Mathing…

Here’s something for the Calculus teachers. And no, it’s not about how Starcraft 2 is going to drop the AP scores for the boys (and some girls) this year. Even though, there is a good chance one of your students bought one of the roughly 620,000 copies sold in US on day one.

Names have been blocked to protect the innocent.

Thanks to all those who participated in the GeoGebra Applet Request. I’ve learned quite a bit from this experience.

I want thank Jamie and Mimi for their requests along with comments and suggestions.

I also want to thank the folks on twitter that helped promote this experiment or just gave me encouragement in general. @jybuell @wmcneary @jrykse @thescamdog @carnivalofmath @mathheadinc @scsocha.

I expected to have more applets completed, but I guess I didn’t take into account Hofstadter’s Law. I guess that’s part of learning. Much of the time was spent learning how things worked in GeoGebra. I spent a lot of time in GeoGebra Documentation and GeoGebra Forums. I also spent a lot of time just experimenting with commands and functions to see how they worked.

Below are links to all the posts along with links to all the applets for your convenience. For these applets press F9 to re-randomize values (e.g. Dotplot vs Boxplot and Plane from 3 Points in Space) and to start or stop animation on a single slider Right-Click on the slider and click on Animation On menu item to toggle the animation on and off. The play button will play and pause the animation on sliders that are turned on.
GeoGebra Applet Request started it all.

GeoGebra Applet Request – Statistics (Dotplot vs Boxplot) was Jamie’s request. There are multiple solutions to this. Try turning off the Easy Mode (integers only).
Dotplot vs Boxplot (applet link).

GeoGebra Applet non-Request – 3D Coordinate System was my first response to Mimi’s request. I was, um let’s say, a bit off the mark. It may still be useful for other things.
3D Coordinate System (applet link).

GeoGebra Applet Request – Plane from 3 Points in Space was my second response to Mimi’s request. I think this was closer to what she wanted.
Plane from 3 Points in Space version 1 (applet link).

Plane from 3 Poitns in Space version 3e (applet link).

After some correspondence with Mimi who suggested this applet, I think I have a better idea now. The followup comments she put in the original post for GeoGebra Applet Request also helped.

Mimi :

“Fix” is a term (I guess used more commonly in science??) that means that a variable has taken on a particular value. Last year I tried to explain to kids, like, if you have a rigid plane (ie. cardboard paper) and you “fix” (ie. stop moving / assign a location to) two of its corners, the piece of paper can still flap around that hinge, but once you hold onto the third corner, the paper is now fixed in place and can’t rotate anymore. Does that make more sense?

Like, a door doesn’t move because it’s got three “fixed” points: doorstop, top of the door hinge, and bottom of the door hinge. If you take away the door stop, the plane is now free to move / become other planes.

I think this version is much closer to the original request than my last previous attempt where I was moving an airplane around. I have no idea why I thought that. I’m going to say it is because I don’t teach Geometry. For some reason, planes don’t conjure up “abstract surface which has infinite width and length, zero thickness, and zero curvature” or, if you prefer, “surface which lies evenly with the straight lines on itself.”

Some things I learned working on this applet.

• determinant[] was useful for this application. Just give it a matrix and GeoGebra will do the calculations.
• A matrix in GeoGebra is a list of lists. It was much easier to use than expected.
• Sliders can be switched from oscillating to increasing or decreasing. Use a trigonometric function like sine or cosine and increase the number of periods by some random integer factor and offset the trigonometric function and we get a randomized but periodic motion starting at randomized locations. F9 key which recalculates the GeoGebra applet will also recalculate the random function to give a new value.
• Polygon[] takes points and creates a polygon with those points as vertices. A nice feature to have for a future version will be for the Polygon[] command to be able to take a list of points instead. It would’ve been helpful in this case when I wanted to draw a polygon for the portion of the plane under the XY plane. I used a clunky if[] statement to test for all 3 possible scenarios.

Remember to right-click on the slider and click on Animation On. Double-click or right-click and edit object properties of the slider if you want the slider to go faster or slower. It’s the textbox under Animation, Speed.

I highly recommend that you save the applet and run it from your computer. Click below for the applet.

You can determine for yourself if the applet is an effective visual.

UPDATE: Here’s the updated applet with those additional controls along with options to keep the applet window decluttered. Version 2 is no longer available. For some reason it wasn’t loading properly. Try version 3 below instead.

UPDATE2: Click below for version 3. Just click play button on the bottom left. Once you’re ready, try the other drawing options and experiment with the slider controls.

Mimi :

Not sure if you’d be interested in making this (since it’s only 9th-grade math), but I’d really like an applet where you have a plane that moves around uncontrollably, until you fix one of its points, then another, then another. Each time you fix one of the points, the plane should decrease its degree of freedom, but still rotate around the fixed point(s). This would help me illustrate why 3 points in space are required to define / fix a plane!

Thanks,

Mimi

I completely misunderstood Mimi’s request. So the first thing that came to my mind when plane was mentioned was an airplane! I imagined an airplane moving in the air where the movement along one dimension is restricted at a time. I thought it was unusual to have an airplane moving that way. An UFO, hummingbird, or dragonfly would have been better. It wasn’t until I was close to finishing the applet that I finally (I think) understood what Mimi’s request was. I imagine that’s how students get distracted in class. You talk about a term and their brain is thinking of something else.

