Year 5 to 8 algebra
As secondary maths teachers, how often have we considered how much algebra knowledge students come to us with from primary school?
More importantly, how often have we considered what that knowledge is, and how it is impacted by their age?
I can hold my hand up and say I considered students to be almost a blank slate algebraically, maybe able to generalise numerically, but requiring algebra to be taught from its most basic concepts. That was until the 5-8 Continuity Project revealed my own lack of understanding, not just about what students come to me knowing about algebra, but also about algebraic concepts in general. I want to share the following data from the course, which illustrates not just at what age do students understand algebra, but also break down the types of ways algebra can be understood.
A short note on the graph - the higher the bar, the fewer students understood the letter in that form.
This examination of the understanding of an algebraic letter is fascinating. One question this prompted in me was whether I’d even considered the different nature of the letter, never mind how understanding of a letter in one way might or might not easily lead to the next. But this also matches a lot with my experience as a teacher of how students approach algebra - the first instinct is to evaluate the letter, as we’d expect given the amount of understanding that form has, but then when we look at the age of the students who have that understanding doesn’t that mean that I should be moving onto the other ways to consider the letter - as a variable, or as an unknown, faster, and spending more time on those definitions? And that leads to considering the sequencing of steps which would move a student’s understanding into those more complex areas, whilst still having the knowledge that the letter could also be something to be evaluated. This prompted a lot of discussion and thought on the 5-8 Continuity Course, and even just speaking from a Secondary Maths teacher perspective, I can say that this simple diagram really developed my own understanding of how students see algebra.
