So I "donated" an on-line Algebra course (1/2 semester) as part of a fundraiser for my kids HomeSchool Choir. You can categorize this under "Well if I commit to something publicly, I will figure out a way to do it." I should have categorized it under "Be careful what you ask for, you might get it". My motivation was:
I wanted to help the choir
I enjoy working with kids
I was looking for a way to experiment with on-line learning
I would like to develop a curriculum using open source materials
While I agree with Papert "it doesn't much matter what mathematics we teach them as long as they are learning to reason like a mathematician." That said if your are going to reason you need to reason about something, so I picked Algebra.
Here is the "Course Description" I sent:
An introductory On-Line Algebra/Geometry course for kids from 7th to 9th Grade:
Description: This course will help students not only be proficient in basic Algebra and Geometry manipulations (which are needed for Standardized tests) but also provide concrete experiences to help children develop a deeper understanding of mathematical concepts. Course material will be based upon a variety of material including some Open Source, AlgebraTextbooks, Geogebra, Scratch, Etoys and other materials. Students will have homework assignments, quizzes and tests during the semester.
Topics Covered:
Expressions, Equations and Functions
Schedule - The One Semester Course (18 weeks) will meet on-line for 90 minutes (mornings 8-9:30am, actual day will be negotiated amongst those signing up and the teacher). There may be one or two "in-person" and time will be allotted (at least four 30 minute sessions per student for one-to-one tutoring via the Internet)
Teacher: Steve Thomas - studied for his Masters in Mathematics Education at Rutgers with Robert B. Davis. He has also developed mathematics course material as a member of the education committee for Etoys which is part of One Laptop Per Child.
I am working on some education projects to provide education and clean water for Haiti (and others) through OLPC and Waveplace. The goal is to teach kids about clean water and have them build their own solar stills. Working on developing engineering challenges for the kids and providing them materials to design and build their own solar stills.
This Etoy Minute was created in response to an email on the OLPC mailing list, where someone asked for a program to do word sorts. So I created an Etoys project which is hopefully easily modifiable by others to allow folks to create their own Word Sorts (an activity where students arrange groups of words/picture by common characteristics, such as spelling patterns, meaning, sounds or other shared characteristics)
In the video and in the Etoys project I created a button to duplicate a page, I think this was making it too easy, I should have simply shown folks how to duplicate a page from the book menu (the menu icon at the top of the book between the next page and previous page arrows. If you click on it is has an option "duplicate page".
Feedback and suggestions for improvements always welcome.
Balance Scales is part of a set of the ELVM (Etoys Library of Virtual Manipulatives) I am working on. The advantage of ELVM's over other Virtual Manipulatives is that being in Etoys the kids and teachers can not only play with them, but also:
Use them in journal entries created in Etoys
Kids and Teachers can create their own versions of the EVLMs
Look inside and see how they work (just get the halo and look at the scripts)
Hi Steve, If I were trying to do this (and it is just the right thing for a parent to do) I would definitely start off with "a stick and some sand". Algebra is basically a symbolic form of arithmetic in which the art and skill is to "see/develop" strategies which can be turned into tactics that preserve equality (mostly, and sometimes other relationships). A lot of it has to do with the idea that "a number is all the ways to make it" and that the basic arithmetic operations have inverses. This last sentence is the one that is missed in most "school math" (which isn't "real math"), and part of the many difficulties which arise is that the children are pushed into trying to deal with "numbers as numerals (that is, their "names" in positional notation)" rather than as ideas which have analytic properties (they can be taken apart and put back together). And in general one of the difficulties in "school math" is that it winds up concentrating on how ideas are written down using societal conventions, rather on the ideas themselves. (And this is perhaps even more so with regard to science ideas.) A physical/geometric approach to these ideas is a very good one for all (especially younger) children. There are several good references here, including Hadamard's "Psychology of Invention in the Mathematical Field", a rare and valuable assessment of how mathematicians do their thing by a great mathematician himself. The bottom line in this study is that most real mathematicians do their thinking outside the written down forms, and mostly visually (and configurally) and for about 20% (including Einstein) kinesthetically. A lot of the real mathematics that is worth learning and understanding was invented to help with science in characterizing observations and results in the real world. This has been perverted in a sense by even some of the well meaning texts which try for "relevance" and to have lots of "story problems" that are situated in the world. But most of these are