Progressions in Polygons

You know how it is. You start tinkering around with an idea and before you know it, it's a month later and you've written 40 pages' worth of stuff. That's what happened when I started messing around with patterns in the interior angles of polygons this summer. The picture above is of an octagram whose angles form an arithmetic progression.

I started out by looking at simple alternating angle patterns, then moved onto APs and GPs, and finally quadratic sequences. It's not an exhaustive piece of work by any means, but there are lots of interesting discoveries in there. For example, the AP relationships in a quadrilateral (illustrated below) force any such quadrilaterals either to be cyclic, or trapezia! I love it when this kind of unexpected simplicity pops out of what appears to be a complex investigation.

There are lots of places to go with this, too... specific sequences such as polygonal numbers;  into three dimensions with angular deficiency or skew polygons, etc. It's not difficult mathematics, but I suspect I may have poked round in the odd unexplored corner, even if it's only because nobody else could be bothered!

Mathematical Idea Analysis

I was switched onto George Lakoff and Rafael Núñez' seminal work Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being this summer. Understanding it was quite difficult for someone like me who's not a cognitive scientist, but the writing is very clear and the ideas are fascinating. When we finally got all the way to the Euler equation in the fourth case study I felt like applauding!





I do have some issues with their interpretation of the consequences of the theory as a total refutation of the Platonic position (regarding the independent existence of mathematical objects), but that doesn't invalidate what they say regarding the cognitive structures behind mathematical thought.

However, I'm looking forward to sharing some of this thinking with this year's cohort of trainees. It's always good to look at the "nuts and bolts" of our subject, but here we'll be investigating how the nuts and bolts themselves are made!

Royal Institution Maths Masterclasses

Significant lengths in a pentagram...

...are related by the golden section.

I've been fortunate enough to be involved with these for the last couple of years. The Lincolnshire masterclass series for Year 8 pupils is organized by John Slater, with support from Yvonne Croasdaile of the Further Mathematics Support Programme and Robert Heathcote of Queen Elizabeth's Grammar School, Horncastle.

It was my turn to deliver on Saturday 10th March: my class is called "What Happens Eventually?" and is basically about iterative processes, with refreshment stops at the Golden Section and Stupidly Large Numbers! However, I've been finding that there's a lot of unused material left over, so I think next time I'll do the remainder, once I've checked it will work standalone.

The masterclasses run from 10am until 12.30pm, with a short break; we had just over 50 students in one of the larger maths classrooms at Lincoln Christ's Hospital School. The two-and-a-bit hours seemed to flash past and student engagement seemed high - I'm awaiting feedback!

National Numeracy

According to the National Numeracy website, "Poor numeracy is a huge and neglected problem. According to the most recent Skills for Life survey, almost 17 million people in the UK have numeracy skills below those needed for the lowest grade at GCSE – for literacy the comparable figure is 5 million…"

The new charity was launched this week. Their website contains sections on what numeracy is and what the issues are surrounding current attitudes to numeracy in the UK. The resources section has links for teachers/tutors, parents/carers and learners; the resources for teachers currently comprise links to government and Ofsted documents, rather than "chalkface-ready" teaching resources, but there is an invitation for users of the site to contribute in this regard.

I've signed up for regular updates, so I'll keep watch and comment on anything I deem of interest...

NTU Virtual Schools: ESCalate case study

The case study I wrote for the ESCalate initiative Working with Diverse Groups of Learners in the Digital Age is now online: here's a link to it: case study page.

NTU Virtual Schools is a campus-level wiki provided by PBWorks.

Responses from the current PGCE/GTP cohort are being evaluated at present, and these will help us to improve Virtual Schools for next academic year. It looks like I'm going to be shooting more support videos!

Teachers TV

There are numerous places you can find the Teachers TV video archive.  You can find a list of these here.

However, I particularly like www.teachersmedia.co.uk, as it appears to be the only one whose player doesn’t mess up the aspect ratio of the picture when you go to full-screen.

School Holidays



Logo from website frontpage

If, like me, you have to visit trainee teachers in schools across a number of different counties, keeping track of the idiosyncracies of their holiday timetabling can be a chore. Help is at hand in the form of schoolholidaydates.com. I was intending to plod round the various county websites to acquire the holiday information for 2011-12, and stumbled across this. Their initial aim is to offer the school term dates for all counties, but eventually to have the dates for individual schools, taking into account training days, etc.

Having tested a few counties, it seems that some of the information is currently partial, e.g. for Nottinghamshire I was only able to find dates up until Christmas 2011, even though they have been published on the County Council's website. The data for Lincolnshire, Leicestershire and Derbyshire were complete, though a recent change to the Summer half term dates for Leicestershire had not been amended.

None of the school names I entered was recognised, but I understand that the site is very new and they haven't got a great deal of individualised school data yet - this should improve with time.

So with the above provisos, I think this is a worthy venture and should prove to be a useful resource.

First Post

Well, there I was, reading Blogs, Wikis, Podcasts, and Other Powerful Web Tools for Classrooms by Will Richardson on my shiny new Kindle, when the idea hit me that I ought to start a blog of my own. This is the result, and you're reading the first post.

My job is an interesting mixture of teaching maths to intending teachers and supporting those intending teachers once they begin their training. That's why the title Teaching Maths Teaching seemed appropriate. So expect to read posts coming from both of these angles.

I have no idea how frequently I'll be able post - we'll see. The current cohort of PGCE and GTP trainees have just completed their courses, so there should be some time in the near future.