Tools to Play/Learn/Teach with - M&M Fractions and Multiplicaiton

M&M Artifacts for Multiplication and Fractions
(you need to download Etoys to play/view)

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Etoys is a media-rich authoring environment that encourages deep learning through experimentation. 

Children use Etoys to make their own models, stories, and games, which keeps them engaged because it's a lot of fun. But Etoys isn't just child's play. Etoys makes abstractions more palpable, allowing children to visualize and explore new ideas. 

Etoys allows you to construct things from a set of basic building blocks which is its strength and also (IMNSHBOWO¹) its weakness.  It requires that you build everything from those basic building blocks.   I wanted to explore the idea of providing higher level "artifacts" that allow the user to play with ideas without having to start from first principles.  So I am working on a set of "Tools to Play/Learn/Teach with" (or to Think with or Play with) that allow kids, teachers and anyone else to play and learn.

I created this Etoy to explore how we can help kids with ideas such as fractions and multiplication.

My end goal is to see Etoys and the higher level artifacts used by teachers, kids and parents to facilitate and improve learning.  You are free to modify the tools you see here and/or create your own. As such they are Creative Commons licensed under the Share and Share alike  (see sidebar for license for all content on this site).

¹ IMNSHBOWO - In My Not So Humble But Often Wrong Opinion

Taking Tic-Tac-Toe to the next level

If you give a child an answer,
you solve a problem for the day.
Teach a child to find the answers,
you prepare her for a life.

So, how do you "Teach a child to find the answers?" Let's illustrate by example.
Parent Ground Rule:

You can't tell the child the rules of the game, let them figure it out for themselves, they'll retain more and feel better about themselves

The Game Example

Parent: (Stage Direction: Create a grid of dots on a piece of paper like this)
. . . .
. . . .
. . . .
. . . .
Parent: Lets play a game on this board I have created.
(Stage Direction: Look at your always beautiful, and sometimes frustrating child)
(Say your child's name) Pick any two numbers from 0-10.

Child: okay 2 and 8

Parent: Great, Now lets go to the game board.
(Starting in the lower left corner of the board, count from ZERO to the first number your child said. See diagram below:
. . . .
. . . .
. . . .
0 1 2 .
(next using the second number your child gave you start counting up from the dot you just picked. See diagram below:

. 4
. . 3 .
. . 2 .
. . 1 .
. . 0 .
(when you get to four, ie: you are off the board stop and say) Sorry that's off the board, my turn.

Parent: I pick 1 and 2
(Again count from ZERO, starting with the dot in the lower left corner and pointing to each dot as you count. Now mark an X a shown)
. . . .
. X . .
. . . .
. . . .
Parent: Your turn pick two more numbers between 0 and 10
Child: I pick 2 and 3
Parent: Okay lets check it out.
(Start counting from the dot in the lower left corner of the board using the first number your child gave you. Then start counting up from the the first number using the second number and mark your childs spot with an 0, as shown:
. . O .
. X . .
. . . .
. . . .
Parent: (say it with enthusiasm and pride: state your child's name) Congratulations, you seem to have figured out the rules of the game!
(Teaching Tip: here you are giving specific praise on something your child probably struggled with at first then figured out all by themselves)
Game Teaching Suggestions:

1. Your child most likely won't figure this out on their second guess, it will probably take them a while, but have patience they will figure it out.
   
2. If you have multiple children, teach the game to your younger child first (if they can play tic-tac-toe, they can play this game) and don't let your older child see you playing. Then have your younger child compete against her older brother. Then sit back and watch the sense of pride as your daughter's face beams as she womps her older brother. He will get frustrated, but that frustration will drive him to learn the game. This is good frustration channeling.
3. If they get too frustrated, STOP. Our goal is to help them be success. If you sense your child's frustration level is too high, change the way you ask the question, such as "pick two numbers between 0 and 3", then switch back on the next turn to between 0 and 10.
4. Always start counting from zero It took us humans thousands of years to discover zero, its an important number. More history on Zero in a later posting.
   
5. After a few games have your child explain the rules to you and how the game works. This also helps your child to start reflecting on what they are learning.
6. Its okay to win the first game. Your child will feel a greater sense of accomplishment if they lost the first game and then came back to win.

What your child's learning:

1. Geometry - Cartesian Coordinate System
2. How to communicate what you know (see teaching tip #5)

Now try it with your child and please let us know how it went by clicking on the comments link below. We also appreciate any suggestions and editorial corrections you have in the comments section.
Coming Soon:

1. Books suggestions that go along with this lesson
2. Taking tic-tac-toe to an even higher plan
   1. Getting kids to think about Second Order Consequences
   2. You can't do that (or introducing negative numbers)
   3. "History" lessons
      1. Rene Descartes and "Mom, there's a fly in my room."
      2. Why on earth did it take so long to discover Zero and why is it so important anyway. Can you figure it out? If not ask your kids, its okay if they don't have an answer, some of the best questions are ones that it takes a while to figure out.

Thanks to:

• Robert B. Davis - Bob Davis was my professor at Rutgers in the Masters in Mathematics Education Program. This is based on a warm up he taught teachers for the Madison Project. Bob was a true master teacher and a heck of a nice guy. He also ate the second worst banana I ever saw.
• You, for taking the time to learn how to help your child learn by doing.