Have a go at some of these:
An athlete's best time to run a mile is 4 minutes and 10 seconds. How long would it take him to run 5 miles?
It takes one orchestra one hour to play a symphony. How long would it take two orchestras to play a symphony?
On a ship, there are 13 goats and 12 sheep. How old is the captain?
Among schoolchildren, the most common answers to these questions are: 20 minutes and 50 seconds; half an hour; and 25 years old.
Hence the title: where are these thoughtless, silly answers coming from?
The bizarre and somewhat frightening thing is that this is a well-attested finding in many different countries and schools. School students predominantly seem to think that anything involving calculation, in the classroom at least, is a matter of doing a simple arithmetic operation on the numbers given, without any kind of sense-checking or thinking about the real situation behind the numbers.
This strange phenomenon demands explanation, not to mention fixing. In this episode, we look at several articles concerning this issue, why it's there, and what to do about it.
Enjoy the episode.
Dr Amanda Serenevy is a mathematician and mathematics educator, focussing on outreach through the medium of Math Circles, and on teacher training. This episode appears as number "27+" because the previous episode, Consider the Circle, was about how Amanda rescued a young girl from a terrible time with maths at school.
She is the founder and director of Riverbend Community Math Centre in South Bend, Indiana, which works to improve mathematics education within the local community. She runs teacher training courses throughout the year, both to help teachers with their pedagogy, and with their knowledge of maths itself. She also has many local children and young people come to her Math Centre to engage in mathematical activities, the most prominent of these being Math Circles.
In summer, she is the main organiser of the Summer Math Circle Institute at the University of Notre Dame, which is a course for learning how to run Math Circles, and is the place where I met her. She also finds time to spend almost two months a year in Navajo Nation helping to run maths outreach programs, including a three week long summer camp.
She did her undergraduate degree in mathematics at the University of Indiana at South Bend, and her PhD in dynamical systems at Boston University. Interestingly, she declined academic positions at university in favour of doing more maths outreach, and so her choice of career is very deliberate, and she is committed to her cause.
From getting to know Amanda personally, I can say that she is both very personable and very dedicated to her work. It is easy to see how much positive effect she is having on her community, particularly on the children who have clearly gained so much from her help, guidance, and activities. While she has a thorough understanding of the problems with maths education in her country, she somehow isn't completely disillusioned, which is a feat in itself. I was greatly privileged to be able to shadow her for a week while in the US and pick her brains about maths, education, and why America is such a strange place.
Enjoy the episode.
A very short episode about an article written by a young girl concerning her experiences with maths.
At school, she is faced daily with the same worksheet, always refusing to do it. Her teachers continue to give her the sheet every day for months, keeping her out of the normal classroom. She becomes resentful and angry at maths and at school, and continues her protest of inaction.
When she discovers Math Circles, a different approach to maths education, then she stops feeling neglected and starts, gradually, to engage. With time she not only gains confidence in the maths she is "supposed" to know, but also discovers mathematics as a field full of things to explore - and things she is capable of exploring.
Having gained confidence and understanding from Math Circles, she eventually graduates from high school and enrols in university. (A happy ending, one presumes.)
We will be talking a good deal about Math Circles, so this little story makes a good anecdotal introduction to their potential benefits. It sounds a bit like an advert, but Eliza Vanett is a real person who really underwent these experiences and volunteered to write this herself. You'll hardly see adverts for Math Circles on television.
Enjoy the episode.