Now that I’ve completed Jo Boaler’s ‘How to learn Math’ MOOC, I thought I’d share some more of the concepts which particularly caught my attention as I worked though the material, and those that have remained with me since I finished.
One of the sections in the course was Number Sense. In this section Jo shared the view that an ease with numbers is a very good foundation on which to build the more complex maths concepts. This is a view that I have long held myself. One of the most enlightening exercises that Jo has shared on the course relates to number sense. She shared an example of a ‘Math Talk’ where students were given a calculation to do without a pen and paper or a calculator. They had to come up with an answer and then share how they came up with that answer. The calculation they were given was 18 x 5. Some of their workings are as follows:
- 18 x 2 = 36 : 36 x 2 = 72 : 72 + 18 = 90
- 18 / 2 = 9 : 9 x 5 = 45 : 45 + 45 = 90
- 5 x 10 + 5 x 8 = 50 + 40 = 90
- 18 / 2 = 9 : 9 x 10 = 90
- 20 x 5 – 2 x 5 = 100 – 10 = 90
Others shared variations of these solutions. For me the really important part came in the discussion around the way the students came up with their solution. Being aware of the various ways of performing these calculations, and talking them through with the group, really showed a flexibility in Maths that many don’t see. Having to really explore what you do and why, helps students to gain a deeper understanding of the concepts. When asked about their perceptions around Maths, many people mention an inflexibility, and a formulaic way of approaching it, that is as a result of the Maths we teach, and the way we teach it. I often find that students zone in on “the” way to solve a problem when in fact there are many different ways to get to the solution. I have always tried to help students to develop their intuition around Maths and to hone their number sense and the course has helped me to refocus my efforts on this in my classes.
Helping students to discover maths by exploration is another area that Jo probed in quite a lot of detail through the course. This is an area that I myself struggle with. It can be easy to fall into the trap of thinking that you must cover the concepts first before introducing the contexts in which those concepts can be used. This idea of learning through exploration is one of the most powerful aspects of CoderDojo and it is one of the areas where I think the formal education system can learn from Dojo.
It’s been a few weeks since I finished the course and it has had an impact on my teaching in many subtle ways. I love how it has reinforced some ideas for me and how it has made me rethink so many more.