Author: tombennison

A while ago I posted about “Increasing Cognitive Load at A-Level” where I discussed removing the leading steps from some FP1 questions. I think this is an even more powerful technique for the mechanics modules as these questions can be made significantly more difficult by simply removing the diagram that is attached to the question.

I have always thought that at least half of a mechanics paper should have questions where the student needs to draw the diagram themselves.

As an example, consider Question 1 from the Edexcel M1 Paper, June 2014  

  The first part of the question is just a guide to finding the answer to the second part so removing that and the diagram makes the question a bit more challenging.   

As another example, consider question 6: 

 and my increased difficulty version:  

 My full increased difficulty version of this June 2014 M1 paper can be downloaded here.

Last night at 8pm I was sat at home nervously awaiting the start of the first #mathsjournalclub discussion. I really wasn’t sure if anyone would take part – especially after I had found the article relatively hard going! The article didn’t turn out to be what I had expected, but once I had got through the first few pages I found it very interesting and it gave me lots to think about. 

Thankfully, lots of people took part and I really enjoyed hosting the discussion (even if it was surprisingly tiring!). There were some great points made and lots of excellent discussion- see below for some of these. 

If you didn’t take part this time please consider it next time. I will be releasing the poll to choose the article next week so if you have a suggestion send it to me or to the @mathjournalclub account. 

To try and distill the discussion I created the following storify… Please don’t be mad if all of your tweets didn’t make it – there were so many of them!

On the 24th August between 8pm and 9pm the first #mathsjournalclub discussion took place. We were talking about the article “A Glimpse into Secondary Students’ Understanding of Functions” by Brendefur, Hughes and Ely. Discussion was frantic – this is an attempt to provide some kind of record.

On the 24th August between 8pm and 9pm the first #mathsjournalclub discussion took place. We were talking about the article “A Glimpse into Secondary Students’ Understanding of Functions” by Brendefur, Hughes and Ely. Discussion was frantic – this is an attempt to provide some kind of record.

On the 24th August between 8pm and 9pm the first #mathsjournalclub discussion took place. We were talking about the article “A Glimpse into Secondary Students’ Understanding of Functions” by Brendefur, Hughes and Ely. Discussion was frantic – this is an attempt to provide some kind of record.

https://storify.com/tajbennison/getting-started

Very short post today to just promote the first #mathsjournalclub discussion tonight between 8pm and 9pm. We are going to be talking about “A Glimpse into Secondary Students’ Understanding of Functions” by Brendefur, J, Hughes, G and Ely, R which is available here if you haven’t read it yet.

Last week I posted some possible themes for the discussion, for convenience I have reproduced them below:

• What did you think were the key points of the article?
• Do you agree with the four ways given that “students typically represent functional relationships: graphs, tables, verbal descriptions and equations” ?
• Has this article impacted on how you introduce and teach the understanding of functions?
• What are the limitations of the article/research?

The more people who can take part the better the discussion will be so I really would love it if you could make it tonight.. Don’t forget to use the hashtag #mathsjournalclub in all your tweets so that I and others can follow the discussion.

After writing my original Matlab program to plot Barnsley’s fern I thought I would look into it in a bit more detail and read his original paper here and have had a play around with the parameters in the program. I have been trying to generate a fern that looks a bit like one that I saw at Bradgate Park in Leicestershire.

  After a while of adjusting the parameters and getting ferns that I wasn’t completely happy with I decided to look online and see if anyone had come up with some parameter sets already. It turns out they had, and using the given parameters for the Cyclosorus fern  I can come up with something pretty good.

In the notation of the previous post, the affine transformations are given by

\( \begin{align} f_1(x,y) &= \begin{pmatrix} 0.000 & 0.000 \\ 0.000 & 0.250 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} 0.000 \\ -0.400 \end{pmatrix} \\ f_2(x,y) &= \begin{pmatrix} 0.950 & 0.005 \\ -0.005 & 0.930 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} -0.002 \\ 0.500 \end{pmatrix} \\ f_3(x,y) &= \begin{pmatrix} 0.035 & -0.200 \\ 0.160 & 0.040 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} -0.090 \\ 0.020 \end{pmatrix} \\ f_4(x,y) &= \begin{pmatrix} -0.040 & 0.200 \\ 0.160 & 0.040 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} 0.083 \\ 0.12 \end{pmatrix} \end{align} \)

with associated probabilities \(0.02, 0.84, 0.07, 0.07\). These give the following plot after a million iterations.

Have play with the parameters and see what you can come up with. I have also found a very nice bit of html5 and javascript code that generates Barnsley’s ferns, this is here – take a look at it.

When I was teaching mean from a frequency table I remember looking on MyMaths and seeing the questions they had (I don’t use MyMaths that much to be honest), and they had this….

Not holding back now…. I think this is an awful question. This is mainly because of the third column that is titled \(fx\). At no point in the question is either \(f\) of \(x\) defined!! Maybe I am being a bit pedantic, but to me because of this having a column titled \(fx\) is meaningless and sloppy. Ok, I know that \(fx\) seems to be often used in this context, but I really don’t like.

Surely this just sets a bad example for students… especially once they get to A-Level and beyond. Clarity of mathematical exposition is important, and it should make logical sense. It’s like if a student writes \(E(X)\) without first defining the random variable \(X\) – makes me want to cry a little!

If you follow me on Twitter then you probably know that I am pretty passionate about engaging with academia, both in terms of bringing current mathematical research into the classroom (if possible) and by engaging with the mathematical education community.

I feel pretty lucky in that I am based near Nottingham with the University of Nottingham on my doorstep. Not only has it got a beautiful campus and a great maths department but is also the home of The Centre for Research in Mathematics Education (CRME) convened by Malcolm Swan

Among others, Jeremy Hodgen (@JeremyHodgen), Colin Foster (@colinfoster77), Peter Gates @petergates3), Geoff Wake (@geoffwake1), Diane Dalby, Andy Noyes and Mark Simmons (@simmo1363) are all based at the CRME.

They hold an excellent series of seminars during term time, which I try to go to – I think I went to most of them this year – and are well worth the time.

If you have something similar near to you I would recommend that you get involved, and if you are near the CRME come to some of the seminars next year.

Back in May, there seemed to be a craze of posting “shelfies” of our book collections; as mine are spread out over numerous shelves I collated all of mine into a blog post.

Unfortunately I can’t remember who started this (if it was you please come forward!) but many of us on Twitter shared photos of books and briefly mentioned some of your favourite ones. I said about how it would be good to have a central list of books that have either been recommended or reviewed by us on Twitter, maybe listing some of the things that were good about the books.

After this, Stuart Price (@sxpmaths) set off and created website where we could submit books and links to reviews etc to do exactly this. I couldn’t really believe how quickly he got this website up and running.

Unfortunately until now, I haven’t gotten around to submitting any reviews or mentions, but this academic year I plan to change this. I am aiming to give myself some reading time every day (even if it is just 15 minutes) so that I can start to work through my large backlog of books, post reviews on my blog and then send to Stuart to update his site.

I’d really like to encourage other people to submit books and reviews to Stuart too, I think it could become a valuable reference if collaboratively we build it up so that it is fairly comprehensive.