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Types of Data

Here’s a simple resource I’ve created that I like. It was based on a tweet I sent asking for examples of discrete data that aren’t integers and aren’t shoe sizes.

I’ve combined those suggestions along with some continuous and qualitative types (both of which are far easier to come up with!) and made them into a tick sheet. Students work collaboratively on the first set of examples, then, after going through those answers together, there’s another set for them to have a go at by themselves.

Worksheet 1 Types of data

Thanks to all those that contributed and feel free to use this yourself.

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Core Maths – reflections so far

I’ve been teaching Core Maths for 6 weeks now and I think it’s about time for some reflections. A lot of this focuses on things that I’d like to improve/modify for next year but it’s worth pointing out that plenty has gone well!

If you have any suggestions, hints, tips or solutions, please leave a comment.

Estimation

This was a great choice to start with. It’s punchy, attention grabbing and ‘different’ to GCSE maths. It feels like it’s relevant to do and there are easy links both to real life but also to more generic ‘good skills to develop’. A lot of my students have really enjoyed the liberation of not having to focus on the right answer.

Students starting late

Due to the nature of post 16 courses, there were quite a few students who missed some of the first lessons. I need to think of a ‘catch up’ system that doesn’t take up too much of my time. This is also true for students that miss a lesson.

Homework

This has broadly gone well (they were expecting to get homework) but I’d underestimated the length of time it’d take to mark them. I’ll probably stick with it next year and see if just being more aware of the marking time helps.

Resources

There just aren’t that many out there (mine are here and updating as I go). I’m trying really hard to make mine good quality and therefore reusable so it is taking a long time per lesson.

Twitter

Having said that, there is a strong group of teachers that are very good at sharing and giving advice on twitter. If you’re not already on there, I’d really recommend it just for this! The hashtag #CoreMaths is well worth a look every now and again.

Correlation/regression

This was the first topic that really lost some of the students, particularly those with lower grades at GCSE. Unsurprisingly, their straight line graph work wasn’t secure and the complicated nature of the regression lines was a bit much. I also think that the correlation topic was a bit complex and I need to consider how to deliver this better (maybe just more slowly) next time.

Calculators

They don’t all have them. I want them to have the Casio fx991-Class Wiz but they’re up to £30 each! There’s the possibility of us doing a loan scheme but I do think the lack of calculators in general did not help with correlation and regression. There was, unfortunately, a correlation with those that did less well at GCSE tending to be the ones that did not have calculators.

AMSP

The Advanced Maths Support Programme is fantastic. They are busy on twitter and working hard behind the scenes to support maths teachers in delivering this course. They are running some CPD sessions soon and, in a pretty much unprecedented turn of events for CPD, they asked what sort of things we’d want to be included and then have actually made a course focussing on those things. What more could you want? If you’re not registered to get their emails, do it now!

So, in summary, obviously a mixed bag with this new course but lots of positives and some things to work on for next year.

How funny were the jokes?

I ran a survey recently asking people to rate some jokes so that I could use the results with my Core Maths classes. Several people said they were interested in the results and I thought I’d share them along with what I plan to do with them here.

The jokes

There were 10 of them and they’re presented here in no particular order:

  • I can’t stand Russian dolls. They’re full of themselves.
  • When I worked as a librarian, if anyone ever asked where the books on paranoia were, I’d always whisper, “They’re behind you.”
  • Someone complimented me on my driving the other day. I got back to the car and there was a little sign saying “Parking: Fine”, which was nice of them.
  • I used to train racing snails. One day, I took the shells off to see if they’d go faster. It didn’t really work and, if anything, it made them more sluggish.
  • I had a job drilling holes for water – it was well boring.
  • Cheer leading exams are easy. You go in and shout “Give me an A”.
  • I got really emotional this morning at the petrol station. I don’t know why, I just started filling up.
  • I’ve started a business selling ejector seats to holy people. Prophets are through the roof!
  • Thanks for explaining the word ‘many’ to me. It means a lot.
  • I’ve always wanted a job putting up mirrors. It’s something I can really see myself doing.

