Mixed Ability Grouping in Mathematics: Promoting Equity Part 2

Despite the numerous research studies that support the idea that streaming aka tracking has a negligible impact on student outcomes, many mathematics classes around the world, particularly in the UK, Australia and US, still group students according to ability. Mixed attainment grouping is perceived to be too time-consuming to plan, unconventional and results in a “too challenging” teaching environment. Johnston and Wildy (2018) reported that despite research findings, teachers preferred the ability grouping model as there is a false belief that streaming can help manage student behavior and address the demands of teaching to different ability levels.

Boaler (2008) reported that heterogeneous grouping with a specific set of pedagogical strategies can allow students of different socioeconomic and cultural backgrounds, as well ability levels, to interact in a meaningful way that promotes respect and diversity. All students should be given opportunities to solve complex mathematical problems through collaboration with others and being exposed to different perspectives in order to truly promote equity in the mathematics classroom.

There is much evidence to support that mixed ability grouping in mathematics appears to strongly benefit the majority of students (Venkatakrishnan & Wilaim,2003; Boaler, 1997; Linchevski & Kutscher, 1995), which includes lower attaining students.

In order to cater for all students in a mixed attainment setting, teachers to need to include differentiated learning opportunities and design mathematical tasks which are high ceiling, low threshold. These types of tasks allow students to enter the learning engagement at their own levels of achievement and exit the learning experience according to their background knowledge and capability. Differentiated learning can also be supported by differentiated content, product or process (Tomlinson, 2003), and Boaler et al. (2000) reported that a mixed attainment class was more likely to employ these practices than a tracked class. In the same study, students also reported that teachers were more likely to give work that was more appropriate to their level and pace in a mixed ability setting. In order for teachers and schools to be more open minded to adopt a mixed attainment system, exemplars of effective mixed attainment strategies and curriculum materials need to be made readily available.

The current trend in UK mathematics education is the adoption of the mastery approach which was developed from Asian mathematics programs such as the Shanghai and Singapore math teaching models. The focus on mastery mathematics from Shanghai is on depth of understanding through conceptual variation or procedural variation (Gu et al., 2017). The whole class moves in a mixed attainment setting through the same content and the emphasis is on learning concepts on a deeper level rather than on a faster level. Differentiation is achieved through this depth rather than through acceleration. The mastery method also borrows from the Singapore mathematics Concrete Pictorial Abstract (CPA) or also called the Concrete Representational Abstract (CRA) model (Bruner, 1966). Both models support a mixed attainment setting, holding a strong belief that every student is capable of learning mathematics on a deep level.

Research indicates that ability grouping in mathematics is not beneficial for student attainment and several negative impacts of ability grouping include lower self-esteem issues with students and low expectation from teachers in lower attainment groups.

Further reading

Archer, L., Francis, B., Miller, S., Taylor, B., Tereshchenko, A., Mazenod, A.V. & Travers, M.C. (2018). The symbolic violence of setting: A Bourdieusian analysis of mixed methods data on secondary students’ views about setting. British Educational Research Journal, 44(1), 119–140. https://doi.org/10.1002/berj.3321

Boaler, J. (1997). Experiencing School Mathematics: Teaching Styles, Sex, and Setting. Buckingham; Philadelphia: Open University Pres.

Boaler, J. (n.d.). Fluency without Fear. Retrieved March 20, 2019, from YouCubed website: https://www.youcubed.org/evidence/fluency-without-fear/

Boaler, Jo. (2008). Promoting ‘relational equity’ and high mathematics achievement through an innovative mixed‐ability approach. British Educational Research Journal, 34(2), 167–194. https://doi.org/10.1080/01411920701532145

Boaler, Jo. (2013). Ability and mathematics: the mindset revolution that is reshaping education. FORUM, 55(1), 143. https://doi.org/10.2304/forum.2013.55.1.143

Boaler, Jo, Wiliam, D., & Brown, M. (2000). Students’ experiences of ability grouping - disaffection, polarisation and the construction of failure. British Educational Research Journal, 26(5), 631–648. https://doi.org/10.1080/713651583

Bradley, K. (2016). Evaluating the effects of mastery learning in postsecondary developmental mathematics (Ed.D., University of Louisiana at Monroe). Retrieved from http://search.proquest.com/docview/1799648934/abstract/D066F4692CB242DFPQ/1

Bruner, J. S. (1966). Toward a theory of instruction. In Toward a Theory of Instruction. Cambridge, MA, US: Harvard University Press.

