Embracing the Ridiculous in order to enhance student engagement

As a maths teacher, for many years I have heard that in order to improve student outcomes in mathematics, you need to improve student engagement, this I agree with.  However the most common suggested way of doing this is to make it relevant to them or the lives they will have, this is something I do not completely agree with.

Common ways we try to make it relevant is to link it to their life beyond school, caluclating wages, taxes, bills, budgetting how much mulch you would need for irregular garden bed.  These are all valid, relevant ways of engaging with the mathematics, but how many teenagers want to think about the responsibility of bills and taxes, what ever money they earn, they spend, they don't want to have to think about budgeting for something, if they have spent all their money they try to get more from their parents or just go without. Over many years I have found that teenagers just want to be teenagers and as much as they want to be treated as adults they are not necessarily all that interested in having the same level of responsibility as adults, nor should they to a certain extent.

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Photo source: 
http://robertkaplinsky.com/work/in-n-out-100-x-100/

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the other way we try and make the work relevant is by linking the work to their interests using things such as sport to calculate statistics and optimal angles, but due to many students dislike of mathematics quite often what comes back is "why are you trying to ruin football for me my making it into a maths lesson".  They enjoy the sport and playing it, but don't want to know about the maths involved.

The argument about relevance also becomes about who it is relevant to.  If you make the lesson about football, then it is not personally relevant to anyone who does not like that sport, this could easily be more than half of your class. 

The idea of relevance can be used very successfully for engagement, there have been some highly relevant lessons that I have taught, that students have also found highly engaging.  But I have also had some highly relevant lesson fail miserably.  Over the last few years I have found that embracing the idea of presenting students with ridiculous problems has increased student engagement more than anything else.

So how do I define an ridiculous problem

1. the problem must have direct links to the real world
2. The problem must push the context far outside it's normal limits
3. All the basic elements that make up a good problem solving type question must be present (e.g. multiple solution paths, excess or deficiency of information, group work and discussion).

Some of the questions of this type I have had success with in the past are as follows

• How much does the 100x100 in and out burger cost? (photo shown above, thankyou to Robert Kaplinsky for this great lesson)
• How much money will fit in this classroom?
• How many Post-It notes will it take to cover the whiteboard and how long will it take?
• What is the maximum number of chicken nuggets that you cannot order?  (credit to Numberphile for the idea for this question)

All of these questions immediately gained the students interest, the looked at me like I was insane, but also had that look of "I want to know the answer to this".  As can be seen they are all very much related to something they have seen before, money, burgers, post-it's nuggets but it takes how they have thought about these things far outside the realm of what we consider "normal".  It is this deviation from the normal that students find really interesting and the work they have produced on these sort of tasks has been quite stunning.  In my observations of students working on these type of tasks it is clear that they are discussing the work more with others, coming up with stronger, well reasoned responses and also add value to the task for looking at ways they can extend it such as looking at how many calories in the 100 x 100 burger or the cost of a 1000 x 1000 burger.  In particular the chicken nuggets question still continued to have students talking about it 8 weeks after the task had finished, students even went to McDonalds and tried to order that number of nuggets to see what they would say.