This week, a workshop on inquiry maths led me to my own 'aha!' moment, as I finally grasped the difference between growth and fixed mindsets, and how it relates to my students.
But how to lead the students to their own 'aha!' moment, without doing the thinking for them?
But how to lead the students to their own 'aha!' moment, without doing the thinking for them?
1) Students were presented with the following problem:
"It is possible to write some numbers as the sum of consecutive numbers. For example, 9 is the sum of 4 and 5.
Can you write the numbers 1 to 25 as the sum of consecutive numbers?"
Can you write the numbers 1 to 25 as the sum of consecutive numbers?"
Working in their books or on whiteboards, students then set to work on this problem. After an initial period of 'thinking time', they were allowed to discuss their thoughts, ideas and strategies with each other. Myself and the learning support teacher were able to ask them questions to draw out their thinking, but did not give them any extra help with the task.
As they grappled with this, we observed their behaviour, and recorded any statements they made.
I then showed this image on the board. Before they went to play, students were challenged to make a connection between this and the statements they had made about their learning.
A few were able to make a connection, some were able to explain what they thought the cartoon was trying to show, while some, comfortable in their fixed mindsets, wrote 'there is no connection' or 'it doesn't make sense.'
A few were able to make a connection, some were able to explain what they thought the cartoon was trying to show, while some, comfortable in their fixed mindsets, wrote 'there is no connection' or 'it doesn't make sense.'
3) After play, we got back together as a group. We revisited two terms from our language lessons - 'antagonist' (an adversary who tries to stop the story) and 'protagonist' (an advocate who wants to continue the story) and I explained that in this lesson I wanted students to reflect on whether they were antagonists or protagonists in their own learning story.
I then introduced the terms 'fixed' and 'growth' mindset, sharing the example from Carol Dweck's research (summarised here on Brainpickings.org):
'In another study of hundreds of students, Dweck and her colleagues gave each ten fairly challenging problems from a nonverbal IQ test, then praised the student for his or her performance — most had done pretty well.
But they offered two types of praise, some students were told: “Wow, you got [X many] right. That’s a really good score. You must be smart at this,” while others: “Wow, you got [X many] right. That’s a really good score. You must have worked really hard.” In other words, some were praised for ability and others for effort. The findings, at this point, are unsurprising yet jarring:
The ability praise pushed students right into the fixed mindset, and they showed all the signs of it, too: When we gave them a choice, they rejected a challenging new task that they could learn from. They didn’t want to do anything that could expose their flaws and call into question their talent.
In contrast, when students were praised for effort, 90 percent of them wanted the challenging new task that they could learn from.'
4) The students then asked if they could sort out the statements again, this time into indicators of fixed and growth mindsets. This prompted some very interesting discussion and ideas as they debated where each statement should go.
'I think all the questions should go under growth mindset, because questions never end, so they are open to learning.'
'I think the person who said they felt bad might still have had a growth mindset, if they were still trying to work it out. But if they decided that they were no good and gave up, that's fixed. We need more information.'
I then introduced the terms 'fixed' and 'growth' mindset, sharing the example from Carol Dweck's research (summarised here on Brainpickings.org):
'In another study of hundreds of students, Dweck and her colleagues gave each ten fairly challenging problems from a nonverbal IQ test, then praised the student for his or her performance — most had done pretty well.
But they offered two types of praise, some students were told: “Wow, you got [X many] right. That’s a really good score. You must be smart at this,” while others: “Wow, you got [X many] right. That’s a really good score. You must have worked really hard.” In other words, some were praised for ability and others for effort. The findings, at this point, are unsurprising yet jarring:
The ability praise pushed students right into the fixed mindset, and they showed all the signs of it, too: When we gave them a choice, they rejected a challenging new task that they could learn from. They didn’t want to do anything that could expose their flaws and call into question their talent.
In contrast, when students were praised for effort, 90 percent of them wanted the challenging new task that they could learn from.'
