We aspire to inquire!
This week I will be watching a video critique about Khan Academy by Michael Pershan and an article on inquiry maths by Andrew Blair.
It is interesting that both the article and video consider the discussions and pursuit of mathematics through questions of utmost importance. This is akin to the beliefs of Dan Mayer who disagrees with the current American style of teaching which focuses on text books and answering questions. Indeed Michael Pershan says the same and looks at the differing styles from other countries where the students are presented a problem with no solutions and asked to discuss how to solve it.
I notice that this is often how we are taught at university, with teachers prompting discussions and students bouncing ideas between each other when trying to come up with a proof or method for solving a problem. It allows us to explore gaps in our understanding and consolidate new methods and approaches we might have never thought about. However there are some distinct differences between us and GCSE students. We’ve come from different backgrounds and been exposed to many concepts already which means we benefit from a rich pool of experiences. In a system that rarely challenges most of its students it would be very difficult and even unfair to expect them all to come up with these ideas on their own without sufficient input from the teachers.
With that said Andrew Blair and Michael Pershan seem to believe that it is where our education system should be headed. To me the current system of education encourages decoding and formulas over real conceptual understanding and so I would push for the same system that Blair and Pershan have in mind. However I think we need to be careful when introducing this into a classroom and understand that there is a culture of education and that our ideas would be vastly different to what students are used to. Therefore more needs to be done in lower years and primary to encourage this kind of growth mind-set and approach to problems so that they are confident about approaching a new problem and wielding their mathematical arsenal.
Andrew Blair believes that by having these discussions students think more about their approach to questions and that it is the only way to harmonise conceptual mathematical knowledge and the method of learning. Firstly we should think about whether there is an entirely second curriculum being lost in the American system, which is getting students to learn how it is they learn. In my own experience I’ve suffered with a lot of confidence issues when I haven’t been able to understand a topic. The general solution was often to be shown how to do it and then be told to repeat it and I was often hard on myself for it when it felt difficult. When I got to my A levels I realised I did much better when working with other students then I did working in revision classes with teachers or tutors and I became aware of my ideal learning environment. We would often link mathematical problems to models from games or puzzles and from there I came up with many original ways to model the Mathematics. It was then that I started to feel less anxious about the mathematics and more open to problem solving.