Fractal patterns

As part on an ongoing inquiry into pattern and in response to an emerging interest in the concept of infinity, I showed the children some images (click here for some great examples) and YouTube clips of fractal patterns. This provoked a huge interest. The children have asked again and again to watch the clips. They are particularly interested in Mandelbrot’s fractal shape.

The videos have inspired the children to experiment with pattern making themselves and there has been an injection of enthusiasm for pattern exploration.

Today we talked about patterns in nature.

If your child is interested, you could extend this inquiry by looking for interesting patterns at home and when you are out and about.

Exploring non-standard units of measurement

Having measured Nathan, the children decide that we need to find out everyone’s height. I assign the children partners, taking into consideration the personalities and developmental levels of the children. Apart from that, I do not to give any guidance, but instead step back and observe how the children go about the measuring project over the next few days.

As I observe I see that the children know a lot about measurement already. I see evidence that many children understand the need to start at the bottom and continue to the top and see the need for accuracy. Most children know that the measurement needs to be taken in a straight line, with no gaps. Some children measure using lengths of paper or wool and then realize that they don’t have a way to communicate the length of their wool (how long is a piece of string?); they are discovering that a measurement must have a numerical value. Some children realize that their “number” will have to be greater or less than their partners depending on their height.

The children record their data in a table as they measure. After a few days, when I feel the children have exhausted their measuring inquiries and are ready for the next step, we look at the information in the table. Several children can see problems:

  • How can Yungi be 200,000 and Angus is only 5? That can’t be right!
  • Yungi is too much.
  • Because I count in tens
  • I noticed that Aiden has two different highs, 45 and 65.
  • Maybe he growed?
  • No, how can he grow from yesterday?
  • I think we measured wrong.
  • Yeah, I think there was a muddle.
  • It’s a bit tricky because it keeps changing.
  • And Angus has two as well! 107 and 5. Huh?
  • That’s because I was 107 unifix cubes and 5 meters when I measured with books.
  • How many books?
  • 5! I already said! 5 meters means 5 books.
  • Well we had a problem because Nathan is really smaller than me but when we measured the first time he had more than me because he had more than 100.
  • Yeah, that happened to us and we had to measure again.
  • I think the problem is everyone is measuring with different things. That’s why we all have different answers. Because a cube is smaller than a book so you have to be more cubes.
  • That’s why it’s so tricky.
  • I agree! It’s so confusing.

From this conversation I decide that the children are ready to start exploring measurement with standardized units.

A reply from KinderPals

A few days ago we tweeted our Kindergarten buddies in Canada the measurements for our Nathan in KC.

We got a reply from KinderPals saying they needed more information.

Hmmm! More information! We wondered what information we could give KinderPals so they could know how tall KC Nathan was.

  • Scarlett: That’s what I said but no-one was listening! Because how will they know what we used?
  • Jaiden: So we need to tell them about the pencils, that we measured with pencils
  • Yungi: Orange, yellow, red

At this point I chose to intervene and ask the children whether they thought the color of the pencils was important information that would help KinderPals.  After some discussion the children reached a consensus that this was not necessary information. Together we composed a reply to KinderPals explaining that we used coloring pencils.

But now we have a problem:

  • KC Nathan is 11 middle pencils tall
  • KinderPals already told us their Nathan is 66 cubes tall.

Which is taller -11 middle pencils or 66 cubes?

We tweet KinderPals back and ask them if they can please measure their Nathan in middle pencils so we can compare the heights. Scarlett suggests that we could measure our Nathan in cubes.  There is a buzz of agreement. The children look around for some cubes. Oh oh! Which cubes? We have several different sizes of cubes.

We have no more time, so we leave our cube collection and agree to continue our discussion at another time.

Our measuring inquiry continues

Today we measured Nathan. We wondered what to measure him with. Aidan suggested cubes, Angus suggested books, Azi Hedeleen and Leander thought wooden pegs would be good. Leona volunteered to do the measuring. She chose red pencils.  Nathan lay down and Leona laid the pencils out in a line. Jaiden pointed out that the pencils didn’t start at the bottom of Nathan’s feet. Leona corrected this and carefully placed the pencils in a line to the top of Nathan’s head. However Scarlett noticed the pencils were not touching, “so there is gaps that didn’t get measured“. Leona made sure the pencils we all touching. Once everyone was satisfied, we all counted the pencils. 14. “That means Nathan is 14.” said Aiden.  “Yeah” agreed Jaiden. “Not 14 like his old, but 14 high.

Shoei wanted to have a turn.  There were only two red pencils left, so he decided to measure Nathan using orange pencils. Nathan was 8 orange pencils long. Now we had a problem- was Nathan 14 or 8?

Lovisa decided to solve the problem by measuring Nathan one last time. She got the yellow pencils and carefully laid them out. Oh oh! Nathan was 11 yellow pencils!

Jaiden noticed that the pencils were different lengths; red pencils were the shortest, the yellow pencils were the next longest and the orange pencils were the longest of all. (We had an interesting conversation about why that might be. A few children figured out that the red pencils must get used more and therefore concluded that red must be most people’s favorite color – a lovely authentic survey and data collection and graphing opportunity that I let go (for now) as I wanted to focus on the measuring.)

I asked the children what answer we should tweet to KinderPals. Some children thought we should tweet all answers. Others thought we should choose the biggest answer. One person thought we should tweet the yellow answer as yellow was her favorite color.  After much discussion, the children reached a consensus that we should tweet all three answers and explain that one was short, one was a little bit long and one was the longest. Scarlett suggested that we needed to mention “one what? They need to know what the thing is, like a pencil“. She was out-voted. I decided not to interfere at this stage, but to wait and see how the inquiry unfolds; finding out for oneself is a much more powerful learning experience than being told.

