The current Mathematics GCSE is quite a difficult subject to learn and a very difficult subject to teach, but I often feel that people don’t quite appreciate the subtleties of why this is.
The subject is broken up into lots of different, discrete skills (sometimes these skills are related to other skills, sometimes they’re not) and each individual skill needs quite a few approaches in order to target as many people as possible.
I can’t think of another subject that works like this.
Most other subjects, let’s take English as an example, have a few main skills which are constantly refined with new knowledge and applied to new situations. In English Literature it might be critiquing a text. Students do this their whole school career, moving onto different texts, but still using the same base processes on each one. Hopefully after doing this numerous times, their ability to critique a text becomes better and better.
This isn’t how the Maths GCSE works. Each lesson, or series of lessons, students are introduced to a new concept that they have to understand and apply to new problems. These concepts can link back to earlier concepts (which can create a chain of misunderstanding if you’re not careful) or they could be entirely new concepts unrelated to other things for students to get their head around.
This creates a problem, which I think why ‘I don’t get it’ can be so prevalent in maths. In other subjects students usually go into the lesson with an understanding that they are working on skills they’ve been using their entire school careers. In mathematics students come in and it’s likely they’ll be immediately hit with something they’ve never done before.
This difference between maths and other subjects also crops up in something that I’ve been thinking about recently.
In most subjects, a single question can be answered at many different ‘levels’, but in mathematics, it’s very rare that this is the case. This creates a big problem for maths teachers to think about when it comes to hitting the objectives, or at least heavily signposting hitting the objectives, in lesson observations in regard to differentiation and personalised learning.
Often we want to teach a skill, or have a student discover a skill, and then apply that skill. In maths each skill tends to have it’s own level assigned so it’s not really possible to teach that skill at numerous levels. Differentiation becomes harder.
I’d love to hear other people’s comments below, on how they get around this. Or if people think this is something that needs to be taken into consideration more on observations.
Hi Richard. I teach maths to adult learners who mostly have left school without achieving a maths qualification such as a GCSE. The biggest problem I encounter is low confidence and ability in the basic rules of arithmetic. I use lots of fun activities as a way of practising these skills, building self esteem and breaking down the ‘I can’t do this’ attitude. Like GCSE maths, the maths I teach has to be ‘functional’ to the learners in order for it to meaningful. I totally agree with you when you talk about a chain of misconceptions. Unfortunately I see this all too often in my classes and it can be challenging to figure our exactly how deep the problem lies (and so rewarding when you/if it can be resolved 🙂 ).
Problem solving is also challenging since the problem has to be interesting enough for the students to want to solve it! My students range in age from 18 to 70 so the mix allows for good discussions ;).
Theresa
Thank you for addressing this difficult question. You provided excellent food for thought to a question that plagues teachers and administrators throughout the world. I would like to add that it is possible to teach math skills through differentiation at different levels but that it is very difficult, if not impossible, to do so appropriately if the gap of background knowledge and math intuition is too large.
Sean