weak stretches compared to what's interesting about real science. So I would put a lot of effort into combining "real math" and "real science" as much as possible. A nice observation here is that quite a lot of really good math can be garnered by treating "math as a science" -- that is: where interesting constructions are made and then analyzed (this is like "bridge science", which is studying and modeling the phenomena that bridges manifest). Back to algebra. The main initial games here are to find ways to "preserve equality by adding 0s and multiplying by 1s). There are scaling games, relationship games, etc. And many of these have nice visual and tactile representations. For example, multiplications can be represented as rectangles, and many of the simple abstract multiplications -- such as (x + y) * (w + z) -- where any or all combinations of lengths can be used for the sides. A good one to start with is (x+y)*(x+y), and to see how this generates the standard formula from visual inspection alone. A nice end point is to actually derive "The Quadratic Formula" by "completing the square". I remember being so pissed when I was a kid to be given this formula without any explanation about why it works, when it is a "simple" derivation using algebra(there's an immense irony here). It's worth trying to understand "simultaneous equations" as simply manifestations of the "main initial games" -- that is, to try to avoid the routinization of method here, but to think what it means to "remove a variable" in algebraic terms. (Another irony here, because much of the second and third steps in algebraare derivable using the first steps. The thinking processes are of the same kind as the way geometry should be taught and learned.) Functions are often very mysterious for a number of interesting reasons. It is often the case that one part of this mystery can be dispelled by making dynamic interesting relationships using computer graphics. Functional relationships can be learned before formal parameterization. For example, the "Drive a Car" project in Etoys (a favorite early one for 10 year olds) exhibits this in a very memorable form when the heading of the steering wheel is connected to the turn command of the car. For most kids, this is a huge hit of understanding about variables (with the more subtle grasp of the "functional relationship" between the heading of the car and the heading of the steering wheel. Another good one is to think through what "turn" means and make your own version of "turn 10" from "car's heading <- car's heading + 10" and then make the turn function itself (Etoy scripts can be parametrized). The same kinds of things can be done in Logo (and experiments in parametrization and function making are fun to do in Logo). Another way to think about a lot of mathematical thinking from numeracy onwards is to use the metaphor of "projection". A mathematical thinker is always *projecting outwards* combinations and dissections of the materials (often numbers) in front of them, and those who haven't gained these skills just let them lie there. (This is also a center of what it means to be a programmer.) One very good route that is often neglected is "mental math". This is hard for most children because they are rarely exposed to it (and I have to cover the screen of their computer or their book when I want them to start thinking internally). So one of the things I would start doing with your son is to pose "in your head" problems. They can start with just simple arithmetic and progress.(You should do them too.) The idea is to get them to internalize their thoughts so they can visualize both images and symbols. (My brother and I had this fun with our Dad (who was a physiologist). A typical example for a 12 or 13 year old -- but after a few years of working up to it -- would be "find the volume of a sphere 35 centimeters in radius". This can take a while, but the results are some great "sticks and sand" in your head that can work on lots more complicated things later on!) The mantra here is "The music is not in the piano" -- i.e. "The math is not in the computer (or the book or the stick and the sand)" You are trying to help your son become a kind of musician (where the music is "relationships about relationships" (as von Neumann termed it)). Cheers, Alan
Suggestions and feedback always welcome. If you have a request for a new Etoy Minute or a new Etoy project you can use in your classroom, simply post a comment here and I will get back to you.
With Etoys, children can draw their own sketches then bring them to life by writing "scripts" that tell the sketches what to do. This post will explain how you can specify when scripts should run.
After watching the video, see if you can figure out what "MouseDown" and "MouseStillDown" do. Play around and run some tests to figure it out.
You can also learn about scripting by reading excerpts from the soon to be released Etoys Manual or just playing around and running some tests.
Excerpts from soon to be release Etoys Manual
3.6 Script Editor
Although some object actions can be controlled in the object's viewer, the script editor is where you assemble the tiles to create more complex actions or scripts. In the script above two of the object sketch's tiles have been dragged from sketch's viewer and dropped into the Script Editor. When the tile is in place to be accepted by the Script Editor, the area around the tile turns green and when the tile is released an audible click is heard if sound is enabled.