4) The students then asked if they could sort out the statements again, this time into indicators of fixed and growth mindsets. This prompted some very interesting discussion and ideas as they debated where each statement should go.
'I think all the questions should go under growth mindset, because questions never end, so they are open to learning.'
'I think the person who said they felt bad might still have had a growth mindset, if they were still trying to work it out. But if they decided that they were no good and gave up, that's fixed. We need more information.'
5) At the end of the lesson, students discussed how their thinking had changed:
‘I used to think it was how good you are, but now I think it’s more about how hard you try. Even if you’re really good at maths, if you’re not open in your thinking then you won’t ever really challenge yourself, you’ll just keep doing the same stuff because it’s easy… because it’s safe.’
'At first I thought this was a math lesson to wrap my brain in a heap of hardness. But now I don't think it was about the maths at all, but about what I did when it got difficult.'
'I actually think that smart is kind of a bad word because it's either one or the other, you either are or you're not, and that's not what learning is like. Learning just keeps going and going and you're not always going to get it but that doesn't mean that you're not smart, just that you haven't found the answer yet.'
'Yeah, let's ban the word smart!'
‘I used to think it was how good you are, but now I think it’s more about how hard you try. Even if you’re really good at maths, if you’re not open in your thinking then you won’t ever really challenge yourself, you’ll just keep doing the same stuff because it’s easy… because it’s safe.’
'At first I thought this was a math lesson to wrap my brain in a heap of hardness. But now I don't think it was about the maths at all, but about what I did when it got difficult.'
'I actually think that smart is kind of a bad word because it's either one or the other, you either are or you're not, and that's not what learning is like. Learning just keeps going and going and you're not always going to get it but that doesn't mean that you're not smart, just that you haven't found the answer yet.'
'Yeah, let's ban the word smart!'
Reflection
During the lesson, I had observed one student with interest. Normally a risk-taker in her learning, as soon as she was challenged by the task she had said 'this is impossible', written the word 'NO.' in large letters on her whiteboard, and then spent the remainder of the time doodling. At the end of the lesson, she shared:
‘I don’t think you either have a fixed mindset or a growth mindset and that’s it, that’s you. I think it can change. For me, I normally try and I don’t give up, but today I gave up straight away because I was feeling upset about something that happened at playtime. This makes me think that your mindset depends on how you are feeling. So if you feel sad and alone you won’t want to try and you’ll be fixed. But if you are happy then you will have a growth mindset. Well… not definitely but you are more likely to have a growth mindset if you are feeling happy.’
Through resisting my natural instinct to manage and redirect her, I had allowed her to come to this realisation about herself and how she learns on her own. An important lesson for her, but for me, too. A reminder of the importance of learning to let go: to unlearn the habits which undermine student inquiry and ownership of their learning.
Resisting the impulse to manage and direct, taking a step back, and allowing students time and space to come to understanding on their own is the first step towards facilitating authentic inquiries.
During the lesson, I had observed one student with interest. Normally a risk-taker in her learning, as soon as she was challenged by the task she had said 'this is impossible', written the word 'NO.' in large letters on her whiteboard, and then spent the remainder of the time doodling. At the end of the lesson, she shared:
‘I don’t think you either have a fixed mindset or a growth mindset and that’s it, that’s you. I think it can change. For me, I normally try and I don’t give up, but today I gave up straight away because I was feeling upset about something that happened at playtime. This makes me think that your mindset depends on how you are feeling. So if you feel sad and alone you won’t want to try and you’ll be fixed. But if you are happy then you will have a growth mindset. Well… not definitely but you are more likely to have a growth mindset if you are feeling happy.’
Through resisting my natural instinct to manage and redirect her, I had allowed her to come to this realisation about herself and how she learns on her own. An important lesson for her, but for me, too. A reminder of the importance of learning to let go: to unlearn the habits which undermine student inquiry and ownership of their learning.
Resisting the impulse to manage and direct, taking a step back, and allowing students time and space to come to understanding on their own is the first step towards facilitating authentic inquiries.