Professor Kim Beswick from the University of New South Wales discusses her research into Mathematics success and engagement at the secondary level, highlighting the importance of teaching low attainers to act like high attainers, and learn in the same ways that successful learners learn.
I recently had the pleasure of working on a grant application with a colleague with whom I had not worked before. He has been successful in these endeavours in the past, so I expected to learn things – and I did. The chance to observe his processes and thinking will help me to write better applications in the future. The experience prompted me to reflect on Mathematics classrooms and how we might provide similar learning opportunities for students.
Mathematics classes in secondary schools are typically streamed by ability at least by Year 9. Although there is still a wide range of attainment in these supposedly homogenised groups, lower attainers have no opportunity to learn from the best Mathematics students. It is worth considering whether low attainers, and indeed any students, might do better if they were taught to do what the best students have figured out how to do.
When I asked a group of 18 secondary Mathematics teachers to describe their most and least capable students, the most commonly mentioned characteristics of the skills and knowledge of poor students were their lack of basic computational skills, poor understanding, lack of prior knowledge and difficulty grasping new concepts. Conversely, the best students were described as fluent with multiplication tables, understanding concepts, having broad background knowledge, being able to pick up new methods and explanation quickly and able to grasp concepts intuitively.
None of that is surprising but the non-cognitive characteristics they mentioned suggest ways teachers might intervene. Poor Mathematics students were described as disliking Mathematics and being unwilling to attempt difficult work, whereas their capable peers had positive attitudes towards Mathematics and even a love for the subject. The weakest students miss lessons, are inattentive, disruptive, unwilling to seek help and have poor concentration. The best students attempt the hardest problems, approach problems methodically, take initiative to figure things out, set goals, make lots of effort, and learn from mistakes.
We cannot simply tell students to feel differently about Mathematics, to be more confident or motivated, or to have a growth mindset. It is understandable that students who have not been successful would not like the subject and might find ways to avoid experiencing failure again. Teachers in this study seemed to recognise this. When asked how they would help these students make progress they said that these students needed to develop confidence and motivation and that they would assign them work that was easy enough for success to be likely, provide lots of hands-on practical tasks and tasks that were relevant to them. Successful students would be provided with challenging, open-ended and problem-solving tasks, and encouraged to work hard and extend their knowledge.
At one level this is logical and certainly well-meaning but how will low attainers ever learn to attempt difficult tasks, or to persevere if they are not offered challenging tasks that come with a risk of failure? Is succeeding at work you know is below the standard expected of most students really likely to build confidence and motivation? Might it not simply reinforce that you are not capable of learning Mathematics? If that is the case, why would you try? Teachers’ good intentions tend to play out as low attainers being given a mathematically impoverished diet of repetitive low-level tasks aimed at strengthening basic number work with the intention, at best, of laying the groundwork for higher level tasks sometime in the future. This progression almost never happens. Rather, the usual outcome is more avoidance and disruption (or passive tuning out), increasing dislike for the subject and continued under-achievement. So, what might we do instead?
However students are grouped, they must know, not simply be told, that their teacher truly believes they can learn Mathematics. This means expecting them to learn the mandated content of the Australian Curriculum (or state-based version thereof) and teaching them how to do that. If students know that success at ‘proper’ Mathematics is possible and that failure is safe, they will work hard and enjoy the satisfaction of hard-earned success. For example, if capable students approach problems methodically, how can other students be taught to do that? What does it look like? What exactly is it that capable students do? What might students do when they don’t know what to do? What do successful students do in these circumstances? How can students learn from getting things wrong? These kinds of questions develop students’ metacognition.
Students who are currently low attainers have gaps in their knowledge, often of quite basic things like number facts and almost always have problems with major concepts like proportional reasoning. It is important to remember that learning primary school content as a 14 or 15-year-old is different from learning it as a primary school student.
Filling the gaps does not have to take a lot of time and, most importantly, does not need to prevent learning year level curriculum.
If teachers start from an assumption that all students can learn the year level curriculum and convey this belief to students through their actions – i.e. teaching that curriculum to all of them and framing difficulties as shared problems that need to be tackled and solved together – almost all students will rise to the opportunity (once they believe the teacher thinks they can learn). Students need to also be taught how to learn better by challenging them to think about how successful students learn and how they can do those things as well. Students need to know that solving problems they encounter in their learning requires them to do their best. They also need to know that their teacher sees student difficulties not as evidence of inability but as opportunities to reflect on their teaching and to find new ways to represent and explain concepts, and to understand student thinking in order to address misunderstandings that result from gaps in prior learning.
In my experience, the most relevant concern of teenagers is to fit in with their peers and to avoid looking foolish in the eyes of those peers. The opportunity to succeed at the same Mathematics that their peers are learning is highly motivating and means that filling gaps in prior knowledge in the context of learning year level appropriate Mathematics is much easier and more likely to be effective than trying to address the gaps in advance.
No matter how successful they already are, everyone can learn by considering how others learn and think, and learning to reflect on their own learning processes. Teaching low attainers to learn in ways that successful students learn, and believing they can, can help high expectations lead to high attainment.