Archive for January, 2011

Maths on the underground

January 27, 2011

As I was on my way to catch the train home this evening, I received a text from a friend with the following question:

Two flagpoles, heights a and b, are separated by a horizontal distance d. The top of each flagpole is joined by a wire to the bottom of the other pole. At what height do the wires cross?

I solved it on the metropolitan line with a few minutes’ thinking and scribbling time. Let me know how you get on, and feel free to share your methods in the comments.

Its own reward…

January 17, 2011

I had an interesting thought the other day. It was about motivating students by offering them rewards. Someone suggested to me that I could enthuse some students I was working with by bringing some sweets for the team who finished first, and my knee-jerk response to this was that I didn’t want to do that.

I went away and analysed my knee-jerk response, and came up with a few thoughts as to why I was so reluctant to offer rewards. Firstly, there have been many times when I’ve been given something to do in competition with others, and the nature of the competition has caused me to want to opt out. After all, if there’s a risk of coming second, of not winning, then at least by opting out I can say that I CHOSE not to compete. I think I am far from alone in this, so I prefer not to introduce competition into the maths activities I offer to students.

Secondly, I want the students I work with to think positively about maths. I don’t want them to work hard on a problem because they’ll get a mars bar if they do, I want them to work hard on a problem because it engages and interests them, and they are curious about the result. I want them to work on the maths for its own sake, not because they want to please me and win a prize.

Thirdly I’m aware of studies showing that although offering rewards can increase motivation in the short term, in the longer term groups who are not offered rewards catch up and then overtake the rewards groups.

Students often ask the question “Why do I have to do this, miss?” It has always seemed to me that an answer about the benefits to the student’s mathematical understanding and progress in the subject is a more honest and better answer than “Because if you do, I will reward you with a mars bar/A grade/not giving you a detention!”