[논문]중학생들의 수학 흥미와 성취도의 종단적 변화에 따른 잠재집단 분류 및 영향요인 탐색: 다변량 성장혼합모형을 이용하여

김래영; 한수연

doi:10.7468/mathedu.2024.63.1.19

중학생들의 수학 흥미와 성취도의 종단적 변화에 따른 잠재집단 분류 및 영향요인 탐색: 다변량 성장혼합모형을 이용하여
Classification of latent classes and analysis of influencing factors on longitudinal changes in middle school students' mathematics interest and achievement: Using multivariate growth mixture model 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.63 no.1, 2024년, pp.19 - 33

김래영 (서울대학교) , 한수연 (한국교육과정평가원)

초록
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본 연구는 중학생들의 수학 흥미와 성취도의 종단적인 변화 양상을 알아보기 위해 경기교육종단연구 4-6차년도 데이터를 분석하였다. 다변량 성장혼합모형을 이용하여 분석한 결과 학생들의 수학 흥미와 성취도의 변화 양상에 이질적인 특성이 존재함을 확인하였고, 종단적인 변화 양상에 따라 학생들을 4개의 잠재집단으로 구분하였다. 학생들은 흥미와 성취도가 모두 낮은 저수준 유형, 모두 높은 고수준 유형, 학년이 올라감에 따라 증가하는 중수준-증가 유형, 학년이 올라감에 따라 감소하는 중수준-감소 유형으로 구분되었으며, 유형마다 흥미와 성취도의 종단적인 변화 양상이 다르게 나타나는 것을 확인하였다. 또한, 다변량 성장혼합모형의 초기값과 기울기 사이의 상관관계를 분석한 결과, 수학 흥미와 성취도는 초기값뿐 아니라 변화율에 있어서도 서로 긍정적인 영향이 있는 것으로 나타났다. 잠재집단의 결정에 영향을 미치는 요인을 개인, 수업방식, 가정 변인으로 나누어 그 영향력을 살펴보았고, 학생의 교육포부와 사교육 시간은 수학 흥미 및 성취도에 긍정적인 영향을 미치며 선행학습의 경우 그 정도에 따라 영향력이 달라지는 양상을 확인하였다. 학생이 인식한 수업방식의 경우, 교수자 중심 수업은 흥미와 성취도가 높은 집단에 속할 확률을 높이고, 학습자 중심 수업은 흥미와 성취도가 낮은 집단에 속할 확률을 높이는 것으로 나타났다. 본 연구는 다변량 성장혼합모형을 통해 수학교육에서 흥미와 성취도를 비롯한 다양한 특성에 대한 학생들의 변화 양상을 분석하는 새로운 방법을 제시하였다는 점에서 의의가 있다.

Abstract ▼ AI-Helper

This study investigates longitudinal patterns in middle school students' mathematics interest and achievement using panel data from the 4th to 6th year of the Gyeonggi Education Panel Study. Results from the multivariate growth mixture model confirmed the existence of heterogeneous characteristics in the longitudinal trajectory of students' mathematics interest and achievement. Students were classified into four latent classes: a low-level class with weak interest and achievement, a high-level class with strong interest and achievement, a middlelevel-increasing class where interest and achievement rise with grade, and a middle-level-decreasing class where interest and achievement decline with grade. Each class exhibited distinct patterns in the change of interest and achievement. Moreover, an examination of the correlation between intercepts and slopes in the multivariate growth mixture model reveals a positive association between interest and achievement with respect to their initial values and growth rates. We further explore predictive variables influencing latent class assignment. The results indicated that students' educational ambition and time spent on private education positively affect mathematics interest and achievement, and the influence of prior learning varies based on its intensity. The perceived instruction method significantly impacts latent class assignment: teacher-centered instruction increases the likelihood of belonging to higher-level classes, while learner-centered instruction increases the likelihood of belonging to lower-level classes. This study has significant implications as it presents a new method for analyzing the longitudinal patterns of students' characteristics in mathematics education through the application of the multivariate growth mixture model.

