Hypothesis testing for correlation

I’ve recently started teaching statistics and have the pleasure of teaching both Year 1 and Year 2 side by side.

As I was searching around for a homework to set my Year 13 class, I was inspired to go hunting for some correlated data and this worksheet is what I produced.

Please feel free to let me know if you spot any errors in either the worksheet or the solutions.

Disclaimer: I am not a statistician, so please do tell me if I have made any serious errors!

A change of perspective…

… is sometimes all you need. I made a move to my third school in January, and I haven’t even completed my second year as a qualified teacher yet. The latest move has found me now in a positive and supportive environment. This change has reignited my passion for teaching mathematics, and has finally enabled me to start developing and improving my teaching practice. With this in mind I am now hoping I can make the return to (irregular) blogging and more regular engagement on Twitter.

New AS level maths SAMs

Having spent most of my Saturday this weekend working through the new AS level sample assessment materials for each exam board I thought I would briefly summarise my thoughts so far. Being a little rusty on statistics and mechanics I have brushed up mostly on M1 and S1, so all the binomial distribution and hypothesis testing questions I haven’t touched for now.

As I am currently teaching the Edexcel specification and so decided to attempt their materials first. They are the only exam board who have proposed a 2 hour core pure paper and a 1 hour applied (statistics and mechanics) paper. The material in both papers seemed reasonable and at similar level to the current qualification.

I then looked at the AQA material which seems to be ever so slightly ‘easier’ than the Edexcel papers. AQA, like OCR A and OCR MEI, have gone with two 1 hour 30 minute papers split into pure and applied. For some of the new material, particularly applicable to differentiation from first principles, AQA have designed a ‘guided’ question (see question 8 in paper 1). In contrast, a question on this topic when assessed in all other boards is just asked up front, e.g. Differentiate $f(x)=3x^2$ from first principles (Edexcel paper 1 question 9). There are also some multiple choice questions which, following a brief conversation on Twitter with Tom Bennison, I am informed is similar to their GCSE papers. This, I think, could be seen in both positive and negative views. It’s quite nice to be able to get students thinking about some of the misconceptions and really thinking about their answers in the exam, however some students could get frustrated over the quantity of work they might need to do for a single mark (I make this statement with respect to my year 12 class who showed me their AS physics sample paper in which they sometimes needed to do large amounts of work to find the correct choice).

OCR A were the next papers I looked at and I very much enjoyed these ones. Some more interesting and different questions cropping up and the statistics element taking up what felt like half the first paper. I particularly liked the trigonometry and vectors questions in paper 1 (question 5 & 6) and the proof question in paper 2 (question 6). The papers were slightly more difficult that the Edexcel papers in my opinion, though with some similarities.

Finally, I looked at the MEI materials. The first paper opened up with a nasty looking question in comparison to other papers, but most of the content again seems to be on par with the OCR A sample materials. Interestingly, MEI are also the only exam board to mix the pure and applied questions together, rather than separate the sections.

I still need to look over the physical specifications for each board, but at this stage I think my preferred set of sample materials for the AS in mathematics are those provided for the OCR A.

Next, I think I will look over the A level mathematics materials before I look at some of the further maths. But before that I need to revise some mechanics and statistics!

Edit (12/06/16): Note also that OCR A has included binomial expansions as part of their statistics section, whilst Edexcel and AQA included this within pure.

The NQT year is almost over…

It has been an interesting first year in teaching to say the least. Aside from development in school I have particularly enjoyed engaging with the Twitter community in the sharing of ideas and resources, as well as getting involved with chats and attending CPD events. I have also had the privilege to be involved with the mathematics magazine, Chalkdust.  In this post I hope to document some of the things I have made use of or got involved with during this year.

One of the first Twitter chats I was able to get involved with was #mathsjournalclub which is hosted by Tom Bennison. A new chat which also started last year, the discussions have a mathematics education research paper as the focus, though discussions have also developed around ideas and suggestions which are raised during the chat. Past discussions can be found on Tom’s Storify page. The sixth chat is up for voting until the 9th June here and will take place on Monday 11th July at 8pm. If you don’t already take part, the discussions have all been very interesting and it would be great if you got involved!

I have also tried to get involved with the weekly #mathscpdchat and #mathschat discussions and have had the pleasure of hosting two #mathscpdchat discussions this year (Wild Maths and Marking at A-level). These discussions always have an interesting topic of focus with lots of fruitful discussions. Following a break for half term both of the discussions should be very exciting next week with a special #mathschat webinar and #mathscpdchat focusing on working collaboratively on teaching, learning and assessing mathematics.

I have attended ChristMaths and MathsMeet Glyn (organised by Jo Morgan), MathsConf6 (La Salle Education) and Maths in the Sticks (organised by Stuart Price). All of these event provided excellent presentations and provided me with lots of things to take away and think about. My next planned event is Tom Bennison‘s East Midlands KS5 Mathematics Conference which already has an excellent line up! I would highly recommend getting along to any good CPD event, especially when they are free!

I now frequent many maths teaching resource websites. For A level I tend to find myself looking for something on Integral Maths. For homework, Jo Morgan and Kathryn Forster’s Pret Homework website provides quality and worthwhile worksheets designed by teachers. In addition Jo Morgan’s Resourceaholic website provides access to some outstanding resources which can be used from KS3 to KS5.

I have without a doubt used an extensive list of other resources, however these have been of particular help when struggling to find something good to incorporate into a lesson.

I will be returning to my second PGCE placement school for my second year of teaching and I am looking forward to a change in dynamic and continuing to make use of the outstanding resources that have been made available by fellow mathematics teachers.

Parametric equations card sort

Recently I taught an observed lesson on the introduction of parametric equations (Core 4). One of the tasks which I used towards the end of the lesson was a self-designed card sort activity. This task requires students to match a set of parametric equations with their corresponding Cartesian relation and graph. Within one set of cards there are five groupings, with some of the Cartesian relation and graph cards remaining blank.

A key idea that one grouping in the card sort helps to address is how restrictions upon the parameterised equations may not result in the full Cartesian graph.

The parametric equations used in the task are $x=\sin^2{t}, y=\cos^2{t}$, which for all values of $t$ only gives $x$ and $y$ values between $-1$ and $1$. This results in the Cartesian graph of $x+y=1$, but only a small segment of it (see graph on the left).

When I implemented the task students got engaged with it quickly, some making matches and others getting stuck with manipulating equations to eliminate the parameter. There were certainly a number of challenges encountered, though I thought that the task itself really helped to test their understanding of what they had learnt during the lesson, and provided me with a better idea of who needed more support.

Parametric and Cartesian equations cards

Graph cards

Solution sheet

Please feel free to provide me with any feedback on this task, I would be particularly interested in general thoughts or any suggestions on further developments that could be made to improve the task.

Please also let me know if you make use of this activity and if it is successful!