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.

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!

First half term as an NQT completed…

… And hasn’t it been tough?! An ‘interesting’ start to the year resulted in a number of timetabling (and therefore class) changes, which meant having to go through the introductory stage with classes again after two weeks! I have enjoyed experimenting with a number of ideas and resources I have seen this half term, and the idea of this post is to document some of these, much like my previous post ‘First two weeks as an NQT’. I shall try to ensure that these ideas are ‘new’ and that I am not repeating things which are mentioned there!

First off I want to talk about marking. Whilst I have by no means found the ‘best’ approach to marking, this sticker shared by a member of my department has helped me to share feedback clearly with students. What I really like about it is not only the ‘RAG’ style effort rating bar, but that you can invite students or peers to assess work in their books using the sticker. I am still looking for effective marking methods, so please share your strategies with me!

We have used the diagnostic questions website (@MathsDQs) this half term with year 7 to assist with placing them into ‘appropriate’ sets after half term. These were an excellent resource and I would recommend use of the website across key stages. I imagine the GCSE collections would be invaluable to assist students and teachers in becoming (more) aware of what areas still need to be addressed, and where misconceptions are most often occuring. There is also a collection focusing on the new AQA specification which would also be of benefit.

Due to our mixed ability year 7 classes there were a few occasions when the work was not sufficiently challenging for some pupils. To tackle this I looked at the ‘My Classroom’ post from @solvemymaths which I mentioned in a previous post. I had recalled seeing a section called ‘extension activities’, and when reviewing the post I found the link to resources from mathschallenge. The questions are excellent and challenging, so I printed some of these out which solved the problem of not always having sufficient material to occupy students in the lessons!

With KS5 I have been making use of MEI’s integral maths on a regular basis as well as looking at Jo Morgan’s (@mathsjem) bank of resources on resoureaholic. I am awaiting word on login details for CMEP having seen a selection of these resources at an FMSP development session at UCL earlier in October. I have also started blogging for my KS5 students (see ‘Blogging for KS5’ post) after each lesson, providing them with access to the lesson resources and some additional follow up material. After half term I am beginning a KS5 enrichment club which is starting off as training for the senior maths challenge hosted by the FMSP before developing into a less specific enrichment club. I hope to continue improving where I go to find resources so as to provide my sixth formers with engaging lessons and encourage them to see the real beauty and excitement of mathematics.

Another thing I saw via Jo Morgan is the website Create A Test (@createatest). I consequently took a look and on finding it to be free, signed the school up. It is an outstanding resource for producing assessments and exam style questions with the ability to generate variations of one particular type of question. I really like the website and have already begun to encourage other members of my department to take a look and make use of this FREE resource.

Monday 19th October saw the second maths journal club discussion on Twitter (@mathjournalclub/#mathsjournalclub). This was a nice ‘break’ from teaching, diving back into the research and taking part in an interesting discussion. This focused on Colin Foster’s paper “Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts”. There were a number of great ideas in the paper which I hope to now implement in my future teaching. Check out the storify of the discussion put together by host Tom Bennsion (@DrBennison) here. Also, next discussion is on Monday 7th December!

I am still developing my bank of resources and ideas and the maths education Twittersphere has been one of the effective places for me to do this. Thank you to everyone who freely shares their teaching ideas and resources, so many of us appreciate your hard work!

Chalkdust magazine

I visited UCL for a training course last week and I took the opportunity to catch up with the Chalkdust team, acquiring some copies of their magazine. This is a reasonably new ‘mathsy’ magazine which is being published by students in the mathematics department at UCL.

I’ve not had a proper chance to look thoroughly through it yet, but it looks both professional and full of exciting maths! Congratulations go to the Chalkdust team!

You can view an online version of the magazine in this link if you are interested!

Blogging for KS5

I set up a blog for my KS5 students a couple of weeks ago as a way of providing them with a reference for covered lesson content and extra resources (it also saves me some printing credit too!).

The posts have so far included all the resources used during the lesson (i.e. presentations, PDF of interactive whiteboard teachings, activities, etc.) along with a ‘run down’ of what has happened during the lesson. This provides an opportunity to remind students of how we overcame some misconceptions that may have been raised during the lesson. At the end I have included a homework/private study reminder (with links to worksheets when appropriate) and then some ‘follow up material’. This has generally been extra material such as links to revision videos, extra worksheets and the occasional STEP or UKMT question. Some students have really appreciated this opportunity to ‘stretch’ their knowledge.

This felt like a really good idea at the time and it has been well received by my students so far! I keep plugging it in lessons to ensure that they are all visiting the blog and using it to help with their studies. I hope to include some more posts when I start my KS5 enrichment club after half term as well!