021a). Using the virtual–representational–abstract with overlearning instructional sequence to students with disabilities in mathematics. The Journal of Special Education, 54(4), 228-238.
  • Park, J., Bryant, D. P., & Shin, M. (2021b). Effects of interventions using virtual manipulatives for students with learning disabilities: A synthesis of single-case research. Journal of Learning Disabilities, 8(4), 418-437.
  • Peltier, C., Morin, K. L., Bouck, E. C., Lingo, M. E., Pulos, J. M., Scheffler, F. A., ... & Deardorff, M. E. (2020). A meta-analysis of single-case research using mathematics manipulatives with students at risk or identified with a disability. The Journal of Special Education, 54(1), 3-15.
  • Piaget, J. (1952). Play, dreams and imitation in childhood. W W Norton & Co.
  • Ramirez, M. C., & Rodriguez Devesa, R. A. (2019). A scientometric look at mathematics education from Scopus database. The Mathematics Enthusiast, 16(1), 37-46.
  • Root, J. R., Browder, D. M., Saunders, A. F., & Lo, Y. Y. (2017). Schema-based instruction with concrete and virtual manipulatives to teach problem solving to students with autism. Remedial and Special Education, 38(1), 42-52.
  • Sanyal, D. K., Bhowmick, P. K., & Das, P. P. (2021). A review of author name disambiguation techniques for the PubMed bibliographic database. Journal of Information Science, 47(2), 227-254.
  • Satsangi, R., & Bouck, E. C. (2015). Using virtual manipulative instruction to teach the concepts of area and perimeter to secondary students with learning disabilities. Learning Disability Quarterly, 38(3), 174-186.
  • Satsangi, R., Bouck, E. C., Taber-Doughty, T., Bofferding, L., & Roberts, C. A. (2016). Comparing the effectiveness of virtual and concrete manipulatives to teach algebra to secondary students with learning disabilities. Learning Disability Quarterly, 39(4), 240-253.
  • Schiebel, E., Bianchi, D., & Vernes, A. (2017). A Bibliometric Framework to Identify and Delineate Subfields of Research on Tribological Wear. In M. Gäde, V. Trkulja, & V. Petras (Eds.), Everything Changes, Everything Stays the Same? Understanding Information Spaces. Proceedings of the 15th International Symposium of Information Science (ISI 2017) (pp. 192—202). Glückstadt: Verlag Werner Hülsbusch.
  • Sekeris, E., Empsen, M., Verschaffel, L., & Luwel, K. (2020). The development of computational estimation in the transition from informal to formal mathematics education. European Journal of Psychology of Education, 1-20. [Advance Online Publication] https://doi.org/10.1007/s10212-020-00507-z
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  • Spooner, F., Root, J. R., Saunders, A. F., & Browder, D. M. (2019). An updated evidence-based practice review on teaching mathematics to students with moderate and severe developmental disabilities. Remedial and Special Education, 40(3), 150-165.
  • Stroizer, S., Hinton, V., Flores, M., & Terry, L. (2015). An investigation of the effects of CRA instruction and students with autism spectrum disorder. Education and Training in Autism and Developmental Disabilities, 223-236.
  • Tucker, S. I., Lommatsch, C. W., Moyer-Packenham, P. S., Anderson-Pence, K. L., & Symanzik, J. (2017). Kindergarten Children's Interactions with Touchscreen Mathematics Virtual Manipulatives: An Innovative Mixed Methods Analysis. International Journal of Research in Education and Science, 3(2), 646-665.
  • Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal Of Applied Developmental Psychology, 18(1), 37-54.
  • Wang, T. Y., & Hsieh, F. J. (2017). Taiwanese high school students’ perspectives on effective mathematics teaching behaviors. Studies in Educational Evaluation, 55, 35-45.
  • Wang, T., & Cai, J. (2007). Chinese (Mainland) teachers’ views of effective mathematics teaching and learning. ZDM, 39(4), 287-300.
  • Westenskow, A., & Moyer-Packenham, P. S. (2016). Using an iceberg intervention model to understand equivalent fraction learning when students with mathematical learning difficulties use different manipulatives. International Journal for Technology in Mathematics Education, 23(2), 45-62.
  • Wong, N. Y. (2007). Hong Kong teachers’ views of effective mathematics teaching and learning. ZDM, 39(4), 301-314. Xin, Y. P. (2013). Conceptual model-based problem solving: Teach students with learning difficulties to solve math problems. Springer.
  • Yakubova, G., Hughes, E. M., & Baer, B. L. (2020). Supporting students with ASD in mathematics learning using video-based concrete-representational-abstract sequencing instruction. Preventing School Failure: Alternative Education for Children and Youth, 64(1), 12-18.
  • Zhao, D., & Strotmann, A. (2008). Author bibliographic coupling: Another approach to citation‐based author knowledge network analysis. Proceedings of the American Society for Information Science and Technology, 45(1), 1-10.
  • Zupic, I., & Čater, T. (2015). Bibliometric methods in management and organization. Organizational Research Methods, 18(3), 429-472. http://doi.org/10.1177/1094428114562629
Toplam 92 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Alan Eğitimleri
Bölüm Research Articles
Yazarlar

Huan Chın 0000-0003-0991-7299

Cheng Meng Chew 0000-0001-6533-8406

Menaga Suseelan Bu kişi benim 0000-0002-9319-8284

Proje Numarası Fundamental Research Grant Scheme with Project Code: FRGS/1/2019/SS109/USM/02/13
Yayımlanma Tarihi 1 Temmuz 2022
Kabul Tarihi 1 Nisan 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 9 Sayı: 4

Kaynak Göster

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