Dreaming about Maths

I've only been back at work three weeks and I've already started to dream about maths again. And not in a good way. I mark a set of homeworks and dream about the answers - they swim around my head all night long, tormenting me. Perhaps I shouldn't mark in the evenings.

I also lie awake at night thinking about lessons that didn't go well. I know, I know - don't dwell on them - after all, I learn from my mistakes and they make me a better teacher.

Today I want to focus on the good lessons. This post is about three things that went well this week. As well as being therapeutic for me, hopefully there'll also be some ideas here to inspire you.

1. Angles
At the end of a sequence of lessons on angles with Year 7 I gave out this vocabulary check. I told my students to try to fill it in without referring to their notes. I was pleased that some high quality work was submitted:

It turned out to be a really worthwhile exercise for revealing misconceptions. The most common misconception was that co-interior angles are equal. There were also a lot of sketches missing the correct parallel line notation:

Just forgetting the arrows or unaware the lines must be parallel?

A few more surprising misconceptions came up too:

Worrying misunderstanding of the definition of parallel

Confusion over vertically opposite angles

Normally I'd avoid an activity that doesn't actually involve solving maths problems, but I think I'll use this one again because it was so revealing.

I took a first look at my Year 7's books this weekend. Some were a big mess so I need to do more work on improving their presentation. I think it's really important to establish good working practices in Year 7. The picture below shows one of the best books in the class. This is why I want to use iVisualiser in my classroom - I want to show this student's book to the class as an example of how classwork should look (margins, sketches in pencil, clear workings, underlined answers etc).

2. Problems
At the end of a sequence of lessons I often make an A3 sheet of problems relating to that topic. The questions come from a variety of sources including Median Don Steward and Brilliant.org, and sometimes I include one or two past GCSE questions. My students work in pairs answering the questions in any order - sometimes this is for a whole lesson, sometimes half a lesson. The example below is one I used in a Year 10 quadratics lesson, after they'd completed a card sorting activity.

The radius problem (bottom left) originated from Chris Smith's newsletter and I've mentioned it in a couple of blog posts before. I told my Year 10s I'd be very impressed if anyone managed to solve it. The next lesson, two girls brought me the correct solution and talked me through their method. I love it when students do maths 'voluntarily' in their own time, and I love it when they surprise me by figuring out the solution to a challenging problem.

Solving the radius problem

I gave the same problem to my Year 9s. A few girls came up the solution 36 - although it was incorrect, their thinking was interesting. They correctly argued that the circle must be in a square - they thought that the top must be a multiple of 9 and the side must be a multiple of 8, so the sides of the square must be a multiple of both 9 and 8 (ie 72). I like their reasoning and they explained it well, but there's no reason why the sides of the square have to be a multiple of 8 and 9. Actually the radius is 29, so the square has sides of length 58.

I've been doing a lot of problem-based lessons this year (using up my school's stocks of A3 paper!) and I've been very impressed by my students' efforts so far. They seem to enjoy these lessons, so I'll keep doing them every now and then.

Lovely problem for a surds problem solving lesson

3. #LikeAGirl
This isn't maths, but it does have a link to maths so bear with me.

I've taken on a Year 11 tutor group this term. They're lovely girls, if a little loud at times. I have three 20 minute afternoon registration slots to fill each week. This week I showed them the brilliant #thisgirlcan video, but they didn't seem particularly inspired. I think it has more of an impact on women my age than teenage girls. The Head of PE then recommended the #likeagirl video and this one got a better reaction. If you haven't seen it, do have a look.


It struck me that this video has parallels with gender issues in maths and science. I work at a girls' school where these gender issues are non-existent. We have over 200 sixth form students taking maths - it's the most popular subject in the school - and there is absolutely no perception of it being a 'male' subject. I admit that there are some disadvantages of single-sex education, but this freedom from the influence of gender stereotypes is one of the clearest advantages I've seen. If I was to tell my students that maths and science are male-dominated, they'd be surprised and perplexed. But in many schools (and in society in general), doing maths 'like a girl' is considered an insult, like throwing like a girl or running like a girl.

The video really got me thinking about the maths gender debate so I'm going to put 'discovering this video' down as my third success of the week.

The rest
Please don't think that every lesson I teach goes well... far from it! Many lessons aren't worth commenting on, and some could actually be classified as disastrous... I tried Plickers for the first time with Year 7 on Friday. At the last minute my iPad app randomly froze so I had to use my iPhone instead. Scanning the room took far too long. In fact, it was painfully slow. We gave up after four questions, which was a shame because I'd spent a while setting it all up. I still really like the idea though, and my students seemed to like it too. So if I can get it working again on my iPad, I'll definitely try again another day.

Speaking of trying new technology, I've set up a multiple choice test for my Year 10s on Monday which I intend to mark using Quick Key. I'll write about how it goes next week.

Polygraph was the absolute highlight of the week for me but I haven't featured it here because I wrote a separate post about it (as soon as I got home from school on Wednesday, because I was so excited!).

That's it from me. I hope there's been some helpful ideas in this post. I think all teachers would find it really worthwhile to reflect on a few things that went well each week. If you want to sleep soundly, don't dwell on the bad stuff, but pat yourself on the back for the good stuff. And don't mark after 9pm!