Tag Archives: Geogebra

The Day the Scaffolding Fell Apart (and Got Put Back Together)

The Setting

Being in only my 3rd year teaching at this school, my principal still wants to do semester observations on us “newbie teachers”, and so I decide I’m going to show him another 3 Acts lesson since the first one went so well. (Side note: this is not a nervous or bad experience for me, not because I think I’m an awesome teacher or anything like that, but because our principal is so approachable and dedicated to helping us teachers grow. He’s “on our side”.)

The Lesson

In Precalculus, we’re still getting used to (read: remembering) different functions and their various representations. After much debate with myself, I decided to use Dan Meyer’s “Will It Go In The Hoop”, where he shoots a basketball, freezes it halfway and asks the students to predict.

I’m learning how to better “hook” students, and this time I did it by record a simple “yes” or “no” next to each student’s name after asking them “Do you think the basketball will go in the hoop?”  Takes 30 seconds, engages them for the rest of the lesson–at least the first leg of the lesson.

I then put Dan’s Geogebra applet, complete with the picture of the ball, sliders, and parabola (he did all this), onto my website for students to access. Geogebratube wasn’t working the night before for me, so I didn’t want to take chances and actually had them download the .ggb file.  The downside is that it’s a few small steps to use that on the Chromebooks. Fortunately, Geogebra has a Chrome applet, so (1) the had to install Geogebra on their Google account, (2) download the .ggb file from my website, (3) open Geogebra (not just click on the file like they’re so used to), and then (4) go to “file–>open–>open”.  Not very many steps for any competent computer user, but as we all know, most teenagers are woefully incapable when using the computer doesn’t involve Facebook or Youtube.

Crash & Burn

So they open the file, and of course they’re all moving at different speeds: some figured out what the sliders do right away.  If you’re wondering, the variables in this particular applet are a, h, and k in the equation y=a(x-h)^2+k.  I decided I would remind them of parabolas & equations at the same time as teaching them to use Geogebra.

That was my first mistake.

The first two .ggb files had sliders already built, but I actually deleted Dan’s work so they only had the picture because I wanted them to want (and then create) the sliders and not just take them for granted. They need to understand what they do and why they’re so nice and helpful.  However, we ran into a few “speed-bumps”. (Hitting speed-bumps when travelling 60 mph isn’t smart, btw.)

  • Creating and using sliders is much tougher in the Chrome applet than with the desktop version. For one thing, I never figured out how to edit the max and min on the slider unless you create a new one.
  • Having to click the “mouse” button on Geogebra always throws students for a loop (although these were doing better than in the past).
  • Students’ understanding of variables is tentative at best, so connecting the slider to the equation via a variable almost always had to be explained explicitly (“Type in exactly what I tell you…”)
  • Even I find using a mouse much easier than a track-pad, especially if there’s no clear button to click outside of the touch-pad. Clicking and dragging items are trickier.
  • The screens on the Chromebooks are just a tad smaller than it seems the applet was created for, so they had to shift and zoom the sheet to see the equation, the picture, and all the lines.
  • One girl at the front became very flustered and frustrated with herself and her computer, which can quickly change the dynamic of the whole class.

I felt the class slipping away from where I had them when I recorded their guesses. We managed to get through two of the shooting videos fine, but when I took away the slider, they became “disengaged”.  I guess I should have known it was their first time using Geogebra as I’m the only teacher in the school to use it.  I just need to give them a better intro than one where they crash & burn so they come to appreciate how easy it can make things.

It really felt like I had pulled too much out from under them and they were collapsing under all that they were required to do. This is one of those cases where the technology was becoming a hindrance rather than supporting more dialogue and investigation.  On the one hand, giving them sliders felt like making it too easy for them. Yet taking away that simple tool made it much more difficult.  I’ll need to try to tread the line between challenging/engaging and frustratingly, pointlessly complex.

The Putting Back Together

I should have pulled these out sooner as a “recap” to help the students bring together their thoughts, but in the excitement, I honestly forgot about them at first.  (Fortunately in my 2nd precal class of the day, I corrected my error and they got this as a summary immediately). I attended a conference where I learned about these “Link” sheets.  This is excellent because it brings together four representations of a function: in this case (1) equation, (2) verbal description, (3) table, and (4) graph.  Sometimes I fill in some parts and they fill in others, but for this I wanted them to take their Geogebra & the video and put it onto the sheet. Here’s a word version (LINK-Blank Linear v 2)  if you’d like to edit it.

After all that technology, I think some students were honestly relieved to have a piece of paper in front of them that they could write on. This helped them to see what the goal of this activity was in the first place.  We’re still not to the point where they understand how to translate any given function, but we’re more used to seeing functions and connecting equations, graphs, tables, and verbal descriptions, which is not a bad block period. The afternoon went better, mostly because I never took the sliders away from that group.

My Analysis

I think I need to do a better job of deciding what I want the students to get out of my 3 Act lessons. I’m trying to remain flexible and “go where the students want to go” in case they mention some great ideas, but I also need to have a plan and something in mind that I want them to learn, rather than just generic “understand & play with functions”. That’s on me.  More planning than I am sometimes motivated to do, if I’m being honest.

And of course there’s also the technology aspect.  I am fairly comfortable with new technology (I find installing operating systems and customizing them fun, for example), so it is very difficult for me to understand how little technology some of my students understand. (One unfortunate girl started at me questioningly when I asked her to “reload” the current web page. My mind was blown, and not in a good way.)  Somehow I became good at being patient with them when they don’t understand math, but I get much more frustrated and tired when they are so slow with technology. Perhaps it’s because I’m not expecting it: they grow up with technology all around them, but they can’t transfer it, mostly (I suspect) because they don’t want to as badly. Figuring out how to find the most popular Youtube video is more essential to their lives than figuring out how to open a file through a program other than the browser you just used to downloaded the file. Ugh. Well maybe next time I’ll be more mentally prepared.


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A Way to Use Geogebra

So I just assumed everyone knew this, but just in case, this is a nifty way for students to quickly send you what they’ve done on any program such as Geogebra or Desmos: just use the “Print Screen Button”!  It actually works really well–it copies something onto the invisible computer clipboard and if you open a Word document and “Paste”, the entire screen will show up there!  Here are some examples of my students sending me things they were actually excited (and proud) to do.  I just assumed that my students could “see” reflections, even across the y=x axis.  Not true!!  So yeah, they pasted 4 or 5 of these in a Word document and e-mailed it to me (most students could do this at school during lunch or their break–I try to be sensitive toward those students without internet/computers at home).  And yes, I gave them a handful of Participation Points to sweeten the deal.


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Dilation and Translation of Functions in Geogebra

So I created a handful of activities because I love using Geogebra.  I can’t believe I didn’t know that there are spreadsheets in Geogebra (I’ve never read the manual :/), and I’m definitely going to look into using Kevin’s lesson when we get to trig functions and graphs.  But as a review for my Precalculus students, I created a discovery activity where students get to see functions dilating and translating (I call them “stretching” and “shifting” or “sliding” because I think it’s more intuitive for the students… and I often forget the official names).

Here are two of the activities that we’ve used so far, and I like the activities because it starts assuming that the student has never used Geogebra.  Later activites, I get to assume that the student is experienced with Geogebra and I don’t have to write each step explicitly down, but I was shocked at how few of my students were able to follow such clear step-by-step instructions, even though they are all juniors or seniors in high school!

EDIT: Even after doing this for one year, students found some wrong problems, so I’ve edited the second packet to include these corrections:

Let me know if you have suggestions for these activities!

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