Assuming you’re still with me and not uncontrollably laughing, here’s a bit more detail about my survey design.

Survey design and distribution

  1. I deliberately made it an anonymous survey and didn’t ask for any details other than “How funny are these?” I think this probably means that people are more happy to answer but it does mean I can’t do as much about drilling into the data.
  2. A scale of 0 to 4 allows a sensible “This isn’t funny = 0” rating and also allows enough scope for differentiating between jokes without forcing people to decide “Is this an 8 or a 7?”
  3. Each person that answered the survey had the jokes presented in a random order to avoid the potential issue of skewing results. For example if a mediocre joke followed a poor joke, then the mediocre one may get an unfairly high score.
  4. I shared my survey mostly via Twitter so it has been answered by the kind of people that follow me (and the people that follow them).
  5. I asked people to retweet the link just to get more responses.

The results

There were 585 responses and you can see a spreadsheet of the raw results here. (You’re welcome to use them however you like.)

What am I going to do with them?

Correlation

One main reason for doing this was to be able to look into correlation. For that, I’m going to do a statistically very dodgy move of finding the mean average rating for each joke. This is something you shouldn’t do with Likert scale data as the scale isn’t linear (ie 4 isn’t twice as funny as 2). However, I do think it’ll give a sense of which jokes were rated more highly and I’ll have to hope the Stats Gods will let me off. I promise I’ll discuss this in class.

I’ve also asked each of my classes to rate the same jokes and I’ll get them to see if there’s a correlation between the rating they gave and my followers. I’ll also get them to see if there’s a better correlation between their average ratings and those of the other class.

I did consider giving them one fewer joke to rate and use regression to predict their rating. However, I suspect the correlation will be weak and therefore the regression will be a poor predictor so I’m a little wary of showing them a scenario where regression doesn’t seem to work.

Averages and Spreads

I’m also going to use the data later in the course as the basis for a discussion about the types of averages and pros/cons of each. Modal response is probably not very helpful as they’re mostly just ‘3’ (on Twitter responses at least) and Median has a similar problem.

I will also (committing the same Likert scale crime) use the data to find the standard deviation of each joke to find the most ‘marmite’ one. Those with lower standard deviations may well have been more consistent in their ratings while those with a larger sd may have been more polarising.

Here are the mean average results in case you’re interested:

Mean Twitter Class C Class M
Russian Dolls 2.356 2.333 1.778
Paranoia 2.471 1.889 1.222
Park Fine 2.132 2.111 2.333
Racing Snails 2.535 2.111 1.556
Well Boring 2.047 1.111 1.333
Cheer Leading 1.941 2.222 1.556
Filling up 1.925 1.333 1
Ejector Seats 2.502 2.111 2.444
Means a Lot 2.55 1.556 2.333
Mirrors 2.341 1.333 1.667
Charts

These make some fairly nice bar charts that are interesting to compare and explore/discuss. I might see if there’s anything dodgy I can do to make my favourite joke/s appear more popular than they actually were and let the students play detectives with my misleading graphs!

Using computers

I may also use these as a ‘large data set’ for students to play with on computers. That’s only just occurred to me so I can’t say I’ve given it much thought but I’m sure there’s something there! Will probably be worth looking into if there are any weird results or any cases of people just rating some of the jokes and how we might deal with that.

Comparing to last time

I have done this experiment before (you can see the results here). It wasn’t all the same jokes although you’ll see that there are some repeats. There’s likely to be something we could do along the lines of “Did the jokes that featured both times seem to rank in approximately the same place each time?”

Thank you

Finally, thanks to everyone that read the jokes and rated them. Thanks also to everyone that retweeted the link so it could be seen by a wider audience. If you do something interesting with this data, do let me know!

