Archives
Current issue
About
About us
Aims and Scope
Abstracting and Indexing
Editorial Office
Open Access Policy
Publication Ethics
Journal History
Publisher
Follow us: Twitter
Contact
For Authors
Editorial Policy
Peer Review Policy
Manuscript Preparation Guidelines
Copyright & Licencing
Publication Fees
Fee Waiver Policy for Doctoral Students
EJMSTE Language Editing Service
More
Statistics
Special Issues
Special Issue Announcements
Published Special Issues
LITERATURE REVIEW
35 years of fraction learning: Integrating systematic review and bibliometric analysis on a global scale
1
Faculty of Education, Universiti Kebangsaan Malaysia, Bangi, MALAYSIA
Online publication date: 2024-11-26
Publication date: 2024-12-01
EURASIA J. Math., Sci Tech. Ed 2024;20(12):em2543
KEYWORDS
ABSTRACT
Fraction learning is a fundamental yet challenging component of mathematical education, critical to students’ broader mathematical development. This study presents a comprehensive review of fraction learning research spanning the years 1989 to 2024, integrating a systematic literature review with bibliometric analysis to explore the evolution, trends and gaps in this domain. Utilizing data from the Web of Science database, we reviewed 725 articles, identifying key themes through co-citation analysis and categorizing the literature into three primary clusters: cognitive and conceptual understanding of fractions, developmental and educational aspects of fraction learning and teacher knowledge and its impact on mathematics teaching. Our findings reveal a shift from early research focused on conceptual foundations to more recent studies emphasizing educational interventions and teacher preparation. The analysis also highlights significant geographical imbalances, with most research originating from Western countries, particularly the USA. Despite advancements, critical gaps remain, particularly concerning the long-term retention of fraction knowledge and the effectiveness of adaptive learning strategies. This study underscores the importance of a multifaceted approach to improving fraction learning outcomes and calls for future research that addresses these gaps, particularly in diverse educational contexts. The findings provide valuable insights for educators, policymakers and researchers, guiding future efforts to enhance fraction education globally.
REFERENCES (126)
1.
Addington, S., Clemens, H., Howe, R., & Saul, M. (2000). Four reactions to principles and standards for school mathematics. Notices of the American Mathematical Society, 47(9), 1072-1079.
2.
Alshahri, A. (2020). The effectiveness of using the Dunn and Dunn model in teaching the unit of regular fractions for fifth-grade primary students in developing achievement and mathematical intuition skills. West East Journal of Social Sciences, 9(1), 23-42. https://doi.org/10.36739/wejss....
3.
Aria, M., & Cuccurullo, C. (2017). Bibliometrix: An R-tool for comprehensive science mapping analysis. Journal of Informetrics, 11(4), 959-975. https://doi.org/10.1016/j.joi.....
4.
Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455. https://doi.org/10.1016/j.jecp....
5.
Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Developmental Science, 17(5), 775-785. https://doi.org/10.1111/desc.1....
6.
Baker, H. K., Pandey, N., Kumar, S., & Haldar, A. (2020). A bibliometric analysis of board diversity: Current status, development, and future research directions. Journal of Business Research, 108, 232-246. https://doi.org/10.1016/j.jbus....
7.
Ball, D. L. (1990a). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144. https://doi.org/10.2307/749140.
8.
Ball, D. L. (1990b). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466. https://doi.org/10.1086/461626.
9.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/002248....
10.
Barbieri, C. A., Rodrigues, J., Dyson, N., & Jordan, N. C. (2020). Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. Journal of Educational Psychology, 112(3), 628-648. https://doi.org/10.1037/edu000....
11.
Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 296-333). Macmillan Publishing Co, Inc.
12.
Behr, M. J., Lesh, R., Post, T. R., & Silver, E. A. (1983). Rational number concepts. In R. Lesh, & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91-125). Academic Press.
13.
Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15(5), 323-341. https://doi.org/10.2307/748423.
14.
Blanco-Mesa, F., Merigó, J. M., & Gil-Lafuente, A. M. (2017). Fuzzy decision making: A bibliometric-based review. Journal of Intelligent & Fuzzy Systems, 32(3), 2033-2050. https://doi.org/10.3233/JIFS-1....
15.
Booth, A., Sutton, A., & Papaioannou, D. (2016). Systematic approaches to a successful literature review (2nd ed.). SAGE.
