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!”

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:

- Feedback must help students to improve.
- Feedback must be useful to teachers.
- 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 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.

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!”

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 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)”

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”

In my maths department we are starting on a journey of building a new curriculum based on the principles of mastery. To find out what mastery is, read Mark McCourt. Implementing something different comes with all sorts of challenges but, if it’s a good thing to do, it brings benefits too. One of the benefits I am finding this year is the liberation from the compulsion to produce a three- (or four- or five-) part lesson with objectives and mini-plenaries and some kind of forced activity to (falsely) demonstrate the “progress” my students have made over the course of an hour. By having a curriculum with clear aims and (hopefully) coherent thinking underpinning every aspect I feel more confident to teach the way I feel will be most effective rather than making my lessons a conflation of lots of “best practice” techniques in order to satisfy a checklist. Continue reading “Adventures in Mastery 4: Lesson Sequences”

When rewriting our scheme of work for years 7 to 11 I was conscious that there were some perennial problems I wanted to try and solve. One such problem was that of algebraic misconceptions that arise year-in, year-out. I decided that I would try to address these with what I can best describe as *prognostic practice, *which is practice that directly prepares the students for the algebraic work earlier on in the year. Here are some of the problems, and the associated practice we will do: Continue reading “Adventures in Mastery 3: Prognostic Practice”