OK, so yesterday it was MathsConf 15. I’ve got loads of takeaways.
- The first session I went to was Jo Morgan’s session on indices. It was phenomenal. Jo puts a lot of work and research into her sessions and it really shows. If you ever get to see her do an ‘In Depth’ presentation, do.
The crux of the presentation was this: Jo used to cover the 3 main indices rules in one lesson. In fact, so did I! I even have a resource on it on TES! What jo, showed, though, is that by doing this we’re denying students the ability to go properly in depth with the topic and gain a proper understanding. For a start, I’ve been getting the language wrong.
The ENTIRE thing is the power. The little number is the index.
We also refer to power in so many different ways that it can be confusing for children
There’s also loads of subtitles in even the multiplication index law. Maybe by going too fast we’re missing talking about a lot of subtleties that could trip pupils up. (Hat tip to Ben Gordon for these pictures, btw)
There’s also a lot of practice we can do. Just because we don’t want to talk about what negative and fraction indices are yet, doesn’t mean we can’t have fractional and negative indices in our answers. It makes them less scary and special when encountered later. We can also start using this as an excuse to practice negative number work, or fractions work or algebra work. Hey, why not ask questions like this:
As you can see, there was loads of content in this talk. But there were a few things I will take into my teaching straight away:
Atomise. Don’t try an do too much at once.
Instead of moving on, go deeper
Don’t miss chances to practise negative numbers at every opportunity.
- Next I went to Peter Mattock’s measuring session. Measuring seems so simple, but there’s so much in there. My 1/U borderline year 11 this year really struggled with a question where a pylon was 11.5 x the height of a man. They couldn’t see how you could have half a man. The multiplicative reasoning of measures hadn’t been embedded. Once more, we need to think more deeply about what we do.
- I then went to a session PRESENTED BY ME! I’ve never done a session before at something like this, and I was really nervous. I even wore a full suit as a kind of ‘suit of armour’ to protect the nerves. I got even more nervous when I got there and MR BARTON WAS IN MY SESSION. Mr Barton is a maths legend. It’s because of his ‘resource of the week’ that I first started sharing my resources. I wanted to be resource of the week. And I was eventually! It was such a buzz. I can’t be the only one that started sharing my resources because of him. Add to that the impact his book has made and his impact in maths teaching in the UK is incalculable.
My session went OK. It was on GapMinder. But the best thing about it was the amount of people who came up to me afterwards to share ideas or resources and the amount of people who pointed me to great stuff on Twitter. Some people got in contact to disagree, which I loved. I don’t want to be right, I want to have a conversation.
If you’re in two minds about doing a session at MathsConf, do. You get so much out of it.
If that wasn’t enough, I was mentioned on the Mr Barton Maths Podcast! This is genuinely the proudest moment of my professional career. I am still beaming.
- Fourth was Mr Barton, Jess (I’m sorry I didn’t catch her last name, which makes me feel bad) and Ben Gordon’s session on variation. It was flipping brilliant. They talked about making student’s think more deeply about the structure of what they’re being asked. Anyone who has read this blog recently knows it’s something I’m into at the moment. And they launched a new website variationtheory.com with loads of variation exercises and stuff. It is, obviously, brilliant.
- This last takeaway is something I really debated putting down. But as much as I enjoyed the day, I also found it really hard. I am generally a very socially anxious person, especially in crowds. MathsConf was very crowded. I found the ‘networking’ sections really, really difficult. Mingling with strangers. It’s something that I’ve always found hard, although teaching has certainly helped me improve in this area. You always worry that you’re either boring people, or attaching yourself onto people like a limpet. I also repeat myself a lot when I do this. I can also sometimes be a ‘bit much’. If I did this to you, I apologise.
However, if you’re someone who is socially anxious, I would still recommend going (maybe bring a friend? Having a friend there has helped me). The people at MathsConf have always been very friendly, and put up with me brilliantly. I would like to thank Jo Morgan and Peter Mattock in particular for both always finding time to talk to me and being really friendly. In fact, everyone at mathsconf is always been friendly. I’ve not had one negative encounter. It’s worth the anxiety.
- Follow Paul Rodrigo on Twitter. He’s a good egg.
Download the word file here
This one was hard. I spent ages rearranging questions and looking at what should be added. Specifically, I had a massive dilemma when it came to introducing fractions. I was trying to point out the ways in which simplifying fractions and simplifying ratio were similar, but I’m not sure that I haven’t just led students down the wrong path thinking they’re equivalent. For instance 5 : 6 is 5/11 and 6/11, not 5/6. Hmmmm.
The variations I used for section A.
- An example where you can use a prime divisor
- The opposite way around. What happens to our answer. Order is important!
- Half one side. 8 : 5 becomes 4 : 5
- One that’s already as simple as possible. Time for some questioning? How do you know you can’t simplify it?
- It’s not just reducing the numbers down. Here you have to multiply up. Deals with what simple is. I have changed this from the picture to make only one number vary from the previous question.
- Needs a non prime divisor. This isn’t really a variation, though. It has nothing really to do with the previous questions!
