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

Etoys Class Reflections

Taught a class today, 4 kids (8, 10, 11, 12, 14) and 2 adults (Mom and Dad of two of the kids). First class with this group.

Started with "Daemon Castle" and then had them do "Etoys Challenge".

Observation:I had one child. Nick, who was laughing hysterically.  I went over and found him playing around making the car go tight circles, bounce off walls and he eventually figured out how to make it bounce off the walls until it reached the goal.  His father who sitting next to him, got a bit upset and told him he needed to focus on what he was learning and be more disciplined.  

Thoughts:
This reminded me of something another coach told me while coaching Soccer "Never coach your own kid, (a) they won't listen to you and (b) they will listen better to another adult".  While I don't fully believe (a), I think they do listen, they just don't want to act like they do, especially in front of the friends, he made a good point. Also, in my observations parents are harder on their own kids then they are on others, especially with their first child.

I love to see kids laugh and having a good time in class, this means they are having fun and to me fun means MOTIVATION. I firmly believe motivation trumps most other things, as kids will work hard when motivated.  That said the father had a good point and I needed to find a way to turn that "silly fun" into what others have termed "hard fun".  So I let him finish his "Etoys Challenge" then when he told me he was done I stepped back and ran his scripts on each step.  I then challenge him to reach the goals using just one script.  I have observed a number of kids who use multiple versions of the script changing it along the way until they reach the goal. Again I let them do this and congratulate them on a creative way of solving the problem and pointing out there are many ways to solve the problem, but can they find a simpler more elegant way using only one script which doesn't change?

I always try to have one part of the class where I get them AWAY from the computers and preferably outside.  Today I broke them into pairs and have them "program" each other. One child, the programmer, would give instructions to another child "the computer".  I first had them try and program each other to "walk a square".  At some point one of the kids will say "turn" and the other knowing he is supposed to walk a square will dutifully turn 90 degrees.  I then jump in and ask the child to program me. When I am told to turn I will turn some random value (usually either a very small turn or a 360 degree turn) and they will get the idea and then ask me to turn 90 degrees.  One kid got excited and came up with the idea of I can go forward 10 steps, turn 90 degrees and repeat forever.  After complimenting him (kids love compliments) I asked him what was like repeat forever in Etoys? He said a ticking script.  At some point I made the connection, wish I could remember what brought it up, to how the cells in our bodies are like millions of little ticking scripts doing their own things responding to stimulus and working together to make us and how it is amazing that is.

IMPORTANT TEACHING NOTE: I try to never give a child an answer.  Instead I will either ask them a question or give them another problem that will help them figure out the answer themselves. Basically a hint in problem or question form.

What to do with kids who finish early?  

There are always those who finish faster than others I have a couple of strategies to deal with this:

1. Have some problems or other Etoys Challenges they can work on
   For this lesson I had "Etoys Game Challenge" which the kids like because they can create their own games, very motivating for kids.
2. Teach them to teachThis means having them help other kids, but the danger here is they will simply show the other kids the answers they found. I do my best to impress upon the kids that they should never give them the answer, but instead help the other child find the answer themselves by asking questions or getting them to think about how their program works (aka play computer). I try to model this and point it out explicitly a bunch of times early in the lesson so the kids understand my preferred style before I ask them to help teach. I then monitor the kids closely when they first start "teaching" other kids.
3. Have the child teach an adult in the class
   The kids get a big kick out of teaching adults.When there are adults this is especially fun, the kids get a big ego boost (and motivation from feeling they are better that an adult at something) out of teaching an adult, and it shows them the adults don't know everything (a valuable lesson in life that kids figure out faster than most adults would like to believe).  The adults are usually good sports, but read your people some peoples ego's are fragile and you need to be sensitive to that.
4. Have them improve or extend their current work
   For example their script may not be the simplest or most elegant (ex: turn 90, turn -45; one kid had turn 45, turn -45) or having a forward 10 tile in the YES and NO of a test
   Some kids will instantly see what they can do with Etoys and start creating games or other fun stuff. If I see this and they have completed the main task (sometimes even if they haven't) I will encourage them to improve their games or show them some basic Etoys functionality that they can use to improve their game or do what they want.

