Differences in students’ mathematics knowledge in homogeneous and heterogeneous groups

Boris Černilec 1, Mara Cotič 2, Darjo v 2, Daniel Doz 2 *
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1 Zavod za Gluhe in Naglušne Ljubljana, Ljubljana, SLOVENIA
2 Faculty of Education, University of Primorska, Koper, SLOVENIA
* Corresponding Author
EUR J SCI MATH ED, Volume 11, Issue 1, pp. 15-32. https://doi.org/10.30935/scimath/12431
Published Online: 08 September 2022, Published: 01 January 2023
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ABSTRACT

The question of grouping students into homogeneous and heterogeneous groups is not new, but it does not find an unambiguous answer in the literature, especially in mathematics. In this paper, we address the question of whether grouping students into homogeneous and heterogeneous groups in mathematics improves their knowledge. The quasi-experiment involved 126 8-grade (i.e., 13-14 years old) Slovenian primary school students, who were divided into two equal groups: the control group worked in homogeneous groups, and the experimental worked in heterogeneous groups. The results of the post-test show that the students from the experimental group had better results in mathematics, which indicates that heterogeneous groups should be preferred in mathematics. Lesson observations have identified differences in teacher behavior: educators working in homogeneous groups tend to give students with lower competencies tasks from lower taxonomic levels, and teachers favor abler groups. Such differences have not been observed among teachers working in heterogeneous groups. The implications for educators are also discussed.
Keywords: mathematics, homogeneous groups, heterogeneous groups, differentiation

CITATION

Černilec, B., Cotič, M., v, D., & Doz, D. (2023). Differences in students’ mathematics knowledge in homogeneous and heterogeneous groups. European Journal of Science and Mathematics Education, 11(1), 15-32. https://doi.org/10.30935/scimath/12431