- Again, double one side
- Double both. Our answer does not double!
- Adding a third part of the ratio. Changes the answer significantly.
- Doubling two parts here. Our parts don’t double in our answer!
If you amend this and it works better, please let me know!
Download the word file here
- A question to start
- Reversing the terms. Does balancing still work?
- A take-away. How does this effect our balance.
- Does reversing the terms still lead us to the same answer
- Increasing the constant by one. What happens? Also: a decimal answer.
- We can have a negative answer
- Divide x, instead of multiplying it.
- Increasing co-efficient of x by one. What happens to our answer?
- Doubling co-efficient of x. Not sure about these last two. I think they may be a step back from question 7. This is the problem with presenting these in a linear format. These questions are variations on question 1, not question 7. I might experiment with some kind of spider diagram.
- Doubling the divisor from 7. Again, maybe the linear way these are written is a bit rubbish.
Don’t know how I like the order of these questions, but there’s lots to think about and something to tweak.
I have found the transition to asking ‘why have they asked you that question? What are they trying to tell you?’ has been difficult for some students, but I think it’s worth devoting time to it. If students are inspecting questions for things like this, maybe they’re more likely to read the question thoroughly and pick out it’s mathematics. Big hope, I know.
I talked a little about the idea for Maths spelling-type tests here.
I’ve used them this year, but I’m not really sure how effective they’ve been. I’m not sure pupils have fully bought into the idea of using learnt facts.
The other thing I noticed is that I hadn’t really presented them in a way that was useful, so I’ve redesigned them and made enough for an entire half term. You can download the pdf here or the PowerPoint file here.
Now for each week/test you get a version with everything filled in to give to the students to revise (two to a page to save on printing), and on the next page there are two of the tests, with blank sections for pupils to fill in from memory.
As always, feedback appreciated.
A student sent me this.
I’ve started a ‘bad maths’ category. Does showing students this kind of stuff and asking for them to be aware/send examples to you make them more mathematically aware?
Lack of updates. Sorry. Crunch time (plus exciting personal stuff). I will get on doing some things in a few weeks. PowerPoints to be done. More variation stuff to work on. More timed questions to set up.
In the meantime: These are GREAT.
I teach a lower attainment year 11 and they often struggle to revise. I like this idea of just doing one question every day to keep the mind fresh.
Lets Get Ready – More Revision Calendars
We’ve gone through some past month’s ones, too.
A little bit of maths each day
I know I’d said I’d do simplifying a ratio first but I got distracted.
PDF Here | Editable excel file here
Another ‘vary and twist’. This time on inverse proportion. Download it here.
I have added a section at the top making explicit that students should make an expectation of the answer before working it out, as I think this is where the power of these types of activity come from.
- A question to start
- Does swapping x and y matter? If not, why not?
- Doubling x, what happens to y? What you expect?
- Doubling y in our initial relationship. Why does this differ in it’s result from doubling x from before?
- As above, but for x
- What happens if we half the value of x we want? Maybe this should be moved up in the list to question 4.
- A multiplication of 10 from the original. Does it hold up to more than halving?
- Now we’re finding x not y!
- We’ve doubled the y. What happens to x? Does the relationship work both ways?
- A decimal answer
As always, feedback would be lovely. I’m not sure I’ve correctly hit the sweet spot between making links and confusing the pupils. I’m also not sure that they flow the way they should.
I guess since I’ve done dividing in a ratio, proportion and inverse I should finish off the module. Expect simplifying a ratio and recipes (which will be a challenge to lay out) to come next.
I’m going to call these Vary and Twist.
Section A is some variation practice. Here’s my thinking behind the variations:
- Simple example
- Context change, numbers stay the same
- OK. Now double what we require. answer doubles
- Amount needed triples, answer triples. Also 6 x first one
- We’ve doubled the number of pens in the first one. essentially having the price…
- Now doubling the price
- Halving the price. Link between 5? Maybe 6 + 7 should be swapped around
- Less pens then initially. Answer will get smaller for first time
- Rounding introduced.
- Don’t just quadruple your answer from 9! You’ll introduce a rounding error!
Sections B and C add a little extension, but they use the idea of spaced practice to make students think a little more than standard blocked practice.
Worksheet is here.
Think I might be using this format for more exercises. I’ve done the table layout now. Took me ages.
I’ve found it’s a little limited, though. Tried to do a sheet with probability trees and it quickly became unmanageable with images.
I’ve been using Mr Barton’s SSDD Problems with my year 11 class. I think they’re really good. They do a really good job of making students pick out what they need to do.
Here’s a great one.
This is great because it makes pupils read the question. It was fantastic for revision because we got to discuss 4 topics in one lesson.
There are loads of great SSDD problems. I recommend Socks in a drawer, this nice circles one and this difficult formula one.
Some are less good, though. This one for instance:
I made this one. I’m not sure it’s a proper SSDD. It’s just 4 different questions based on the same image. Not sure it quite fits the SSDD criteria. I’m also not quite sure I can put my finger on exactly what the SSDD criteria is.
As ever, thoughts appreciated.