At the end of class I wanted to set them up for their homework (working on the 40 Mathematical Shapes challenge) and had them try and get their car's to "Draw a Square"

(Hmmmm, another idea to get them out of the computer and use the knowledge they already have is to have them "program" their hands to draw a square on a piece of paper).  While doing this one child asked: "What's this symbol here do?" He was pointing at the "add a variable" icon in the top bar of the viewer (looks like a arrow head in a pink background pointing down).  At the time we had a script on the screen to draw a circle (forward:5, turn:5) when I had a brainstorm.  Okay we can use variables to change the value for forward and turn (I am slow I can't believe it has taken me this long and a 14 year old kid to finally figure this out!!!).  So I showed him how to add the two variables and dragged the variables into the scripting tiles to replace the 5's and then asked him to make a square without changing his script. When he looked confused (a feeling I recognize because of my vast experience with this emotion) I pointed out,  a couple of times, that the car would move forward and turn by the variables we had setup. I did NOT point this out by saying it explicitly. Instead I simply pointed to the variable (i had dragged a detailed watcher onto the screen for each variable) and then pointed to the forward tile and asked him how far it would move forward. He eventually got the idea and I went to work with another child who had been asking questions. Then all of a sudden I heard and excited voice saying "Hey I made an Octagon!!!"  I then made a big deal out of his great discovery and pointed out how with one script he could make multiple shapes just by changing the variables. Then i asked him what other shapes he could make and left him to have fun.

Towards the end of class I sent them outside again to program themselves (as opposed to others in this case) to follow a road.  I drew a sample road and then gave each of the kids some chalk and observed.  Each child drew a different shape and I asked them what there program was for following the road. Fortunately one of the dad's who was there said the scripts we wrote reminded him of a robot they have at work do deliver mail.   I told the kids some folks have been paid a lot of money to write programs just like the ones they wrote today to follow the road (when my son heard this he asked for $100K).

The kids got the idea of programming a car that could drive itself, so I challenged them to program the "Car of the Future" and asked them to think about what kinds of challenges they would have and how they would handle them (other cars, pedestrians, traffic lights). One of the parent's suggested they test their program by having multiple cars drive in Etoys world at the same time.

Anyway a lot of fun was had by all and I had to kick the kids out as they wouldn't stop working on Etoys when the class was done. (a good sign and one I always see when kids are first exposed to Etoys).

Mr. Steve

Note for future reflection: On teaching kids to think about multiple ways to solve a problem and learning how to compare solutions.

Etoys Challenge - Game Controls

The following post contains teaching tips and ideas for Etoys Game Controls  (click on link to get project) which is an Etoys project designed to help kids learn to create their own games. Etoys can be downloaded here.

Etoys is tool that can be used by teachers to:

• Create Curriculum
• Assess children's understanding
• Provide skill practice
• Motivate students
• Help children learn useful and powerful ideas

Etoys is a tool that can be used by students to:

• Write Reports
• Communicate Ideas
• Create their own Stories
• Learn from each other
• Create Games
• Develop a deeper understanding

Teaching Tips for this Project:

• Try not to give the kids the answer, they will figure it out for themselves eventually. Instead you can ask them questions or have another student help them.
• Train students to help others by asking them questions and not giving them the answer directly. For example: Esteban, can you help Leonardo, now please don't give him the answer, instead give him hints and try asking him questions that will help him figure it out for himself.
• Ask the kids if they have seen a similar problem before.
• Ask the kids if they have seen another project that solved the problem or did what they are trying to do. Then ask them to study that project to figure out how they did it. You can even point them to a project that can help them. For Example, on Step 4, you can ask them if they have seen anything that sends the car back to the start.
• Towards the end of class if there is time, look at the different ways kids have written scripts and pick out two that used different methods to solve the same problem. Then ask the class do both work? Which is better? Why is it better? Is there another way?
• Encourage kids to look at their scripts and "play computer" ONE STEP AT A TIME to figure out what it is doing.
• Questions to ask while Teaching with this project: "How can we make the game harder?" and "How can we make the game easier?" Invert, always invert' ('man muss immer umkehren') - Carl Jacobi)

Things to look for while Teaching with this project:

• Look For: Kids who change the forward value from 5 to a higher number.
• When you see it: Ask the child why they did that, then praise them for such a good idea, tell the rest of the class "Pablo, came up with a neat change to his script" then ask Pablo to show the other kids what he did. Then you could ask the other's why did Pablo's idea work?

• Listen For: Kids who come up with ideas for improving the game or new games
• When you hear it: Tell the child, out loud so others can hear it, something like: "Sadie, that is a great idea to improve the game." Then ask her to share her idea and ask the other kids to come up with ideas to improve the game or make their own games. Ideally you should only have to do this once or twice to "prime the pump" and get kids talking and sharing ideas on how they can improve the game or make their own games.

• Listen For: Kids who ask "Is negative 5 turn to the left" or any question about how a tile works.
• When you hear it: Tell them: "Good question, how can you find out? Is there a Test you can run to figure it out?" Then when they run the test and discover the answer for themselves, praise them and tell the rest of the class "Hey folks, look at what Ines did!  She wasn't sure what this tile did then she created a test and found out the answer for her self. (While saying this ideally you can show or have Ines show the question she had and the test she ran).  The goal is to encourage kids to test things and find the answer themselves.

• Listen For: "Hey I can make a two player game" I have heard this when the realize on Step 4 that the arrow keys ( and were changed to a,s,d,w.
• When you hear it: Say "That's a great idea, i'd love to see that'
• NOTE: There will be problems when a child creates a two player game with the techniques shown in this project. That's okay, its good for kids to get frustrated once and a while. I will post another project and blog post on how to deal with that later.

