One of the blogs helping me is Undefined, which I can now find easily thanks to my figuring out how to make a blogroll. In it, you can find an actual draft of a list of stats standards for the first unit. I like the list, but it also helps clarify questions for me. Here are some items on her list:
- Create a histogram
- Create a box plot
- Create a scatter plot
- Sketch a line of best fit
- Use a calculator to find a line of best fit
- Understand correlation coefficients
- Distinguish between a normal and a skewed distribution
- Work well in a cooperative group
These are all things I want my students to do. And here are some questions. I hope SBG luminaries look at this and tell me all the answers…
- What about the create vs. interpret aspect of graphs I mentioned in that other post? Are those separate standards? (I mean, sketch or find a regression line is really different from interpret a regression line.) I don’t mean to be all obsessive about this, but if they are separate, man, that’s starts to be a lot of standards; and if they’re not, each standard has a lot of aspects and it’s hard to imagine the artifact—the piece of student work, whether a quiz answer or a part of a project or a discussion—that is convincing evidence of understanding. Or is it easier than that? Do you know it when you see it?
- What about things that overlap? A simple example: which box plot corresponds to this histogram? I can imagine students who can construct and interpret box plots and histograms who can’t do this. So: is this another standard? (This particular example may be lame; do we care? But in general, I’m really interested in students integrating more atomic skills into [let’s call them] molecular understandings. Where does that fit into the scheme?)
- Higher up in this hierarchy (cellular? Maybe the metaphor has run its course…) we find some of the things I have nattered on about elsewhere. I think they stretch from ideas such as “Articulates why a particular choice of graph to support a claim is effective” to habits of mind such as “integrates different perspectives (numeric, graphical, symbolic, etc) when solving problems.” Related to this, an interesting list appears in the common core, which I want to talk about separately.
I currently think these are different animals from the ones that can possibly be assessed in a quiz. They seem best addressed with, say, portfolio and oral discussion. But then, what’s the balance? Anybody dealt with this well?
- What is the balance in time, effort, emphasis, and grade weight between the obviously mathy standards and vital but less-mathy standards like “works well in a cooperative group?”
Here’s what I find interesting about this post, reresding it before pressing Publish: I really care about this, and am losing sleep over it. And I bet that by Thanksgiving this entire maelstrom will be gone. It will either be obvious once reality sets in, or it will be superseded by a bigger constellation of questions. Isn’t it always the way?