A Way In

metal doll 2
Metal Doll from Mexico


I used to wonder why it was that students who traveled more and did more things seemed to learn better than students whose worlds were more limited. Intuitively this seemed correct to me, but for a long time I carried around the question about why this was. Finally, there was moment that I realized that knowledge needs an entry point, and that children whose had more experiences have more ways to relate to, and thus integrate, new information.

 Rasberry Leaf, inked and pressed by hand
raspberry Leaf, inked and pressed by hand

I not only do hands-on work with students, but I also believe in the value of it. Lately one of my projects has been to develop flip books to animate math concepts to enhance student understanding. There are numerous absolutely outstanding on-line technologies that can do what I am laboring over, but what they are doing happens only in the virtual world. I am using the tools available to me through technology to design interactive books that are completely off-line and non-electronic. One question has popped up repeatedly: is there an advantage of creating a manipulative when such excellent 0n-line resources exist?

pencil drawing by Paula Beardell Krieg
Unripe Tomato

The short answer is that on-line resources are richer in information than any book I can make. Each book I make illustrates just one concept, whereas any on-line resource can illustrate what looks like an infinite number of concepts. An on-line resource doesn’t require extra purchases, it doesn’t get lost, it disappears once you click off of it so won’t clutter up your house. It won’t get stolen. Actually, books about math generally don’t get stolen either, so maybe I should leave it out of this list.

Hand and Friend, pencil drawing by Paula Beardell Krieg
Hand and Friend, pencil drawing

We’re always looking to relate what’s inside of us to what is outside of us. So, when I make a book that illustrates an idea in math that can be experienced visually, but that can also be picked up and flipped through, then stopped. then made to go forwards and back, when I hear the click of it in my hands, feel it’s weight, well, then, somehow, it begins to feel like mine.  Now, here’s a GIF of my most recent set of pages for a flip book. If it’s not animating, click on it.

equations of a Line, changes in B
equations of a Line, changes in B

I really like the image that happens with the changes in this equation, especially when I let them stack on top of each other. But if I want to share this with someone who has less than a positive history with numbers and equations, I have to deliver it in a way that they will accept it. Opening my computer and opening a graphing program is just not going to do it.

At this point, at gatherings of friends, I’ve pulled out some of these little books. People become engaged immediately, they ask questions and they want to share them with their children. One friend of mine said he never understood the equation of the line until he looked at my little books. Graphing equations always seemed so random to him. This understanding gives us one more entry point into information and deciphering relationships between things, which can feel really good. Then, maybe after this world of numbers feels better, it’s more possible, then, to explore things beyond the few little books that I create. But to get there, it’s good to have a friendly way in.

Quarry Road
An Invitation to Enter


4 thoughts on “A Way In

  1. there’s the poem by the chinese monk that I don’t know if I remember about if you tell me something (I learn whatever) if you show me something ( ) but if I do it, I learn it. Especially with making books and also with math principles. That’s why in the Montessori school, they have students handle buttons and beads and things to learn counting. I was a reading tutor for awhile with the lower grades and we had various ways of teaching them, because some kids are visual, some are aural, some are tactile and most are a combination. I learned some new ways of teaching that time, the tactile impressed me the most, because I was one of those people that just instantly ‘got it” when i was quite young. Didn’t mean for this to be so long, but when I was teaching english to foreign students, I also did it by relating things to them. Example: I’m sitting on a chair, the chair is on the floor, the floor is in an apartment, and so on. This helped several people, also things like taking them grocery shopping, and handling and naming the food.


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s