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The World Is Maths

Mathematical Stories 2 (or Shakespeare never saw a decimal point)

I wrote a blogpost on some interesting stories in the history of maths a couple of years ago which I was reminded of chatting to some historians on Twitter yesterday. The history of maths is not something you really meet until you’re an undergraduate mathematician, and that tends to be only an introduction. It’s something you have to choose to pursue to find much out.

Over the years I have read more and more and the thing that strikes me repeatedly is the way our subject has evolved over time. Take any one topic and its current incarnation seems to be the result of thousands of years of both disparate and conjoined thought across many people on almost every continent, which makes tracing their history quite difficult. Over a few posts I am going to take some topics and look at where they have come from. Continue reading “Mathematical Stories 2 (or Shakespeare never saw a decimal point)”

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Directed Numbers

I’ve been teaching directed numbers to Y7 recently. It’s a topic that always gets me thinking. I am not happy with “two minuses make a plus”, although I was taught it that way (you know, where you circle – – and write + above it). When used as one of the main methods of instruction it can lead to things like -7 + -3 = 10 because the students don’t really know what’s going on. They have an aide-memoire without knowing when to apply it. (And that, for me, is the thing with aides-memoire – I have no issue with them if students know when they are and aren’t applicable or appropriate. When they become the source of the teaching we get problems). Continue reading “Directed Numbers”

More Thoughts on ITE in Maths

Last year I wrote a post on subject knowledge and maths ITE, where I argued that we cannot take for granted the subject knowledge of someone beginning to teach maths. There are many reasons for this, which you can read in the post if you are so inclined, but the tl;dr is that most of us (maths teachers) are good at maths at school, move on from it, and never have to think about school maths in any great depth once we’re on group theory or fluid dynamics or the Poisson distribution.

One thing I mentioned in the post that I want to pick up here is that there is so much fragmentation in our system of ITE that guaranteeing a consistent quality experience for trainees across the country is practically impossible. Continue reading “More Thoughts on ITE in Maths”

Entrance requirements for A Level Maths

UPDATE 16/11/17: After I wrote this post I was contacted by Steve McCormack from the NCETM to discuss the issue directly with Charlie Stripp on the first NCETM podcast. You can listen to the discussion (30 mns), also with the NCETM’s Carol Knights and Secondary maths teacher Rob Beckett, here.

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The new GCSE in mathematics is considerably harder than the old one which has resulted, not at all surprisingly, in very low grade boundaries.  For the Edexcel Higher paper in Summer 2017 a score of 79% across three papers earned the highest possible grade, a Grade 9, and this grade was achieved by around 3.5% of the population across all exam boards.

The changes to A levels in England, with no more modular exams, terminal papers at the end of two years, and difficulty increased just like at GCSE, have resulted in most schools and colleges insisting students take only three subjects.  Where previously a student would study four in Year 12 and “drop” one at the end of the year to continue with three into Year 13, now it is imperative that students are on the correct course from the beginning.  There is no halfway house where they can bin off their worst subject, there are no modules to resit and up their final grade.  Get it wrong and two years of study can end with little to show for it. Continue reading “Entrance requirements for A Level Maths”

To talk or not to talk? That is the question.

People have been talking about silence and dialogue lately.

Is silence golden?

Do talking and collaboration improve learning?

Does it matter whether or not pupils talk?

What type of talk is good talk?

This is probably one of those edu-topics that gets people all partisan, so I’m going to nail my colours to the mast and see what happens. Continue reading “To talk or not to talk? That is the question.”

Guest Post for the Learning Scientists

I was very excited to have written a post for the Learning Scientists last month, whose work is fabulous in spreading the word about effective (and ineffective) strategies throughout the teaching community.

I wrote for them about how I created a mathematics scheme of work trying to embed effective learning strategies from the outset.

You can read the post on their blog.

Algebra: you use the letter ‘x’ more than you ever have done in your whole life!

I started my first algebra unit with Year 7 on Monday.  It’s the essentials of algebraic manipulation: adding, subtracting, multiplying and dividing terms, including those with indices, as well as expanding and factorising single brackets, all pretty standard beginnings in algebra.  In the past I think my first lesson on algebra would consist of a brief introduction then some simple collecting like terms.  From what I’ve seen, that’s generally what comes up first in most schemes of work.  This time, though, I’ve tried to be more deliberate and more pedantic over the details.  Really, really pedantic, because it’s insecurity with the small details that causes so many mistakes for the rest of our students’ experience.  I’m starting out by assuming they have done no algebra.  Many of them have done a little but I’m not prepared to risk that all their different primary experiences were the same, or solid.  (This is a not a criticism of primary teachers, more that I want to take sole responsibility for something so important). Continue reading “Algebra: you use the letter ‘x’ more than you ever have done in your whole life!”

Designing a Feedback (not Marking) Policy

I wrote in this post about how many examples of poor feedback and ridiculous marking I have come across in recent years, much of which is still going on now.  Examples of ridiculous and pointless marking include tick-and-flick, “dialogic” or “triple” marking, anything that makes more work for teachers than students, and anything that provides feedback far too long after the original work was completed (we all know how short our students’ memories are!)

I also mentioned how we are trying to find a better way in our maths department, and the exit ticket forms the basis of this.

After discussions with SLT I’ve designed a new Feedback Policy for the department (note, not a Marking Policy).  As with everything I do, it’s a work in progress and I want to get things right.  When thinking about feedback I have three overarching aims:

  1. Feedback must help students to improve.
  2. Feedback must be useful to teachers.
  3. The benefits must outweigh the costs.

I will come back to these at the end, but first here is the policy. Continue reading “Designing a Feedback (not Marking) Policy”

Truncation

Truncation is new to the National Curriculum and the GCSE and there aren’t many resources out there (textbooks or worksheets).

I found a decent presentation by Rory Mathews, with some handy quick-fire questions on it.  It comes with a worksheet, but there is only a handful of truncation questions on the worksheet before it goes into rounding, so I’ve made a very simple worksheet with practice questions on truncating and writing the error interval for a truncated number.

After spending time on the basics, we’ve done this really nice activity by Peter Mattock which pretty much finished off the topic (apart from all the times we’ll revisit to stop them forgetting, of course!)

That’s it.  An appropriately short post I hope.

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