This is an answer that as a teacher I used to hate, or should I say rather than hate, it absolutely frustrated me. "Can you tell me how you solved that?"
"I just knew!" or the good old shrug of the shoulders, where a child would have the right answer, but had absolutely no idea how to explain how they solved the problem.
So many times I remember waiting patiently, giving them time, trying not to throw my voice in there, and in the end basically answering my question myself. I often wondered why they were unable to explain their strategies to me.
Since I participated in maths PLD, a few years ago now, I have had a few lightbulb moments and come to realise why the stock standard answer was "I just knew it."
There are several reasons in fact.
1) The way I presented maths encouraged children to be fast, and very much valued knowledge, children felt that they were successful if they did have the answer straight away. They knew this was what I wanted and therefore it was the answer I got. Even if they had used their fingers to solve a problem, or had to use counters, or some other strategy, they didn't feel that this was a valued way of working and they actually wanted me to think that they 'just knew.'
2) They actually didn't know who they had solved the problem. We didn't talk deeply about how we solved problems, so articulating this was difficult for them. Explaining a strategy is something that needs to be modelled and taught.
3) We very rarely explored problems that had more than one step, often the problems could be solved with pure knowledge with little strategy needed. Word problems were not common and usually the questions asked had just the one answer.
4)The children worked largely in groups that were ability based, this meant that often the children in the group would have similar understandings and therefore couldn't build on the understandings of others, or hear different strategies.
So what has changed?
Well loads of things have changed, but thinking specifically about the response "I just knew" I suddenly realised the other day that this has not been an answer I have heard for at least two years. I think there are some very valid reasons why.
1) We work as a whole class in mixed groups. Discussion and sharing is valued. Agents get to build on each others understanding and piggyback from each others ideas. They are always keen to share.
2) We use visual images like dot talks and other images to discuss what we see and what we notice, this noticing is valued and there is not one answer. We regularly use the sentence starter "I notice..." for a range of activities.
3) We use talk moves. Children are encouraged to talk about the strategy they have used and Cowgirl will scaffold or revoice this. They still use knowledge, but they know that it is the strategy that is valued, the problems are sometimes multi-faceted and require deeper thought. They are usually quite challenging. Materials and fingers are valued. We listen to each others strategies and agents have to think about whether they agree or disagree and if their strategy is similar. These are the statements we use as sentence starters when sharing...
"I agree"
"I disagree"
"I think the answer is,------- because..."
"I have a similar strategy..."
Cowgirl will revoice their strategy and clarify what they are trying to say if they get a little lost.
Obviously discussion is highly valued, having a 'Goodie' with this specific role in the form of Cowgirl Calculation adds weight to the process.
I am happy to see an end to the answer "I just knew" and glad to see the back of maths that values speed and the correct answer, to maths that values discussion, strategy, open ended questions and visual images.
Authentic maths - makes "I just knew" a thing of the past.
"I just knew!" or the good old shrug of the shoulders, where a child would have the right answer, but had absolutely no idea how to explain how they solved the problem.
So many times I remember waiting patiently, giving them time, trying not to throw my voice in there, and in the end basically answering my question myself. I often wondered why they were unable to explain their strategies to me.
Since I participated in maths PLD, a few years ago now, I have had a few lightbulb moments and come to realise why the stock standard answer was "I just knew it."
There are several reasons in fact.
1) The way I presented maths encouraged children to be fast, and very much valued knowledge, children felt that they were successful if they did have the answer straight away. They knew this was what I wanted and therefore it was the answer I got. Even if they had used their fingers to solve a problem, or had to use counters, or some other strategy, they didn't feel that this was a valued way of working and they actually wanted me to think that they 'just knew.'
2) They actually didn't know who they had solved the problem. We didn't talk deeply about how we solved problems, so articulating this was difficult for them. Explaining a strategy is something that needs to be modelled and taught.
3) We very rarely explored problems that had more than one step, often the problems could be solved with pure knowledge with little strategy needed. Word problems were not common and usually the questions asked had just the one answer.
4)The children worked largely in groups that were ability based, this meant that often the children in the group would have similar understandings and therefore couldn't build on the understandings of others, or hear different strategies.
So what has changed?
Well loads of things have changed, but thinking specifically about the response "I just knew" I suddenly realised the other day that this has not been an answer I have heard for at least two years. I think there are some very valid reasons why.
1) We work as a whole class in mixed groups. Discussion and sharing is valued. Agents get to build on each others understanding and piggyback from each others ideas. They are always keen to share.
2) We use visual images like dot talks and other images to discuss what we see and what we notice, this noticing is valued and there is not one answer. We regularly use the sentence starter "I notice..." for a range of activities.
We like to use images that the children have created through other activities.
What do you notice?
How many....? How do you know?
Could we sort them a different way?
What do you notice?
How many, how do you know?
We like to use images in groups and share our understandings before we talk as a whole agency.
3) We use talk moves. Children are encouraged to talk about the strategy they have used and Cowgirl will scaffold or revoice this. They still use knowledge, but they know that it is the strategy that is valued, the problems are sometimes multi-faceted and require deeper thought. They are usually quite challenging. Materials and fingers are valued. We listen to each others strategies and agents have to think about whether they agree or disagree and if their strategy is similar. These are the statements we use as sentence starters when sharing...
"I agree"
"I disagree"
"I think the answer is,------- because..."
"I have a similar strategy..."
Cowgirl will revoice their strategy and clarify what they are trying to say if they get a little lost.
Obviously discussion is highly valued, having a 'Goodie' with this specific role in the form of Cowgirl Calculation adds weight to the process.
I am happy to see an end to the answer "I just knew" and glad to see the back of maths that values speed and the correct answer, to maths that values discussion, strategy, open ended questions and visual images.
Authentic maths - makes "I just knew" a thing of the past.
Cowgirl Calculation helps to revoice and clarify understandings "So I hear you saying...?"
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