How do you engage children in ways that help them verbalise their thinking and help them learn?

The children organise their own day and always make time for their ‘own time’ or free inquiry. This provides me with so much evidence of learning.

During these sessions I observe the children to see:

Where their passion lie (e.g. lists for the space ship or making paper planes).

What their current understanding are, and if they are applying taught skills (e.g.reading writing, number strategy)

What vocabulary the children are using.

How the social dynamics of the class are developing.

Does this mean children miss out on the taught curriculum?

Not at all. I knew we needed to carry out work on measurement, for example. I set about looking for a real reason to measure that would get the children excited. I have never been so happy to have a paper plane knock into my head! The answer literally feel in my lap. Waiting for a reason that sparks learning saves time because the children already have something to reference their developing understanding to.

Teacher generated, child supported learning.

Every time we need to find something out we discuss the best method. Sometimes I may make a suggestion. Come and look in the classroom, we are making a display of different methods. Of course the best example is the children’s ‘Who will do the calendar chart’. I am now looking to see if the children apply their taught skills, let me know if you see something at home.

Generating the inquiry.

As you can see from the video this has given me so much data on the vocabulary of measurement the children have. I also know something about their level of understanding about measurement. I took one of the planes made last week and started thinking out loud about it:

I was wondering if all planes go the same distance? Why not?

Do they go the same distance each time? How do you know that?

What is the best plane? How can you be sure?

These questions can not be answered with ‘yes’ or ‘no’. There are many possible ways of thinking. Try out such questions at home.

Molly is in England and we all miss her very much. The good news is we can stay in touch and continue learning together. The children decided the best way to share their maths with Molly was to make her a video. They decided what they wanted to share. Here it is.

The children decided to call the it the ‘beautiful maths for Molly video’.

You say you do maths, but what about adding and subtraction?

There are five areas of maths we teach in kindergarten: pattern and function, shape and space, data handling and number.

Let’s start with number. We divide number into two parts, number knowledge (understanding that there is a naming system for numbers i.e. 3 represents ***). We also teach number strategy.

We teach number on a daily basis. As teachers we are always looking for ways to make maths part of the curriculum. So we have teaching time in: maths, unit of inquiry, reading, writing and even recess times. There are explicit skill develop times and other times when we provide opportunities for children to show their understanding.

O.K, but there just little kids, How much thinking do they do about adding and subtraction?

To be a successful mathematician children need to be able to express their thinking using mathematical vocabulary. We listen to their words as they explain what they are thinking and help them develop a vocabulary for thinking. This is called meta-cogntion, or thinking about how you think!

Here is a poster that shows the level of thinking we are developing in kindergarten

Children pass through many stages of development as they explore number strategy, at every stage they need to be able to express their ideas and findings. Children are reflecting on their learning. Any way of recording their understanding is valuable and may include: drawing, diagrams, words or symbols.

If children think in many different ways, how do I know what these stages are?

The Beginning

I am learning to count a given number of objects. I am learning that a number has a value that does not change (three is always three). I know that there are things called numbers. I am learning to count in sequence order but can’t quite manage this yet (1,3,3,5,9).

One to one Counting

I can count sets of objects up to ten. I can make groups of objects up to ten (1,2,3,4,5,6,7….).

Counting From One on Materials

I can put together two numbers like five sweets and three sweets. I need to use objects such as my fingers to help me. I also need to count each object in the sets to get the answer (1,2,3,4,5,…6,7,8).

Counting From One by Imaging

I put my fingers behind my back or under the table to count (shielding). I can see a problem in my head as pictures or numbers. I count all the numbers from one to get the answer.

Advanced Counting (Counting On)

I understand the number at the end of my set tells me about the whole set (1,2,3,4,5,6). So if I want to add 6+5 I will put ‘6’ in my mind and count on from there (6… 7,8,9,10,11).

Early thinking about the Parts of a Whole Number

I can work in my head with numbers and take them apart and put them back together in different ways (10+6=16 so 9+6=15). I can work with number facts I know like doubles (7+8=…. 7+7 is 14, so… 7+8 is 15)

How many ways can you be right?

What’s the missing Number? We have a set of number cards and turn over at least one cards so the children can’t see the number. The children then work out the missing number. Most importantly they have to give the strategy they used.

What are the strategies they used ?

Molly: I looked at five and seven. I looked at the number before and after.

Matthew: I counted from zero.

Taiki: I counted from nine… backwards.

Mai: I looked at all the numbers and I didn’t see six.

SojiroI: I counted forward and backwards and there hasn’t six, so I know it’s six.

Julia: I look at five and six is missing so I know it’s six.

Hashu: I counted down from nine and when I was counting down there wasn’t six… so it might be six.

Jolie: I looked at the number before and after. I didn’t see six.

Here is a video of us carrying out this activity.

I want to know how I can help at home?

We do maths every day so there is no need for you to feel pressure to do things at home. You might find it helpful to look at these activities so you are helping your child think mathematically.

Talk about how you use addition to calculate what you need to buy e.g. “We have 2 tins of tomatoes and we need three more. How many will we have then?

Play games, there is so much maths involved (counting on 1,2,3… and counting back 4,3,2,1…) snakes and ladders and Uno are good games.

Take a set of objects like cubes and see how many ways you can make 5 and work up to 10.

Get children to grab 2 handfuls of materials and compare them. Which set has more? How do you know it has more? Can you add them together and count how many you have? Can you take one away from another? What strategy did you use?

I know my child needs to explain things in their own way to show understanding, but what mathematical words do you us?

My child is learning English, can we talk about maths in our home language? I am worried they will be behind the other children.

There is so much research to support a strong home language. If you understand an idea (adding) in one language, when it comes time to learn the vocabulary in another language you can apply your existing knowledge. We would like your help in explaining (in simple words) the ideas and vocabulary listed below to your child in their home language.