주제어

표/그림 (9)

표 Table 1. Questions used for math interest and achievement
표 Table 2. Questions for independent variables
그림 Figure 1. Structure of multivariate growth mixture model.
표 Table 3. Descriptive statistics for mathematics interest and achievement
표 Table 4. Descriptive statistics for independent variables
표 Table 5. Model comparison based on the number of latent classes
그림 Figure 2. Trajectories of mathematics interest and achievement for each class.
표 Table 6. Estimated correlation coefficients (standard error) of intercepts and slopes for mathematics interest and achievement
표 Table 7. Results of multinomial logistic regression analysis

참고문헌 (48)

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716-723. https://doi.org/10.1109/TAC.1974.1100705

상세보기
Chang, O. (2013). A study on the effect of the private in-advance learning in mathematics among humanities-orientedtrack high school students [Doctoral dissertation, Dankook University].
Cheong, M. J., Kim, H. K., & Moon, Y. H. (2015). The relationship between teaching methods accepted by learners and academic achievement factors on academic achievement. Korean Journal of Youth Studies, 22(7), 129-150.
Choe, S. H., Park, S., & Hwang, H. J. (2014). Analysis of the current situation of affective characteristics of Korean students based on the results of PISA and TIMSS. Journal of the Korean School Mathematics Society, 17(1), 23-43.
Choi, J. S. (2020). Theoretical conceptualizations of educational interest focused on mathematics learning. Journal of the Korean School Mathematics Society, 23(1), 1-23. http://doi.org/10.30807/ksms.2020.23.1.001

원문보기 상세보기
Choi, J. S., & Sang, K. A. (2019). The effects of educational context variables on achievement and interest in mathematics in high and low achieving students. Journal of the Korean School Mathematics Society, 22(2), 163-182. http://doi.org/10.30807/ksms.2019.22.2.004

원문보기 상세보기
Chung, H., Won, J., & Park, S. (2018). Classifying the academic achievements and core competencies of adolescents and testing the effects of variable factors. Studies on Korean Youth, 29(2), 185-215. http://doi.org/10.14816/sky.2018.29.2.185

상세보기
Chung, J. Y., Lee, H., & Kim, S. (2014). A hierarchical analysis of the factors influencing on student achievement - Using the teacher and student factors of TIMSS 2011. The Journal of Korean Teacher Education, 31(2), 53-75. http://doi.org/10.24211/tjkte.2014.31.2.53
Chung, Y. K., Lee, S. Y., Song, J. Y., & Woo, Y. K. (2017). Differential relations of students' perceived instructions to their motivation, classroom attitude, and academic achievement: The moderating role of self-efficacy. The Korean Journal of Educational Methodology Studies, 29(1), 211- 235. http://doi.org/10.17927/tkjems.2017.29.1.211

상세보기
Hallquist, M. N., & Wiley, J. F. (2018). MplusAutomation: An R package for facilitating large-scale latent variable analyses in Mplus. Structural Equation Modeling: A Multidisciplinary Journal, 25(4), 621-638. https://doi.org/10.1080/10705511.2017.1402334

상세보기
Hertzog, C., von Oertzen, T., Ghisletta, P., & Lindenberger, U. (2008). Evaluating the power of latent growth curve models to detect individual differences in change. Structural Equation Modeling: A Multidisciplinary Journal, 15(4), 541-563. https://doi.org/10.1080/10705510802338983

상세보기
Jang, J., & Ko, Y. (2020). Perception and characteristics of teachers and students on teaching methods: A latent profile analysis. The Korean Journal of Educational Methodology Studies, 32(4), 575-605.
Jang, J., & Park, I. (2019). Analysis of the actual status and effect of mathematics prerequisite learning of elementary, middle, and high school students in Gyeonggi-do. The Korean Journal of Educational Methodology Studies, 31(1), 45-66. http://doi.org/10.17927/tkjems.2019.31.1.45

