Education Bookcast

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 artic