16.
Booth, J. L., & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37(4), 247-253. https://doi.org/10.1016/j.cedp....
17.
Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23(3), 194-222. https://doi.org/10.2307/749118.
18.
Boyack, K. W., & Klavans, R. (2010). Co-citation analysis, bibliographic coupling, and direct citation: Which citation approach represents the research front most accurately? Journal of the American Society for Information Science and Technology, 61(12), 2389-2404. https://doi.org/10.1002/asi.21....
19.
Byrne, E. M., Jensen, H., Thomsen, B. S., & Ramchandani, P. G. (2023). Educational interventions involving physical manipulatives for improving children’s learning and development: A scoping review. Review of Education, 11(2), Article e3400. https://doi.org/10.1002/rev3.3....
20.
Chadegani, A. A., Salehi, H., Yunus, M. M., Farhadi, H., Fooladi, M., Farhadi, M., & Ebrahim, N. A. (2013). A comparison between two main academic literature collections: Web of Science and Scopus databases. Asian Social Science, 9(5), 18-26. https://doi.org/10.5539/ass.v9....
21.
Chang, C. C., & Silalahi, S. M. (2017). A review and content analysis of mathematics textbooks in educational research. Problems of Education in the 21st Century, 75(3), 235-251. https://doi.org/10.33225/pec/1....
22.
Common Core State Standards Initiative. (2010). Common core state standards for English language arts & literacy in history/social studies, science, and technical subjects. https://learning.ccsso.org/wp-....
23.
Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111-144. https://doi.org/10.2307/749646.
24.
Desimone, L. M., Smith, T. M., & Phillips, K. J. R. (2013). Linking student achievement growth to professional development participation and changes in instruction: A longitudinal study of elementary students and teachers in title I schools. Teachers College Record: The Voice of Scholarship in Education, 115(5), 1-46. https://doi.org/10.1177/016146....
25.
Dietrichson, J., Filges, T., Seerup, J. K., Klokker, R. H., Viinholt, B. C. A., Bøg, M., & Eiberg, M. (2021). Targeted school-based interventions for improving reading and mathematics for students with or at risk of academic difficulties in grades K-6: A systematic review. Campbell Systematic Reviews, 17(2), Article e1152. https://doi.org/10.1002/cl2.11....
26.
Donthu, N., Kumar, S., Mukherjee, D., Pandey, N., & Lim, W. M. (2021). How to conduct a bibliometric analysis: An overview and guidelines. Journal of Business Research, 133, 285-296. https://doi.org/10.1016/j.jbus....
27.
Ellegaard, O., & Wallin, J. A. (2015). The bibliometric analysis of scholarly production: How great is the impact? Scientometrics, 105(3), 1809-1831. https://doi.org/10.1007/s11192....
28.
Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education: Development status and directions. ZDM, 45(5), 633-646. https://doi.org/10.1007/s11858....
29.
Faulkner, G., Fagan, M. J., & Lee, J. (2022). Umbrella reviews (systematic review of reviews). International Review of Sport and Exercise Psychology, 15(1), 73-90. https://doi.org/10.1080/175098....
30.
Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17. https://doi.org/10.2307/748969.
31.
Fuchs, L. S., Fuchs, D., & Compton, D. L. (2013). Intervention effects for students with comorbid forms of learning disability. Journal of Learning Disabilities, 46(6), 534-548. https://doi.org/10.1177/002221....
32.
Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Jordan, N. C., Siegler, R., Gersten, R., Changas, P., & Cirino, P. T. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology, 105(3), 683-700. https://doi.org/10.1037/a00324....
33.
Fuchs, L. S., Schumacher, R. F., Sterba, S. K., Long, J., Namkung, J., Malone, A., Hamlett, C. L., Jordan, N. C., Gersten, R., Siegler, R. S., & Changas, P. (2014). Does working memory moderate the effects of fraction intervention? An aptitude-treatment interaction. Journal of Educational Psychology, 106(2), 499-514. https://doi.org/10.1037/a00343....
34.
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 293-304. https://doi.org/10.1177/002221....
35.
Gesuelli, K.-A., & Jordan, N. C. (2024). Fraction arithmetic development: An examination of students’ patterns of growth and errors across the intermediate grades. Journal of Educational Psychology, 116(3), 377-395. https://doi.org/10.1037/edu000....