The Script Editor allows you to assemble tiles and test out your ideas for creating a simulation in the Etoys world. Getting into the habit of testing your ideas is a very powerful concept. You can use the results of these test scripts to simulate and determine the attributes and behaviors of the objects in your world. Getting into the habit of testing your ideas or at least thinking about how you could test your ideas (and what other people tell you is true) is a wonderful "habit of the mind". Let your imagination reign.
Collapse button
The round brown button with the black enclosed circle at the upper left collapses the script back to the viewer. The script can always be viewed in the Script Editor again by dragging it out onto the world from the object's viewer. Name of the Player being Scripted.
The text to the right of the collapse button is the name of the object for which you are creating the script. You can not change the objects name here.
Name of script.
The text to the right of the object's name is the script's name. It's a good idea to give a good name to the script (e.g. If its a script that moves the player, you can call the script 'move', etc.). Exclamation point.
The yellow exclamation point in the center of the Script Editor runs the script one time. You can also run the script from the object's viewer as shown above.
Tickindicator
The TickIndicator is the clock face to the right of the yellow exclamation point. The TickIndicator is light green when not in use, pink when script is paused and blue when script is ticking. Hold mouse button down and a menu pops up. There you can set the rate at which the script should run. The default is 8 ticks a second. Predefined in the menu are choices from one tick to 100 ticks a second. Last menu option is called other... Here you can type in the number of ticks per second that you want the script to run. A tick rate of 0.5 indicates one tick every other second, 0.1 once every 10 seconds, etc. ScriptStatusControl
This appears to the right of the clock. Click it to get the following menu of options:
normal - run when called
paused - ready to run all the time, will change to "ticking" Status when you press the "Go" button in the "All Scripts" object.
ticking - run all the time, will change to "paused" Status when you press "Stop" button in the "All Scripts" object
mouseDown - run once when mouse goes down the object
mouseStillDown - run while mouse still down on the object
mouseUp - run once when mouse comes back up off the object
mouseEnter - run once when mouse enters the object's bounds with the button up
mouseLeave - run once when mouse exits the object's bounds with the button up
mouseEnterDragging - run once when mouse enters the object's bounds while dragging another object
mouseLeaveDragging - run once when mouse exits the object's bounds while dragging another object
opening - run once when the object is being opened, this only works for World and Pages (contained in a book) objects.
Pop Quiz: Can you figure out how to use this to ensure a Book always opens to the first page when a project is opened? Can you figure out how to use this to reset a Page each time it is opened?
closing - run once when the object is being closed. This only applies to World and Pages objects.
More events:
connectedTo - run once immediately after a connector has connected to the object
disconnectedFrom - run once immediately before a connector is going to disconnect from the object
KeyStroke - executed when any key is pressed, this is only available from World and Playfield scripts
acceptedTextContents - executed when text is accepted, which can be when you tab to the next text field or hit return (if accept on CR is checked), this is only available for Enhanced Text objects.
Gold chest.
Clicking on the gold chest to the right of the ScriptStatusControl allows access to the following special tiles:
test tile
This tile has three holders into which you can place one or more tiles: Test: You can place any tile that contains an attribute of any object. For example, you could test whether Ellipse's y value is less than 5 as shown. To accomplish this grab the left side of the Ellipse's y tile from Ellipse's viewer. Make sure you aren't to the right of the tile and have the red box surrounding Ellipse's y and its value at the right, because then you will obtain an assignment phrase for the tile and not its attribute. You can test on almost any attribute (numeric, color, graphic, etc) of any object.
Pop Quiz: How could I define a test to see if a car passed a finish line in a race? Yes: Tiles placed in the "Yes" holder will be executed when the "Test" is true. If y<5, then Ellipse will turn blue.
No: Tiles placed in the "No" holder will be executed when the "Test" is false. If y>=5, then Ellipse will turn blue.
Note, that many tiles can be used in the "Test" holder of the "Test Yes No" tile. Some can also be used as watchers, which can be useful when debugging your scripts. While you may think a "Sketch obtrudes" or a "Sketch is under mouse" the Etoys system may think differently. Being able to see this as a script runs can help.
repeat tile
This tile has one holder called "do" into which you can place a script:
You can repeat the script you drop into the "do" placeholder the number of times set in the number box at the top of the tile.
random tile
The random number will range from 0 to the number in the number box (in this case 5). It can be dropped into the end of a command that requires a number or function. This is a special case of a function tile.
function tile
You can choose a function by clicking on the arrows at the left or clicking on the function name (in this case "abs") to get a drop down list of functions to choose from. Most of the common functions are available in the list. The function can be dropped into the end of a command that requires a number or function.
button up?
