Nuggets

Freddy: “Mr Pearce, we found your blog.”

Me: “Yes?”

Freddy: “It’s all about teaching.”

Me: “What did you expect?”

Freddy: “Some mathematical nuggets?”

Me: “I’m a teacher, not an entertainer.”

OK, so I’m still quite happy with my last line, just because I like the ring of any line of the form “I’m not a …”, which I stole from a friend Sam Bartlett who employs it comedically better than I ever could. But I was being rash – a teacher is, to some extent, an entertainer.

I clarified by saying that I think there is rather a glut of mathematical nuggets out there and so I’m looking to provide something different.  However, I do like nuggets, so I’ll allow myself one (and only one) blog post to share some of my favourites:

The Movie Maths Quiz

movie-maths

Don’t work hard…

dont-work-hard-work-intelligent

The Venn Diagram of Bollocks

venn-diagram-of-bollocks

George Ford on Countdown

Report Cards for Mathematicians

maths-reports

The Three-Switches Problem

three-switches

An interesting problem

Causes of Death

 

DIY Homework

Virtually all of my teaching ideas are stolen, but I think I came up with this one myself last summer.  Maybe that’s a bad sign.  I’d love to hear from others who have tried something similar…

It’s not exactly complicated: students choose their own homework.  Obviously they require some guidance. Click here for the document I show the students outlining my advice.  The basic structure:

  1. Students must choose questions which they can check the answers for (so I’m expecting that they’ll mostly work from the textbook, which has answers at the back – and this has turned out to be the case)
  2. I suggest a minimum of 90 minutes per week for most of my classes, rather than a specific number of questions.
  3. Students should try to challenge themselves, and find questions with which they struggle.  If they’re doing the final few (most difficult) questions from each exercise fully correctly, that’s fine, but otherwise I expect to see mistakes and (attempted) corrections, with questions for me if they can’t get to the correct answer.

I should point out that this is not very different to my usual expectations for homework.  I have always asked students to check their own answers, so that I can focus my time on helping with the problems with which they’ve struggled.

What Went Well

The quantity of work done has impressed me – normally more than I would have set. I obviously can’t tell if a student has actually spent 90 minutes but in general, I think they have done so and many have done much more.

There has been much better differentiation in the difficulty of problems tackled: some students have tackled drill problems from the starts of exercises, others more varied problems from the harder end, and some have extended themselves with Olympiad or university entrance exams.

There has also been differentiation of the topics covered: students have spent different amounts of time on different topics, according to their needs. Some students have also varied the topic they’re working on, and worked on topics covered some time ago, giving them a chance to constantly revise.  I continue to encourage all to do this.

It has encouraged greater reflection and independence: I’ve seen more evidence than before of students learning from their mistakes, and many have engaged in very useful written dialogue with me, asking specific questions about how to tackle a particular problem and letting me know exactly what they don’t understand.

Even Better If

As I discovered in my end of term report, some students have found it difficult to choose questions and hence haven’t enjoyed the freedom as a result. I feel that this issue will diminish as they get more used to the approach. I do suggest a set of questions on each topic during classwork, so if they really don’t want to use initiative, they don’t have to!

A couple of students wanted to be more frequently in a situation where they weren’t able to look up the answers, so that they are forced to check their work more carefully. This is a fair criticism and so I’ll balance DIY homework with occasional ‘assessment homework’ next term.

It is taking me a little longer than previously to give written feedback, as I have to look through a variety of different topics and often have to find the relevant questions for my reference. I don’t mind this too much as I have enjoyed the process of engaging with my students more than writing repetitive comments on a set of near-identical work.

I’ve been keeping a record of which questions each pupil has struggled with, and so far not many have been good at returning to these questions in future homework. I need to continue to encourage them to do so, and this term I’m going to set up a shared spreadsheet to check their progress on them.

Overall

It was probably a bit much to go for this approach with all my sixth form homework this term: when I have a new idea, I do tend to go for it in quite a big way!

However, I do feel that the WWW’s outweigh the EBI’s and so I will continue to use it for at least half of sixth form homework time, probably more.

I’d love to hear from anyone else who has tried something similar and has suggestions on how to make it more effective.

New Year’s Resolutions

Many of these ideas come from a survey of my pupils at the end of last term. So this starts with a brief summary of that rather long post.

  1. Ensure that I’m providing enough guidance and support when asking pupils to investigate unfamiliar problems, by creating more guided resources, and preparing a back up text-book option for certain pupils.
  2. Refer more frequently to the skills from Thinking Mathematically to encourage pupils to know what to do when stuck on a problem and other strategies from Helen to help them develop a growth mindset.
  3. Make use of mini-tests: Mathsbot looks like it will be a good source for these in KS3+4, I need to source something similar for KS5.
  4. Set one or two summative homeworks per class per term, in addition to supporting pupils in choosing their own questions by using Google sheets to share questions which pupils have found difficult and track their progress in re-attempting them.
  5. Take opportunities for whole-class interactivity, particularly with year 10, making use of Dan Meyer’s 3 act tasks.

And others which don’t come from the survey.

  1. Ensure I always make clear the Headache before providing the Aspirin.
  2. Write (type where possible) board notes more clearly and slowly; learning Spanish and trying furiously to copy quickly-disappearing notes down from a board has taught me this!
  3. Continue trialling Inquiry Maths lessons, in particular bringing them to sixth form as well as younger pupils.
  4. Use shared Google doc with each pupil to track their general progress and targets, alongside my target setting form.
  5. Build a website to share my approach to providing summative and formative feedback, both directly to pupils and in written reports.

Trigonometry

The Resource

This is an approach to introducing trigonometry I took from my previous department at Highgate.  It focuses on just the tangent scale factor in this initial intro – we would then return to introduce sine and cosine a month or so later, following a spiral curriculum.

I would start with an introduction on the aim of the lesson: we want to find a link between the sides of a triangle and the angles within it. This could make use of the 3-act math format alongside a real life problem such as finding the height of a mountain: personally I often do this with one of my favourite tracks playing the background: Everest by Public Service Broadcasting.

The worksheet guides pupils to discover that if you divide opposite by adjacent for similar right angled triangles, you always get the same number.  This gives us the link we are looking for. It can be followed up (or proceeded) with a note on why you would expect triangles with the same internal angles to have the same scale factor.

Then for homework, pupils can be each given their own angle to work out this special number for.  At the start of next lesson, I would tabulate the pupil’s results and encourage the class to look for patterns: any incorrect/wildly inaccurate values for tan will stand out and can be quickly corrected.

I’d then demonstrate how we can use this table (for now avoiding the calculator tan button) to estimate sides / angles.  Using the pupils’ own numbers gives them a sense of ownership over the method, which adds a lot of value to the approach.

Suggestions for alternative approaches welcome as ever.