Art and Math

Finger Tracing

Hand of a four year old
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.
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!

Addendum July 21, 2016

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 Universitys
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:–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 .

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.


8 thoughts on “Finger Tracing

  1. Thanks for the mention in the addendum

    Yeah, silly me. I thought quite a bit about using words instead inequality signs. (They’re the alligators in the classroom — sorry, couldn’t resist.)

    For a long while I have been suspicious of some of the claims of Jo Boaler and Carol Dweck — I thought they were pushing things too far. But now, after more than a month chasing down other sources, I don’t dismiss it so readily.

    Great post Paula.

    Liked by 1 person

    1. What I’m attracted to is the conversation about different ways of thinking about teaching and learning, and how I can respond to what other people are doing with modest materials. It’s not about discovering the best methods, as even the best ideas and research can be implemented ineffectively. But these are exciting things to think about, and I love when I read thoughtful posts that express what other people are observing. I read your post all the way through a few times, and will be looking at it again (making it part of this post is my best way to keep track of things I want to go back to!) Thanks for your comments.


    2. BTW here’s my very short rant about the inequality signs: I am looking at math from a point of view of compassion. We see so many people really suffering because of math, and, the way the inequality signs are taught adds to this. A young girl pointed out to me that the open mouth of the alligator would go towards something smaller than it’s mouth, which, actually makes perfect sense, but this interpretation got her in trouble plenty! That said, your intention with the graphic was perfectly clear and I loved your post.


  2. It reminds me of something I used to do with my kid to help her calm down. I would trace a letter or a word on her back and she’d tell me what I had written. She used to suffer intensely from intense sensory processing issues so I probably got the idea from resources related to SPD.

    Also, did I ever tell you my kindergarten-traced-hand-with stars on the fingers memory?


    1. Wow…I’m going to remember this tracing-on-the-back for settling down a young child. I can imagine how that could be helpful. You did at some time mention a stars and finger memory: I would love if you would repeat it here. ❤


  3. As I’ll be teaching 5 year olds in September, this is timely for me, Paula: I found Jo Boaler’s thing about fingers interesting; but it doesn’t particularly chime with anything I’m conscious of personally. But if finger-number sense is critical, this seems like a good way to play with it and develop it; the addenda too!

    Liked by 1 person

    1. If you do some finger-sense games with this age group I think you’ll be impressed at the range of awareness that students have of their fingers, and how quickly you can help them support this awareness. Whether or not it really has impact on number sense is unknown, but it certainly can’t hurt! I will look forward to hearing about your work with 5 year olds. It’s been my experience that it’s a profound time in their lives, a time when you can have great influence. Can’t wait to exchange thoughts with you about this!


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