Why on earth, is the Head of STEM, writing about History in a school newsletter? The question about why some students have a rising performance pattern, whilst others have a falling performance pattern, might have a simple answer. Sometimes, it is about effort. More often than not, however, the answer can be found in the complex interrelationship of a number of factors – from effort, to habit, to the graduating difficulty of course structure, to the shift in focus from fluency to problem solving, to the framing of mathematical questions in word problems.
On occasions, teachers are asked this question: “My son was on an A last year, what happened?” More often than not, this question comes at a pivotal juncture in the schooling transition – the move from the junior to the middle phase. I’ll unpack this statement in more detail shortly, but first I’d like to reflect on the nature of Maths for our students.
Students who achieve success in Maths broadly sit in two categories in primary school. The first category might be referred to as those with natural capacity. Typically, it is comprised of those who have an affinity for numbers and are naturally and easily able to work with the patterns and processes involved in Maths. The second category might be referred to as ‘the workers’ – those who need to be industrious in order to achieve success (completing every homework and revision task). Some students fall into different groups, at different times. Upon entering Middle School, these students exhibit some characteristic traits. ‘Naturals’ tend to be those students who need to be pressed to show their working. ‘But sir/miss, I know the answer. Why do I need to write out all of that working?’ Sometimes they also fail to copy the examples from the board. ‘But sir/miss, it’s all in here (pointing at head). Why do I need to copy that?’
As teachers, these attitudes can be difficult to deal with, particularly in those cases when the student performs quite well on their initial tests in middle school. These results appear to support the students’ hypothesis that they really don’t need to do all of the additional work of setting out and copying notes to achieve success.
The complexity of problems increases throughout middle school with questions requiring more and more steps to reach a solution and at some point the ‘naturals’ reach a point where they can no longer hold that much information in their working memory. This is the critical juncture where it all falls apart for these students. They are no longer able to rely on their ability to pluck the answer out of the air AND they haven’t developed the skills of setting out a problem step-by-step. Not surprisingly, their grades suffer.
‘Workers’, on the other hand, have always battled to gain an understanding of the content. They’ve meticulously copied examples and shown working. They see an increased complexity as a few more lines of working which they are skilled at completing. Their marks tend to be much more consistent through this period. Often, their marks will rise. These are broad generalisations but I believe they help to reflect on the original question relating to the basis for success.
Fortunately, in most instances, success can be learned. Failure, or a dip, can be instructive. In failure, the German army, and those that followed it, realised the error of creating a war on two-fronts. If only they had taken the opportunity to learn from the failings of Napoleon, who had done the very same thing, some time earlier. The measure of success in moving forward, is not whether a student’s performance has declined in a Semester. It is whether the student, in partnership with teachers and parents, can learn from their errors and adopt strategies which reduce the risk of a further slump.
In Mathematics, this requires the student to focus on their mathematical communication. Put simply, this involves copying all notes and examples from the board, and increasing the time spent completing problems and homework.
This is a lesson that must be learnt by all students before entering Senior School where the complexity and higher order thinking requirements increase exponentially. In 10 years of teaching senior maths, I’m yet to teach a student who is able to be successful in Maths B or C with natural ability alone. Hard work must become a part of the ethos of the student and it is this attribute which will best determine their success in Maths and in the future.
Mr Mark Watson, Head of STEM