Press play button on the lower left to start the animation. Right-click on the slider bar in the bottom of applet and click on the checked Animation On menu item to stop the motion along that dimension.

Click below for the applet.

I might update this later to display octants as the point moves around in space.

GeoGebra Applet Request suggestion by Jamie for a GeoGebra applet for statistics.

Jamie :

How about one for statistics?

Have a dot plot (line plot) on top and a box plot below. As a user adds points to the dot plot the box plot changes to match the data. Help students see connection between the two. Also can help them see why a whisker might be longer on one side compared to other side. See connection between shape of dot plot and shape of box plot.

It would be nice if when a student adds a point to the dot plot they can click a spot on the dot plot to add a point instead of adding a value to a table. To make it easier to do some investigations, only allow integer values or integer values and halves?

Getting really fancy, put a second box plot on the bottom that is generated randomly. Student adds points to their dot plot to make their box plot change to try and match the second box plot.

This was a much tougher to make than I had anticipated. However, I learned a lot while building this applet.

• GeoGebra has many upcoming features in GeoGebra 4. It’s currently in beta and is a work in progress. I would recommend it only to the more adventurous users who want to play with it to learn about upcoming features. There are still unfinished features and (probably) bugs and there isn’t enough documentation to help you if you’re stuck. Though I must say that from reading the beta forums, I found the folks at GeoGebra very helpful in their replies to questions from users.
• BoxPlot[] – GeoGebra actually has boxplot features built in the current version. You can give it a list, or give it a 5 number summary and some basic settings and it’ll do the rest.
• Object[] – If you give the name of an object as string and pass it to Object[] it allows you to access that object. While creating this, one thing I used while experimenting with the commands and features was Object["A"+j]. I wrapped it inside a sequence[] command to build a list sequence[Object["A"+j],j,1,100]. That command created a list with the contents inside cell A1, A2, A3,…, A100. Later I found quicker way to do this.
• CellRange[] – CellRange[A1,A100] essentially does the same thing as the above sequence-object command.
• CountIf[] and KeepIf[] – I haven’t found a good way to count the number of items in a column. So I created a list using CellRange[] and then counted the number of numbers that are greater than zero. Not a great solution, but works for now.
• I wasn’t initially how to re-randomize the settings. The Online GeoGebra Documentation was very helpful. To recalculate values in an applet, simply press F9. If a random function is used in the applet, it is recalculated to a new random value.
• RandomBetween[] – It takes 2 integers and find a random number between those 2, inclusive (meaning RandomBetween[2,11] could potentially give you 2 or 11).
• min[], q1[], median[], q3[], max[] – These commands do what you think they do statistically. Among other things, useful for when you need to create boxplots
• Textfield can also take if[] statements. if[mymin==targetmin && myq1==targetq1 && mymedian==targetmedian && myq3==targetq3 && mymax==targetmax, "Good Job!", "Keep Trying!"] will congratulate you when your boxplots match.

Other Observations

• It was helpful to use the a Check Box to show and hide objects and also sliders while working on this. It made it easy to move elements on the screen around.
• In this version of GeoGebra, I couldn’t find a good way to switching between 2 settings like in a radio box where options are mutually exclusive. Checkbox is not useful here. So I repurposed a slider and added some text to allow for switching between settings.
• GeoGebra has (as of version 3.2.44) limited interactivity capability. This might be because GeoGebra is a work in progress (where features will be added later) or because it was designed that way (GeoGebra may be designed to meet only certain needs so that it does what it does really well). However, I think that some things that GeoGebra doesn’t do well yet can be made up using JavaScript. One issue that came up for me was how to reset many values in the applet to some original/default state. I’ll have to learn how to set up a GeoGebra applet to work with client-side JavaScript. Another issue was how to capture a click on the applet so that I add a data point in to the list automatically depending on where it was (as suggested by Jamie). So I used sliders.

You can see for yourself if it’s dynamic enough or useful to demonstrate how change in data can affect the dotplot and boxplot. Don’t be put off by the visual noise in the user interface (UI). I’m not a UI designer and elements can be moved around the screen and simplified.

I got about a week before school begins. I’m going to use this last week to learn some of the other features in GeoGebra that I haven’t touched thus far. At this point I’d like to take requests for GeoGebra applets. To be honest I don’t know if I’ll be able to make the applets requested, but I think at least I’ll learn about what I know and what I don’t know. I am hoping I get to use features that I haven’t used thus far, but even if it’s something simple and I don’t do anything difficult, I’d like to help other teachers get interested in using GeoGebra in the classroom.

If all goes well, you get an applet for use in class and I get to learn a little more GeoGebra. I’ll do as many as I can in the next week. I’m guessing one applet a day if it’s hard, more applets if I can get them done quickly. If I can’t do it, I’ll reply with a comment after giving it an attempt and hopefully someone more capable can help you out.

Send me your request(s) by placing a comment below,  tweeting or direct messaging @mrhodotnet, or sending me an e-mail through my Contact page. Here is a sample of what I’ve done so far with GeoGebra.

UPDATE1: Jamie’s suggestion for an applet on dotplot vs boxplot can be found here.
UPDATE2: My first attempt at Mimi’s suggestion can be found here.
UPDATE3: I think I got it right this time. Mimi’s suggested applet is here.
UPDATE4: Thanks for the help/support/encouragement. Last post is here.