### Archive

Archive for January, 2016

## A conic extention

This week has been a strange one, I’ve been trying to shake an illness but it keeps on getting worse,  and my lessons have been disrupted a little bit by mock examinations. This, however, has given me a chance to work.woth small groups in some classes and to see how some classes are getting on with their courses.

In one of further maths lessons a student who takes maths but not further maths asked if he could.sit in the classroom and revise for his maths, asking if he needed help, I said it was fine and started the lesson,which was a review of the conic sections topic and an assessment sheet to identify any areas of weakness that may be apparent. I gave the none further maths student a spare copy of the assessment sheet, told him it was basically C1 skills but applied in a much more algebra heavy context, and asked him to have a crack.

Not only did he have a good crack at it, he answered it near perfectly. I was extremely pleased with his resilience in working through a question that has way more algebra than anything he’s looked at before and was glad he could make the links to the C1. His thoughts on the question were interesting, and I think they allowed the rest of the class to see more clearly how the conic section of FP1 fits with, and build on, the coordinate geometry sections in C1 and 2.

I think that in future I will use these parabola and hyperbola questions with all my high attaining AS maths students.

This was cross-posted to the “One Good Thing” blog here.

Categories: #MTBoS, A Level, Maths, Teaching

## Unstructured problems

Currently I’m in the process of completing a dissertation based around problem solving in A level mathematics and how this can be improved. This is a focus as in our setting students have struggled with this in the past. It was timely, then, that the article picked for this week’s Maths Journal Club was around the same subject.

The article was by Sheila Evans and was entitled “Encouraging Students Formative Assessment skills when working with non routine problems”. Available here.

The article itself was interesting, it set out an approach to teaching based around these unstructured problems and designed student responses to get students talking and thinking about the way they are approaching the questions. The article seems to suggest that students with an instrumental or procedural understanding are less likely to succeed at this type of problem than those with a relational understanding, and that is something I’ve been thinking myself.

I think the approaches mentioned in the article sound interesting and I am going to tailor them to students and trial them in my own context to see if there is an effect.

It’s certainly an article that has got me thinking and has given me ideas for things to investigate in teaching, as well as signposting a raft of other pieces of literature that I want to investigate further too.

## The core curriculum

This post was originally published here, by Labour Teachers on 29th December 2015

Curriculum, it’s an issue that plays on my mind a fair bit, and I think the reason for that is that I don’t really know what I think is best. I don’t mean the maths curriculum here, I mean the overall curriculum.

I’ve been asked before by students “why do we need to study maths”, and this is really the sort of thing I mean. I can see that some skills are necessary for all. We all need to know how to read, to write, to understand the laws of the land and our democratic model. But the rest of it? I’m not sure I could argue that knowing Hamlet is more or less important than knowing how tectonic plates work, or that knowing how to use trigonometry is more or less important than understanding the difference between a bass clef and a treble clef.

These thoughts lead me to understand an argument for a really slimmed down core curriculum and plenty of option choices to allow students to choose a really unique and bespoke curriculum. The slimmed down core would include numeracy, literacy, digital literacy and citizenship. And everything else would be optional, allowing students to choose their own truly bespoke path.

In many ways I love this idea, but in many ways I hate it too. At what age would we teach a wider core curriculum and at what age would we introduce this wide choice?  Would we start it at KS3? KS4? KS2? The current system sees a choice given at KS4 -typically started by 13 or 14 year olds (depending on whether the school counts Y9 as KS3 or 4). Do 13 year olds have enough knowledge of themselves, the world, the subjects and the future careers they feed to be able to make an informed choice? Do 16 year olds for that matter?

These reasons lead me to see the alternative argument too, perhaps there should be no real choice for education. Perhaps a broad base which covers all subjects is the best option? That way all students would have a fair crack of the whip. They would be able to make a much more informed choice on their future, when the time came, given their broader knowledge base. But who chooses that broader base? Who decides what bits of the curriculum are the most important? We certainly wouldn’t have time to fit all of all the subjects in if there were no opt outs. At what age would we then allow choice? Would it come at A level? Or would we wait until undergraduate study? Would this cover both academic and vocational subjects? Answers either way to that could see some students put at a disadvantage.

Would some sort of middle option be better? Or would that make it worse? I really don’t know, and I’m conflicted massively on this issue. I’d love to hear others thoughts on the topic.