Author: tombennison

On the 9th of May we discussed “Fifty years of A-level mathematics: Have standards changed?” by Ian Jones, Chris Wheadon, Sara Humphries and Matthew Inglis. A pre-print of the article is available here since the published article is behind a paywall.

https://storify.com/tajbennison/mathsjournalclub-discussion-5-a-level-standards#publicize

We were lucky enough to have one of the author’s take part in the discussion and he provided some important insights. I feel that having the authors take part in the twitter chats is very powerful and something I hope we will see more of in the future.

Later this week I will release a poll for the next article, you have a few days to send me any suggestions – please make sure that they are open access 🙂

I will also announce the date for the John Mason article chat as soon as I have one.

Following on from my FP1 Revision Clock activity I have made one for FP2. 

As before the generic clock template is available here. 

The questions are a mix of ones that I have written myself and past exam questions. 

You can find the questions and solutions on my website. 

It took my class slightly over the hour to complete. 

Aiming to do an FP3 and S2 one this weekend. 

Something that I have been meaning to write about for ages and seemed pertinent to today’s #mathscpdchat hosted by Rob Beckett (@RBeckett_Yd) is the idea of mathematical style. 

I’m often saying to my A-Level students that mathematics isn’t just about succeeding at getting an answer. The steps to the answer are the most important along with being able to structure a mathematical argument that is stylish. 

Style and mathematical elegance is of course subjective, but I am beginning to think style should be assessed in A-Level examinations. The proposed problem solving questions with multiple possible approaches would be ideal for this. I believe a comparative judgment on “the most mathematically elegant” approach would be a robust way of assessing this. 

As an example, to me, for the below question the first approach is significantly more elegant than differentiating! 

What do you think? 

Inspired by posts from Mel (@Just_Maths), a nice C1 revision activity from Jo (@mathsjem) and a Core 3 version from Eve Pascal (@Pascal1Eve) I decided to make an FP1 “Keeping Time” Revision Clock activity.

The questions are a mix of my own and past exam papers. I haven’t used it with my class yet, but all being well they will be able to complete all 12 questions in an hour.The questions are here and the generic clock template for printing on to A3 is here.

Please use 🙂 I’m hoping to have an FP2 one done before the end of the week too!

UPDATE: Solutions now available here.

Today (Monday 9th May) we are going to be discussing the recent paper by Ian Jones, Chris Wheadon, Sara Humphries and Matthew Inglis entitled “50 Years of A-Level Mathematics: Have Standards Changed“. . As the article is pay-walled we will be looking at a pre-print version available Here.

Anecdotally most people seem to agree that over time A-Level mathematics has got easier. From my own experience the current C1 module for example contains less than the P1 module that I took – but is scoping down definitely leading to easier exams?

The article we are going to be looking at aims to answer that question by using a comparative judgement approach (see the No More Marking Ltd company that one of the authors runs).

It’s a shame that there weren’t any scripts available to be included in the study from the 1970s and 1980s – why is this I wonder?

To me, this study is certainly stronger than previous comparability studies and they have taken lots of measures to address (and in some cases eliminate) problems associated with this kind of study.

A few things to think about:

• Does the fact that no questions had to be excluded reflect the “constancy” of maths over time?
• Does the concept of “the better mathematician” vary?
• Does the outcome of this study fit with our perceptions?

Join me at 8pm!!

A very short post tonight to share a resource that I made last week in an effort to make the beginning of an FP3 revision session a bit more interesting.

I have created 40 integration questions to be used in a bingo format. The presentation with the questions is available here and there are some pre-made bingo cards available here.

Some of the integrals are quite tricky – the possible answers are shown in the grid below.

I hope you can make use of it 🙂

Tomorrow I am hosting the NCETM’s #mathscpdchat on the topic of GCSE revision.

I thought that I would briefly post tonight with a few thoughts and possible ideas for the discussion tomorrow.

For me, in an ideal world GCSE revision wouldn’t be necessary as if there is true understanding I don’t believe that you should have to coach towards a particular exam, as long as the content has been covered. I also think that it tends to be the time of year where (needs must) we aim to get marks, possibly at the expense of understanding, wheeling out things like formula triangles, “keep change flip” etc to get marks for the precious grades that go towards performance measures. I always try to steer clear of these and of “teaching to the test”, but with the current GCSEs it is easy to create questions for students to practise that are very similar to exam questions see my recent post “Edexcel November 2015 GCSE Paper” .

Some things that I would be interested to discuss tomorrow:

• How do you teach students to revise mathematics?
• Do you feel that GCSE revision dilutes the purity of the subject?
• What are the best ways you can get your students to revise?
• Do you do anything exciting / different in revision lessons?
• How does GCSE revision tie in with intervention?

Looking forward to discussing it all tomorrow 😉

I’ve just enjoyed reading Anne Watson’s latest blog post “Finding Nemo and Dissection” on the Oxford Education blog and at the end of it was something that I haven’t noticed before.

If you represent discrete data as a bar chart, then the arithmetic mean of that data is a number such that if you draw a line at that value on the \(y-\)axis then the area of the bars above the line is the same of the area of the gaps below the line.

For example, consider the data set \(\{6,4,7,2,8,3\}\) which has arithmetic mean \(5\). As you can see from the diagram below the areas above and the gaps below the line (plotted at the arithmetic mean of the data) are equal.

You may have seen that I was a bit stupid and we missed the date of the next #mathsjournalclub because I put the incorrect date in my calendar. 

We were due to discuss the article “Reasoning Reasonably in Mathematics” by John Mason et al on the 11th April, which due to my mistake was moved to the 16th April. However, John Mason has said that he cannot make that date as he will be in Oklahoma, so I am proposing that we postpone it to a date that John can make. I believe, that where possible, having one of the article’s authors taking part in the discussion can improve the discussion significantly, so I hope no one is too frustrated at the repeated re-scheduling. I will let everyone know when I have a suitable date; I have been looking forward to discussing this one as I have tried one of the tasks with a few classes.

However, I would like to have a #mathsjournalclub discussion soon, and given the coming changes to A-Level mathematics  I think looking at the recent paper by Ian Jones, Chris Wheadon, Sara Humphries and Matthew Inglis entitled “50 Years of A-Level Mathematics: Have Standards Changed” would be useful. I am proposing that we discuss this on Monday 9th May at the usual time of 8pm. As the article is pay-walled we will be looking at a pre-print version available Here.

As a bit of a taster, here is a graph from the paper….