Just a quick post this time. I’m aware there’s a lot of information to take in during the Core Maths course and that it’d be silly to wait until the end to try and revise it all.

I’ve put together this simple list of questions as an in-class quiz. I’m planning on allowing them to look in their notes so that this task will also serve to see how organised their folders are.

Here are my questions (based on covering Fermi estimation, Correlation/Regression, Numerical data analysis).

Give a suggestion for the size of the population of a small town. |

What is “primary data”? |

What word beginning with R is another one to describe a line of best fit? |

Complete the sentence, “Interpolation is generally _____” |

What is the average life expectancy in the UK? |

How many countries are there? |

What is “discrete data”? |

What is a reasonable suggestion for the height of a house? |

What are the highest and lowest that the correlation coefficient, r, can be? |

T/F In science, a line of best fit can be a curve. |

T/F Standard deviation is linked to consistency of results. |

Briefly describe how a systematic sample is done. |

What is the average number of hours sleep per night? |

As the second term begins, I’ve been thinking about my planning for Core Maths. The short and honest truth is that it’s been taking me *ages*. I want these lessons to be of a quality that I can share with others and I intended to put the time in now, as I go along so that they only need tweaking next year once I have more experience.

I’ve been pulling ideas from Twitter, other teachers and text books to make some resources I’m really proud of and you can download them on the TES. I felt like I wanted to make some resources for Estimation (as there simply isn’t that much around) and I knew I could adapt my numerical analysis, correlation and regression lessons from A level to suit the course.

However, it’s very time consuming and my next topic (see the scheme of work here) is graphical data analysis, which something I’ve really taught much of as it hasn’t been in the AQA S1 and S2 modules. Since these are mostly GCSE topics anyway, I’m going to go down the route of adapting resources I can find and treating this module more as a collation exercise. I’m sure I’ll be writing new material for some other topics and eventually for these ones too but I can’t do it all and there are some great resources out there already anyway!

So, I’m going to have a few posts that are simply a collection of resources, in the order I intend to use them. I’m going to teach each of the graphical methods and then tie them together into a task. First up is:

#### Stem and Leaf diagrams

Beat the Teacher (described here by Jo Morgan)

http://www.resourceaholic.com/2014/07/stem-and-leaf.html

Stem and leaf explanation ppt (Craig Barton)

https://www.tes.com/teaching-resource/stem-and-leaf-powerpoint-lesson-6030328

Creating Stem and Leaf Diagrams (Jo again)

https://drive.google.com/file/d/0B9L2lYGRiK2bOFlobFFDMzE5QW8/edit

Stem and leaf diagram very simple worksheet (only use for very weak students if needed) (nottcl)

https://www.tes.com/teaching-resource/stem-and-leaf-diagrams-worksheets-6018092

Interpreting/reading S&L diagrams inc back to back (I’ll adapt to include some IQR) (Dannytheref)

https://www.tes.com/teaching-resource/interpreting-stem-and-leaf-diagrams-6387426

GCSE exam questions (Maths Genie)

**What does average mean?**

When putting together some slides for this section of Core Maths, I put in the question “What does average mean?” I realised I didn’t actually know where the word comes from so I used Google’s etymology search and found that it comes from a time when cargo ships would be transporting goods around. Sometimes the goods would be damaged and the French word *avarie* is “damage to ships or goods”. The decision as to how to **fairly share out the costs** was developed and the suffix -age from the word damage was used. Eventually, this word came to be associated with a more general sense of sharing things out as is done in the mean.

#### How does Standard Deviation work?

I’ve also been teaching the Standard Deviation. I made a point of going through the long calculation (even though it’s not needed for this course) as I think it’s important to try and understand *what is going on* rather than blindly use a calculator. It’s not a complex process and most students were fine with following it along. I also think it gave them an even better appreciation for the power of practising with their calculator modes (given the alternative process!)

#### When does Standard Deviation matter?

To help come up with situations where standard deviation is important I asked Twitter to suggest scenarios and got a nice list. I’m working on putting these into a worksheet (which I’ll share once it’s ready) but I wanted to thank all those that contributed. I discussed this and the etymology of average on episode 61 of my podcast Wrong, but Useful.

#### Mean and Standard Deviation in Psychology

In terms of comparing data sets using mean and sd, I went looking for other questions and found this one on an AQA A level Psychology paper. (Note that there’s no expectation for them to be able to calculate the sd in that course.)

I think it’s worth noting that it’s 4 marks and looking at the mark scheme is interesting too:

The Examiner’s report on this question is eye-opening too:

Although there were some strong responses, generally students found this harder than anticipated.A number failed to receive any credit due to simply defining the mean and the standard deviation. It was also far too common for students not to understand and answer the ‘justify’ component of the question. Many students simply restated information from the table or provided possible explanations or conclusions, as opposed to justifications. Although students generally saw the mean as showing a difference, there was often the claim that music hindered performance, with confusion regarding time being a higher score, meaning slower.

Worryingly, some students still have little understanding of standard deviation.

Hopefully that’s given you some things to think about regarding this topic and our course will help with that bolded section above!

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.

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

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.

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

- 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.
- 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?”
- 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.
- 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).
- 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 | 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:

*Thanks for explaining the word ‘many’ to me. It means a lot.**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’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.

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.