what else...
Have you got a mathematical brain?
Find out with Professor Brian Butterworth's mathematical ability test below ...in conjunction with our Mental capital and wellbeing: Dyscalculia event, Cheltenham Science Festival 2008.
Question 1.
The distance from Boston to Portland is 200 km. Three steamers leave Boston simultaneously for Portland. One makes the trip in 10 hours, one in 12 hours and one 15 hours.
How long will it be before all are in Portland?
show me the answer
1. If you attempted any addition, subtraction or multiplication of 10, 12 and 15, then sorry, but no points for you.
2. But if you picked 15 hours, congratulations, give yourself 2 points.
Question 2.
Estimate 3.21 x 5.04
a. 1.6
b. 16
c. 160
d. 1600
e. no idea
show me the answer
1. If you attempted an exact calculation, no points.
2. But if you estimated 16, then give yourself 2 points.
Question 3.
How many black squares in this array?
show me the answer
1. If you counted the squares, no points!
2. If you multiplied 7 x 7, divided by 2, and got 24.5 no points
3. If you multiplied 7 x 7 and noted that the corners are black, well done, 2 points.
Question 4.
Five hundred and sixty three soldiers need to be moved from Camp Alpha to Fort Baxter. Each bus can take 40 soldiers. How many busses will be needed for the journey?
show me the answer
1. 14.075 = no points!
2. 14 = no points!
3. 15 = two points, congratulations!
Obviously you cannot have 0.075 of a coach, and if you have rounded down, three soldiers would be left behind.
Answers 1 and 2 show that your mathematical brain has been captured by the numbers.
Question 5.
(273+273+273+273+273) ÷ 5 =
show me the answer
1. If you added the 273s and then divided by 5, no points.
2. If you saw that there were five 273s, and reasoned that therefore the solution had to be 273, award yourself 2 points.
Question 6.
Jane's field is 270m long by 80m wide, while George's field is 280m long by 70m wide. Who has the larger field?
show me the answer
1. If you calculated 270 x 80 (21600) and 280 x 70 (19600), and said that Jane has the bigger field, no points.
2. If you solved the problem without calculation. For example, by reasoning that Jane has 10 more big segments (10 x 270) while George has 10 more small segments (10 x 70). If you did this, you get 2 points.
3. And if you solved the problem by drawing rectangles like this, then you also get 2 points.
Question 7.
Find the sum of the numbers from 1 - 100.
show me the answer
1. You added 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 ... 100, no points
2. If you thought that the sequence could be folded on itself so that you could add 100 + 1, 99 + 2, 98 + 3, 97 + 4, 96 + 5 ... so that you only had to do half the additions, and you then went on to carry out 50 additions, we'll give you 1 point.
3. If you went one step beyond this, and saw that sum of the whole series was the sum of the first and last digits multiplied by half the number of digits, wow! - you may award yourself 2 points.
Question 8.
Is it possible to colour faces of a cube with only three colours and none sharing an edge?
show me the answer
You have to imagine a cube with two opposite faces, say the top and bottom faces in the same colour, and the faces between them in alternating colours.
1. If you got the correct answer without drawing, take 2 points
2. If you had to draw it first, 1 point.
3. And no points for the wrong answer!
This is a test of spatial ability, which is really important when thinking about geometrical aspects of mathematics.
Question 9.
Imagine the following situation. I am standing in front of you holding a metre cube by the top and bottom corner. How many corners can you see (including the ones I am holding)?
show me the answer
Was your answer 5? If so, you imagined not a cube on its point, but an octahedron - two pyramids joined at the bottom, so no points there.
This problem is a stiff test of your logical construction of objects in space.
If you answered 7, then you get 2 points. If you drew a cube first, then just 1 point.
How did you score?
If you scored 18, then you have survived school with your mathematical brain intact. If you had special difficulty with the last two questions, then you have lost the ability to imagine objects in space.
Did you fail miserably?
Or do you have a mathematical brain?
OK ...here's how to get rid of your maths anxiety
Professor Brian Butterworth, the UK's dyscalculia expert, from the Institute of Cognitive Neuroscience, University College London - www.mathematicalbrain.com
Here is my three-step programme for ridding yourself of maths anxiety. Of course, I cannot give a you specific recipe since I don't know what level of mathematics you have reached. But the principles I will propose can apply at any level.
Step 1.
Slow down
Much of maths anxiety comes from trying to do things too fast. Speed has always been stressed in maths tests. Children at the abacus juku are taught a procedure for solving a problem type, and simply practice that. Of course, they do get faster and more accurate. But because they are not taught alternative procedures, nor encouraged to develop them for themselves, abacus training will not help them see that there are alternatives.
Professor Giyoo Hatano of Keio University, Tokyo, has found that abacus skills do not promote understanding. We have found that estimating the answer before calculating aids understanding, and we have used this method successfully with people who think themselves very poor at maths. This gets both sides of your brain working: the estimation processes of the right hemisphere and the sequential processes of the left hemisphere. It also gives you a check on your answer.
Step 2.
Don't learn anything new, just try to understand what you think you already know
Try to find new ways to do old things. Take something really simple: 5 x 6. You probably "just know" the answer; you don't have to work it out. But take a moment to find another way to do it.
For example, you could transform the problem into 10 x 3. This is very obvious, but it depends on an understanding that n x m = (n x a) x (m/a) = (n/a) x (m x a), or, in words, if you do one thing to one term and do the inverse to the other term, you won't affect the final answer. If you simplify, you will see that what is happening is that you are multiplying the whole problem by 1, because what you have actually done is multiply 5 x 6 by 2/2. You can check that this rule holds by applying it to a new problem, e.g. 98 x 18. (Now there is a danger in the verbal formulation. You may think that because subtraction is somehow the inverse of addition, this problem is the same as 100 x 16 because you have added 2 to one term and subtracted 2 from the other. This is not the case, and the unconfident mathematician will find it very useful to see why.) Why not use a calculator to scale up the idea. If you were thinking through the implications of the 5 x 6 problem, you could test them out with very large numbers.
Doing all this may not help you not help you solve 5 x 6 faster, but it will help you understand multiplication, and how multiplication relates to division, subtraction and addition.
Step 3.
Do it upside down
Don't repeat the same problems. Drill won't aid understanding. Try to see one problem from different perspectives.
When you look at a familiar face standing on your head, or in a mirror, you will notice symmetries and asymmetries you had never noticed before. With mathematics, this can be achieved by trying to see a multiplication as an addition, or a subtraction, or combination of different operations. Do not worry about the answers, but about seeing mathematics and an integrated system. This is really a broader version of Step 2. Follow these three steps when you are faced with a maths problem, and your worries will ease and eventually disappear.
Good luck!
