Standards of Mathematical Practice

I was one of the many people unable to attend the NCTM conference in NOLA.  Instead I followed along with many of my favorite people on twitter as they shared their impressions and opinions of the various presenters and programs.  It was interesting hearing from in many cases both presenters as well as people who attended the presentation.

@woutgeo (Avery Pickford) commented that there are 385 content standards occupying 60 pages and 8 practice standards in 3 pages.  If the practices standards are so important, why are they given so little focus.

I said that it is much easier to assess, check off the boxes, the content standards than it is to evaluate (with fidelity) the usage and performance with regard to the practice standards.

I have started to work on coming up with a couple of ways to address this problem.   The first one is that I made up a sheet on which I start a problem and ask the students to identify what practice(s) were used to get to that point in the problem.  The students then need to complete the problem and reflect on what practice they used to finish it.

The problems do need to be carefully considered, as I don't want a problem which only uses a single practice and has a good place to split it so that the work still assesses whether the student understands what they are doing.

Here is the first one I used with my students this spring.  I have a couple ideas for other problems to use, but I haven't done them yet.

Practice Standards Assignment

I am happy with the results I got from this first assignment.  I am required to have students complete a math-based essay as part of the final exam given each trimester.  I hope to use one of these at the end of this school year as the required essay.

Practices student work

Made For Math Monday *Rational Expressions*

Been a while since I've written one of these.  I am finding that my students are slowly, but surely getting the concept of identifying discontinuities in graphs of rational expressions.  We've been looking at them pretty piecemeal up until now, though.

I wanted to get them practicing and its always more fun when there is folding and coloring involved, so we made cootie catchers!  I used a template from Teach Inspire Prepare Students (TIPS) which was a lifesaver as I am really not good at getting word to do what I want with regard to writing sideways in text boxes.

When completed the cootie catcher is assessed by simply looking at the colors each of the innermost pieces are colored.  I am including the file I made (from the earlier mentioned template) as well as the instructions and a scanned completed page.

Here is the pre-solved cootie catcher Cootie Catcher Rational Discontinuities.  Below you can see a completed version.  I liked having the students do different colors for the various discontinuities because high school students always love an excuse to color something in (and it makes it sooo much easier to see how the students have done).

As an aside, primarily because I started this posting 3 weeks ago, I can say that the group of students with whom I used this activity did particularly well on the portion of the rational expressions assessment which dealt with discontinuities.