Today I had the opportunity to work with a math teacher from another school. We spent the afternoon playing with Wolfram Alpha. Our goal was to play around with widgets to learn how we could use them to help students with their understanding of math concepts.

That's right two math geeks spent an afternoon collaborating during their vacation. It was great. We both learned a lot from each other and a lot that neither of us knew. I really enjoyed working with a teacher that I have a great deal of respect for, but never get to work with. How do we make this sort of thing happen more often? How can we harness our professional development time to make more connections like this? The last time I had an opportunity to collaborate with other teachers within my district was four years ago. I find it odd that I connect with teachers around the globe more often than I connect with teachers within my own district. Somehow we need to use our professional development time to allow for collaborative exploration of ideas that will advance education in all subject areas. After all, if we hope to teach our students to be 21st century learners, don't we need to become 21st century learners.

What does your school or district do to allow for collaborative professional development?

Also, if you're interested, here is a sample of what we were working on today. We were trying to get make it easy for students to use Wolfram Alpha as a computer algebra system. The widget allows users to enter an equation and then enter the inverse operation that would take them to the next step. The process can be repeated until the equation has been solved.

## Thursday, December 30, 2010

## Sunday, December 5, 2010

### Looking For Wrong Answers

I have, in the past asked students for wrong answers rather than right answers to my questions. When I've done it, it's usually because nobody knows the right answer or how to find it. So I ask for wrong answers to start the thinking process. When a student gives a wrong answer I ask why it's wrong and then we try to narrow down the correct answer from there.

I've been reading Dan Meyer's blog for a while now. He's a big supporter of asking for wrong answers but he doesn't just ask for them when nobody knows the answer. He asks for wrong answers all of the time. I tried the technique last week before asking for the correct answer. I was blown away by the quality of wrong answers I was getting. Here's the graph we looked at:

We had just calculated the slope of the blue to be -1. I added the red line to the graph and before asking what its slope could be I asked for what its slope can't be. I originally expected a lot of ridiculous answers. I was pleasantly surprised.

Here are some of the responses I received:

I've been reading Dan Meyer's blog for a while now. He's a big supporter of asking for wrong answers but he doesn't just ask for them when nobody knows the answer. He asks for wrong answers all of the time. I tried the technique last week before asking for the correct answer. I was blown away by the quality of wrong answers I was getting. Here's the graph we looked at:

We had just calculated the slope of the blue to be -1. I added the red line to the graph and before asking what its slope could be I asked for what its slope can't be. I originally expected a lot of ridiculous answers. I was pleasantly surprised.

Here are some of the responses I received:

- Can't be negative 1, since the slope is different from the blue line (nice segue into slopes of parallel lines)
- Can't be zero since it's not a horizontal line
- Can't be -1000 (a little silly but nailed down that our solution needed to be between -1 and 0)
- Can't be undefined

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