HOME | Journal Archives | About | For Contributors | E-submission |

Sorry.

You are not permitted to access the full text of articles.

If you have any questions about permissions,

please contact the Society.

죄송합니다.

회원님은 논문 이용 권한이 없습니다.

권한 관련 문의는 학회로 부탁 드립니다.

Journal of Educational Research in Mathematics -
Vol. 31 ,
No. 1

[ Article ] | |

Journal of Educational Research in MathematicsVol. 30, No. 4, pp.625-648 | |

Abbreviation: JERM | |

ISSN: 2288-7733 (Print) 2288-8357 (Online) | |

Print publication date 30 Nov 2020 | |

Received 28 Sep 2020 Revised 05 Nov 2020 Accepted 05 Nov 2020 | |

DOI: https://doi.org/10.29275/jerm.2020.11.30.4.625 | |

An Analysis of Domestic and International Research Trends of Mathematical Reasoning through Topic Modeling | |

Hwang, JiNam ^{*} ; Pang, JeongSuk^{**}^{, †}
| |

*Graduate Student, Korea National University of Education, South Korea (whiyoung10@naver.com) | |

**Professor, Korea National University of Education, South Korea (jeongsuk@knue.ac.kr) | |

Correspondence to : ^{†}Professor, Korea National University of Education, South Korea, jeongsuk@knue.ac.kr | |

Abstract

In order to understand the research trends in mathematical reasoning since 2000, this study analyzed 262 papers published in seven KCI journals and 381 papers published in five SSCI journals via topic modeling. The overall research topics were compared and contrasted between domestic journals and international journals. A more detailed analysis was conducted by considering different publication periods. The results showed that the main domestic research topics included, in order, geometry proof, mathematical justification, problem solving, pattern generalization, proportional reasoning, and statistical reasoning, whereas the main international research topics included, in order, proof and argument, teacher education, geometric reasoning, pattern generalization, problem solving, and statistical reasoning. The results of this study also showed that gifted students represented the most popular research target of domestic studies, while the process of mathematical reasoning was the main focus of international studies. This paper closes with implications on research targets including teachers, attention to the mathematical reasoning process, diversity of research topics, and new research topics that may guide future research on mathematical reasoning.

Keywords: mathematical reasoning, topic modeling, research trends |

References

1. |
An, S. Y., & Kim, G. Y. (2014). Exploring students' thinking in proof production in geometry. The Mathematical Education, 53(3), 383-397. |

2. |
Australian Curriculum, Assessment and Reporting Authority (2015). https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics |

3. |
Baccaglini-Frank, A. (2019). Dragging, instrumented abduction and evidence, in processes of conjecture generation in a dynamic geometry environment. ZDM, 51(5), 779-791. |

4. |
Barrett, J. E., Clements, D. H., Klanderman, D., Pennisi, S. J., & Polaki, M. V. (2006). Students' coordination of geometric reasoning and measuring strategies on a fixed perimeter task: Developing mathematical understanding of linear measurement. Journal for Research in Mathematics Education, 37(3), 187-221. |

5. |
Biehler, R., Frischemeier, D., & Podworny, S. (2018). Elementary preservice teachers' reasoning about statistical modeling in a civic statistics context. ZDM, 50(7), 1237-1251. |

6. |
Bjuland. R. (2012). The mediating role of a teacher's use of semiotic resources in pupils' early algebraic reasoning. ZDM, 44(5), 665-675. |

7. |
Blanton, M. L., & Kaput, J. J. (2005). Helping elementary teachers build mathematical generality into curriculum and instruction. ZDM, 37(1), 34-42. |

8. |
Blei, D. M. (2012). Probabilistic topic models. Communications of the ACM, 55(4), 77-84. |

9. |
Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent dirichlet allocation. Journal of Machine Learning Research, 3, 993-1022. |

10. |
Brousseau, G., & Gibel, P. (2005). Didactical handling of students' reasoning processes in problem solving situations. Educational Studies in Mathematics, 59(1-3), 13-58. |

11. |
Byun, G. M., & Chang, K. Y. (2017). Seventh graders’ proof schemes and their characteristics in geometric tasks. Journal of Educational Research in Mathematics, 27(2), 191-205. |

12. |
Cho, W. Y., & Jung, B. N. (2003). An analysis of proof factors in the intuitive geometry for seventh grade. Communications of Mathematical Education, 15, 141-146. |

