As Maths teachers we are constantly telling students that Maths is all around us but do we really show them? Yesterday I read a blog post by Ira Socol titled ‘Changing Gears 2012: maths are creative, maths are not arithmetic‘. This blog post gets at the crux of the problem and has given me plenty to think about as a Maths lecturer first and a Mathematician secondly. For me this order is really crucial – I have come across some amazing mathematicians in my years in the Maths sphere. Many were Maths geniuses but sometimes these people were so comfortable in the Maths zone that they found it difficult to pass on these often complex concepts to others. I will always be a Mathematician by trade but over the years I have become a Maths lecturer first and foremost. I am very aware that it’s not enough for me to understand the concepts, for my students it’s all about whether or not I can help them to understand topics which they will need as Computer Scientists. I am very conscious that concepts that I just get leave others completely baffled.
A simple example is that I have been dealing with functions with my students over the past few days. I have discovered over a number of years that students often just don’t get functions – they can take a function definition such as f(x) = -4x + 9 and calculate f(3) and f(-2) etc. but when asked to deal with a real application many struggle. Because of the success of my Java coding in Maths class last term I have decided to teach functions through coding this term. We dealt with the above example by writing the Java code to implement it using x and y as variables, reading in x as the input and calculating the output y = -4 * x + 9 and printing out the y values. We then used the test data (f(3) and f(-2)) to make sure that our program worked as it should. We then worked through some basic pay calculations such as ‘A person gets paid €8.50 an hour. They get paid time and a half for any hours worked over 40 hours and double time for any hours over 60. Calculate their pay.’. If we ignore the complication of overtime this is a basic function y = 8.5x. Adding in the overtime complexity is often where students struggle. Seeing the different ways that students see this problem and work through their way of performing the calculation is fascinating. I’m not sure that us Maths teachers do enough of this allowing students to find their own way – there isn’t only one way of doing things and the discussions that follow when exploring these different ways often throw up issues with the approach taken or performance issues associated with a certain approach.
In Ira’s blog post he mentioned Fibonnacci and coincidentally I came across a Youtube clip by Vi Hart about Maths doodling which also referenced Fibonnacci.
I love this clip and it has provided me with an opportunity to talk to my own children about Maths in a way that they can connect with. We’re going out to buy cauliflower and pineapple at the weekend to count the Fibonnacci spirals contained therein 🙂 I came across another great clip by Vi Hart called infinity elephants which I’ll be using when I’m teaching infinite sequences in future.
I feel that as a Maths lecturer I do a good job. I’ve helped many students to overcome the genuine terror that they feel towards Maths. But can I honestly say that I do enough to connect my students with Maths? I’m not sure that I do but that can change!