But if you think you really get them, try a little experiment: ask a small group of math teachers what they think "Attend to Precision" means. What does it look like if a classroom task requires it? What does it look like when a teacher is facilitating it? What does it look like when students are doing it? Here are some responses you might hear:

- Rounding correctly according to the directions
- Rounding sensibly based on the problem's context
- Being careful when plotting points
- Labeling axes and diagrams correctly
- Drawing sketches and diagrams to scale
- Using an appropriate number of sig figs based on the precision of the measuring device
- Using precise mathematical terms in written and verbal communication
- Defining variables and symbols

I've spoken to teachers who express their understanding with numbers 2, 6, and 7, but I've talked to teachers whose understanding hews closest to numbers 1 and 3. Which is not to pass judgment, but is to say: it might be wise to be aware that you and your colleagues could have different, and potentially incorrect, assumptions about the SMPs.

And "Attend to Precision" seems like one of the more concrete ones. See what your colleagues have to say about "Look for and express regularity in repeated reasoning," and I bet the answers will be even more all over the place.

Another observation: it can be really hard to evaluate which SMPs are highlighted or emphasized in a classroom task. When I try, I tend to go "uummmm...all of them...?"

So what kind of task lends itself to "Modeling with Mathematics"? What does it look and sound like when teachers and kids "Look for and Make Use of Structure"?

I'd like to point you to a recently published resource: A

__Rubric for Implementing Standards for Mathematical Practice__. It was written in July of 2011 by Danielle Maletta, Mimi Yang, and Mariam Youssef as part of the Visualizing Functions working group at PCMI. It gives an observer specific items to look for in a task, as well as specific teacher behaviors, to help evaluate how faithfully a standard is being met in a particular lesson. The accompanying Resources document will also give you a deeper understanding of each standard.
Also, heads up that Illustrative Mathematics, in addition to the Herculean undertaking of trying to illustrate every K-12 content standard, has put a significant amount of effort into illustrating the Standards for Mathematical Practice using both sample videos and classroom tasks.

Check them out. Share widely.

Will Do! Thanks for the head's up.

ReplyDeleteThe "A Rubric for Implementing Standards for Mathematical Practice" link appears completely broken -- any ideas?

ReplyDeleteSounds like some fantastic resources and I very much agree that we need to do a lot more with examples (such as the videos you linked to) and discussion to clarify what the Practice standards really mean in, well, practice.

Thanks!

Thank you! It should be working now.

ReplyDeleteThose videos are so great for clarification. I've been to a few pd's about the SMPs and we always end up saying "ummm... all of them" too.

ReplyDeleteThanks for the helpful links!

I'm especially eager to see how the #sbar crowd handles the Standards of Mathematical Practice. As I see it, "attends to precision" should probably mean a lot of different things, depending on context.

ReplyDeleteHere in Georgia, we've had process standards very similar to the SMP for a few years. I found that "teaching" the process standards was virtually impossible. Like you said, even identifying which one(s) were highlighted in a task was tough.

Perhaps these standards go well in a rubric. As in, "did you attend to precision? (here's a description of what that means in this task's context)".

In the Uk we have the National Curriculum. Over the years whole forests have been used to convey what should be taught, with many examples of what is expected. But I do query wether this has actually raised standards. In addition despite repeated attempts to pin down these standards is still open to interpretation and if the inspector looking at your lesson interprets them differently to you conflict arises. Actually this is not true the inspectorate is always deemed to be right and the teacher wrong.

ReplyDelete