• Look For: A child who is stuck and their script isn't working the way they expect.
• When you see it: Ask them to look at their script and explain what it does. You may want to ask what a specific tile does (the one that is causing the problem. The goal is to encourage them to look at their scripts and "play computer" and figure out what the computer will do. Remind them the computer only does what you tell it to do AND it does EXACTLY what you tell it, not what you want it to do.

• Look For: NOTE: In this project on the first two steps the scripts start in "Ticking" state so as soon as they put in a tile that action is taken.  This will hopefully surprise some kids and lead them to ask "Why did that happen" If they do ask or notice ...
  
• When you see it: ... Ask them to look at the scripts "Ticking" state. Hopefully they will realize that is the reason (with guided questions if neccesary). Then ask them what the different states do and when they give you an answer (right or wrong it doesn't matter at this point, really!), ask them to "Prove It!"  Ie: "How can you design a test to prove that's what it does?The goal being to get the kids in the habit of designing tests and testing their ideas.
  

• Look For: Kids who finish a step early. In a large class (and even in a small) one this will happen.
• When you see it: Ask the child if there is another way to solve the problem. Always good to get kids thinking about alternate approaches to solving a problem. I had one student who in step 2 used forward and turn for the same arrow key and it to my surprise it worked!  Ask the child to help another child who may be struggling. Remember to train them to ask questions and give hints, NOT answers.
• Look For: Kids who finish a step early. In a large class (and even in a small) one this will happen.
• When you see it: Ask the child if there is another way to solve the problem. Always good to get kids thinking about alternate approaches to solving a problem. I had one student who in step 2 used forward and turn for the same arrow key and it to my surprise it worked!  Ask the child to help another child who may be struggling. Remember to train them to ask questions and give hints, NOT answers.

• Look For: Kids who put a Test tile inside the "NO" section of another Test tile. Most kids I have seen put one test after another.  
• When you see it: At the right time, perhaps towards the end of the class when you ask kids to look at the different ways kids have solved the problems (ie: the different ways of writing the scripts) you could ask them are these the same?

• Listen For: "Oh I get it"
• When you see it: Smile to yourself, this it the Joy of teaching and learning. Then ask the child what they discovered and if appropriate share it with the class.

• Look For: Two kids using different tiles for "reset" on Step 4. Both "Car reset" and "Car do reset" do the same thing.  Frankly I wasn't sure if I should include this or not. 
• When you see it: Let me know what you think about the reaction and dialogue of the kids. Thanks!

Things to Add/Next Steps:

• Time Trials (A challenge to show kids how to create their own timer) This should lead the kids to try and make harder mazes and change the values for move forward and turn from 5 to higher numbers. Of course some may make easier mazes.
• Provide a Top Ten Times lists where kids can post their high scores. This will require prompting for names, lists and sorting. Will work on a project to teach this later.
• You have three lives to get through the maze without touching the wall
• Consider adding a "background" script in Step 3, so kids can't go through walls.
• Consider adding a sound in Step 3 when a car hits a wall. 
• Have the child Enter their name at the beginning of the project and customize the certificate with their name. Ideally print it or email it at the end. Need smalltalk/squeak script to do this.

How to relate this to "School Curricullum"

• turn teach about degrees in a circle (need to create a lesson plan on this for teachers to make the connection more obvious for the kids)
• the x and y in reset teach about Geometry
• teaches programming
• Etoys can be used to create curricullum
• Etoys can be used for students to create reports and explore ideas

Prerequisites:
Students should have completer the Etoys Projects: Demon Castle and Etoys Challenge which can be found in the "Tutorials and Demos" from the Etoys Home Project.

Acknowledgements:
The design of this project is based upon Etoys Challenge by  Toshio Miyasaka. The beauty of his design (and Etoys which allows you to do this) is that you can design the learning environment so that the child has only those things necessary to solve the problem visible and is not distracted by all the powerful scripting tiles available within Etoys.

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.

Teachable Moments: A Rotten Banana

During a break in class Bob Davis pulled out what had to be the second ugliest banana I ever saw. It was a deep dark brown, without a hint of yellow anywhere. As soon as he pulled it out the whole classroom went quiet and everyone stared at Bob wondering "is he really going to eat that thing?"

Professor Davis, never one to miss an opportunity to teach, looked up at the class and said:

When I was a kid, all the bananas at the fruit stands and grocery stores were brown. That is when they are at their ripest and taste best. The problem was they didn't have a very long shelf life. So the folks in the banana companies started an ad campaign to convince the public that yellow bananas were best. This would give them a longer shelf life and more time to get them to markets farther away from the ports.

He then took a bite of the banana. A true master teacher sensing a teachable moment and then teaching us an economics lesson in math class.