A hasty post on problem solving in maths: more English is the answer
Email just in from a teacher:
“How you are tackling problem solving? Our learners and staff are finding it a challenge and I feel the key is to ensure it is right lower down in the school so that pupils have more skills to tackle problems when they are at KS4.”
And my response, copied here in case it’s useful…
My problem solving strategy would be, as frequently and as early as possible, to give students questions/problems that meld two or more topics together. For example in year 7 when you’re doing algebra, bring in angle problems that require some collecting of like terms. When you’re doing fractions bring in an area question where the side lengths are mixed numbers. With indices make the powers an algebraic expression.
As you get up to year 11, you’ll have to be creative and often invent random maths concoctions. It’s a worthwhile team planning exercise to write out things like: vectors, transformations, probability, trig, quadratics, volume, speed, angles in polygons, bearings, etc. on separate cards and then choose two at random to make a question from. For example if you choose speed and probability, can you and your partner invent a mash-up question?
I’m saying this because there aren’t enough of these combo problems to draw on at GCSE yet but that’s the direction they’re going. So for the time being we’re going to have to make them up and force ourselves (i.e. the teachers) to make the connections in the maths.
On the more reasoning type of problems, the total AO3 questions, you’ve got to make sure your school is prioritising English and reading in a big way from year 7. I mean like 8 hours of English a week plus 40 minutes of silent reading a day, plus any interventions required for the weakest.
Language is a pre-requisite for thought. The better your language skills the better your ability to think. You simply can’t reason without language. So until their literacy is supreme, their reasoning is going to suffer and no amount of highlighting keywords is going to really tackle the issue.
Every school should be a big reading school. Speak to your HoD, the English HoD, the school librarian, your HoY or even your Headteacher to find out how to give English and reading more prominence in year 7.
Just my thoughts quickly cobbled together. Discussions welcome in the comments.
Hi Bruno your idea of mashing two ideas together is an interesting one. Lots of exciting ideas out there come through mash ups. But maybe mashing maths with maths is more difficult to sell the real world application which often gets students really puzzling to solve things.
I teach in primary and we have found mashing maths with programming can be a great way to sell the problem solving. Students put in lots of extra time writing programs to translate shapes when we would have been struggling to generate this much interest in maths alone.
We are also beginning to discover that we need to be more explicit in what we think good problem solving attitudes are such as persistence, the ability to cope with complexity, tolerate ambiguity, deal with open ended problems and communicate etc alongside computational thinking ideas such as think through the steps or rules of a project (create algorithms), break up complex projects into chunks (decompose and recompose), look for the most important part of a project, (abstract), adapt ideas and reuse them in other contexts (generalise).
Maybe there might be some mileage in looking at maths problem solving through the prism of computing problem solving techniques rather than just more literacy.
Anyway just a thought I suspect maths has its own raft of problem solving techniques as well and many would overlap
Hi Bruno, it might be interesting to work with the English department and do a ‘mash up’ of English/maths GCSE style questions. Maybe you could use the text from the problem solving questions in maths and apply the English GCSE style questions to it. E.g. List all the information about … It might encourage students to think about applying their ‘English’ skills to the maths context.
I wrote a blog post a while ago about teaching new vocabulary terms in maths, which is sort of related. I’d be interested to hear your thoughts: http://blog.bedrocklearning.org/blog/maths-academic-vocabulary.
Olivia