On a cold and breezy Sunday afternoon, with cup of tea in one hand and red pen in the other, I found myself marking a stack of Year 7 assessment papers. The students had generally performed well on things like areas of shapes, written methods of calculation, even simple algebra, and I felt my mood lifting. Then came Question 18:
Paul has 15 T-shirts. The information below shows the colours of his T-shirts:
2 dark blue
1 light blue
Paul is going to take one of his T-shirts at random:
(a) What is the probability the T-shirt will be red?
(b) What is the probability the T-shirt will not be black?
(c) Paul takes one of his blue T-shirts at random. What is the probability it is light blue?
Would anybody like to guess what the most common responses were from this bright bunch of Year 7s?
(a) Not likely
(b) Quite likely
(c) Sort of likely
I wanted to cry.
Probability is (probably) my favourite topic in maths. I love the way that it is practical, useful, often surprising, and how it creeps into many parts of everyday life. However, I despair at how poorly it can be understood by even the brightest of students, and how much it can be detested by even the keenest young mathematicians.
So, I put my pen down, wiped away my tears, and thought about how I would solve this problem if I was in charge of the World of Maths.
Firstly, I would ban the use of likely and unlikely as a mean of introducing students to probability. Who is to say what likely actually means. Is 4 out of 7 likely? How about 51 out of 100? And once students are used to describing probabilities as likely or unlikely, it is incredibly difficult to wean them off it and get them using actual values, as the example above shows.
Secondly, I would ban the use of decimals and percentages to describe probabilities, and stick to fractions. I know there is a pretty strong argument for not teaching fractions at all in the computer-dominated world, but with probability I believe fractions make intuitive sense. In the question above, the reason that the answer to (a) is 3/15 is because 3 of the 15 T-shirts in Paul’s colourful collection are red. I feel bringing decimals and percentages into play makes it harder for students to conceptualise. More importantly, if students struggle with place value or adding decimals, then their journey to understanding probability is off the tracks before it has even begun in much the same way as a poor knowledge of equations of straight lines stops students being able to carry out reflections. Get students understanding probability as a concept first, worry about the different forms answers can take second.
Finally, I would ban questions that don’t make sense. The probability Tony has chips for tea is 0.2. Good for Tony. But why is that the probability? How does Tony know? Ask the students and they may just be able to figure out that perhaps Tony has kept a record of his previous 10 teas and he has noticed he has had chips twice. Is this a good way of estimating probability? Before you know it, you are venturing into the areas of experimental probability, sampling, bias and independent events, all with real life situations that students can understand.
There are some amazing probability resources on TES, involving games, puzzles, lotteries and interactivities. They can help bring the subject to life, engaging students in a topic that they can relate to. Will all of this help students better understand probability and encourage them to enjoy the subject? I’d say it is quite likely.
Craig Barton is an AST from the Bolton area. He is also the creator of www.mrbartonmaths.com and can be found on Twitter using @mrbartonmaths
Topic Special – Probability http://www.tes.co.uk/article.aspx?storyCode=6080845
Improving Learning in Mathematics: Mostly Statistics – http://www.tes.co.uk/article.aspx?storyCode=6088333