REFERENCES

  • Adamič, M. (1996). Model sukcesivnega kombiniranja temeljnega in nivojskega pouka ter dosežki nivojskih skupin [Model of successive combination of basic and level education and achievements of level groups]. Sodobna Pedagogika [Modern Pedagogy], 47(1-2), 39-48.
  • Askew, M., & Wiliam, D. (1995). Recent research in mathematics education. HMSO/Osted.
  • Blanco Diez, J. C. (2018). Learning contexts available for Japanese teachers in a top tier public high school: Encompassing a demanding work environment with adult education needs. https://www.diva-portal.org/smash/get/diva2:1222725/FULLTEXT01.pdf
  • Boaler, J. (1997). Setting, social class and survival of the quickest. British Educational Research Journal, 23(5), 575-596. https://doi.org/10.1080/0141192970230503
  • Burris, C. C., Heubert, J. P., & Levin, H. M. (2006). Accelerating mathematics achievement using heterogeneous grouping. American Educational Research Journal, 43(1), 137-154. https://doi.org/10.3102/00028312043001105
  • Dawson, M. M. (1987). Beyond ability grouping: A review of the effectiveness of ability grouping and its alternatives. School Psychology Review, 16(3), 348-369. https://doi.org/10.1080/02796015.1987.12085298
  • Dee, T. S., & Jacob, B. (2011). The impact of no child left behind on student achievement. Journal of Policy Analysis and Management, 30(3), 418-446. https://doi.org/10.1002/pam.20586
  • Denton, J. (2017). Working with the IMPaCT taxonomy: Encouraging deep and varied questioning in the mathematics classroom [PhD thesis, University of Warwick].
  • DiMartino, J. (2005). Reaching real equity in schools. Education Digest, 70(5), 9-13.
  • Esposito, D. (1973). Homogeneous and heterogeneous ability grouping: Principal findings and implications for evaluating and designing more effective educational environments. Review of Educational Research, 43(2), 163-179. https://doi.org/10.3102/00346543043002163
  • Fox, L. H. (1979). Programs for the gifted and talented. In: A. H. Passow (Ed.), The gifted and talented: Their education and development (pp. 104-126). University of Chicago Press.
  • Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Karns, K. (1998). High-achieving students’ interactions and performance on complex mathematical tasks as a function of homogeneous and heterogeneous pairings. American Educational Research Journal, 35(2), 227-267. https://doi.org/10.3102/00028312035002227
  • Gagne, R. M. (1985). The conditions of learning and theory of instruction. Holt, Rinehart & Winston.
  • Galeša, M. (1995). Specialna metodika didaktike [Special methodology of didactics]. Didakta.
  • Gall, M. D., Gall, J. P., & Borg, W. R. (2007). Educational research: An introduction. Pearson.
  • Grabbe, J. W. (2015). Implications of experimental versus quasi-experimental designs. In: K. D. Strang (Ed.), The Palgrave handbook of research design in business and management (pp. 141-152). Palgrave Macmillan. https://doi.org/10.1057/9781137484956_10
  • Gregory, R. P. (1984). Streaming, setting and mixed ability grouping in primary and secondary schools: Some research findings. Educational Studies, 10(3), 209-226. https://doi.org/10.1080/0305569840100302
  • Huang, M. H. (2009). Classroom homogeneity and the distribution of student math performance: A country-level fixed-effects analysis. Social Science Research, 38(4), 781-791. https://doi.org/10.1016/j.ssresearch.2009.05.001
  • Ireson, J., & Hallam, S. (2001). Ability grouping in education. Paul Chapman Publishing. https://doi.org/10.4135/9781446221020
  • Kerby, D. S. (2014). The simple difference formula: An approach to teaching nonparametric correlation. Comprehensive Psychology, 3, 11-IT. https://doi.org/10.2466/11.IT.3.1
  • Kulik, C. L., & Kulik, J. (1984). Effects of ability grouping on elementary school pupils: A meta-analysis [Paper presentation]. The Annual Meeting of the American Psychological Association.
  • LeBlanc, V., & Cox, M. A. (2017). Interpretation of the point-biserial correlation coefficient in the context of a school examination. The Quantitative Methods for Psychology, 13(1), 46-56. https://doi.org/10.20982/tqmp.13.1.p046
  • Leonard, J. (2001). How group composition influenced the achievement of sixth-grade mathematics students. Mathematical Thinking and Learning, 3(2-3), 175-200. https://doi.org/10.1080/10986065.2001.9679972
  • Linchevski, L. (1995). Tell me who your classmates are and I will tell you what you are learning. PME, XIX(3), 240-247.
  • Liu, F. (2007). Personalized learning using adapted content modality design for science students. In Proceedings of the 14th European Conference on Cognitive Ergonomics: Invent! Explore! (pp. 293-296). https://doi.org/10.1145/1362550.1362612
