Fluency in Mathematics: Part 3
October 8, 2014I gave a talk in March at Pedagoo London (my first public appearance) and again the weekend before last at the La Salle Education maths conference on fluency in mathematics. This post is based on those talks and so, inevitably it has taken several posts and revisits some old ground. Parts 1 and 2 are here and here.
Finally we come to my advice for teaching for fluency. Firstly, something I started doing this year, is starting all learning objectives with “know” or “practise”. I find this covers everything that’s worth teaching and establishes what you are trying to achieve. But the big challenge is over resources. Here are my recommendations.
1) math-drills.com This is an American website (note the lack of an “s” in “math”). However, it has a wide range of free worksheets that emphasise practice. It’s particularly good for number bonds and times tables.
2) Ten Ticks. Probably already known to every maths teacher reading and very common in schools. But there is often a sniffy attitude that Ten Ticks sheets have too many questions on. I beg to differ. If you are using them sensibly (don’t just read off the levels) then they provide the right amount of practice, and usually the right level of increasing difficulty.
3) Mymaths. Again I’m recommending something that is already widespread. However, what I want to point out, to those who already have access, are the many “Beat the Clock” activities. These are absolutely ideal for developing fluency.
Beat the Clock game on Mymaths
4) Make your own worksheets on Excel. If you need students to repeat very similar work then you can create worksheets in Excel which can then be significantly altered by changing only a few cells. So, for instance, by making the answers random numbers it is possible to generate similar but different equation questions repeatedly.
An Excel Spreadsheet. The answers are randomly generated and can be easily changed to generate different versions of the same worksheet (below).
5) Old Textbooks. The fashion for letting students look things up themselves and the hostility to practice has seen textbooks expand their explanatory material and decrease the number of questions. Most of the high achieving maths departments I’ve worked in, or visited, have had textbooks from ten or more years earlier.
A page from a textbook published in 1919
A page from a textbook published in 2008. Those 2 questions are the only ones covering those topics.
The most important principle is not having to hide that you are doing any of these things. Teachers should be allowed to get kids to practise.
If you have any other resources that are good for developing fluency, please suggest them in the comments. Two things that came up in the questions after the talks are Times Table Rock Stars and mental mathematics practice. The latter is one I use a lot, particularly where it is possible for students to hold up answers.
Okay, this isn’t me giving my talk at the maths conference, but if you look closely, it is me sat behind Johnny Ball. Really.
Scenes From The Battleground 
[…] Continued in part 3 […]
Oldandrew, this is slightly offopic, but I thought you would enjoy a look at the piece of “educational research” to be found here:
Click to access FULLTEXT01.pdf
The “researcher” videotaped Finnish maths teachers and was appalled to find they use a lot of traditional methodology (he describes this as “an intelligence and emotional wasteland”). He then solemnly concludes that, since it is clearly inconceivable that such teaching practices could in anyway contribute to Finnish success in PISA maths, the explanation must therefore lie OUTSIDE of the classroom, in cultural factors!
Hello. I teach maths to adult learners who don’t have GCSE. I’ve just discovered mathsdrill.com and my (older) students love it!
I’m wondering if this is because this style of worksheet feels familiar and comfortable to them? The younger students are less keen although they can see the benefit of practice!
We use (and love) TTRockstars too. I love watching my oldest student (72) beating the young guys! Fantastic!
Thanks for the excel idea! Genius :=))
I am interested in the balance between speed and accuracy when developing fluency in the way you describe. Both are important but accuracy is more important. I try to run ‘races’ a similar to those you describe where pupils have five minutes to answer as many questions as they can (times tables, number bonds, short division that sort of thing). They try to beat their personal best. Unfortunately some have taken to rushing too much so their success percentage is not high enough (80% right) but they crunch through a lot more questions. I thought about doing a sort of ‘wipeout’ system where the result is invalidated if they get three wrong or something but I fear this will be ambitious for my very low ability and kill self-esteem.
Any suggestions?
Those text books look scarily like ‘Level Up’, am I right? My school has those (and only those) and I hate them.
I would treat Hattie’s “research” with some caution. His work and use of statistics has been called into question. Search this blogsite’s archives to find more. Kelvin Smythe was the chief inspector on New Zealand schools. http://www.networkonnet.co.nz/index.php?section=education&id=124
I like certain Ten Ticks worksheets and at the start of my career I couldn’t have done without them but as time goes by I rely less and less on them and my teaching has improved dramatically as a result. The problem is that since pupils rarely get to the end of them they miss out on the opportunity to practise the most difficult questions and have only practised a long list of easier questions. They also look very ugly and dated with their Times New Roman font, irritating clip arts which only encourage pupils to doodle on the sheets and poor formatting (fractions are created by underlining text for example). On the other hand, many modern textbooks such as the current Oxford University Press series for GCSE have exercises which are far too short and it amazes me that the authors seem to think that each double-page spread, half of which is explanation, amounts to a lesson’s worth of material. Three resources which I think are a good half-way house between the two are:
1. Sum Books: (http://www.sumbooks.net/) these are slightly shorter exercises than ten ticks but it’s the same idea
2. The Maths MEP pdf files from Plymouth University: (http://www.cimt.plymouth.ac.uk/projects/mep/) I can’t believe I was teaching for over 4 years before I discovered these. I felt betrayed by my PGCE provider that they had never been pointed out to me, presumably because my University thought they were too old fashioned.
3. MathsWatch: (http://www.mathswatch.co.uk/) MathsWatch are best known for their revision videos but their discs also contain excellent worksheets in pdf format. Again, it took me all too long to discover these.
My whole point regarding Ten Ticks is that there is often a lot more to be gained from doing lots of easier questions than we think. Sum sheets I do sometimes use, I just think they are less consistent than Ten Ticks. The Mathswatch sheets are really good for homework, but not so good for learning a new topic.
I guess it depends on your definition of easy. There’s no point in practising something you have already mastered. Personally I think pupils learn the most when they are attempting a problem which is only just within their capabilities, although that’s not to say that there isn’t a place for consolidation.
‘There’s no point in practising something you have already mastered.’
Really? Isn’t that a definition of revision?
No. There’s a difference between being taught something in a lesson and mastering it. The definition of revision is looking at something a second time (or perhaps a third or fourth time). This is necessary because very often it was not completly mastered the first time. But once you have truly mastered something you don’t need further practice. You only need to learn how to ride a bike once.
Isn’t riding a bike considered an exception to the usual state of affairs? i.e. it is singled out as an example of something you don’t forget, unlike most other things.
Also, you can always get better at riding a bike through practice.
“There’s no point in practising something you have already mastered.”
How about to get better at it?
[…] Fluency In Mathematics Part. I Gave A Talk In March At Pedagoo Londonmy First Public Appearance And Again The Weekend Before Last At The La Salle Education Maths Conferenceon Fluency In MathematicsThis Post Is Based On Those Talks And So Inevitably It Has Taken Several Posts And Revisits Some Old GroundParts And Are Here And teachingbattleground.wordpress.com […]