## Saturday, October 19, 2013

### The Gift of Being Wrong

All week I've been watching my students' geogebra assignments progress by watching successive versions of them pop up in their epearl portfolios. Fascinating, truly fascinating to find out that I was wrong about so many things. Wrong about what I thought would be difficult and easy. And I'm trying to see these as gifts.
• I thought the easy part would be understanding what I wanted them to do, because, as I always tell people, I am so good at communicating. WRONG:
• A lot of kids interpreted "Create a geogebra file about the linear function that displays the graph and equation of any linear function y = ax + k for any values of a and k."  as "Draw one particular linear function, using whatever value of a and k that you feel like at the moment." What I wanted was sliders for the slope and the initial value. So maybe, just maybe, I should have said that in the first place.
Gift #1: A wake-up call. Get over yourself.
• I thought the hard part would be figuring out how to get the zero and y intercept to always be in the right place, regardless of which linear function is currently set by the sliders. WRONG:
• Once the sliders were in and working, many did this just by using the "Draw a point" button and placing a point right on the axis, no algebra needed. Which is not what I wanted.
• Darn geogebra is too nice - it assumes that when you put a point on the x-axis, that you always want it to stay there, even as the function changes. SO I had to edit the assignment description to say that the intercepts have to be done WITHOUT using a drawing button - use the input bar only.
Gift #2: A reminder that there's more than one way to skin a cat.
• That feels lame somehow, I mean if there's an easier way to do something, who wouldn't choose that? But too bad, there it is, this is an opportunity for them to gain conviction in algebraic formulas. Deal with it.
• I thought the easy part would be figuring out the formulas for the x and y intercepts of the linear function - in fact, I thought they'd already know them, considering these are gr 11 kids, and strong students, who have already studied the linear function for 2 years. WRONG:
• They didn't know those formulas, or they didn't remember them. So okay, fine, we spent some time solving equations like  a|x - h| + k = 0, so they could use the same method to solve the linear equivalent. Well no one could! It was no problem for them to solve 2x + 3 = 0, but it was another thing entirely when they had to treat the a and k as if they were known numbers.
Gift # 3: A surprise - I found a huge gaping hole in their algebraic toolboxes! Let the mending begin....
• I know that many people would say "Why get them to use formulas when it's more important that they understand and be able to figure it out from first principles?" But at this point, I think it's important for them to be able to generalize using algebra, and to use it to save time and cognitive load.
• Besides, if they have to derive and then type in Z = (-k/a, 0) for the zero, and then immediately see that it works, then they get to own that formula, and believe it. And lo and behold, once that happened, I got a lot of "Oh! Cool! It works!"  It seemed like the idea that algebra always tells you the truth was new to them!
• I thought that very few would try the bonus points, and I predicted who those few would be. I don't have the final versions yet, they're due tomorrow, but so far, RIGHT:
• One student put in almost all of the bonus features PLUS checkboxes
• One student wrote a text that contains, instead of inert letters, an object that changes with the sliders. I only just figured that one out last weekend.
• One student couldn't figure something out so she went online and read the geogebra manual! I wept when I read that in her reflections.
• The rest are doing the basic stuff, which is fine. It still feels like they're learning about the linear function in a whole new way.
I'll share their work and reflections here, once I get their permissions of course. For now, I plan to upload their work to geogebratube, or embed them right here, but once they have their own blogs going, they'll be doing all that themselves. Hmmmm.....I wonder if there are already any geogebras on geogebratube that came from students instead of teachers?