  • Nachar, N. (2008). The Mann-Whitney U: A test for assessing whether two independent samples come from the same distribution. Tutorials in Quantitative Methods for Psychology, 4(1), 13-20. https://doi.org/10.20982/tqmp.04.1.p013
  • Oetzel, J. G. (1998). Explaining individual communication processes in homogeneous and heterogeneous groups through individualism-collectivism and self-construal. Human Communication Research, 25(2), 202-224. https://doi.org/10.1111/j.1468-2958.1998.tb00443.x
  • Østbø, I. U., & Zachrisson, H. D. (2021). Student motivation and parental attitude as mediators for SES effects on mathematics achievement: Evidence from Norway in TIMSS 2015. Scandinavian Journal of Educational Research, 1-16. https://doi.org/10.1080/00313831.2021.1939138
  • Page, R. (1992). Lower track classroom: A curricular and cultural perspective. Teachers College Press.
  • Raftu, G. (2016). Methods and techniques of instruction individualization and differentiation. Learning through cooperation or group work. Bulletin of the Transilvania University of Braşov, Series VII: Social Sciences and Law, 9(1-Suppl), 83-90.
  • Rahbarnia, F., Hamedian, S., & Radmehr, F. (2014). A study on the relationship between multiple Intelligences and mathematical problem solving based on revised Bloom taxonomy. Journal of Interdisciplinary Mathematics, 17(2), 109-134. https://doi.org/10.1080/09720502.2013.842044
  • RIC. (2005). RIC. https://www.ric.si/mma/izhodi%C5%A1%C4%8Da%20npz%20v%20o%C5%A1/2006070611531042/
  • Saifi, S., & Mehmood, T. (2011). Effects of socioeconomic status on students achievement. International Journal of Social Sciences and Education, 1(2), 119-128.
  • Schullery, N. M., & Schullery, S. E. (2006). Are heterogeneous or homogeneous groups more beneficial to students? Journal of Management Education, 30(4), 542-556. https://doi.org/10.1177/1052562905277305
  • Slavin, E. R. (1990). Achievement effects of ability grouping in elementary and secondary schools: A best-evidence synthesis. Review of Educational Research, 60(3), 471-499. https://doi.org/10.3102/00346543060003471
  • Slavin, R. E. (1987). Ability grouping and student achievement in elementary schools: A best-evidence synthesis. Review of Educational Research, 57(3), 293-336. https://doi.org/10.3102/00346543057003293
  • Strmčnik, F. (1992). Problemski pouk v teoriji in praksi [Problem-based lessons in theory and practice]. Didakta.
  • Strmčnik, F. (1993). Učna diferenciacija in individualizacija v naši osnovni šoli [Learning differentiation and individualization in our elementary school]. Zavod Republike Slovenije za šolstvo [Institute of the Republic of Slovenia for Education].
  • Strmčnik, F. (2001). Didaktika. Osrednje teoretične teme [Didactics. Central theoretical topics]. Znanstveni inštitut Filozofske fakultete [Scientific Institute of the Faculty of Arts].
  • Tallarida, R. J., & Murray, R. B. (1987). Mann-Whitney test. In R. J. Tallarida, & R. B. Murray (Eds.), Manual of pharmacologic calculations (pp. 149-153). Springer. https://doi.org/10.1007/978-1-4612-4974-0_46
  • Učni Načrt. (2011). Učni Načrt. https://www.gov.si/assets/ministrstva/MIZS/Dokumenti/Osnovna-sola/Ucni-nacrti/obvezni/UN_matematika.pdf
  • Valenčič Zuljan, M., Cotič, M., Felda, D., Magajna, Z., & Žakelj, A. (2015). The efficiency of homogeneous and heterogeneous grouping of students in mathematics. Verlag Dr. Kovač.
  • Venkatakrishnan, H., & William, D. (2003). Tracking and mixed ability grouping in secondary school mathematics classrooms: A case study. British Educational Research Journal, 29(2), 189-204. https://doi.org/10.1080/0141192032000060939
  • Wendt, H. W. (1972). Dealing with a common problem in social science: A simplified rank-biserial coefficient of correlation based on the statistic. European Journal of Social Psychology, 2(4), 463-465. https://doi.org/10.1002/ejsp.2420020412
  • Wyman, P. J., & Watson, S. B. (2020). Academic achievement with cooperative learning using homogeneous and heterogeneous groups. School Science and Mathematics, 120(6), 356-363. https://doi.org/10.1111/ssm.12427
  • Žagar, D. (2004). Nivojski pouk v devetletni osnovni šoli [Level lessons in a nine-year primary school]. Šolsko Polje [School Field], 15(5/6), 29-51.
  • Žakelj, A., Cankar, G., Bečaj, J., Dražumerič, S., Kern, J., & Rosc Leskovec, D. (2009). Povezanost rezultatov pri nacionalnem preverjanju znanja s socialno-ekonomskim statusom učencev, poukom in domačimi nalogami. Poročila o raziskavi [Correlation of national test scores with students’ socioeconomic status, lessons, and homework. Research reports]. Zavod Republike Slovenije za šolstvo [Institute of the Republic of Slovenia for Education].