Post date: Jan 31, 2014 7:48:41 PM
Recently I was involved in a discussion about the value of some of the mental maths workbooks that are available in this country. Personally, I do think these books have a value; the varied range of quick-to-answer questions that they usually include, may help improve children's mathematical fluency, speed and ability to readjust to questions from a wide variety of topics. They can be very good revision aids and because children generally can do these independently, they can provide teachers with easy options for home work tasks, or busy work in a multi-class situation.
However, I do have a major issue with these books using the word mental in their titles. Mental math is about the ability to visualise and manipulate numbers. It is about strategies based on mathematical understanding. And these books don't teach that; nor do they show teachers how they could address oral and mental maths in their classrooms. Worse still, they give teachers the impression that by doing one of these books with their class, they can tick off the oral and mental maths requirement of the curriculum.
So what does the Curriculum say about Mental Maths?
“This mathematics curriculum places less emphasis than heretofore on long, complex pen-and-paper calculations and a greater emphasis on mental calculations, estimation, and problem-solving skills. Rapid advances in information technology and the ready availability of calculators have not lessened the need for basic skills”. (Primary School Maths Curriculum, p. 7)
So what does this mean? Well, my interpretation is this:
…less emphasis on long, complex pen-and-paper calculations…
What‘s the point of doing long complex calculations by hand? It’s not very time efficient. And if I can (or can’t) do a shorter version of the algorithm, then a long 3 or 4 step one isn’t going to improve my understanding of what’s going on. Rather, if it's long and/or complex calculations, then I’m probably going to opt for a calculator.
…greater emphasis on mental calculations…
The children need to be taught how to calculate in their heads, to be able to manipulate the numbers and visualise the connections between them, in order to organise them in way that makes sense. This also means recognising when it would be more efficient to calculate it mentally, or when a written algorithm or calculator would be preferable. One way that teachers can do this is by using Think Aloud, where you explain to the class how you might do this, and invite other children’s suggestions. Realising that there is nearly always, more than one way to calculate or solve something in maths, can be a very liberating experience for a child and their perspective of and understanding of maths.
…the ready availability of calculators
Calculators, calculator apps, mobile devices are here to stay. I, personally, find that, in the classroom they can be a fantastic incentive to encourage the children to have a go, particularly when it comes to problem solving. However, they do soon discover that having a calculator does not guarantee arriving at the correct answer, and this emphasises again the importance of understanding what is going on.
… not lessened the need for basic skills…
Even with a calculator everybody still needs to know the basic number facts (aka Tables). And not only should we teach these to children, we should also teach them other strategies that enable them to do calculations mentally.
So, before we go any further, I want you to stop and work this out:
18 x 5 = ?
What’s the answer?
And more importantly, how did you calculate it?
This example was inspired by a post from the Scholastic Frizzle blog, and is one that I was exploring recently with both my fifth class and a group of teachers. Most children from the end of third class up should be able to calculate this using the short multiplication algorithm, but how many of those children could calculate it mentally?
Even in my own class, most of those who could calculate the answer mentally, did it by doing the procedure of the algorithm in their heads.
A small number recognised that 18 = 1 Ten and 8 Units and did (5x10)+(5x8).
With prompting from me, one or two made the connection between 5 times a number being the same as half the ten times and so worked out that if 18x10 was 180 then 18x5 was half that ie 90 (even though we had been using the half 10 times strategy when we had been revising the basic facts of 5).
The teachers, of course, had all these ways above and some more e.g. if you half one factor and double the other you will get the same product ie 18x5=9x10, 14x5=7x10.
Another way is to round 18 to 20 times 5= 100 less 10 (the extra two times 5) = 90
So in a nutshell, why teach oral & mental maths?
It helps children make the links between known and unknown facts
It emphasises that learning mathematics is about methods as much as it is about getting the right answer
Explaining how you worked something out is a powerful way of learning
It helps children realise there is more than one way to solve a problem
It helps build children's confidence
Have I convinced you to go mental with me?! If so, look out for my next post in which I outline some activities that you could use to teach oral and mental maths in any class.