Tuesday, 31 January 2017

Maths is Creative Thinking: Measuring Time

Maths involves creative thinking.

When kids are given opportunities to discover this and why creative thinking is important to mathematical thinking, even those who might harbour negative feelings, become much more open-minded towards maths. They start to rethink and understand that maths is not about getting an answer.  It helps them to understand that mathematical thinking is about coming up with your own ways to try to solve problems. It is about creating your own strategies and then reflecting on their effectiveness. It involves analysing strategies to find their pros and cons. 

Often, in traditional maths learning classrooms, children are spoon-fed strategies to replicate and then repeat. That robs them of rich opportunities to create their own strategies and to really delve into the concepts being explored. When we give children opportunities to creatively come up with their own strategies (and allow those strategies to be mad or ineffective) we help tear down those misconceptions that there is only one way to solve problems. We also help tear down feelings of apprehension some children harbour fearing they are not doing the 'right' thing. 

When we ask children to be creative in maths, we are giving them the much needed freedom and opportunity to explore the way their mind works. 

That's important.

We all think differently and we should be encouraging children to develop their own thinking processes, not programming their brains to think a certain way.

To begin our investigation into ways we can measure elapsed time, we used a Padlet and shared our initial understandings by answering the question: 

How and why is creative thinking important in maths?

Padlet is a wonderful way to give a voice to everyone in the class, not just those courageous enough to share their thinking.

After ideas were shared, we were asked to find someone else's thought that made is think about it differently then we had. 

I like this strategy for a few reasons:

1. It encourages children to actually read and think about others' thinking.
2. It helps validate the thinking of class members and helps them feel their thinking is appreciated.
3. It helps generate deeper levels of discussion. When a student shares another students' idea, we all become more involved in analysing it.
4. It is a more active way of sharing thinking. When we discuss orally, some children miss out of the initial and then struggle to catch up with what is being discussed. Using the Padlet, they can read and see what thought is being discussed and this helps them to think about it more.

We then used another Padlet to share and discuss our understandings of:

How does visualising help us with mathematical thinking?

These thinking and discussions helped 'set the scene' for the sort of thinking and investigation were about to do.

We then looked at the following problem:

Using the phrase 'How many different strategies.........' instantly makes the enquiry open-ended. There are now many possibilities and that is what we are valuing.

To help us understand what we are valuing, I explained how the strategies we create do not have to be the most effective. In fact, we should try to challenge our thinking by also creating mad, ineffective strategies because they will help us with our thinking. We can create strategies that will take a long time to help save. That's alright.  Let's just explore different possibilities.

We used the think-pair-share routine.

Children had 10 minutes creating different strategies on the paper.

After 10 minutes, we discussed what we thought about creative thinking.

Some very in depth and interesting reflections emerged such as:

° Before I thought creative thinking was just about doing something in a fun way. Now I understand that you actually need to think really hard and deeply about something. 

Everyone agreed that creative thinking does require 'hard' and deep thinking.

° I think it's interesting that creative thinking is a balance between hard thinking and fun thinking. 

° I get different answers with the different strategies I created and I'm trying to find out why.

This last comment is exactly where we want children to be: without being prompted, find reasons why a strategy is working or not. We all agreed this was a great thing she was doing.

I then explained we were going to do a 'silent gallery walk' to see what others were experimenting with and exploring as possible strategies.

Why do we think we are going to do this?

- So we can see how creative we can be?

- We could be inspired by other people's ideas and use them?

That's interesting.  Do we think it is alright to use other people's ideas?

- Yes, because we might see an idea and be able to change it to make it even better.

- I don't think we should just copy someone else's idea though. It's the same as stealing their thoughts and pretending its yours.

- But we can be inspired by someone else's idea and see if we can be even more creative with it.

-Its similar to what we did last week with creating logos. We learnt that designers often collaborate and share all their ideas to make a great idea together. If we see someone's strategy we like, we aren't speaking it. I think we are becoming a team with that person. Even if they don't know they are part of the team.

With those ideas we agreed that the purpose is to be inspired. If we find an idea interesting, we should try to experiment and play with it.

Some of our creative strategies:

So many unique and interesting thoughts can emerge when we give children the freedom......

We then silently walked around examine the strategies being created. When children found something inspiring, the returned to their seat and continued creating different strategies to solve the problem.  

After another 10 minutes had passed, table partners then shared their strategies with each other. Some rich discussions took place as they analysed the strategies and the reasoning behind them. The children naturally evaluated the effectiveness and visual creativity without being encouraged to.

To expand our creative thinking further, we then looked at our next task:

The new strategy created needed to have an element from each person. Some initially felt this was too tricky, but after time we all found possible solutions to do this. 

We then shared our new strategies on the data screen.  We explained each person's strategy and then how they were combined.  Their classmates were encouraged to ask them questions about the thinking process rather than the product and that generated some interesting perceptions on what creative thinking entails.

Partner Sample:

Partner A's:

Partner B's:


New Combined Strategy:

Another Pair showing each's strategy and then combining it: 

We then wrote a quick reflection using the following prompt:

Here are some excerpts from our reflections:

° I feel like this is the first time I've ever really understood what creative thinking is REALLY about. I used to think it was just fun thinking, but I know now that it involves hard and complex thinking too. 

° ...we can even take the easiest word problem and make it super complex when finding ways to solve it. 

°......visualising helps me make sense of what I am trying to work out in my mind.

° This helped me discover that I can create many different ideas and I feel more successful as a mathematician. 

°......helps me make more sense of what I'm doing.

° .....When I kept hitting road blocks with the strategies I was trying to make, it made me think of ways I could solve them. Actually, so much thinking went on in my mind doing this. I was amazed that my mind could handle them all so well. 

°I like how there isn't any pressure when we are creating different strategies. Its fun and challenging at the same time.

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