13. |
Choi, J. A., & Kwak, M. H. (2019). Topic changes in mathematics educational research based on LDA. Journal of Education & Culture, 25(5), 1149-1176. |

14. |
Common Core State Standards Initiative (2010). http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf. |

15. |
Conner, A. M., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Identifying kinds of reasoning in collective argumentation. Mathematical Thinking and Learning, 16(3), 181-200. |

16. |
Dvir, M., & Ben-Zvi, D. (2018). The role of model comparison in young learners' reasoning with statistical models and modeling. ZDM, 50(7), 1183-1196. |

17. |
Ellis, A. B. (2007). Connections between generalizing and justifying: Students' reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194-229. |

18. |
Eom, S. Y., & Kwean, H. J. (2011). The analysis of 6th-grade elementary school student's proportional reasoning ability and strategy according to academic achievement. Communications of Mathematical Education, 25(3), 537-556. |

19. |
Ferrara, F., & Sinclair, N. (2016). An early algebra approach to pattern generalisation: Actualising the virtual through words, gestures and toilet paper. Educational Studies in Mathematics, 92(1), 1-19. |

20. |
Garfield, J., Le, L., Zieffler, A., & Ben-Zvi, D. (2015). Developing students' reasoning about samples and sampling variability as a path to expert statistical thinking. Educational Studies in Mathematics, 88(3), 327-342. |

21. |
Griffiths, T. L., & Steyvers, M. (2004). Finding scientific topics. Proceedings of the National Academy of Sciences, 101, 5228-5235. |

22. |
Günther, E., & Domahidi, E. (2017). What communication scholars write about: An analysis of 80 years of research in high-impact journals. International Journal of Communication, 11, 3051-3071. |

23. |
Hallowell, D. A., Okamoto, Y., Romo, L. F., & La Joy, J. R. (2015). First-graders’ spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM, 47(3), 363-375. |

24. |
Hilton, A., & Hilton, G. (2019). Primary school teachers implementing structured mathematics interventions to promote their mathematics knowledge for teaching proportional reasoning. Journal of Mathematics Teacher Education, 22(6), 545-574. |

25. |
Hong, C. H. (2003). Various proofs and educational applications of Pythagorean theorem. Communications of Mathematical Education, 15, 195-200. |

26. |
Hunt, J., & Silva, J. (2020). Emma's Negotiation of Number: Implicit Intensive Intervention. Journal for Research in Mathematics Education, 51(3), 334-360. |

27. |
Hwang, J. N. (2015). A study on the effective use of tangrams for the mathematical justification of the gifted elementary students. Journal of Elementary Mathematics Education in Korea, 19(4), 589-608. |

28. |
Jin, M. R., & Ko, H. K. (2019). Analysis of trends in mathematics education research using text mining. Communications of Mathematical Education, 33(3), 275-294. |

29. |
Jones, K. (2000). Providing a foundation for deductive reasoning: Students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1-3), 55-85. |

30. |
Kang, H. Y. (2007). Generalization and symbol expression through pattern research: Focusing on pictorial/geometric pattern. School Mathematics, 9(2), 313-326. |

31. |
Kang, Y. S., & Kim, M. J. (2013). High school students' reasoning characteristics in problem solving. Journal of the Korean School Mathematics Society, 16(1), 241-263. |

32. |
Kim, J. Y., & Park, M. G. (2011). An analysis of justification process in the proofs by mathematically gifted elementary students. Education of Primary School Mathematics, 14(1), 13-26. |

33. |
Kim, M. K., Heo, J. Y., Cho, M. K., & Park, Y. M. (2012). An analysis on the 4th graders' ill-structured problem solving and reasoning. The Mathematical Education, 51(2), 95-114. |

34. |
Kim, N. G., & Kim, E. S. (2009). A study on the 6th graders' learning algebra through generalization of mathematical patterns. Communications of Mathematical Education, 23(2), 399-428. |

35. |
Kim, S. J. (2003). A study on approaches to algebra focusing on patterns and generalization. School Mathematics, 5(3), 343-360. |

36. |
Kim, Y. K., & Pang, J. S. (2007). An investigation on 6th grade students' spatial sense and spatial reasoning. School Mathematics, 9(3), 353-373. |

37. |
Knipping, C. (2008). A method for revealing structures of argumentations in classroom proving processes. ZDM, 40(3), 427-441. |

