#Mathsconf14 Takeaways

I thought I would use a similar format to my ATM Don Steward takeaways. These are just some quick thoughts. They’re by no means things I’ve thought about for a great deal.

  1. My first session was Peter Mattock’s session on averages. It was great, although in sessions like this I worry I talk too much. On our table we kind of basically agreed we should stop using the term ‘average’ as it’s unhelpful. Mean, median and mode are also different skills. ‘Levelling off’ or sharing, centrality and frequency respectively. Maybe they should be taught as different units. I showed Dudamath, which I love as it has a lovely stats module that does ‘levelling off’ well. Here’s a little video:
  2. I was in Hinal Dhudia and Dani Quinn’s on ‘Making it stick’. They talked a lot on variation theory and questions that make students think. For instance a set of five questions, instead of looking like
    1. 2a + 3 = 7
    2. 3a + 10 = 13
    3. 7a + 5 = 19
    4. 9a + 1 = 10
    5. 6a + 3 = 15You might get something looking more like
    1. 2a + 3 = 7
    2. 4 + 3a = 16
    3. 10  = 2a + 6
    4. 8a + 1 = 5
    5. 5a + 3  = -2
    I’m not sure how I felt about this. I get that we need student’s thinking more. Students often treat work as their doodle. Something to keep their hands busy. And we can play into that by giving them ‘busywork’. Learning is the residue of thought, and all that jazz. I’m just not sure if this is the way to do it. I worry that too much intervention is required between each question, and I’m not sue where this fits in with variation theory.NOTE: This is not to say I didn’t enjoy Hinal and Dani’s session. Quite the opposite. It gave me lots to think about
  3. At lunch I did Martin Noon’s session on braiding. I found it extremely difficult but fascinating.
  4. After lunch came Jemma Sherwood’s session on building effective learning. Lots of good practice in this. I use Corbett Maths 5-A-Day with every class, every day. I really think it helps build up long term memory and it’s effective at building routines.
    Jemma talked about the idea of a three-part lesson being an issue. We fit things into an hour, even if that’s the appropriate amount of time. Not everything needs a plenary after every lesson. I agree with this generally, but I think the idea of ‘episodes’ of learning is useful. Something to ponder.
  5. Last, but not least was Craig Barton’s packed session. The man’s a flipping’ celebrity.
    He talked a lot about only varying one aspect of a question to make students predict what was going to happen. Having predictions either confirmed or rejected is powerful. I am thinking of building this into stuff that I do.
    He also launched two new websites! https://mathsvenns.com with rich tasks and the amazing SSDD problems, which I think are PHENOMENAL. He’s looking for more. I’ll get writing one this week.

As usual MathsConf was ace. I love the conversations you’re able to have and the enthusiasm of everyone there is inspiring and wonderful.

I’ll be going to MathsConf15. I’ll see you there!

Maths in the real world – The Sun’s Brexit percentages

This piece of maths in The Sun was all over Twitter this week. It was retweeted and praised by MP Jacob Rees Mogg. The maths in it is wrong. Wrong, but interesting.

A lot of people tried to correct it on Twitter, but Twitter is not the place for explaining mathematical content.

The Sun has tried to calculate the cost of items – the tariff percentages. I’m not going to talk about things like tariff calculations being based on other things apart from the retail price, or the fact that some of these items are from tariff-free countries. I am merely going to talk about the common percentage misconception and why maths matters.

The easiest way to see the error The Sun have made is by looking at the calculation for butter.

This seems to make sense. 50% of £2 is £1, so take £1 off the price, and presto. Except, working backwards we can see that this doesn’t work.

If butter cost £1, and we applied a 50% tariff to it, the final cost would be £1.50. The maths doesn’t stand up when working in reverse.

How should we do it? 

I think the easiest way to think about this is to call the original price 100%. After the 50% tariff has been applied our new price (£2) represents 150%. To find 50% of this new amount, we actually have to divide £2 by 3, as \frac{150}{3} = 50 . We can then take away our 50%. 2 - \frac{2}{3}

The new price should be £1.33 (and a third).

Does this matter? 

Well, kind of. I don’t think anyone would have been less convinced by the new, accurate figures. I do, however, think that we need to be careful about promoting sloppy mathematical thinking in the public arena. At the very least, it is indeed an example of ‘real life’ maths.

Several people on Twitter have suggested it as a nice activity to do in lesson, to correct the figures. However, I would be careful about the surface of the problem distracting from what is intended to be learnt.