36.
Good, T. L., Wood, M. B., Sabers, D., Olson, A. M., Lavigne, A. L., Sun, H., & Kalinec-Craig, C. (2013). Strengthening grade 3-5 students’ foundational knowledge of rational numbers. Teachers College Record: The Voice of Scholarship in Education, 115(7), 1-45. https://doi.org/10.1177/016146....
37.
Gough, D., Oliver, S., & Thomas, J. (2017). An introduction systematic reviews (2nd ed.). SAGE. https://doi.org/10.53841/bpspt....
38.
Hasumi, T., & Chiu, M.-S. (2022). Online mathematics education as bio-eco-techno process: Bibliometric analysis using co-authorship and bibliographic coupling. Scientometrics, 127(8), 4631-4654. https://doi.org/10.1007/s11192....
39.
Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843-859. https://doi.org/10.1037/a00198....
40.
Hecht, S. A., Close, L., & Santisi, M. (2003). Sources of individual differences in fraction skills. Journal of Experimental Child Psychology, 86(4), 277-302. https://doi.org/10.1016/j.jecp....
41.
Hiebert, J. (1999). Relationships between research and the NCTM standards. Journal for Research in Mathematics Education, 30(1), 3-19. https://doi.org/10.2307/749627.
42.
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400. https://doi.org/10.5951/jresem....
43.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406. https://doi.org/10.3102/000283....
44.
Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143. https://doi.org/10.1080/073700....
45.
Izsák, A., Jacobson, E., & Bradshaw, L. (2019). Surveying middle-grades teachers’ reasoning about fraction arithmetic in terms of measured quantities. Journal for Research in Mathematics Education, 50(2), 156-209. https://doi.org/10.5951/jresem....
46.
Jordan, N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45-58. https://doi.org/10.1016/j.jecp....
47.
Just, J., & Siller, H.-S. (2022). The role of mathematics in STEM secondary classrooms: A systematic literature review. Education Sciences, 12(9), Article 629. https://doi.org/10.3390/educsc....
48.
Kalra, P. B., Hubbard, E. M., & Matthews, P. G. (2020). Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children. Contemporary Educational Psychology, 62, Article 101896. https://doi.org/10.1016/j.cedp....
49.
Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Elementary School Journal, 102(1), 59-80. https://doi.org/10.1086/499693.
50.
Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. A. Lesh, & D. A. Bradbard (Eds.), Number and measurement. Papers from a research workshop (pp. 101-144). Information Reference Center.
51.
Kim, S. A., Bryant, D. P., Bryant, B. R., Shin, M., & Ok, M. W. (2023). A multilevel meta-analysis of whole number computation interventions for students with learning disabilities. Remedial and Special Education, 44(4), 332-347. https://doi.org/10.1177/074193....
52.
Kiuhara, S. A., Gillespie Rouse, A., Dai, T., Witzel, B. S., Morphy, P., & Unker, B. (2020). Constructing written arguments to develop fraction knowledge. Journal of Educational Psychology, 112(3), 584-607. https://doi.org/10.1037/edu000....
53.
Knoll, J., & Matthes, J. (2017). The effectiveness of celebrity endorsements: A meta-analysis. Journal of the Academy of Marketing Science, 45(1), 55-75. https://doi.org/10.1007/s11747....
54.
Koellner, K., Jacobs, J., Borko, H., Schneider, C., Pittman, M. E., Eiteljorg, E., Bunning, K., & Frykholm, J. (2007). The problem-solving cycle: A model to support the development of teachers’ professional knowledge. Mathematical Thinking and Learning, 9(3), 273-303. https://doi.org/10.1080/109860....
55.
Korom, P. (2019). A bibliometric visualization of the economics and sociology of wealth inequality: A world apart? Scientometrics, 118(3), 849-868. https://doi.org/10.1007/s11192....
56.
Kumar, S., Tomar, S., & Verma, D. (2019). Women’s financial planning for retirement. International Journal of Bank Marketing, 37(1), 120-141. https://doi.org/10.1108/IJBM-0....
57.
Lamon, S. J. (2001). Presenting and representing from fractions to rational numbers. In A. C. Albert (Ed.), The role of representation in school mathematics (pp. 146-165). NCTM.
58.
Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 629-668). Information Age Publishing.
59.
