This post is in reflection of some of the things we covered in the How to Learn Math Stanford university MOOC course presented by Jo Boaler.
One of the biggest topics, in my opinion, has been about mindsets - growth mindset vs fixed mindset - what they are, what's important about them and how we affect which one our students will have. The information about mindsets is from Stanford Psychologist, Carol S. Dweck. The basic idea is that people with a fixed mindset believe that there is a limit to how well they can do at something, whereas someone with a growth mindset believes that with effort they can achieve whatever it is that is logically and physically possible for them to achieve - such as excelling in their studies of mathematics. People with a fixed mindset are more likely to reach a point where something becomes difficult and give up, saying that they obviously are lacking in some fundamental area which makes it impossible for them to progress any further, such as lacking a "maths gene" (I cringe as I write that).
So, rather than going into all the gory details about mindsets, which you can read more about on the web or in Carol Dweck's book, I'd like to spend some time brainstorming ideas on how we affect the mindset that children develop and what we can do about it.
We send silent, implicit messages to people all the time, by our body language, by the terms and phrases we use, and even the tone of our voice. As teachers we send implicit messages to students by the type of questions we ask, and by the way we grade work. School administrators send implicit messages to students in the way the school is run - such as the use of tracking/streaming/phasing/sets (different names for the same thing).
When we ask questions, if we always ask closed questions, students start to believe that maths is all about right or wrong, that there is only one way to do things, that there is no creativity in maths, that it is robotic, mechanical and dry. However if we ask open questions, and discuss different ways of solving problems, this sends an entirely different message to students about what maths is. Take a look at the kids in this interview, they're in year 2. Wouldn't you love your students to talk like this about maths? If so, here is an example of those student's teacher in action (please note that the use of technology wasn't necessary, a black/white board would have sufficed, but if you've got access to a smartboard, why not use it).
When we grade work, we also send messages about what constitutes good scholarship. When students receive their work back, all nicely (ok usually messily) graded, we as teachers seem to expect that they're going to labour over it learning from their mistakes - It doesn't happen - It gets chucked into the bottom of the school bag to be recycled as end of year school bag compost, along with the mouldy apples and sweaty lettuce sandwiches. We know, as educators that it is important to find out where we went wrong and that correcting those mistakes can form part of a great learning curve, yet we let that chance slip by our students by not allowing them to fix their mistakes and learn from them. Why?
Some teachers argue that the extra marking isn't worth it - however I'd have to strongly disagree. No, it's not worth it if the only reason you mark things is to put grades into a book to please your administrators, but if you're marking your students work in order to help your students learn and grow, then it seems almost criminal to not stress the importance of working on and fixing your mistakes! Other teachers argue that if all their students were allowed to fix their mistakes, then all their students would get 100%. But I argue, what the heck is wrong with that! What is with this dogmatic need to get a good "spread" of results? Is it good for enhancing student learning, or is it good for administrators and people wanting to rank schools by test scores? If it isn't for the students, then why hold onto the idea so dearly?
Then there are the fixed mindset messages we send our students by tracking. Oh yes, tracking is wonderful, if all you're really concerned with is making teaching easier (yes, it's hard!) - but what it does and can do to students is disastrous! The only stronger message other than tracking that we could send our students that we believe that they have only a fixed capacity to learn a subject would be to tattoo it to the insides of their eyelids! The arguments about how difficult it is to differentiate teaching to a heterogeneous class are starting to become obsolete when teachers now have access to wonderful teaching resources made by people such as Dan Meyer. It doesn't necessarily need to be more difficult to teach to a class of students ranging in their knowledge by 4+ years, it just means (drastically) changing how we teach. We need to get away from how this stuff was taught to us, because it obviously isn't working.
At the very least, the 'take home message' I'd like anyone to take from this post is not necessarily to believe or agree with everything I have said, but to ask the difficult questions about how we do things. Why do we mark the way we do? Why do we think that tracking is okay? What messages are we sending our students? and most importantly, how is it serving the student's best interests?
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