In the late eighth and early ninth centuries there lived a Persian mathematician called Muhammad ibn Musa al-Khwarizmi. Al-Khwarizmi was an official mathematician and astronomer for the Abbasid Caliphate and was the head of the library at the House of Wisdom in Baghdad – an academy in the original sense, a centre of scholarship and learning which followed in the footsteps of the Library of Alexandria a millennium earlier. Continue reading “Mathematical Stories 4 – An historical and international endeavour”
Back in June 2017 I wrote an article for the Learning Scientists on how I had started to try to incorporate their Six Strategies for Effective Learning into a maths curriculum and lessons.
A year has passed since then and the work has been continuing. I’ve spoken at two conferences recently on this theme – MathsConf14 in Kettering and researchED Rugby – and have shared a few more practical ideas, including resources we have found useful along the way. Continue reading “‘Learning Scientists’ Talk and Scheme of Work”
The Ancient Greek Pythagoreans discovered the existence of irrational numbers in the fifth century BCE, to the legendary demise of one of their number, Hippasus, and were perturbed by them since they contradicted the firmly-held belief that everything related to number and geometry came back to natural numbers and their ratios (rational numbers).
The Greeks were rather late to the party, though. It’s thought that Indian mathematicians were thinking about irrational numbers a whole three hundred years earlier – Manava (c. 720 BCE) thought that certain square roots could not be determined – but, as with many things in the history of mathematics, it is not always clear where, or from whom, an idea originated. Much like any academic history, mathematics is a mix of human thought across time and space.
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”
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”
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.
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”
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.”
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.
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!”