I think The Sun could do well to offer a correction, along with a page explaining the mathematics.

Don Steward ATM session: 5 thoughts

I’m trying a new kind of post. I went to the ATM/MA Don Steward presentation on Saturday. It was excellent, and if you get a chance to see Don speak, go. Don has uploaded his slides here. Rather than the daunting task of writing a full follow-up, I thought I’d just write my thoughts down in a quick bullet-point format.

  • It was nice to do some maths.
    Part of the session involved doing some of the activities that Don had devised. It was nice to sit with fellow professionals and actually just do some maths. Lots of interesting conversations were had.
  • Don is a master of task design
    I love the way that Don designs tasks, in both meanings of the word. His worksheets are always beautifully presented, but also very well designed to introduce concepts of generality. I love the way he might introduce something simple like

    and twist it like
    this was in an introduction to the difference of two squares.It was nice to see these tasks introduced by Don, though. Sometimes it’s difficult to tell what someone means from a task by looking at it.
  • I was struck by the importance of subject knowledge.
    Don’s activities go off on interesting tangents, often only made possible because of Don’s subject knowledge. Subject knowledge is always something to work on. We’re all always learning.
  • Sometimes, a nice visual is useful. Here’s a lovely one showing the (n-2) \times 108 rule.

Everyone should read ‘How I Wish I taught Maths’

This isn’t a review. I’m about halfway through Craig’s book, so I can’t offer a judgement as to if the book is good or not. This is simply a suggestion: everyone should read this book, and everyone should read it ASAP.

The book chronicles Craig’s mathematics teaching journey, from being the king of tarsia, to the complete about turn he has taken.

I’m not sure I agree with everything I’ve read so far, but that’s what makes the book great. It’s sparked discussions. Several of us are reading the book at work (I’m trying to get the entire faculty to do so. I’ve persuaded 5/12 so far) and the discussions around the book have been, as Craig would say, flippin’ brilliant.

It’s the book’s willingness to get into the weeds that I really have appreciated so far. This is a book for maths teachers. It’s laser focused, which is what makes it so great. Ever sat in a CPD and though ‘Yes, but how do I do this in maths?’, well this book is the exact opposite of that. It’s full of wonderful examples I wouldn’t have come across (ie : \frac{6}{35} \times \frac{35}{3} \times \frac{11}{14} . These discussions have been gold dust. They’re enthusiasm generators.

One of the things that I think can get lost in teaching maths, is that we are learning along with our pupils. I am trying to teach my pupils maths, but I am also trying to learn how to become a more effective and better maths teacher. Every chapter so far has had me walking into class the next day ready to try something new, and reflect on why it did or didn’t work.

This book is, so far, a wonderful addition to the conversation and I really recommend you read it.

Areas of triangles

I went to an interesting talk by Ed Southall (author of Yes: But Why?) at Mathsconf. He talked about area of triangle problems, which I thought about again as I was teaching it this week.

In his opinion, we often test the wrong skill. That is, we test that students can multiply and half, but not which lengths to multiply and half. He has a nice worksheet where you just identify the height and the width of various triangles.

I was looking for a worksheet on finding the area of triangles, and was reminded of this and struck by how many simply gave two sides. I was also struck by how much of the extension focused on compound shapes (which in my mind is a different skill), rather than on giving students more information that they needed.

In this worksheet I have tried to design a progression. From counting squares all the way up to giving students information overload and expecting them to pick out what to do.

If I were to add more extension I would include the angles. I think it would lead to interesting discussions.

The worksheet is here 

Ben Newmark: Why I killed my starters

So welcome to my lesson. Pens out. One to fifteen in your margins. Nothing new, it’s a review. Question one..

https://bennewmark.wordpress.com/2017/11/13/nothing-new-its-a-review-on-why-i-killed-my-starters/

A thought: Maybe ‘fun’ starters were implemented partly as a behaviour tool. Might also explain the persistence of ‘high pace’ lessons with lots of superficial tasks. Keeps pupils busy, even if it doesn’t result in much learning.
I’ve found the Corbett Maths 5-a-day to be good starters, although Ben’s idea of 5 from the last lesson, 5 from the unit and 5 from anywhere makes sense.
Might start incorporating this into my lessons (when I get around to actually making them again).
Edit: I had a go at making something like this for the first lesson in my equivalent fractions unit. I’m not sure I’ve got the formatting right. It looks a little messy for me.
Download it here. I’ve done two duplicate pages and an answer pages. This allows you to print them off ‘two on a page’ which saves printing. I’ll continue to tinker.