Welcome to the World of Probability

Originally published in the September 2000 issue of Australia’s Hotsource online newsletter

Now that most of you can be considered advanced beginners in using MicroWorlds, this issue will explore a bit more of the language and data structures available to you.

The following activity explores probability while demonstrating how sliders, text boxes and even the screen may be used to collect and report data.

Who’s for two-up?
The core of this task will be to flip a coin numerous times and record the number of times heads and tails appear.

• Start a new project.
• Name the turtle, coin.
• Create two coin shapes in the shapes centre. Name one heads and the other tails. Be sure to make them appear different in some way so that the user can clearly see which one side of the coin lands faceup.
• Change the turtle’s costui-ne to one of the coin shapes. Create a Many Times button with the instruction, flip.

Recording data with text boxes
This part of the project will flip a coin in FLIP, and change the value in the textboxes, headscount, tailscount and totalflips. If you name turtles, text boxes or sliders with unique name you may change them even ii they are on different pages. This allows you to have some action going on between the scenes.

• Make a Startup button on the first page.
• Create a new page from the pages menu.
• Create text boxes named, Headscount, Tailscount and Totalflips.
• Show the names of the text boxes so the user knows what they are reading
• Click the Startup button
• Type the following procedures on the procedures page.

to flip
ifelse coin = ‘heads
[recordheads]
[recordtails]
settotalflips totalflips + 1
end

to coin
if 1 = random 2 [output “heads]
output “tails
end

to recordheads
coin, setsh ‘heads
setheadscount headscount + 1
end

to recordtails
coin, setsh “tails
settailscount tailscount + 1
end

to startup
everyone [settext 0]
end

Click the flip button to start and stop the experiment. You may wish to make the flip button run many times if you want it to keep flipping the coin.

Recording data with sliders
Sliders may be used as reporters (input devices) to change the value of a variable or they may be used as indicators (output devices) displaying the current value of that reporter. Let’s experiment with sliders on a second page of our coin flipping project.

• Create a new page from the Pages menu
• Create two sliders ‘heads and tails, with a minimum of 0 and maximum of 300 at the bottom of the new page
• Optional: Create buttons to switch between the two pages of our project.
• Make the following changes to your procedures.

To recordheads
coin, setsh ‘heads
setheadscount headscount + 1
setheads heads + 1
end

to recordtails
coin, setsh “tails settailscount tailscount + 1
settails tails + 1
end

to startup
settailscount 0
setheadscount 0
settotalflips 0
settails 0 setheads 0
end

Type Startup to init-ialise the variables, click oA the flip button and switch between pages.

Do you see the sliders changing their values?

Extra bonus! Adding a histogram to graph our data
It is easy to add simple graphing functionality to our probability lab with the creation of two turtles and a bit more Logo programming.

• Hatch two turtles on the same page as the sliders.
• Name one turtle, headsgraph, and the other, tailsgi-aph (for heads graph and tails graph)
• Place those turtles above their respective sliders.
• Create two different turtle costui-nes consisting of blue and red horizontal bars. Name the shapes hline and tline.

Make the following changes to your procedures.

To recordheads
coin, setsh ‘heads
setheadscount headscount + 1
setheads heads + 1
headsgraph, fd 1 stamp
end

to recordtails
coin, setsh “tails
settailscount tailscount+l
settails tails + 1
tailsgraph, FD 1 stamp
end

to startup
settailscount 0
setheadscount 0
settotalflips 0
settails 0 setheads 0
headsgraph, setpos [-170 1451]
tailsgraph, setpos [200 145] page2 clean pagel
end

Type Startup and click on the flip button to set the experiment in action! You may even want to figure out a way to stop the graphing when a bar reaches the top. How about a textbox reporting the experimental standard deviation?

The magic of MicroWorlds’ parallelism allows the coin to be animated, text boxes to change, sliders to report and a histogram to be created all at once. You can use lots of software to generate random numbers, but no other title allows all of these things to happen at once. I am confident that you can figure out exciting ways to integrate these programming techniques into much more complex simulations and experiments.

Gary Stager

Veteran educator Gary Stager, Ph.D. is the author of Twenty Things to Do with a Computer – Forward 50, co-author of Invent To Learn — Making, Tinkering, and Engineering in the Classroom, publisher at Constructing Modern Knowledge Press, and the founder of the Constructing Modern Knowledge summer institute. He led professional development in the world’s first 1:1 laptop schools thirty years ago and designed one of the oldest online graduate school programs. Gary is also the curator of The Seymour Papert archives at DailyPapert.com. Learn more about Gary here.