I've been thinking, experimenting and testing out ideas about how to move math instruction forward in my classroom, using technology and Problem-Based Learning (PBL) as much as I can. It's a daunting task even if I've done it before in science....very different set of inputs and outputs in a math class.
I've also been wondering what "Teaching in the Age of Siri" really means. I believe we have students who believe they can Google the answer to anything that is asked. When they run up against questions that aren't Google-able, it stumps them.
This week, I gave students pretty tough problems about functions that involved square roots. They really didn't know anything about square roots. So rather than just telling them....I took a bit to explain that we were going to learn what to do when you can't find the answer on Google or have a friend tell you. I gave them 10 minutes to find everything they could about a square root that seemed like it might help answer the two-part question I gave them.
Update from 12.06.12--- I'm inserting a little revision in here to clarify what I first wrote about last week. I received so many requests for the problem, I thought I'd post it here in addition to leaving it in the comments. I also think I may need to restate that it is really two questions. Knowing about square roots help with answering both questions which is why I called it a tw0-part problem in my original writing.
The problem they were solving is really pretty simple
x----> SQRTx and the second problem was
x----> SQRT ABS(x).
For these problems, they had to define what inputs, if any, were not valid.
I wanted to connect it to the real-world and explained that rarely have I had a boss/supervisor that takes the time to show me how to do my job....most of the time, they expect me to know how already. That was very puzzling for my students. Why wouldn't my boss help me, they wondered? It wasn't until I explained that bosses (or at least the kind I've had) hire me to do something that they I can either already do or that I'm smart enough to teach myself. It wasn't that they were being mean to me. In fact it was the opposite, it was that they had confidence in me to solve the problems of my job assignments. That was a huge flip of a circumstance.....something none of my 8th graders had considered before. I assured them that I wasn't going to suddenly assume they knew all of algebra and be like my boss, but the experimental learning style we were about to do was a first step towards being that kind of independent learner.
They used laptops, the Algebra references books I have in the room, the textbook, notes that I have given throughout this unit, their phones and some even asked Siri for help. I really didn't care where or what they brought back to the table. Then I led them in a class discussion about what they thought was relevant in all that they found to solving the problem. Once the class decided (and I have to tell you that they learned a ton that they didn't need to know but was just there for the learning) what was most helpful, we started a discussion about what do you do now that you've found info that could help you solve the problem.
Honestly....I don't think many of them have ever thought about that kind of reasoning.
Turning found info into useful knowledge and something that solves the problem
And they really loved it....they argued and wrestled with all the info they collected and then built their conjectures. After conjectures they had to use evidence from "tests" they could run with their graphing calculators to see the info they found matched up. My role wasn't to teach...it was to coach them. I helped them realize that once they had info NOW they had to something with it.
It's a bit like taking a recipe and a bunch of ingredients...and creating delicious cookies.
And that was thinking...tying all the little discrete factoids they had from prior knowledge and this mini-research into a new problem. Eventually they correctly solved the problem....along the way we discovered way more than the single answer to the two-part problem. I think they'll probably retain the info better.
I realized most of all....they need some hand-holding and practice as they learn how to take "found" information and "think it" into meaning. I'm definitely doing this again....try to refine the process and sharpen it. This isn't all the way to PBL yet. But I think it's the foundational shift of responsibility for learning onto the student's shoulder that will be a precursor for doing a full-blown PBL or maybe a STEMy kind of lesson.
http://www.morguefile.com/archive/display/541092 ---map picture
Love the way you can read PDF documents on my iPad using the Kindle reader. I don't want to lug my whole computer on an upcoming trip but I have to read a PDF version of a book. Voila! I simply email the PDF to my iPad's Kindle email (who ever knew it had one???) and presto/chango....it appears in the Kindle app. Ready for me to read on the plane. Now that is cool