Here is an exam question from a recent Mechanics module paper: “A particle is moving in a straight line from O to P with a constant acceleration of 4ms-2. Its velocity at P is 48ms-1 and it takes 12 seconds to travel from O to P. Find (a) the particle’s velocity at O and (b) the distance OP.”
Is this a good question? It tests students’ knowledge of kinematics and their use of the SUVAT equations, so in that sense perhaps it is.
But wait a minute: there are three figures given in the question, and it will be of little surprise to anyone that these are the exact same three figures, no more and no less, that are required to answer both parts of the question.
When, in real life, are we confronted with problems to solve where we are given the exact information required to solve them? When do we encounter problems where we do not have to disregard surplus information, or hunt down information that has been left out? If we do not expose our students to these problems at school age, how are we preparing them for adult life?
Step forward Dan Meyer, a former high school maths teacher from the USA, currently studying a Stanford University. In a very popular TED talk, he makes this point, but more importantly, he offers up a solution… 3 Act Math!
In Act 1, students are presented with a “hook”. This hook is usually a photo or a video, and crucially it is a real life problem. One nice example is “Pizza Doubler” where students are shown a picture of a lovely slice of pizza alongside two coupons, one offering to double the sector angle of the pizza and one offering to double the radius. Act 1 concludes with the question, “If you are feeling hungry, which coupon would you choose?”.
And that’s it. The students are waiting for more – after all, they have gown to expect more – but this time they are not going to get it.
And so begins Act 2 – information seeking. What information do the students need to know to solve this question? It is up to them to tell you. Only after some discussion do we reveal the image of the pizza menu. The slice in question was from a 12 inch pizza chopped up into 8 succulent slices. Now the students get to work, searching through their banks of maths knowledge for the particular areas that will be useful in solving this problem.
When the problem is solved, Act 3 can begin – the sequel. Would the best coupon for the slice above work for all slices or just some slices? Tell me under what circumstances I should use one coupon or the other? The possibilities for extension work are endless.
Students are hooked and engaged. They are using the mathematics that they have learnt to solve something that means something to them. They are taking ownership over their work by demanding to know information. They are no longer passive in the problem solving process; they are leading the way through it.
Dan’s bank of 3 Act Math problems is not limited to pizzas. Titles such as “Lucky Cow”, “25 Billion Apps” and Nanna’s Chocolate Milk” intrigue me as much as my learners. I’m not promising you will never be asked “sir, when will I use this in real life” again, but this might just be one step in the right direction, and your students will be all the better for it.
Here is the link to Dan Meyer’s 3 Act Math Collection