The KC children are delighted with their work. I am wondering what KinderPals will make of this information.  I look forward to seeing how KinderPals respond and where this inquiry will go next.

Twitter sparks a measuring inquiry

When we got back after the winter break, we found a twitter message from KinderPals, our Twitter buddies in Abbotsford, Canada, thanking us for the Japanese New Year cards we had sent.  We responded by sharing some exciting New Year news: Willow and Nathan had joined our class. KinderPals tweeted back. It turns out that they have a Nathan in their class as well!

KC were curious to know what KinderPal’s Nathan looked like so KinderPals promised to send us a picture. A few days later we recieved this picture of Nathan in KinderPals class, via twitter.

We tweeted KinderPals a picture of our Nathan.

We have been recording the children’s growth on our door. This sparked a conversation about how tall the KinderPal’s Nathan was. Several of the children thought that the two Nathans would be the same height because they were both called Nathan. Other children disagreed; they did not think that the two children would be the same height just because they had the same name. The KC children tweeted KinderPals to ask them how tall their Nathan was.

Michelle, the KinderPals teacher, and I emailed each other to see how we could extend this authentic inquiry into measurement. We have decided to suggest to the children that they measure their respective Nathans so that they can share this information with the other class. We have planned that we will not give the children much guidance initially; we are interested to see what tools and strategies the children come up with as this will tell us what they already know about measurement. I am intrigued to see how this inquiry unfolds!

Children explaining their thinking

Being able to explain one’s thinking is an important part of the learning process. It is one thing to complete a task, but to explain the process to someone else requires a deeper level of thinking. The children are using fotobabble to help them share their thinking with others. They have been working on speaking clearly and slowly so that others can hear, and on describing details. They make decisions about which work they will share and independently record and tweet the fotobabbles. Check the student tweets tab on the KC blog to see the latest fotobabbles.
Jaiden’s pattern

Ken’s pattern

Leona’s pattern

Kieran’s pattern

Scarlett’s pattern

Conducting an inquiry and explaining mathematical thinking.

As part of our math focus on patterning and sorting we have been exploring different ways of categorizing objects. The ability to categorize and sort what we see in the world around us is at the heart of much that we do. Young children tend to focus on more superficial and easily identifiable attributes such as shape, color and size. We have been challenging and extending the children’s thinking by having them sort irregular objects and then resorting the same objects in different ways. This week the children have had lots of opportunities to sort random bits and pieces from around the classroom and to make collections of objects that share a particular feature. Today the children sorted and resorted their shoes into different sets. The video clip below shows a five minute section of our sorting session.

As you watch the video look out for:

  • the concentration on each child’s face as they select shoes for their set
  • the concentration on the faces of the children watching as they problem-solve to work out the sorting criteria
  • the way the teacher thinks out loud to model problem solving strategies
  • the children’s admiration when someone works out the criteria
  • the way children explain their thinking
  • the way children agree or disagree with, and build on, other people’s theories
  • the “ah ha!” exclamations when a child thinks they’ve figured it out
  • the “oh no!” exclamations when they realize that their theory cannot be correct
  • the children’s delight when the criteria is revealed
  • the independent, focused and respectful way the children engage in the activity and interact with each other
You may need to watch the clip a couple of times to catch all the learning moments.

Explaining thinking: sorting from tasha cowdy on Vimeo.

There are strong connections between our math focus and our second unit of inquiry into How We Organize Ourselves. These trans-disciplinary connections help children to take knowledge and understanding constructed in one setting and apply it to a different setting.

Counting sets of objects

The children have been practicing counting. As in other areas, the children are all at different developmental stages in their understanding of our number system. Engagements are designed so that children can participate at a level that is developmentally appropriate for them. The main focus of this session was to provide an opportunity for the children to count objects. Some children are working on counting up to ten. Other children are working on counting to 20. Yet others are working on numbers over 20.

Counting sets of objects from tasha cowdy on Vimeo.

How many days till Kindergarten? A counting inquiry

Kieran from ELC came to our classroom this morning with a question: “How many days till he started Kindergarten?” Hmmm… Good question! How could we find out? The Kindergarten children thought about it. Well, we have to count said Nikhil. Everyone agreed that this would be a good start. “Wait!” cried Trenton “But what shall we count?” “That’s a very good question!” remarked Hal. Heads nodded as children agreed that it was indeed a very good question.

  • Nikhil We have to count days.
  • Phebe I think it’s seven days.
  • Maya Yes, it’s seven!
  • Trenton I don’t agree with Maya’s idea because it’s too small number.
  • Daan Because it’s not enough, seven.
  • Trenton It has to be more.
  • Daan Maybe one hundred?
  • Nia Well, actually, I don’t know.
  • Hal Well we know it can’t be seven because that’s one week and we know the ELC are not coming to Kindergarten in one week. (Many chuckles at this idea!)
  • Olivia I agree with Hal’s idea, I think it can’t be seven
  • Daan Could it be one hundred, maybe?
  • Nikhil Or ‘finity?
  • Trenton Not infinity!
  • Hal I’ve got it! It’s exactly the same day that we go to grade 1!
  • Olivia Well I noticed that that’s the same as asking how many days till August because I remember that’s when we started in Kindergarten and that’s when Grade 1 starts.
  • Hal At last! We almost have a solution!
  • Trenton We nearly solved our problem!

A group of six children choose to continue to work on finding an answer to Kieran’s question. After much discussion they decided that the next step is to find out which date in August school starts.

As always, the adults observe the children carefully, giving the children time and space to conduct their own inquiries and construct their own understandings but ready to step in and support the learning when the children become stuck and we sense they are getting frustrated. For now, the children are high on motivation and are busy formulating and testing strategies and theories.