The World Is Maths

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”

Adventures in Mastery 4: Lesson Sequences

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”

Adventures in Mastery 3: Prognostic Practice

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”

The Wisdom of the Crowd

Sir Francis Galton was a statistician in the 19th century. Thanks to him we have concepts such as correlation and standard deviation.  Galton, it would seem, thought through the filter of statistics, a genius who produced hundreds of papers and books on fields as diverse as meteorology, historiometry and psychometrics and who pioneered the use of questionnaires to gather better information for his statistical analyses.

Last week, at my school’s Open Evening, we conducted a mathematical experiment based on one of Galton’s observations.   Continue reading “The Wisdom of the Crowd”

Subject Knowledge and Initial Teacher Education

In 2015 the Advisory Committee on Mathematics Education (ACME) released their report Beginning Teaching: best in class? High-quality initial teacher education for all teachers of mathematics in England.  The report found that there are many inconsistencies in the provision of maths initial teacher education (ITE) in England, in part due to the variety of routes available into the profession (including university-based postgraduate courses, School Direct, School-Centred Initial Teacher Training (SCITT) and Teach First)) but in the main due to the absence of a shared standard for maths ITE. Continue reading “Subject Knowledge and Initial Teacher Education”

Adventures in Mastery 2: Writing a Scheme of Work

This is post 2 in a series.  In post 1 I discussed why we’re beginning a mastery scheme of work, some of my initial objections, and a brief description of “mastery” in its current incarnation.

In this post I will describe the process that produced my scheme of work, and share the working draft of the scheme itself. Continue reading “Adventures in Mastery 2: Writing a Scheme of Work”

Adventures in Mastery 1: Starting Our Journey

When you’ve been in education a while you see plenty of fads come and go and you become carefully cynical about the latest big pronouncement or the new product that’s going to “transform” your practice.  And so it was that I responded (in my mind) when everyone started to talk about mastery. Continue reading “Adventures in Mastery 1: Starting Our Journey”

A Plague On Both Your Houses! (Or ‘Why I Don’t Like Observations and Lesson Plans’)

Over the last [insert large number here] years, the lesson observation and associated lesson plan have been the status symbol of the excellent teacher.  Schools living in dread of the next Ofsted inspection elevated them to their position at the top of the individual’s evidence pile.  For any observation, objectives were set out, detailing what ALL must learn, what MOST should learn and what SOME were lucky enough to learn, the minutiae of every activity and its purpose were described, every instance of cross-curricular/social/moral/cultural learning was noted and, in all probability, everything was colour-coded (ok, I made that last bit up, but it wouldn’t surprise me).

The thing is, this doesn’t really help anybody: Continue reading “A Plague On Both Your Houses! (Or ‘Why I Don’t Like Observations and Lesson Plans’)”

Cognitive Load and Problem Solving

I was asked recently to deliver a training session for two maths departments on the topic of problem solving.  After internally balking (problem solving as a discrete entity is something that gets on my nerves, “problem solving lessons” even more so) I decided it was the perfect opportunity to talk about cognitive load and relate it to the requested topic. Continue reading “Cognitive Load and Problem Solving”

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