Dracup, T. (2014) The Politics of Setting, https://giftedphoenix.wordpress.com/2014/11/12/the-politicsof-setting/ Retrieved: 14th April 2019.

Effect Size. (2009, July 18). Retrieved February 13, 2019, from Research Rundowns website: https://researchrundowns.com/quantitative-methods/effect-size/

Francis, B., Archer, L., Hodgen, J., Pepper, D., Taylor, B., & Travers, M.-C. (2017). Exploring the relative lack of impact of research on ‘ability grouping’ in England: a discourse analytic account. Cambridge Journal of Education, 47(1), 1–17. https://doi.org/10.1080/0305764X.2015.1093095

Gu, F., Huang, R., & Gu, L. (2017). Theory and development of teaching through variation in mathematics in China. In R. Huang & Y. Li (Eds.), Teaching and Learning Mathematics through Variation: Confucian Heritage Meets Western Theories (pp. 13–41). https://doi.org/10.1007/978-94-6300-782-5_2

Hallam, & Parsons. (2013). Prevalence of streaming in UK primary schools: evidence from the Millennium Cohort Study Wiley Online Library. British Educational Research Journal. Retrieved from https://onlinelibrary-wiley-com.cmich.idm.oclc.org/doi/full/10.1080/01411926.2012.659721

Higgins, S., Katsipataki, M., Coleman, R., Henderson, P., Major, L., Coe, R. & Mason, D. (2015). The Sutton Trust-Education Endowment Foundation Teaching and Learning Toolkit. - Durham Research Online. Retrieved February 4, 2019, from http://dro.dur.ac.uk.cmich.idm.oclc.org/20987/

Ireson, J., Hallam, S., & Hurley, C. (2005). What are the effects of ability grouping on GCSE attainment? British Educational Research Journal, 31(4), 443–458. Retrieved from http://www.jstor.org/stable/30032578

Johnston, O., & Wildy, H. (2018). Teachers’ perspectives of lower secondary school students in streamed classes – A Western Australian case study. Educational Studies, 44(2), 212–229. https://doi.org/10.1080/03055698.2017.1347494

Lavy, V. (2015). Do differences in schools’ instruction time explain international achievement gaps? Evidence from Developed and Developing Countries. The Economic Journal, 125(588), F397–F424. https://doi.org/10.1111/ecoj.12233

Linchevski, L., & Kutscher, B. (1998). Tell me with whom you’re learning, and i’ll tell you how much you’ve learned: mixed-ability versus same-ability grouping in mathematics. Journal for Research in Mathematics Education, 29(5), 533–554.

Linn, R. L., & Dunbar, S. B. (1992). Issues in the design and reporting of the national assessment of educational progress. Journal of Educational Measurement, 29(2), 177–194. Retrieved from http://www.jstor.org/stable/1434601

Loveless, T. (2001, November 30). The NAEP proficiency myth. Retrieved March 17, 2019, from Brookings website: https://www.brookings.edu/blog/brown-center-chalkboard/2016/06/13/the-naep-proficiency-myth/

Setting or streaming | Toolkit Strand. (n.d.). Retrieved February 2, 2019, from https://educationendowmentfoundation.org.uk/evidence-summaries/teaching-learning-toolkit/setting-or-streaming

Slavin, R. E. (1990). Achievement effects of ability grouping in secondary schools: a best-evidence synthesis. Retrieved February 4, 2019, from https://journals-sagepub-com.cmich.idm.oclc.org/doi/abs/10.3102/00346543060003471

Taylor, B., Francis, B., Archer, L., Hodgen, J., Pepper, D., Tereshchenko, A., & Travers, M.-C. (2017). Factors deterring schools from mixed attainment teaching practice. Pedagogy, Culture & Society, 25(3), 327–345. https://doi.org/10.1080/14681366.2016.1256908

Tomlinson, C. A. (2003). Deciding to teach them all. Educational Leadership, 61(2), 6–11.

Venkatakrishnan, H., & Wiliam, D. (2003). Tracking and mixed-ability grouping in secondary school mathematics classrooms: A case study 1. British Educational Research Journal, 29(2), 189–204. https://doi.org/10.1080/0141192032000060939