Lee, H. J., & Boyadzhiev, I. (2020). Underprepared college students’ understanding of and misconceptions with fractions. International Electronic Journal of Mathematics Education, 15(3), Article em0583. https://doi.org/10.29333/iejme....
60.
Lee, J., Bryant, D. P., & Bryant, B. R. (2023). The effect of a tier 2 multicomponent fraction intervention for fifth graders struggling with fractions. Remedial and Special Education, 44(1), 28-42. https://doi.org/10.1177/074193....
61.
Lewis, C., & Perry, R. (2017). Lesson study to scale up research-based knowledge: A randomized, controlled trial of fractions learning. Journal for Research in Mathematics Education, 48(3), 261-299. https://doi.org/10.5951/jresem....
62.
Leydesdorff, L., & Rafols, I. (2009). A global map of science based on the ISI subject categories. Journal of the American Society for Information Science and Technology, 60(2), 348-362. https://doi.org/10.1002/asi.20....
63.
Leydesdorff, L., Bornmann, L., & Wagner, C. S. (2017). Generating clustered journal maps: An automated system for hierarchical classification. Scientometrics, 110(3), 1601-1614. https://doi.org/10.1007/s11192....
64.
Li, C., Wu, K., & Wu, J. (2017). A bibliometric analysis of research on haze during 2000-2016. Environmental Science and Pollution Research, 24(32), 24733-24742. https://doi.org/10.1007/s11356....
65.
Linnenluecke, M. K., Marrone, M., & Singh, A. K. (2020). Conducting systematic literature reviews and bibliometric analyses. Australian Journal of Management, 45(2), 175-194. https://doi.org/10.1177/031289....
66.
Lo, J.-J., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15(6), 481-500. https://doi.org/10.1007/s10857....
67.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teacher’s understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates. https://doi.org/10.4324/978141....
68.
Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21(1), 16-32. https://doi.org/10.2307/749454.
69.
Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441. https://doi.org/10.2307/749431.
70.
Martin, T., Petrick Smith, C., Forsgren, N., Aghababyan, A., Janisiewicz, P., & Baker, S. (2015). Learning fractions by splitting: Using learning analytics to illuminate the development of mathematical understanding. Journal of the Learning Sciences, 24(4), 593-637. https://doi.org/10.1080/105084....
71.
Mazzocco, M. M. M., & Devlin, K. T. (2008). Parts and ‘holes’: Gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11(5), 681-691. https://doi.org/10.1111/j.1467....
72.
Mazzocco, M. M. M., Devlin, K. T., & McKenney, S. J. (2008). Is it a fact? Timed arithmetic performance of children with mathematical learning disabilities (MLD) varies as a function of how MLD is defined. Developmental Neuropsychology, 33(3), 318-344. https://doi.org/10.1080/875656....
73.
Migliavaca, C. B., Stein, C., Colpani, V., Barker, T. H., Munn, Z., & Falavigna, M. (2020). How are systematic reviews of prevalence conducted? A methodological study. BMC Medical Research Methodology, 20(1), Article 96. https://doi.org/10.1186/s12874....
74.
Montserrat, Á. C., & Gorgorió, P. N. (2016). Conocimiento conceptual y procedimental en matemáticas: Su evolución tras décadas de investigación [Conceptual and procedural knowledge in mathematics: Its evolution after decades of research]. Revista de Educación, 374, 43-66. https://doi.org/10.4438/1988-5....
75.
Mora, L., Deakin, M., & Reid, A. (2019). Combining co-citation clustering and text-based analysis to reveal the main development paths of smart cities. Technological Forecasting and Social Change, 142, 56-69. https://doi.org/10.1016/j.tech....
76.
Moss, J., & Case, R. (1999). Developing children’s understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education, 30(2), 122-147. https://doi.org/10.2307/749607.
77.
Munn, Z., Pollock, D., Khalil, H., Alexander, L., Mclnerney, P., Godfrey, C. M., Peters, M., & Tricco, A. C. (2022). What are scoping reviews? Providing a formal definition of scoping reviews as a type of evidence synthesis. JBI Evidence Synthesis, 20(4), 950-952. https://doi.org/10.11124/JBIES....
78.
National Council of Teachers of Mathematics. (2000). Principles standards and for school mathematics. NCTM.
79.
