Earlier this week I observed some Functional Skills maths lessons in a college. Here we have students with low or no grades at GCSE aiming for a maths qualification that will hopefully give some sense of achievement. Most of the students were taking Level 2 courses in Digital/Media areas but are required to continue their maths studies alongside.

The challenges the teachers of these programmes face is immense. They have a wide topic range to cover and yet many students still struggle with basics. One student needed to clarify that a half is not 0.2 as a decimal. When corrected, he did seem to remember – oh yeah, 0.5, because its 50% – but he couldn’t then suggest the fraction to match 0.2. In other words, his underlying understanding of the link between simple decimals and fractions was very weak. He was guessing, not exploring a clear schema or using reasoning. This was Andy, age 16.

Another student was tackling 56 divided by 4, a calculation derived from a worded question. When I spoke to her, she’d just written out the 4 times table. 4,8,12,16,20,24,28,32,36,40,44,48,52,56… phew, no mistakes,… then was counting up how many numbers she’d written. Is it 13? She’d miscounted. I offered an alternative to this horribly inefficient method eg half and half again. But half of 56 was also too hard. Nope. 4 x 14 = 56 was not remotely familiar to Joanne, 17.

And then there was Karim, working conscientiously through some bus-stop method division. He’d produced this and written 115.2

I asked him if he was sure.. could 8126 divided by 7 be 115.2? He couldn’t see an immediate issue. He wasn’t thinking that the answer should be 1000 and something; we wasn’t troubled by the answer only being in the 100s. Fundamentally he wasn’t thinking about the scale of each number and what a concrete version of his problem looked like. He wasn’t connecting digits to place value ie the 8 means 8000. It was all blind procedure. But, in prompting him, he was troubled by the 0.2 because he’d been told to find a remainder. What had he done? He’d correctly applied the method as far as 7s into 42 goes 6. But then Karim was left with that last 6. Here he became confused with subtraction… so he ‘borrowed’ 1 from the top line 6 to make 16… then added a decimal point because, with some logic, he thought 6 divided by 7 is less than one. All a bit of a mess – but so close. Karim is also 17.

I think this scenario warrants exploration. Karim, Andy and Joanne are 16 or 17, struggling with basic number work they were probably first taught 9 years ago. And here they are on yet another course where their teacher is a) hoping these things are basics that can be built on and b) has a ton of other stuff to cover for them and the rest of the class. And yet the gaps in their confidence and fluency are so evident… still; again.

Why does this happen?

• Do Karim, Andy and Joanne have some fundamental cognitive limit preventing them mastering these ideas?
• Is it that this material is too abtract, removed from ‘real world questions’ that would be more motivating and engaging?
• Is it that this material is too teacher-led, too driven by a DIKR STEM agenda, too removed from what Karim, Andy and Joanne would choose for themselves – ie what’s the point of them knowing this stuff anyway?
• Is it that teaching is all a bit of an art and teachers have been too busy following narrowly defined principles to have had the freedom to teach them properly year after year?
• Is it that students’ resilience and other dispositions weren’t sufficiently attended to over the years?
• Is it because of funding pressures and a lack of support for intervention?
• Is it because of setting, with low expectations bringing them down, when mixed ability teaching would have served them better?

Well, no. I’d say it’s none of these things. For sure, year after year, Karim, Andy and Joanne have fallen through the cracks. No doubt each of their maths teachers have been well-intentioned and worked hard but I also think it’s possible to imagine a world where all three students would have been confident handling these questions – long before reaching the last chance saloon of their FE classroom. For that to have happened, I’d say a few practices and attitudes would need to be different:

1. We’d assert that this kind of foundational maths knowledge is important and needs as much time as it takes to take root in secure schema; you don’t rush on and hope they’ll pick it up later. Evidently this doesn’t just happen. You deal with it head on; you teach them what they don’t know at every stage, even if it means going very very slowly and going back as far as you need and going over it again and again. This means that, yes, a mixed ability class might be a tough place to be; it might not remotely be the answer.
2. We’d be very clear that specific techniques that relate to teaching this content should be well known and continually crafted and honed. We don’t fudge it all into nebulous ‘teaching is a bit of an art’ guff. Not here, not with these vulnerable learners. No, the stakes are too high. We focus hard on sharing and implementing sound maths mastery methods, relentlessly. We face that challenge and keep working on it, not look for ways around it.
3. We also don’t allow routines and regimes around lesson protocols or a predetermined curriculum roadmap that mask the fact that Karim, Andy and Joanne are who they are; people with their particular motivations, insecurities, prior knowledge and rates of learning at any moment. We flex and adapt to teach them and motivate them. Fundamentally though, we recognise that the key driver of motivation in this context is success. We have to build success; we consolidate relentlessly.
4. With all this in mind, yes, it means we might need to pare down the curriculum a bit – in maths itself for sure. I don’t know that more and more time for maths is the answer -because there are other things that Karim, Andy and Joanne need to learn and could succeed at – but certainly the scope to teach less maths content to greater depth and fluency might be part of it.

Overall, to echo the wise word of Mark McCourt, the answer should lie in finding out what Karim, Andy and Joanne don’t know and then planning a curriculum around that, revising it as they grow in confidence. Currently our system is failing them; they fall through the cracks and their FE teachers then have the most difficult task in teaching in my view. But we won’t solve the problem by wishing it away or crying ‘low expectations’. It’s the hard graft of crafting ever more effective teaching methods within a deliverable curriculum that will win through, year after year after year after year.