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Entrance requirements for A Level Maths

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”

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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.”

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.

Please, no more rubbish about times tables!

The human adult spine has 33 vertebrae, the bones that support the rest of the body.  The lumbar vertebrae, in the lower back, bear the weight of the upper body and are very flexible.  If you have lower back problems, it’s often your lumbar vertebrae that are struggling under the weight they have to bear.

Multiplication is a lumbar vertebra in the spinal column of mathematics.  Multiplication supports the weight of, amongst other things: Continue reading “Please, no more rubbish about times tables!”

Adventures in Mastery 5: Making Connections

I taught my year 7 class today and had the most wonderful time.  I really love my year 7s, they’re so enthusiastic.  So far this year we’ve done place value, rounding, four operations (with natural numbers and decimals), powers, roots and primes, negative numbers, order of operations, fractions (including four operations) and are early into our unit on percentages.  Today it was common FDP conversions (quarters, eighths, fifths, thirds, ninths, etc).

We looked at 1/3 and 2/3, which led us to the fact that 0.999999….. = 3/3, which is, of course, 1.  I love teaching this fact, I tell them I’m about to blow their minds, and when I show them the initial reaction is always something like, “but it can’t be 1, it’s less than 1″.   Continue reading “Adventures in Mastery 5: Making Connections”

A Plea to Heads of Maths and Senior Leaders (On Feedback & Marking)

A colleague of mine was leading our TSST (Teacher Subject Specialism Training – for non-specialists who find themselves teaching maths) course this afternoon and was brave enough to mention feedback.  We were chatting at the end of the day and he couldn’t believe the stories he’d just heard.  Mentioning marking and feedback in a room full of teachers from different schools is something I’ve learnt to avoid now, it’s one of the most agonising discussions I encounter.

Let’s make this clear from the start: the evidence of the efficacy of marking is scant (EEF).  Marking is not the same as feedback (Toby French) and the time it takes a teacher to mark a set of books is, most often, disproportionate to the effect that marking actually has on students’ progress (Michael Tidd).  Ofsted does not demand a particular type or frequency of marking (Alex Quigley), so no-one can say they are implementing an insane marking policy thanks to the inspectorate.

Here are some of the worst atrocities my colleague and I have heard: Continue reading “A Plea to Heads of Maths and Senior Leaders (On Feedback & Marking)”

The Importance of Vocabulary

Glaring truism alert!  Subject-specific vocabulary is extremely important. The right academic vocabulary turns a clumsy conversation into an elegant and precise one.

In mathematics we have the issue that certain words have a different meaning in common speech, take “roots” or “degree” for instance (degree has more than one meaning even in mathematics – the degree of a polynomial, degrees in a turn). We also have words that it is perfectly plausible to leave out of the curriculum, and that you will find many students never encounter (such as “commutative” or “subtrahend”). But how much better is it if teacher and student have a shared technical vocabulary, one which helps us to be mutually understood and to express ourselves unambiguously. Continue reading “The Importance of Vocabulary”

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