상세보기
Ju, Y. J., Lee, C. H., & Kim, S. H. (2011). A comparison study between male and female students on academic selfefficacy, interest, external motivation, and mathematics achievement of high school students. Journal of Research in Curriculum & Instruction, 15(4), 1021-1043. http://doi.org/10.24231/rici.2011.15.4.1021

상세보기
Jung, H. S., & Song, H. N. (2020). Detecting types for the influence of mathematics interest and mathematical perception on mathematics achievement in middle school students: Using REBUS-PLS. School Mathematics, 22(4), 853-868. https://doi.org/10.29275/sm.2020.12.22.4.853

상세보기
Kang, M. (2018). Longitudinal analysis of high school students' affective attitude, recognition of teacher's teaching ability, learning strategy, and achievement in mathematics [Doctoral dissertation, Ewha Womans University].
Kang, T., & Song, M. (2012). An exploratory study on IRT vertical scaling for grade 6 through grade 9 educational achievement tests. Journal of Educational Evaluation, 25(2), 287-315.
Kim, H. M., Kim, Y., & Han, S. (2018). A longitudinal analysis on the relationships among mathematics academic achievement, affective factors, and shadow education participation. School Mathematics, 20(2), 287-306. https://doi.org/10.29275/sm.2018.06.20.2.287

상세보기
Kim, K., Kim, S., Kim, M., & Kim. S. (2009). Comparative analysis of curriculum and achievement characteristics between Korea and high performing countries in PISA & TIMSS (RRE 2009-7-2). Korea Institute for Curriculum and Evaluation.
Kim, K., Kim, S., & Park, H. (2010). A Comparison of multi-level models for mathematics performance across Korea, Singapore, Japan and Hong Kong. The Journal of Curriculum and Evaluation, 13(2), 219-238.
Kim, S., & Koh, M. (2007). The factor of effect in growth of academic achievement in adolescent: The use of latent growth model. Studies on Korean Youth, 18(3), 5-29.
Kim, S., & Shin, C. (2011). Academic high school students: the pre-study effect analysis. The Journal of Yeolin Education, 19(4), 87-108.
Kim, S. J., Kim, K, H., & Park, J. H. (2014). The effect of mathematics achievement on changes in mathematics interest and values for middle school students. Journal of Research in Curriculum and Instruction, 18(3), 683-701. http://doi.org/10.24231/rici.2014.18.3.683

상세보기
Kim, Y. (2020). A longitudinal study on the influence of attitude, mood, and satisfaction toward mathematics class on mathematics academic achievement. Communications of Mathematical Education, 34(4), 525-544. https://doi.org/10.7468/jksmee.2020.34.4.525

원문보기 상세보기
Kim, Y., & Han, S. (2020). A longitudinal study on the effects of internal and external factors on mathematics academic achievement. School Mathematics, 22(3), 537-566. https://doi.org/10.7468/jksmee.2020.34.3.325

원문보기 상세보기
Kim, Y. B., & Kim, N. O. (2015). Exploration of student and school factors influencing on academic achievement. Korean Journal of Educational Research, 53(3), 31-60.
Koller, O., Baumert, J., & Schnabel, K. (2001). Does interest matter? The relationship between academic interest and achievement in mathematics. Journal for Research in Mathematics Education, 32(5), 448-470. https://doi.org/10.2307/749801

상세보기
Kwon, J. R., & Kwon, M. (2023). Exploring factors influencing affective characteristics in elementary school students: Focusing on school mathematics education and social environment. Education of Primary School Mathematics, 26(3), 199-217. https://doi.org/10.7468/jksmec.2023.26.3.199

원문보기 상세보기
Lee, C. H., & Kim, S. (2010). Analysis of affective factors on mathematics learning according to the results of PISA 2003. School Mathematics, 12(2), 219-237.
Lee, H., Ko, H. K., Park, J. H., Oh, S. J., & Lim, M. (2022). Exploring the direction of mathematics education to improve the affective achievement of students. The Mathematical Education, 61(4), 631-651. https://doi.org/10.7468/mathedu.2022.61.4.631

