Article published 9th March 2009
It was the lack of a grasp of simple probability that led expert witnesses to conclude wrongly that mothers, with more than one child who had suffered a cot death, were guilty of murder.
Sadly not only the juries but also journalists, reporting on the trials, failed to pick-up on this statistical error.
To fail to communicate in maths is to fail to communicate properly and to link with our world - the world of: science, nature, art, architecture, computers, business, shopping, sport, beauty, music...
Think - time, money, temperature, travel, cooking, directions, construction, research. Simple or complex, logical or analytical; think maths.
What is taught?
For teaching purposes maths is broken into the key areas of: number and algebra; shape and space (geometry) and handling data (statistics and probability). As maths extends, many of the topics overlap and so it is important they are learned not only as a skill but with understanding and an ability to apply the knowledge learned and to solve problems. For this reason 'using and applying mathematics' is often referred to as a primary area of mathematics.
Number and algebra
Arithmetic is essential and a good knowledge of times-tables remains an important pre-requisite to success in 11+ maths.
Children will be expected to know: the four rules of number - that is: how to: add, subtract, multiply and divide (not just whole numbers but fractions and decimals too). How to apply these four rules to: integers (positive numbers and negative numbers), to money and measure (including area and volume) and to have a basic working knowledge of percentages. Good old ratio and proportion raises its head too – from adapting recipes through to the time-honoured,
‘If it takes 4 men 3 days to dig two holes how long will it take one man to dig five holes?’
Algebra will include: writing sequences and spotting patterns, deriving and solving simple equations with one unknown eg 3a + 4 = 10. And to use coordinates in all four quadrants (the positive and negative bits).
Things get tricky at 13+ and it is at this stage that many parents get left behind and appreciate that, where needed, a tutor may well add-up to money well-spent. The syllabus extends, for those studying 13+ higher tiers and / or scholarship to: using and applying simultaneous equations, solving inequalities and quadratic equations. Graph work and equations of lines (mainly linear eg y= 4x + 3) are primarily reserved for higher tiers. At all levels children are expected to check their solutions – not only is this good practice but it means the child can see instantly if they have found the correct answer! If any of this sounds overwhelming, remember your child should be covering this work with specialist teachers at school, not with mum and dad.
Shape, space and measures aka geometry
Time to pop to Smiths for a maths set that incorporates a pair of compasses, a protractor, ruler and set square - a pencil sharpener and eraser usually prove handy too!
This is the part of the syllabus that frequently puts a spanner in the works, able students with no-sense of direction, unable to draw accurately or to see 3-D often find shape and space quite a challenge. Meanwhile, armed with calculator, children who have struggled in the arithmetical areas of maths often find they’re pretty adept with the old set square.
Shape and space can be great fun: exploring and drawing shapes; measuring; reflecting; rotating; enlarging, tessellating – a real hands-on area of maths – at least initially. Arithmetic skills are important for perimeter, volume and area work as well as finding unknowns. There is a strong link with algebra too, especially when using formulae; calculating angles or unknown lengths of lines in triangles via Pythagoras (13+) but trigonometry isn't introduced at this level. Bearings, the circle, scale-factors of enlargement (including fractional scale-factors which actually make a shape smaller), prisms and speed are additional 13+ topics.
Handling data – statistics and probability
Time to purchase a pack of coloured pencils – please no felt tips. Get the computer out too – not just to draw graphs charts and tables in excel but to look at the very many graphs and charts used on the web in everyday life.
Tally charts, pie charts, bar graphs, (histograms – no these are NOT bar graphs) and pictographs are favourites with most children. It’s important they get to grips with data that can be quantified – such as weight, and data that can’t eg favourite colour and the difference between discrete data – the number of children in a family (how many times has a child told me they have 1 and a half-brothers as one’s not all there – siblings!) and continuous data which regrettably includes age, weight, time....
Simple statistical calculations are expected: mean (the meanest because you have to add up all the numbers and divide), median (the middle one when they’re all lined up in order), mode (the most popular or fashionable – à la mode – the tallest bar on a bar-chart) and range (how spread out the values are: the difference between the biggest and the smallest). 13+ includes: grouped data, constructing pie charts, using frequency diagrams and drawing and interpreting scatter graphs.
If you are stuck for real life examples of charts and tables we use lots on this website especially on individual school's pages.
The idea of simple probability is introduced and it's time to get to grips with English as terms such as likely, chance, bias and fair are introduced and predictions made. Dice and cards are perennial favourites. Don’t be afraid to use games such as Monopoly® - what chance getting a double six to start!
You can even discuss why throwing three doubles on the trot and thus landing in jail, really is pretty bad luck.
And of course you can begin to work out why the experts got it so horribly wrong...