How to Learn Math (Session 4)

To see my reflections on session 1, and sessions 2 and 3 click on the links below...

session 1 - http://goo.gl/zGhmxD
sessions 2 & 3 - http://goo.gl/2pjIQR

I was looking forward to session 4 ever since Jo Boaler (@joboaler) had started to refer to Carol Dweck's research in fixed and growth-mindsets. Session 4 was titled 'Teaching for a growth mindset'.
As the session title suggests it focused on how you can teach a growth mindset to your students. There was a really great video at the start of the session that got you to look at a teacher in the states introducing the question of what 1 divided by two thirds would be. The lesson was fantastic in showing an approach whereby the students are invited to show their thinking of a problem and trying to make sense of the problem. The 'how does it make sense' part was key to the lesson where the teacher asked her students to show why they thought their answer made sense, rather than showing a method, getting students to learn and copy that method and then apply it to some questions. What I thought was great in the lesson was how many different reasons were presented by the students and how some of these reasons would not have been discussed had the teacher just taught the method to dividing fractions.
In the lesson you had one student draw circles on the board, split them into thirds and then highlighting 2 of the thirds before exclaiming that you have 1 and a half of the two thirds. Another student used a rectangle, like a strip to show how this could be split into 3 equal parts and then used a similar explanation to show an answer of two thirds. There were one or two students who still couldn't grasp these explanations and persisted with an answer of 6 as they believed the 2 over 3 'line' meant that you multiplied the 2 and 3 together. This misconception was picked up by another student (not the teacher) and explained. The same student then randomly pulled out the number 12 when the teacher was putting the question into context of having a yard of wood (or something like that) and needing to take two third chunks from it. The student that mentioned 12 was asked what they meant to which they replied there were 12 feet in a yard. You could almost here the teacher's mind click before she said yes, and what is two thirds of 12? 8 and then you have 4 left over which is half of this, which makes 1 and a half.
These discussions wouldn't have been discussed had the students not been asked to 'make sense' of the problem, rather than just answering it.

Then, in the session, we were asked to look at a blog post from a teacher who had taken a rather closed question involving mini golf and transformed it into a really interesting and engaging open ended task. This was great to read and it is definitely a lesson I'll be using in the future when teaching similar triangles.
Check out www.fawnnguyen.com!

A few tips I picked up throughout the session were to 1) get students to 'convince themselves, convince a friend, convince a skeptic' and to 2) use a 'number sentence' when explaining their reasons to the class.

As has happened in previous sessions we were asked to do a few peer assessment questions which are read and commented on by other subscribers to the course. These questions/feedback have been really useful in seeing what ideas/opinions other teachers have and what things they are planning to do to get across growth-mindset messages to their classes.

The session also looked at what makes a growth-mindset problem and gave us 5 key things the growth mindset question should be (including having multiple entry points and being open). Jo discussed the problems with setting students in mathematics and what messages this gives them. She also discussed what good (growth-mindset) feedback should look like, why grades shouldn't be given based on research conducted and talked about our 'math brain'.

'Remember, the harder you work, the better you get at math'.

Check out www.map.mathshell.org too.

Go to http://class.stanford.edu to sign up for Jo Boaler's 'How to Learn Math'  now!