원문보기 상세보기
Lee, M., & Kil, Y. (1998). Differences of affective variables related to mathematics learning by the grades and achievement groups. The Mathematical Education, 37(2), 147-158.
Lee, S., & Lee, S. S. (2023). Examining the influence of learner-centered and teacher-centered instruction on middle school students' subject interest by achievement levels. The Korean Journal of Educational Methodology Studies, 35(1), 129-154.
Li, F., Barrera, M., Hops, H., & Fisher, K. J. (2002). The longitudinal influence of peers on the development of alcohol use in late adolescence: A growth mixture analysis. Journal of Behavioral Medicine, 25(3), 293-315. https://doi.org/10.1023/a:1015336929122

상세보기
Lim, S. A., & Lee. J. (2016). Affective factors as a predictor of math achievement: Comparison of OECD high performing 10 countries. Journal of Educational Evaluation, 29(2), 357-382.
Muthen, B., Brown, C. H., Masyn, K., Jo, B., Khoo, S. T., Yang, C. C., Wang, C. P., Kellam, S. G., Carlin, J. B., & Liao, J. (2002). General growth mixture modeling for randomized preventive interventions. Biostatistics, 3(4), 459-475. https://doi.org/10.1093/biostatistics/3.4.459

상세보기
Muthen, B., & Muthen, L. (2019). Mplus: A general latent variable modeling program.
Nylund, K. L., Asparouhov, T., & Muthen, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling: A Multidisciplinary Journal, 14(4), 535-569. https://doi.org/10.1080/10705510701575396

상세보기
Park, C. (2007). The trend in the Korean middle school students' affective variables toward mathematics and its effect on their mathematics achievements. The Mathematical Education, 46(1), 19-31.
Park, S., Chiu, W., & Won, D. (2017). Effects of physical education, extracurricular sports activities, and leisure satisfaction on adolescent aggressive behavior: A latent growth modeling approach. PLoS ONE, 14(4), e0174674. https://doi.org/10.1371/journal.pone.0174674

상세보기
Park, S. H., & Sang, K. (2011). Characteristics of and factors affecting on students' attitude toward mathematics. School Mathematics, 13(4), 697-716.
Ramaswamy, V., DeSarbo, W. S., Reibstein, D. J., & Robinson, W. T. (1993). An empirical pooling approach for estimating marketing mix elasticities with PIMS data. Marketing science, 12(1), 103-124. https://doi.org/10.1287/mksc.12.1.103

상세보기
Reinecke, J., & Seddig, D. (2011). Growth mixture models in longitudinal research. Advances in Statistical Analysis, 95(4), 415-434. https://doi.org/10.1007/s10182-011-0171-4

상세보기
Sang, K., Kwak, Y., Park, J., & Park, S. (2016). The trends in international mathematics and science study (TIMSS): Findings from TIMSS 2015 for Korea (RRE 2016-15-1). Korea Institute for Curriculum and Evaluation.
Sang, K. A., Kim K. H., Park S. W., Jeon S. K., Park, M. M., & Lee, J. W. (2020). An international comparative study on the trend of mathematical and scientific achievement: TIMSS 2019 (RRE 2020-10). Korea Institute for Curriculum and Evaluation.
Schwartz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461-464. https://doi.org/10.1214/aos/1176344136

상세보기
Shin, J. H. (2009). The impacts of prior learning and family environments on the attitudes toward math of applicants to the education center for gifted children in math. Korean Journal of Teacher Education, 25(2), 180-199.
Song, H. S., & Jung, H. S. (2022). Detecting types for the influence of math teaching methods perceived by high school students on math self-efficacy: Using REBUS-PLS. The Mathematical Education, 61(4), 613-629. http://doi.org/10.7468/mathedu.2022.61.4.613

원문보기 상세보기
Song, H. S., & Jung, H. S. (2023). The effects of math teachers' teaching ability and class activity types on learners' affective attitudes: A multilevel structural equation model. The Mathematical Education, 62(2), 195-209. https://doi.org/10.7468/mathedu.2023.62.2.195

원문보기 상세보기

표제어: PCR

동의어: Packet Collision Rate

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