Teaching Maths by @oldandrewuk

Name: Andrew Old
Twitter name: @oldandrewuk
Sector: Secondary
Subject taught (if applicable): Maths
Position: Teacher
What is your advice about? Teaching Maths

1: Do not attempt to teach “conceptual understanding” of something unless you have first checked with somebody with a maths degree that *you* understand it.

2: Practice is the key to fluency. While questions should get harder, never shy away from setting dozens of questions on the same thing.

3: Sort out the basics first: time tables, number bonds and the standard algorithms.

4: There usually is one best way to solve a problem, so teach it and ask students to stick to it until they are good at it.

5: Teach algebra like it is a language, not a set of methods. Explain what is meant by “=”, “solve”, “expressions”, “term”, “find”, “substitute”, “rearrange”, simplify” etc.


11 thoughts on “Teaching Maths by @oldandrewuk

  1. Tom Burkard

    Wonderful–you deserve the William of Occam medal for the year, if not the decade. Alas, you can’t make your career in education by advocating the blindingly obvious or making seemingly ‘complex’ issues simple.


      1. kategladstone

        “The basic facts of addition” can mean either things like “2+3 = 3+2” or things like “2+3 = 5.” Which was your intent?


  2. I agree with two of these, the rest I’m afraid feel antiquated and very shortsighted. Basic knowledge (number bonds, time tables etc) are, for me, the most important. As a Year 6 teacher, I am frustrated by children’s lack of basic knowledge, the basic skills I learnt and mastered by early KS2 (although it was never called that then!).

    Having just started teaching algebra today, I told the children that it is a new language and that they must understand the vocabulary before the concept.

    With regards to conceptual understanding, my understanding is taken from courses, coleagial support and trial and error. Admittedly not the best way but it works and I don’t have access to graduates of pure maths, neither do I need to.

    Repetitive, mundane completion of dozens of similar problems is what I did 30 years ago, it is what turns people off maths and does not show any progress. The appropriate way, nowadays, is to use a small number of problems to develop and embed learning and then challenge children to use their newly acquired skill to demonstrate their ability to apply said skill.

    Finally, some children do need to know ‘one method’ and stick to it but the most appropriate method is the one that the child can do to solve the problem. It may not be the most efficient but if it has the desired output, then we are closer than using an inaccessible method. Of course I always try to encourage efficiency in problem solving but you do need to choose your battles.

    Knowing that @oldandrewuk is a secondary teacher, I wonder if there are a different starterforfive for teaching maths in primary?


    1. Tom Burkard

      I fear that the evidence on teaching alternate algorithms is decidedly against you, especially when applied to pupils who struggle with basic arithmetic. Standard algorithms have stood the test of time because they enable students to automatise basic functions and they free the working memory for higher-order functions. Arithmetic is a lower-order skill and trying to teach computation as a higher-order skill merely wastes time and causes unnecessary confusion.

      The old red herring about teaching ‘number sense’ doesn’t really hold water either. Being able to compute rapidly and automatically will give the child a much better understanding of relative values than counting by twos or fives, ‘chunking’ algorithms, or any of the other bright ideas to emerge from education colleges. When I was conducting research on teacher education, I engaged my step-son (who has a phenomenal IQ) as a researcher. When he calculated the number of teachers who entered ITT and never achieved QTS, I instantly saw that his figure was off by a factor of almost two. He was, of course, a product of modern maths education.


    2. There is a post on primary maths somewhere. https://starterforfive.wordpress.com/2015/11/05/primary-maths-by-antonipolster/

      That said, I stick with my advice. I may not teach primary but I see the results of what happens when it is done badly. And I stick by all those points you challenged. Most of my time at KS3 is spent on getting rid of misconceptions acquired lower down the system, dealing with kids that have been taught something but can’t actually do it because they have never been given the space to practise and, worst of all, teaching new methods to kids that have been taught methods that only work for some problems and then struggling to get them out of resorting to that method in the cases where it won’t work.

      Which is pretty much where my advice came from. Good practice in maths should prepare kids for the next level up, and that means: fluency, no misconceptions and no reliance on methods that only sometimes work.


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