Origami Boats and Meandering Number Line with 4-year olds

August 24, 2016

How to Make an Origami Toy Boat

Full disclosure: I did not try out teaching 4-year olds how to make origami boats. It’s not that I didn’t want to, or that I chose not to, it was just that there were other things I wanted to do more, and my time with these little ones was limited. Much to my delight, though, after we used the boats in  our activity, the children asked me about how they were made. I did a demonstration, with hope that this may encourage an interest in  paper-folding.

origami Boats, stacked

I chose to use these paper boats because they stack. Just for the record, I was curious to see if they floated. Turns out ;Yes! Until the paper absorbs too much water, these vessels are sea worthy. What was more useful for me, though, was that they can stand on their own, so that we could use them as playing pieces for a board game.

During my workshops with these children I noticed that even the most accomplished child in the group could not coordinate counting items with the movement of his hands. In other words, if there was a  pile of 8 stones, these children would end up counting inaccurately because their fingers would move out of sync with the numbers that they were reciting. I was really interested to see this, partially because  I’ve read that there is something about learning to play the piano that  helps children be better at math: this now makes sense to me, as playing notes would help train a person to coordinate fingers with intention.

Toy Boats and Board, drawn on large paper

Wanting to try out a simple, and, yes, frugal, made-from-paper activity to encourage accurate counting skills, I worked out a sweet game that the kids seemed to like . What we did mimics  classic board games where a die is thrown, and the player advances a certain number of spaces along a line. It was, however,  important to me that I didn’t want to create winners or losers.  This is how it went: the playing pieces were these paper boats, and when two boats land on the same space, they become a team, and stacked together. The point of the game is to get all the boats stacked together as a team before any boat reaches the end of the meandering number line, which, just, for no particular reason other than I ran out of space on my paper, was 42 units long.

Beginning at zero

Unfortunately, I didn’t get a photo of the kids playing this game, but, they played in groups of three and four, and they seemed to enjoy watching others play as well as playing the game themselves. Counting spaces, counting the dots on the dice, and (especially!) anticipating what throw of the die would yield the desired outcome were all challenging but doable for these kids.

Each of the five sessions that I worked with these students, one-third of my lesson plan was to focused my interpretation of relationship thinking, such as creating patterns from shaped paper,  developing finger sense, estimating, discussing what was the same and different about shapes and flowers, and this unit counting game.

Other parts of my time of my time with these kids was artful numbers, which I what my next and last post about my time with these students will be about.

I had to learn how to make these origami boats for this project. I looked many different models, but this one that I’ve shown  I found most enchanting. I put together a video of it, that is worth watching because there’s some pointers included that I just can’t fit onto a tutorial page.

Happy boating.

Addendum 5/6/2017 Just came across a tutorial that shows an alternative way of making this boat. An interesting way of altering the folding method https://www.youtube.com/watch?v=xAgzkcbqUYo&app=desktop by Gregor Müller

Finger Tracing

June 16, 2016

Hand tracing by a four-year-old

This post is for people who have the good fortune to be working with four- and five-year olds.

For quite some time I’ve been exploring ways of drawing the attention of young students to their fingers. In my post Counting to Ten, March 2015  I wrote”My thinking here is that I want these students to create a visual that connects the numbers that they are learning to the fingers that they count on.” I see the fingers as the original number line.

Recently I watched a TedX  Stanford video of Jo Boaler, an educator who is involved in research in how to support learning and growth. I’m already of fan of Jo Boaler, but particularly liked this talk of hers and particular like what she says about counting on fingers. Starting at about the point 7:22 on the video, she tells the audience that when we calculate, the brain area that sees fingers lights up. She then goes on to tell us that the amount of finger perception grade 1 students have is a better predictor of math achievement in grade 2 than test scores.

Hand tracing with a cut-out tunnel to fit over the student’s wrist.

After hearing Jo Boaler’s talk, I couldn’t help but wonder if it is possible to modify my finger tracing project in a way that could possibly help children strengthen their finger perception? This isn’t something that I’ve ever thought about before, but I guess that some people are more challenged than others in connecting the sensation of having a finger touched to the finger that is being touched. More simply said, when I touch your finger, do you know, without peeking, which finger I am touching?

First we did some counting together, up to five. Then the children traced their hands. The adults wrote down the numbers on the drawn fingers. We cut out a tunnel so the child’s hand could rest under the drawing. Then a partner would touch a finger, and the child would reference the drawing and say which finger had been touched.

Here’s a few short video clips of how it went:

Mostly it was children doing this with each other, but it was easier for me to use these clips that show the adults working with the students. When the students were working with each other I put little stickers on the student’s hands, labeling the fingers 1-5 so that the student who was doing the finger touching would know what number was matched to the finger that he or she was touching.

It was interesting to see that there was a huge range between how hard and how easy it was for children to identify which finger was touched. One child simply could not make the connection at all. It finally occurred to me to let her see her hand and the map of her hand at the same time, to see if she could develop the connection. This seemed to work out for her. Here’s what it looked like towards the end:

This was my first attempt at this kind of…um….hands-on drawing project/ finger game with young students. It was a really quick, let’s-see-what-happens-if-we-do- this kind of thing, but there seems to be something interesting going on here. and I hope to do more of this, and hope other people will try it out too! Thanks Jo Boaler!

I’m seeing a trend… my addendums are getting more frequent and could become posts in themselves. Seems like once I post something I stumble across something that’s totally relevant, or someone tags me with content that applies. This addendum has both.

Part 1

First, here’s an absolutely accessible, research based activity to do with young children, to help their brains develop its mathematical regions. It’s based on the idea that there’s a correlation between preschooler’s sense of approximation and their general ability to do mathematics. It looks like this:

from a report on the work of Jinjing Wang of John Hopkins University

Looks to me that there’s lots of possibilities for here for books that I could make with kids for them to  bring home. Even though the task here is to estimate which side of the page has more dots, I can see all sort of other kinds of vocabulary that can be come up with 4 year olds that this kind of graphic can facilitate. Here’s a link the the article about this, that Dave Radcliffe @daveinstpaul pointed out to the twitter community:

http://indy100.independent.co.uk/article/the-simple-dot-test-that-can-massively-improve-a-childs-maths-skills–WJ4LCbVq8EZ

Part 2

Ted Lewis saw my post and alerted me to his, which, discussed the  longer and more satisfying exploration and examination of ” number sense and how we create it.” This is the graphic that accompanied Ted’s post:

Okay, this is a perfect reminder that I don’t need a computer screen and Big Bird and Elmo to do this kind of work with students. Ted is using the inequality signs for this exercise. (Silly Ted, inequality signs are the downfall of many, but let’s talk about that some other time….)  The point though, is, if you are interested in visuals and the brain and the want some insights and food for thought, read this post for yourself http://mathinautumn.blogspot.ca/2016/06/its-not-all-snake-oil.html .

I’ll be working, weekly, with four-year-olds starting the first week of July. Can’t wait to see if I can corral them into doing any of the activities that are inspired by these dots and other ways of thinking.