The lack of posting over the last, I dunno, many, many weeks, isn’t due to a lack of classroom fodder. There’s plenty going on around here, but my tongue has been tied up in writing for my National Boards and when I find myself with free time I haven’t wanted to spend any more of it in front of my computer. The good news is that my self-imposed due date of March 1 for having all 4 drafts complete is only a few weeks away, so soon thereafter I’m hoping the creative blog juices will once again flow freely. The real due date is March 31, but I’ll be in Mexico then for spring break, so it’s a good excuse to dot my i’s and cross my t’s well before the deadline.

When I attended the Park City Math Institute last summer I returned home with several promises to myself. One was that I would integrate technology into at least one lesson every day. I find that it’s easy to come up with excuses of why it’s my hands and not theirs which should be on the technology (~~spotty wireless on the mobile Imac lab; spotty memory issues on the downstairs PC lab; not enough time in the district pacing guide to train my students on how to use various programs, not enough patience for their questions which stop them in their tracks, etc, etc~~). I’m sure you’ve experienced them all before.

But I’ve been trying hard, really hard, to get my students’ hands on technology with some regularity. But, I must confess, that my 8th grade geometry students’ hands do a whole lot more ticking of the keyboard than my 8th grade pre-algebra students’ hands do. Which is ironic, and disconcerting, since I could make a very good argument about why it should be the other way around.

SO…I made this packet to help guide my 8th grade pre-algebra students into learning how to graph linear equations on GeoGebra while also discovering important aspects of slope and y-intercept. * (Please note…this is NOT the way I introduced slope and Y-intercept. Prior to doing anything formal, we have done several MARS and Shell Foundation tasks which involve real-world situations involving linear motion and I wrote a few of my own. Students have matched cards of a graph to a t–table to an equation. We’ve looked at slope and y-intercept as they apply to the amount of candy my son ate each day following Halloween. We looked at slope and y-intercept as they applied to water dripping at a constant rate out of one vessel and into another one. And we looked at varying slopes along a car trip which involved a lunch stop and speeding up not miss the start of a movie.)*

But I wanted to use GeoGebra to introduce the more formal definitions and ultimately connect them to the problem solving we have already done.

We’ve only just begun…45 min. in the lab last week to be followed up tomorrow. So far, so good, but from looking at their homework, (which was more of the same, but without the technology), it doesn’t appear that the learning has been made concrete yet. I know there are tons of ready-made applets on graphing linear equations, but I wanted to take the time for the students to learn how to use GeoGebra beyond tinkering with a pre-made applet. The trickiest part for me, of spending a whole period in the lab, is that it’s impossible to have a whole class discussion. I can have them stand with their backs to the computers when I want to talk (and this seems to be necessary for them to actually listen), but there’s only so much talk that can happen when everyone’s backs are to the computers.

So I’m hoping that after 2 periods in the lab, we’ll be able to have a whole class discussion about what they discovered with just 1 set of hands on GeoGebra. We’ll see.

I am looking forward to reading about how your follow-up discussions go!

I think this is a pretty cool activity, it definitely does a great job of walking the students through finding slopes of lines and connecting slopes and y-intercepts to the equation of lines, but as a geogebra novice (I only have been hearing about it from teacher blogs, I just downloaded it to play with) I’m curious to know if there is an advantage to introducing equations of lines through this format or if more traditional approaches (i.e. pencil, paper and x-y tables) are just as effective. I understand that you have two aims in this exercise- to introduce students to equations of lines and to introduce them to geogebra- so in teaching lines this way you are killing two birds with one stone, but personally, (maybe I’m old fashioned?) I like the students to have the experience of producing the graph of the line from nothing more than their own pencil. Then it is truly their creation and they have ownership over their learning. I don’t want to sound critical in any way at all because I’m eager to try using this, but I’m just wondering if you have noticed a change in students’ comprehension of the material since using these graphing programs and is that change entirely positive? My biggest concern is that these programs may make graphing seem a bit magical, but I guess that can be counteracted by doing both a lot of hand graphing and graphing with these programs.

Lizzy: I appreciate your comments about how to introduce graphing. This definitely isn’t the only way we’ve graphed. We started with a week of looking at graphs of real world stuff so students could discover the significance of slope and y intercept in different contexts. We looked at distance/time graph of a car whose speed changed (and what happened to the graph when its driver stopped for lunch). We looked at water height/time graph of water dripping out of a vessel. And we looked at a graph of my son eating Halloween candy (in a linear relationship). So before I had students graphing at all, they had a lot of conversations to interpret graphs. We then talked about plotting points by first isolating an x axis and then isolating a vertical (y ) axis. And then discussing how to plot points when the 2 axis are placed atop one another. After that, we plotted lines using T-tables (and I went home in frustration night after night about how their integer operation skills had been long forgotten). Only after that did we do that GeoGebra worksheet with the big idea being that maybe you don’t want to have to plot points forever. We went to the lab twice in 2 weeks, doing a lot of pencil and paper graphing in between. All in all, I feel like it was a well rounded approach and I do feel like they have a very deep conceptual understanding of what’s going on. BUT…in a textbook, those were probably 2 lessons, and I just spent 2+ weeks on those concepts. But that’s a whole other story…

Thank you for your thoughtful reply. I’m struggling a lot right now with how to use technology effectively in class and I’m trying to see it from all angles. I really like teaching both ways- first by hand, then to technology, then back to pencil and paper but like you mentioned, it’s hard to spare this much class time. I am also both worried that students will lean too much on technology to do the understanding for them, and I’m worried that not using enough technology will leave them ill prepared for this new technology centered math world- and it is true that students can perhaps engage more with conceptual material if they’re freed from the tediousness of hand calculation. I’m feeling pretty torn. I can’t spare the time but can I afford not to include technology?

Lizzy: I think the key is to strike a balance. Technology serves 2 main purposes (for me). 1) There are aspects of topics which are better demonstrated or understood through the use of technology. 2) It’s almost always more engaging for students when lessons use technology, either in my hands, but hopefully more often in theirs.

So, I guess for me, the key is thinking through what are my learning goals for any given unit/concept and then thinking which aspects of that concept would be better taught using technology and which aspects are better without.

I suppose that sounds vague, but how I’d use it depends on each individual unit.