National Mathematics Advisory Panel. (2008). The final report of the National Mathematics Advisory Panel 2008 U.S. Department of Education. https://files.eric.ed.gov/full....
80.
Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. https://doi.org/10.3102/000283....
81.
Ngu, B. H., & Phan, H. P. (2016). Unpacking the complexity of linear equations from a cognitive load theory perspective. Educational Psychology Review, 28(1), 95-118. https://doi.org/10.1007/s10648....
82.
Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52. https://doi.org/10.1207/s15326....
83.
Olijnyk, N. V. (2015). A quantitative examination of the intellectual profile and evolution of information security from 1965 to 2015. Scientometrics, 105(2), 883-904. https://doi.org/10.1007/s11192....
84.
Olive, J. (1999). From fractions to rational numbers of arithmetic: A reorganization hypothesis. Mathematical Thinking and Learning, 1(4), 279-314. https://doi.org/10.1207/s15327....
85.
Olive, J., Makar, K., Hoyos, V., Kor, L. K., Kosheleva, O., & Sträßer, R. (2010). Mathematical knowledge and practices resulting from access to digital technologies. In C. Hoyles, & J.-B. Lagrange (Eds.), Mathematics education and technology-rethinking the terrain (pp. 133-177). Springer. https://doi.org/10.1007/978-1-....
86.
Osana, H. P., & Pelczer, I. (2015). A review on problem posing in teacher education. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing (pp. 469-492). Springer. https://doi.org/10.1007/978-1-....
87.
Özkaya, A., & Karamık, G. (2022). A systematic review of experimental researches on the learning fields of numbers and operations in middle schools: The case of Turkey. Journal for Educators, Teachers and Trainers, 13(2), 190-206. https://doi.org/10.47750/jett.....
88.
Öztürk, O., Kocaman, R., & Kanbach, D. K. (2024). How to design bibliometric research: An overview and a framework proposal. Review of Managerial Science, 18, 3333-3361. https://doi.org/10.1007/s11846....
89.
Pilkington, A., & Fitzgerald, R. (2006). Operations management themes, concepts and relationships: A forward retrospective of IJOPM. International Journal of Operations & Production Management, 26(11), 1255-1275. https://doi.org/10.1108/014435....
90.
Pouta, M., Lehtinen, E., & Palonen, T. (2021). Student teachers’ and experienced teachers’ professional vision of students’ understanding of the rational number concept. Educational Psychology Review, 33(1), 109-128. https://doi.org/10.1007/s10648....
91.
Pramudiani, P., Herman, T., Turmudi, Dolk, M., & Doorman, M. (2022). How does a missing part become important for primary school students in understanding fractions? Journal on Mathematics Education, 13(4), 565-586. https://doi.org/10.22342/jme.v....
92.
Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20(1), 8-27. https://doi.org/10.2307/749095.
93.
Reyna, V. F., & Brainerd, C. J. (2008). Numeracy, ratio bias, and denominator neglect in judgments of risk and probability. Learning and Individual Differences, 18(1), 89-107. https://doi.org/10.1016/j.lind....
94.
Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587-597. https://doi.org/10.1007/s10648....
95.
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346-362. https://doi.org/10.1037/0022-0....
96.
Rodríguez-Martínez, J. A., González-Calero, J. A., del Olmo-Muñoz, J., Arnau, D., & Tirado-Olivares, S. (2023). Building personalised homework from a learning analytics based formative assessment: Effect on fifth-grade students’ understanding of fractions. British Journal of Educational Technology, 54(1), 76-97. https://doi.org/10.1111/bjet.1....
97.
Roesslein, R. I., & Codding, R. S. (2019). Fraction interventions for struggling elementary math learners: A review of the literature. Psychology in the Schools, 56(3), 413-432. https://doi.org/10.1002/pits.2....
98.
Rojo, M., King, S., Gersib, J., & Bryant, D. P. (2023). Rational number interventions for students with mathematics difficulties: A meta-analysis. Remedial and Special Education, 44(3), 225-238. https://doi.org/10.1177/074193....
99.
Schadl, C., & Ufer, S. (2023). Mathematical knowledge and skills as longitudinal predictors of fraction learning among sixth-grade students. Journal of Educational Psychology, 115(7), 985-1003. https://doi.org/10.1037/edu000....
100.
Schneider, M., Grabner, R. H., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359-372. https://doi.org/10.1037/a00138....
