A Maths teacher asks - Volume 1
Written by Dave Taylor Thursday, 18 August 2022
Sukhbir Singh, a mathematics teacher at Akal Academy, Baru Sahib in India, asks…
How can I help the slow bloomers of my class?
Thank you for your question Sukhbir.
'Slow bloomer' is not a term that I’ve ever heard or read before, so when considering my response to this, I thought about two types of pupil that I’ve experienced in my 15 years in the classroom:
- ‘Slower learners’: These are the pupils who seemingly need to ‘do’ more to become fluent in an idea, as well as those who need to ‘practise’ more to develop connections and retain knowledge.
- ‘Late bloomers’: These are the pupils who apply themselves in the latter years of their schooling, when they perceive that ‘it matters’. These pupils develop an intentionality towards their learning, specifically with exam success in mind once their educational next steps become clearer.
The question also brought about thoughts around the key element of the mastery cycle: time. Given an appropriate amount of time - spent on the correct level of mathematics for their current level of understanding - all pupils can learn well. We’ll come back to this point later.
Unfortunately, the logistics of schools and the finite amount of time in the classroom doesn’t always allow the time for every pupil to grasp new ideas in full. I feel that one of the positives of the period of school closures in response to the COVID19 pandemic is the increased use of online platforms. Pupils are more familiar with working at home and accessing work online, which provides an opportunity for further development of fluency and practice work to be set for completion between lessons. It is, of course, important that any additional work isn’t burdensome on teachers, and so setting work that can be self-marked is preferable.
An aspect of cognitive science that may be impacting the progress of our ‘slower learners’ is the idea of forgetting. Perhaps forgetting happens at a faster rate for these pupils, and the aforementioned complementary exercises can provide pupils with more opportunities to revisit ideas at shorter intervals, combatting the forgetting curve and impacting positively on the retention of new ideas. Harnessing this additional learning time is much easier than it was ten years ago, and can have an amazing impact on the progress of pupils.
Of course, there are many aspects which can impact upon the ‘slower learning’ of an idea, and it’s worth also considering whether there are gaps in knowledge which are affecting the progress of these pupils. Are pupils ready to access the mathematics they are being taught? Is prerequisite knowledge well-embedded, so that robust learning can take place? Pupils who hold a solid understanding of the building blocks of an idea will not be overwhelmed by that new idea. Developing a routine within our learning episodes where prerequisite knowledge is checked, consolidated and then built upon is key to robust learning and will lead to successful and motivated pupils, which will then lead to improved outcomes.
‘Late bloomers’, on the other hand, don’t necessarily learn at a slower rate or forget more quickly than the ‘slower learners’, but haven’t applied themselves fully in the formative stages of their learning journey. This could be for many reasons - a poor attitude towards learning, (pre-)teenage angst, or demotivation brought about by a lack of success in lessons. The latter is within our control, and our teaching and curriculum plans must meet pupils where they are - rather than where we want them to be. In my experience, many pupils ‘switch off’ because the mathematics that they’re being shown is beyond them, and they have developed the false idea that ‘maths is for the smart kids’. A ‘late bloomer’ may choose to ‘switch on’ again ‘when it matters’, and this can occur at the beginning of studying towards externally assessed courses, when the shift to an exam-focused scheme of learning offers them a fresh start by revisiting less-complex material - returning to content that gives them a better chance of success, developing motivation in these pupils.
This isn’t desirable, and we must design our curricula so that all learners have the greatest chance of success, so that motivation isn’t lost through a repeated lack of success in the earlier years of their education, and so that undue stress and anxiety doesn’t take hold in the high-stakes final years of their schooling.
By meeting pupils at their current level of understanding, and teaching them the correct level of mathematics, pupils will navigate the curriculum with success and confidence, and when ‘it starts to matter’ and intentionality to improve their grades hits, pupils can do so from a more psychologically positive and mathematically mature starting point.
When considering my response, a third type of pupil came to mind: the Pacifier. These pupils are typically ‘nice’ and ‘well-intentioned’ who think they are doing the right thing, but don’t work hard with the intention of learning content, only with the intention of doing ‘enough’ to keep their teacher at bay and their parents ‘off their back’. These pupils don’t think hard enough about the new idea to go beyond developing fluency and rarely make connections with prior knowledge, which leads to issues with forgetting and retention fairly quickly. Explaining how ‘remembering’ and ‘forgetting’ works with reference to cognitive architecture could redirect their intentions towards longer-term learning. Redirecting their attention to ‘learning content’ rather than ‘doing work’, with a greater understanding that simply completing an exercise is rarely enough to learn a new idea, can harness an inner fire in pupils who then strive for success, causing them to apply themselves in a more concentrated way.
As there are so many variables at play within a learning environment, no one has all of the answers for ensuring that all learners achieve highly - if they do, they should write a book and make a fortune - but I hope that my thoughts shared above go some way to supporting the progress of your ‘slow bloomers’. However, I’d like to leave you with one more point to ponder.
Having committed the above to text, I think it’s worth adding that I do not believe that ‘slow learners’ exist, as I may have done in the past. Returning to a point made earlier in this blog, all pupils can learn mathematics well, and at pace - the defining aspect here is that pupils work hard, and are taught the correct mathematics in an efficient, responsive and pedagogically sound way.
Believing that some pupils are better learners than others can be dangerous to the progress of those perceived to be ‘slower learners’, as their lower rate of improvement in terms of their mathematical prowess isn’t a result of choices made by them, but rather by their teacher.
If the teacher truly believes that all pupils can learn well, low expectations are banished to the past (see a summary of the work of Rosenthal and Jacobsen, 1968, here), and pupils are expected to grasp the novel ideas which are shared with them in a timely fashion. For this to occur, pupils must be taught the correct level of mathematics from their current level of understanding, and the new idea must build upon prior knowledge which is well-established within the pupil’s schema. Choosing the correct level of maths in a class of more than one pupil is challenging, but by following the mastery cycle all pupils stand a better chance of succeeding with learning a new mathematical idea and, over time, we’ll see a huge improvement in the attainment of our pupils.
About the Author
Referred to as 'The Master of Fluency Practice', as the creator of the award-winning 'Increasingly Difficult Questions' web site, Dave has taught for 13 years in challenging circumstances in inner city Leeds. He has spent the last 11 years at his current school, working in and leading a medium-sized department serving 933 students, teaching across Year 7 to Year 11.
This year, Dave has joined the team at Complete Mathematics, stepping down from his role as Joint Curriculum Leader, to have an impact upon our most disadvantaged students on a national scale.