Addressing Gaps with Lower Ability Students
By Dearbhla Cooper, Assistant Head of Mathematics – Stage 4 and Numeracy Coordinator
In 2022, I was confronted with a problem I hadn’t come across in my career of teaching mathematics in Senior School. In my Year 8 Stage 4 MYP Mathematics class, my students had crippling maths performance anxiety. These students felt negatively towards maths, were disengaged, and sat well below average when compared to their peers. It was difficult to even get some of them to put pen to paper such was their complete lack of self-belief.
I did my best to teach these students the curriculum during Term 1, but their level of engagement and attainment was dire under typical curriculum time constraints. Missing some of the maths foundations in their Primary School years due to COVID-19 may have caused part of the reason for this. Many of the students had poor working memory and although they were putting in effort, they were being repeatedly exposed to failure, and I wanted to break this cycle.
Teaching the whole child
Cranbrook’s ethos is to teach the whole child. We look at the student’s strengths and weaknesses, and where appropriate, we pivot our teaching methods to help ensure each student receives an education tailored to meet their individual learning needs.
As part of Cranbrook’s professional development programme, Teacher Inquiry Group, I worked with AIS NSW to frame a study that looked at the best way to bridge the gap when looking at lower ability students. Intervention was clearly needed. I wanted to find a way to balance engagement, retention and heighten attainment. In my preliminary research, I noted that most methods of intervention may not always allow for skills generalisation, and that reteaching skills for mastery is limited once disengagement occurs. I wanted to see what would happen if we prioritised increasing confidence and engagement, and I was driven by ensuring equity; I didn’t want to limit what type of maths these students were exposed to. I also wanted to explicitly teach students metacognitive and study skills to enhance their overall numeracy, ready for today’s world.
Redefining maths curriculum
In collaboration with the parents of these students, Ryan Sadler, Head of Mathematics and Nicholas Jolly, Director of Academics, I designed a bespoke programme that tracked incremental growth and progress in a different way. These students were taken off the common maths curriculum to undertake a parallel maths programme of explicit skill development and were taught maths concepts rather than focusing mainly on maths procedure.
Firstly, I wanted to scope a programme that could be spread across years in such a way to create space for deeper consolidation of ideas to reduce the typical “rush” to cover set content. Then, I chose to focus on broader conceptual topics using discussion, stories and collaboration rather than the traditional procedural “drill-style” skills focus that usually underpins intervention classes. My premise was that enhanced engagement and reduced anxiety could create space for a corresponding growth in attainment.
To start the programme, we took the focus away from procedural questions – away from repetition, assessments, and marks, and instead focused only on engagement, discussion and collaboration. We looked at maths concepts at a slower pace, using interesting real-life examples and open-ended questions. For example, we focused on creating a presentation pitch for a client who had given us a budget to work with. The students were tasked with applying various percentage increases and decreases, developing Excel skills, scale drawings and ratios and rates in contexts. Assessment as learning was key.
The parents of these students were very enthusiastic that we were going to be taking a different approach to their children that may allow them to engage with the subject more, and to focus on real life skills. Students were encouraged to talk about maths at home, to ask ‘but why’ questions, to show younger siblings concepts and to argue about the best way to tackle a problem. The classroom changed from being charged with anxiety to being filled with discussion. For example, when looking at percentage rates, we looked at investing in the stock market. One of the students loved shoes, so we looked at different shoes and different prices, dealing with profit and loss, looking at percentages, depreciation over time. The discussions were rich and diverse, and students were keen to participate in a way I hadn’t seen before.
My research redefined what success looked like for these students. Success was not about the final answer but was on working out how to get there. My research removed the pressure of performing academically, allowed for repeated exposure to incremental success and demonstrated that if a student understands the concepts, procedure can come later.
My plan was to unpack the curriculum and spread it out over three years, hoping that by Year 10, we would be confident these students could meet mainstream benchmarks.
Incredible results
However, I was shocked that at the end of the second term, these students started tracking alongside their peers. In Term 3, these successes allowed us to focus on increasing pacing overall, and further developing our skills on collaboration, communication, literacy and extrapolations with an Interdisciplinary Unit comprised of formative assessments across English and Maths on Sustainability- with data backing up their awareness campaign. By Term 4, students were apace with their mainstream cohort, and our focus changed to study skills, using spaced retrieval, importance of independent work and reflecting and correcting this work, with routine quizzes for exposure to higher stakes assessment styles.
By the end of the year, we were able to effectively re-stream the students, so that they were doing the same content at the same pace as their peers. More importantly, their time on task in the classroom was much higher, they generated their own discussions and questions around given content, and generally took much more ownership in their own learning. Eight of these students were consistently attaining more highly, with these indicative trends also showing in Allwell test results, with six students increasing by two levels or more.
There is a lot of current research that talks about differentiation in the classroom. Typical research in the mathematical space focuses on automaticity as the necessary precursor to conceptual understanding to reduce cognitive load in problems, but as several studies have found, this can easily lead to a circular curriculum returning to sites of historical failures to a students’ detriment. Whilst low floor, high ceiling tasks have been suggested since 1982, sometimes this is hard to do if attempting to focus on procedural tasks as a priority. In my research, I found there was a dearth of research on engagement, recall and retention as equal priorities for learning. In conclusion, the need to find the right balance between maths concept and maths procedure is very topical, especially given the new curriculum from NESA starting 2024.
My research found engagement and a conceptual focus can drive changes more rapidly than just focusing on procedure. This allowed for students to shine and see their progress outside of the testing environment. Importantly, it increased resilience, self-efficacy and commitment to independent practice, which given more time, is promising in terms of further attainment, especially when this was mirrored in increasingly formal assessment tasks. This study raised questions about how to best balance concepts and procedures in maths; and argues that if we start from strengths and higher concepts, enhancing engagement in this way first, then we have a good grounding from which to develop procedural understanding.
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