Thursday, February 10, 2011

Mining for math

The rundown on what the kids are so far doing and not doing on the classblog:

Well the kids' posts are continuing to get better and better! Jeremy's post contained a lot of info, but there were lots of misuses of the vocabulary, and there was no picture in it. Fred's included more math symbols, tables, and an embedded graph. His command of the languages, both mathematical and english, was obvious. He also asked an original question, that is, it wasn't similar to anything I had asked in class:

Then we compared the 2 graphs and found them to be almost exactly the same except for 2 differences.
What are they?

As for the comments.....they are all starting to sound alike....Wow great post, I like the way you organized the doubt this is partly because they are hesitant to critique each other, but they are likely just not used to writing about their math THINKING. Or thinking about their math thinking. They aren't addressing anything remotely mathematical in their comments, for the most part.

A few exceptions, of course. Jeremy's answer to Fred's question:

Now about the difference between the Sin and the cosin function, the cosine function intercepts the y-axis at 1 and the sin function intercepts at 0 :) Also, The sin function always crosses the x-axis at either pi or 2 pi ( or more if mroe than 1 turn occured), in other words, it crosses the x-axis at 0/360 degrees and 180 degrees.

What I have done and will have to get better at:

Well, I realized that I have to get over my hesitation to correct and critique, if I want them to, which means I have to model not only the types of comments I want them to make, but the tone, the respect, the we're-all-in-this-together way to give constructive criticism.

So, first thing in each class, I now upload the post onto our eboard, bring up anything useful that has already been put into a comment by one of them, ask if anyone has anything to add/change etc, then I have at it myself. The first victim of this was Jeremy. After I'd made a few corrections, I asked him, "I hope you don't feel Jeremy, that I am tearing your work apart!" and he said "No, it's ok, I wasn't sure about this part!". Hmm...he was maybe hoping for this? Then as I went through my list of corrections to Jeremy's post, others started to say "Oh yes I noticed that too" or "Wouldn't it have been better to call that an angle instead of a radian".

Here are a few things I will look for from now on in the posts:
  • is everything that was in the lesson in the blog
  • is the vocabulary and notation correctly used
  • is there a sample question
  • is the overall organization good, easy to follow
  • is their personality evident in their writing
  • is there anything new - new symbols, new type of thing inserted
  • are there any citations missing (Fred uploaded an image from a site and didn't give the url)
  • did they make any observations about the content, how interesting it was, how it was presented, how it connects to something, etc
What I will look for in their comments:
  • did they notice any of the above
  • did they answer the question with any depth at all
  • did they make any observations about the content, how interesting it was, how it was presented, how it connects to something, etc
  • did they ask anything that would enrich their understanding

    Meanwhile, back at the voicethread:

    I'm finding that the voicethreads lend themselves to problem solving more than they do as responses to the powerpoint lessons. I have had them contribute one step, with explanations, to a situational problem that they are all working on. It's partly a way for them to check in with each other for reassura, collaborate with each other, and for me to document whether or not they are actually working. Plus, again, it's just great for us all to see each other occasionally! Closest we'll get to f2f!


    1. I found the same sort of comments in my class blogs too. I also found that as the level of discourse in class evolved so did the level of discourse in the comments on the class blogs.

      I think you're bang on when you talk about how important it is model the kind of approach you want kids to take in their comments. Better yet, try to get them to be models for each other by fostering discussion between them in class.

      E.g. when one student said: "Wouldn't it have been better to call that an angle instead of a radian". Follow that up with: "Tell us (not me) why you think that." Eventually they'll run with it.

      Also, you might want to extend the dialogue by using the #comments4kids hashtag on twitter to invite the participation of a larger audience for your kids work. (If you're comfortable with that; it would mean opening your class blog to comments from outsiders.)

    2. Hi Darren!
      Already last night's comments are noticeably more reflective. Matthew is thinking ahead, Andrew is connecting to his physics course, Jeremy zoomed right in on Charlene's insight about the frequency, Rapahëlle gave great feedback about the lesson AND provided some formulas, and Abby just made me laugh out loud!
      I will definitely use your suggestion about fostering discussion today (if my voice holds out - think I have laryngitis). I will do the screen shots like yesterday, but this time, I will point to various parts of the post and get them to tell me what the correction/improvement might be. I might also put them into groups (virtual ones of course) so that they feel a bit more free to talk. You wouldn't think that shyness would be an issue in an online class, but it is!
      Thanks for the hashtag idea too, I will definitely see about how my organization would feel about it. I am fortunate to work for an organization that is pretty openminded and trailblazing!