101.
Shin, M., & Bryant, D. P. (2015). Fraction interventions for students struggling to learn mathematics. Remedial and Special Education, 36(6), 374-387. https://doi.org/10.1177/074193....
102.
Shin, M., Ok, M. W., Choo, S., Hossain, G., Bryant, D. P., & Kang, E. (2023). A content analysis of research on technology use for teaching mathematics to students with disabilities: Word networks and topic modeling. International Journal of STEM Education, 10, Article 23. https://doi.org/10.1186/s40594....
103.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/001318....
104.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-23. https://doi.org/10.17763/haer.....
105.
Sidney, P. G., Thompson, C. A., & Opfer, J. E. (2019). Development of fraction understanding. In J. Dunlosky, & K. A. Rawson (Eds.), The Cambridge handbook of cognition and education (pp. 148-182). Cambridge University Press. https://doi.org/10.1017/978110....
106.
Siegler, R. S., & Pyke, A. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49(10), 1994-2004. https://doi.org/10.1037/a00312....
107.
Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691-697. https://doi.org/10.1177/095679....
108.
Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13-19. https://doi.org/10.1016/j.tics....
109.
Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296. https://doi.org/10.1016/j.cogp....
110.
Simon, M. A. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24(3), 233-254. https://doi.org/10.2307/749346.
111.
Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518. https://doi.org/10.1016/j.lear....
112.
Steffe, L. P. (2002). A new hypothesis concerning children’s fractional knowledge. The Journal of Mathematical Behavior, 20(3), 267-307. https://doi.org/10.1016/S0732-....
113.
Surwase, G., Sagar, A., Kademani, B. S., & Bhanumurthy, K. (2011). Co-citation analysis: An overview. In S. R. B. S. Kademani, & A. N. Bandi (Eds.), Beyond librarianship: Creativity, innovation and discovery (pp. 179-185). B.R. Publishing Corporation.
114.
Talan, G., & Sharma, G. D. (2019). Doing well by doing good: A systematic review and research agenda for sustainable investment. Sustainability, 11(2), Article 353. https://doi.org/10.3390/su1102....
115.
Thompson, P. W., & Saldanha, L. A. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 95-114). NCTM.
116.
Tian, J., & Siegler, R. S. (2018). Which type of rational numbers should students learn first? Educational Psychology Review, 30(2), 351-372. https://doi.org/10.1007/s10648....
117.
Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25. https://doi.org/10.2307/749817.
118.
Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175. https://doi.org/10.1016/j.tate....
119.
Tranfield, D., Denyer, D., & Smart, P. (2003). Towards a methodology for developing evidence-informed management knowledge by means of systematic review. British Journal of Management, 14(3), 207-222. https://doi.org/10.1111/1467-8....
120.
Trujillo, C. M., & Long, T. M. (2018). Document co-citation analysis to enhance transdisciplinary research. Science Advances, 4(1). https://doi.org/10.1126/sciadv....
121.
Tsay, M.-Y. (2009). Citation analysis of Ted Nelson’s works and his influence on hypertext concept. Scientometrics, 79(3), 451-472. https://doi.org/10.1007/s11192....
122.
Tzur, R. (1999). An integrated study of children’s construction of improper fractions and the teacher’s role in promoting that learning. Journal for Research in Mathematics Education, 30(4), 390-416. https://doi.org/10.2307/749707.
123.
Ubah, I. J. A. (2021). The impact of different approaches to the teaching of grade 5 fraction by three experienced teachers. South African Journal of Childhood Education, 11(1), Article a854. https://doi.org/10.4102/sajce.....
124.
Ustinov, A. V. (2015). Three-dimensional continued fractions and Kloosterman sums. Russian Mathematical Surveys, 70(3), 483-556. https://doi. org/10.1070/RM2015v070n03ABEH004953.
125.
van Eck, N. J., & Waltman, L. (2010). Software survey: VOSviewer, a computer program for bibliometric mapping. Scientometrics, 84(2), 523-538. https://doi.org/10.1007/s11192....
126.
Zupic, I., & Čater, T. (2015). Bibliometric methods in management and organization. Organizational Research Methods, 18(3), 429-472. https://doi.org/10.1177/109442....
Share
RELATED ARTICLE
| eISSN: | 1305-8223 |
| ISSN: | 1305-8215 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