Used in Test and its value is true when the mouse is NOT pressed down.
button down?
Used in Test and its value is true when the mouse is pressed down anywhere.
tile representing the player
In this case the player is Ellipse.
number
A number box that can be dropped into the end of a command that requires a number or function.
Script editor menu
The Script Editor Menu button appears on the far right. It has the following options. add parameter
This option adds a parameter to the script. The parameter is passed into the script when it is called from another script. For example if you can create a script that will move an object forward based upon the number, you can add a parameter of type number. Then call that script from one or more other scripts passing in a specific value as the number. To use the parameter in the script simply drag the parameter from the Script Editor's in the top line to the right of the scripts name into your script where any number data type can be used.
There following are the data types that can be used as parameters:
Boolean (true or false)
BorderStyle
ButtonPhase
Color
Graphic
ImageResolution
Number
Patch
Point
ScriptName
Sound
String
TrailStyle
button to fire this script This will create a button object that can be used to fire the script. You can change the button's label from the menu in its viewer by selecting change label. show arrows
When selected the arrows inside scripting tiles will be displayed (ex: the up and down arrows to increase numbers and the left and right arrows to remove and parts of the expression edit balloon help for this script
This edits the balloon help that is shown when you hover over the script name in the scripts category of the Objects Viewer
explain status alternatives
Opens a window with descriptions of the options for "when this script should run" (ex: normal et al)
show code textually Will provide a text version of the script which you can edit. This provides an entry into Squeak programming. To save your changes type show code textually Will provide a text version of the script which you can edit. This provides an entry into Squeak programming. To save your changes type <ctrl><s> (on PC and XO) <cmd><s> (on Macintosh) when done. Note once changes are made you can not revert back to tile scripting without losing your changes. save this versionWhen editing the text version of a script you can use this menu option to save the changes. grab this object Will move the object to the position of the mouse and you can drag it to where you want to place it.
reveal this object Will display the halo for this object so you can find it. This can take a second or two.
tile representing this object Will create a tile representing the script's Object. Tiles representing an object can be used in this or other scripts to replace the Object being acted upon in a script.
open viewer Will open the viewer for this script's object
destroy this script Will destroy this script.
4.9 Viewer Category Scripting
This starts the given script ticking. You can select from available scripts at the right of the tile.
This makes the given script be "paused". You can select from available scripts at the right of the tile. Note: If the script specified is the script containing this tile, the script will not pause until it finishes its current processing of the all the tiles in the script. For example, if you have a "Object forward 5" tile after a "Object pause script script1" tile in a script named "script1", the object will move forward 5.
This makes the given script stop or revert to "normal". You can select from available scripts at the right of the tile.
Note: If the script specified is the script containing this tile, the script will not stop until it finishes its current processing of the all the tiles in the script. For example, if you have a "Object forward 5" tile after a "Object stop script script1" tile in a script named "script1", the object will move forward 5.
This starts the given script and all of its siblings's scripts ticking in the object. You can select from available scripts at the right of the tile.
This makes the given script and all of its sibling's scripts be "paused" in the object. You can select from available scripts at the right of the tile.
Note: If the script specified is the script containing this tile, the script will not pause until it finishes its current processing of the all the tiles in the script. For example, if you have a "Object forward 5" tile after a "Object pause all script1" tile in a script named "script1", the object will move forward 5.
This make the given script and all of its sibling's scripts stop or revert to "normal" in the object. You can select from available scripts at the right of the tile.
Note: If the script specified is the script containing this tile, the script will not pause until it finishes its current processing of the all the tiles in the script. For example, if you have a "Object forward 5" tile after a "Object stop all script1" tile in a script named "script1", the object will move forward 5.
This sends a message to all siblings to run the given script once. The object that executes this will not have its script run, only its siblings will run the script once. You can select from available scripts at the right of the tile.
This runs the given script once, on the next tick. You can select from available scripts at the right of the tile.
This runs the given script in the object and in all of its sibling once. You can select from available scripts at the right of the tile.
Used in Test and its value is true when the mouse is NOT pressed down. 