38. |
Knuth, E. J. (2002). Teachers’ Conceptions of Proof in the Context of Secondary School Mathematics. Journal of Mathematics Teacher Education, 5(1), 61–88. |

39. |
Ko, E. S., & Lee, K. H. (2007). Analysis on elementary students' proportional thinking: A case study with two 6-graders. Journal of Educational Research in Mathematics, 17(4), 359-380. |

40. |
Kwon, J. R. (2020). International comparison of ways in which competencies is reflected in mathematics curriculum: Focused on France, Australia and British Columbia in Canada. Communications of Mathematical Education, 34(2), 135-160. |

41. |
Kwon, S. Y. (2003). A study on mathematical justification activities in elementary school. Education of Primary School Mathematics, 7(2), 85-99. |

42. |
Lannin, J. K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231-258. |

43. |
Lannin, J., Ellis, A. B., & Elliott, R. (2011). Developing essential understanding of mathematical reasoning for teaching mathematics in prekindergarten-grade 8. Reston, VA: National Council of Teachers of Mathematics. |

44. |
Lee, C. H., & Kim, B. M. (2004). Development and applications of mathematical proof learning-teaching methods: The generative-convergent model. School Mathematics, 6(1), 59-90. |

45. |
Lee, C. H., Kim, S. H., Kim, B. M., & Kim, K. Y. (2017). Math reasoning. Seoul: Kyowoo. |

46. |
Lee, E. J., & Park, M. S. (2019). Statistical reasoning of preservice elementary school teachers engaged in statistical problem solving: Focused on question posing stage. Education of Primary School Mathematics, 22(4), 205-221. |

47. |
Lee, J. H. (2011). Study on pre-service teacher' statistics reasoning ability. Journal of the Korean School Mathematics Society, 14(3), 295-323. |

48. |
Lee, J. Y., & Pang, J. S. (2019). A comparative analysis of fraction multiplication in Korean and Japanese elementary mathematics textbooks: Focused on quantitative reasoning. Journal of Educational Research in Mathematics, 29(4), 831-854. |

49. |
Lee, M. G., & Na, G. S. (2012). Examining the students' generalization method in relation with the forms of pattern: Focused on the 6th grade students. School Mathematics, 14(3), 357-375. |

50. |
Lee, M. H., & Kim, S. H. (2020). Analysis of abduction in mathematics problem posing and solving. Journal of Educational Research in Mathematics, 30(1), 89-110. |

51. |
Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM, 49(6), 937-949. |

52. |
Maier, D. et al. (2018). Applying LDA topic modeling in communication research: Toward a valid and reliable methodology. Communication Methods and Measures, 12(2-3), 93-118. |

53. |
Mariotti, M. A., & Pedemonte, B. (2019). Intuition and proof in the solution of conjecturing problems. ZDM, 51(5), 759-777. |

54. |
Mata-Pereira, J., & Da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169-186. |

55. |
Mejia-Ramos, J. P., & Weber, K. (2014). Why and how mathematicians read proofs: Further evidence from a survey study. Educational Studies in Mathematics, 85(2), 161-173. |

56. |
Ministry of Education. (2015). Mathematics curriculum. Notification of the Ministry of Education No. 2015-74. [Vol. 8]. |

57. |
Mkhatshwa, T. P. (2020). Calculus students' quantitative reasoning in the context of solving related rates of change problems. Mathematical Thinking and Learning, 22(2), 139-161. |

58. |
Mouhayar, R. E. (2018). Trends of progression of student level of reasoning and generalization in numerical and figural reasoning approaches in pattern generalization. Educational Studies in Mathematics, 99(1), 89-107. |

59. |
Na, G. S. (2009). Teaching geometry proof with focus on the analysis. Journal of Educational Research in Mathematics, 19(2), 185-206. |

60. |
Nathan, M. J., & Kim, S. (2007). Pattern generalization with graphs and words: A cross-sectional and longitudinal analysis of middle school students’ representational fluency. Mathematical Thinking and Learning, 9(3), 193-219. |

61. |
Obersteiner, A., Bernhard, M., & Reiss, K. (2015). Primary school children's strategies in solving contingency table problems: The role of intuition and inhibition. ZDM, 47(5), 825-836. |

