In this blog post I report on research exploring the use of mixed-attainment pairs in primary mathematics lessons in south-east England. Research into mixed-attainment learning is limited; as a result, in-depth understanding of the potential benefits and challenges of this approach to pupil grouping is also limited. However, much is known about the shortcomings of groupings based on judgments of pupil ability, particularly for low-achieving pupils in relation to their mathematical diet (see for example Dunne et al., 2011), and their learner identities (see for example Hargreaves at al., 2021).

This research examined the merits of mixed-attainment working, using a focus on lower attainers working in mixed-attainment pairs. It examined the mathematical contributions these pupils made and how these contributions impacted on task progress for the pupil pair.

The research took place in three primary school classrooms where I worked in partnership with the class teachers. In each case, teachers were experienced and mathematically confident; all were previous participants in the Primary Mathematics Specialist Teacher programme run at the University of Brighton. The study employed close video observation of pairs of pupils engaged in mathematical activity over four parallel lessons in the three separate primary mathematics classrooms.

The study drew on the construct of mathematical noticing (Lobato et al., 2013), which refers to pupils’ ‘noticing’ of mathematical features of the tasks and activities being undertaken – for example, noticing of mathematical relationships, patterns or commonalities. I view mathematical noticing as an essential precursor to mathematical reasoning but distinct from it. A noticing might be the start of something, it might turn out to be important or it might not. A noticing might emerge in one child’s half utterance and be built on by another. Noticing might be evident in speech, or it might be presented through action or expression. In this research I was particularly interested in pupils’ noticing of mathematical pattern, properties of number and mathematical structure.

The opportunity to closely video record pupils’ actions and interactions was crucial in enabling the noticings of the lower attainer to emerge. In real time in the classroom it is impossible for class teachers to be aware of the derivation of pupils’ ideas. Often pupils talk about what ‘we’ did, and of course, we want shared ownership of collaborative task progress, but for this project I really wanted to hear the voice, and focus on the contributions, of the lower attainer.

‘For this project I really wanted to hear the voice, and focus on the contributions, of the lower attainer.’

So what happened?

Throughout the project and in all classes lower attainers were engaged with the mathematics of the tasks and contributed valuable noticings of mathematical property, pattern and structure. On several pivotal instances lower attainers noticed key task features in advance of their higher-attaining partners; frequently, their noticings were instrumental in task progress for the pupil pair.

There is insufficient space in this short blog to detail the many valuable noticings (see Barclay 2021 for more details), but below I briefly detail some of the factors that may have been instrumental in enabling the lower attainers to contribute in the way that they did.

What might be some of the reasons for this?

• We chose exploratory investigative tasks that did not rely on swift recall of facts or procedures.
• We promoted the use of manipulatives for practical exploration, sometimes structured number resources such as Numicon or Cuisenaire, but also number cards.
• Teacher questioning focused not on solutions but on noticings; importantly, questioning tried to focus pupils on where to look – so not just ‘what did you notice?’ but ‘what is the same about all these numbers?’, ‘what do these have in common?’
• Teachers aimed to facilitate a supportive, conjecturing atmosphere in which pupils are encouraged to talk and share their noticings, even if some turn out not to be important.

Lower attainers may not always be able to contribute in the ways described above and more research is needed to understand how mixed attainment can best operate to the benefit of all pupils. However, as the quote in the title of this blog post demonstrates – from a lower attainer whose contributions clearly exceeded her expectations of herself – mixed-attainment learning can sometimes bring real delight.

References

Barclay, N. (2021). Valid and valuable: Lower attaining pupils’ contributions to mixed attainment mathematics in primary schools. Research in Mathematics Education, 23(2), 208–225. https://doi.org/10.1080/14794802.2021.1897035

Dunne, M., Humphreys, S., Dyson, A., Sebba, J., Gallannaugh, F., & Muijs, D. (2011). The teaching and learning of pupils in low-attainment sets. Curriculum Journal, 22(4), 485–513. https://doi.org/10.1080/09585176.2011.627206

Hargreaves, E., Quick, L., & Buchanan, D. (2021). ‘I got rejected’: Investigating the status of ‘low-attaining’ children in primary-schooling. Pedagogy, Culture & Society, 29(1), 79–97. https://doi.org/10.1080/14681366.2019.1689408

Lobato, J., Hohensee, C., & Rhodehamel, B. (2013). Students’ mathematical noticing. Journal for Research in Mathematics Education, 44(5), 809–850.  https://doi.org/10.5951/jresematheduc.44.5.0809