The ‘actual’ results

Given all of the Likert caveats I mentioned above, here’s my tentative suggestion for top three performing jokes:

  1. Thanks for explaining the word ‘many’ to me. It means a lot.
  2. I used to train racing snails. One day, I took the shells off to see if they’d go faster. It didn’t really work and, if anything, it made them more sluggish.
  3. I’ve started a business selling ejector seats to holy people. Prophets are through the roof!

Their bar charts are below and their mean averages are above. See if you agree.

ejector seats

Ejector seats

Means a lot

It means ‘a lot’

racing snails

Racing Snails

 

Organisation from year 11 to year 12

A lot happens to a student between the end of year 11 and the start of year 12. They find out how the last few years of study has paid off, they make final choices about what to study in year 12 and they get the longest summer break they’ve ever had. However, they don’t suddenly learn how to organise their notes and deal with a ring binder system after the security of an exercise book is taken away.

It’s pretty common for some students to be struggling with organisation and to pick up some concerns for this. One teacher commented how a student didn’t have a system at all and was simply putting their loose bits of paper into their school bag.

To help combat this while also providing course material, I’ve made a set of subject dividers for Core Maths. I created some mind maps using mindmup  and copied them into publisher along with a bit more information. Our reprographics department printed each one out on to a different colour of card and then hole punched them. They look great and some of the students were very excited by them. They now don’t have any excuse for knowing exactly where to file each bit of work!

The files are aimed at the AQA course and, specifically the paper 2A option. If you’d like them, you can find them (free) in my Core Maths bundle on TES.

Is Zero even?

Jo Gledhill (@JoLocke1) asked this on Twitter:

… thoughts on 0 being even or neither!! Some of my dept say neither I say even as a multiple of 2 sorry?!?!?

Here’s my thoughts about what makes something even as it’s something that comes up in my classes often when I’m doing the caterpillars investigation.

Even numbers end in 0, 2, 4, 6 or 8

This one often comes up with students and I’d agree with the caveat that we’re talking about integers. I wouldn’t want to have to say that 1.2 is an even number for example.

Even numbers are (integer) multiples of two

Passes this test. 0 = 0 × 2

Stacking up a pile of blocks

If you stack up the blocks into two piles, the top is level (even). This works with 0.

Sharing it out

When you share an odd number of things equally between two people, you have an odd one left over at the end (remainder one). That doesn’t happen with two.

It fits the pattern

-3, -2, -1, 0, 1, 2, 3

odd, even, odd, even, odd, even, odd

So, in conclusion

0 is even

*******************************************

In other 0 related news:

0 is neither positive nor negative

0 may be a natural number or not, depending on which definition you use!

 

 

Correlation and line of best fit

Correlation

Soon, I’ll be moving on to the topic of correlation and regression with my Core Maths classes. It’s a topic that I think often makes intuitive sense (you can have a feeling of what correlation you might expect) while also being something that it’s easy to see as being useful.

For me, it’s important in Core Maths lessons that they are more than ‘just about the maths’ when possible so this seems like a good time to talk about spurious correlations and also to have some fun. I’ve made four scatter graphs that relate to some well-known sayings. See if you can figure out what saying each one is!

Bigger they come harder they fall All workEarly bird Empty vessels

They’re just meant to be a bit of fun and a nice way in to the topic. (I’m well aware they are bending the exact meanings of the sayings in some case.)

Line of best fit

I’ve been talking to a couple of the science teachers in my school (this one and this one) about some of the things we do differently in maths in science. It turns out that are just some different phrasings that are used and I don’t think we are going to get a collective agreement. So, it makes sense to explicitly point these out to students so that they just get the idea that we deal with things differently. Here’s a slide from from my correlation and regression lesson notes. You can find the whole powerpoint over on TES. (Along with some other resources.)

line of best fit

30 Second Challenges Starter

Just a really quick post to share a resource that I like. This one is a site made by Christian Lawson-Perfect that recreates the 30 second arithmetic challenges found in some newspapers.

arithmetic challenge

Great for projecting on to the screen for the class to do and is even useful for tutor time.

The link is here http://christianp.github.io/30secondchallenge/