62. |
Pang, J. S. et al. (2019). Domestic research trends of mathematics education: An analysis of journals published from 1963 to 2019. Journal of Educational Research in Mathematics, 29(4), 709-739. |

63. |
Park, J. H., & Lee, S. J. (2020). Relationship between proportional reasoning and covariational reasoning of 7th grade students. Journal of Educational Research in Mathematics, 30(2), 281-305. |

64. |
Park, J. Y., & Kim, S. J. (2016). An analysis on the proportional reasoning understanding of 6th graders of elementary school: Focusing to ‘comparison’ situations. Journal of Elementary Mathematics Education in Korea, 20(1), 105-129. |

65. |
Park, K. M. et al. (2015). 2015 revised national mathematics curriculum plan development study. Research Report BD15110001, Korea Foundation for the Advancement of Science & Creativity. |

66. |
Pfannkuch, M. (2011). The role of context in developing informal statistical inferential reasoning: A classroom study. Mathematical Thinking and Learning, 13(1-2), 27-46. |

67. |
Perkins, J. (2010). Python text processing with NLTK 2.0 cookbook. Packt Publishing. |

68. |
Powell, S. R., Berry, K. A., & Barnes, M. A. (2020). The role of pre-algebraic reasoning within a word-problem intervention for third-grade students with mathematics difficulty. ZDM, 52(1), 151-163. |

69. |
Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM, 40(1), 83-96. |

70. |
Reid, D. A., & Vallejo Vargas, E. A. (2019). Evidence and argument in a proof based teaching theory. ZDM, 51(5), 807-823. |

71. |
Russell, J. S. (1999). Mathematical reasoning in the elementary grades. In L. V. Stiff (Ed.), Developing mathematical reasoning in grades K-12 (1999 Yearbook, pp. 1-12). Reston, VA: National Council of Teachers of Mathematics. |

72. |
Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4-36. |

73. |
Shin, D. J. (2020). A comparative study of domestic and international research trends of mathematics education through topic modeling. The Mathematical Education, 59(1), 63-80. |

74. |
Son, J. W., & Crespo, S. (2009). Prospective teachers' reasoning and response to a student's non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235-261. |

75. |
Song, S. H., Heo, J. Y., & Yim, J. H. (2006). Analysis on the types of mathematically gifted students' justification on the tasks of figure division. Journal of Educational Research in Mathematics, 16(1), 79-94. |

76. |
Steele, M. D. (2005). Comparing knowledge bases and reasoning structures in discussions of mathematics and pedagogy. Journal of Mathematics Teacher Education, 8(4), 291-328. |

77. |
Stylianides, A. J., & Ball, D. L. (2008). Understanding and describing mathematical knowledge for teaching: Knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11(4), 307-332. |

78. |
Stylianides, G. J., Stylianides, A. J., & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 237-266). Reston, VA: National Council of Teachers of Mathematics. |

79. |
Warren, E., & Cooper, T. (2008). Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking. Educational Studies in Mathematics, 67(2), 171-185. |

80. |
Wilkerson, M. H., & Laina, V. (2018). Middle school students' reasoning about data and context through storytelling with repurposed local data. ZDM, 50(7), 1223-1235. |

81. |
Wilkie, K. J. (2014). Upper primary school teachers' mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17(5), 397-428. |

82. |
Yu, M. G., & Chang, H. W. (2017). Comparative analysis of generalization and justification of the mathematically gifted 6th graders by learning styles. Journal of Educational Research in Mathematics, 27(3), 391-410. |

Copyright ⓒ statement 2012, Korean Society of Educational Studies in Mathematics All Rights Reserved.

Submitting manuscripts for peer review as well as other correspondences can either be made via online by an email (ksesm@daum.net) or sending a mail at Secretariat of

Journal of Educational Research in Mathematics, #1305 Daewoo The'O Ville, 115 Hangang-daero, Yongsan-gu, Seoul, 04376, Republic of Korea (Tel: +82‐2‐797‐7780, Fax: +82‐2‐797‐7750).

Submitting manuscripts for peer review as well as other correspondences can either be made via online by an email (ksesm@daum.net) or sending a mail at Secretariat of

Journal of Educational Research in Mathematics, #1305 Daewoo The'O Ville, 115 Hangang-daero, Yongsan-gu, Seoul, 04376, Republic of Korea (Tel: +82‐2‐797‐7780, Fax: +82‐2‐797‐7750).