April 10, 2016

Building Portfolios of Math Practices

This is a follow up post. I wrote about the original idea in August and how the first round went in November. The goal was to find an authentic way to assess the Standards of Mathematical Practice and the method was to have students build a portfolio of exemplars throughout the school year. They would submit their portfolio quarterly using this Student Form.

We just finished third quarter (so I'm writing this post while procrastinating grading!) and I had students complete this form for the third time. It was again a task for the last day of the quarter. Most of my students have figured things out by now and are good at this, it was just one task of many that class. Not everyone remembered all of my expectations though. A few of them only heard "find four examples of good work" and tuned out before I reminded them to give evidence of how they used a math practice in the exemplar they chose. Those students provided evidence such as "I did well on this." I went back to those students and had them read the quotes again and add more detail. Listening to my co-teacher (who has also worked in English classes) work with students to remind them to "use words from the prompt" - as I checked in with a student whose 'evidence' was to copy over the example I provided word for word - made me realize that this is a cross-curricular assignment. Our ELA data has shown that students need more practice explaining how evidence relates to their claim. They are good at making a claim and picking out the relevant piece of evidence, but communicating why the evidence supports their claim is a challenge. When I designed this portfolio task I didn't expect the writing to be a challenge, but now that I've done it a few times I think this is exactly the kind of challenge students need. Asking students to describe their evidence requires them to interpret the practice standards. Overall the results have been fantastic!

Here are some of the examples and responses students wrote this quarter:

Make Sense of Problems and Persevere in Solving Them
  • Quad HWDespite having difficulty completing the square and graphing I was able to factor.
  • Systems of EquationsFor problem 1 on the back, at first for the x-value I got the wrong answer, but instead of just quitting like I was about to, I chose the other equation instead which I found to be much easier.
Reason Abstractly and Quantitatively
  • Complex Numbers I switched back and forth between thinking about i as a variable and sqrt(-1).
  • I used the equation to make an easy to understand graph.
Model with Mathematics
  • I used both the box method and long division.
Use Appropriate Tools Strategically
  • Students listed a wide variety of tools including: Desmos, tables, graphs, multiple methods for solving quadratics, their conics dichotomous key... This list is much better than first quarter when tools were pretty much rulers and calculators!
Look for and Make use of Structure
  • Operations with complex numbersI already knew how to solve these problems without imaginary numbers and could still solve with them. 
Look for and Express Regularity in Repeated Reasoning
  • ConicsThe equations of circles, parabolas and hyperbolas are different. I discovered the pattern of the equation for each one. 
  • Powers of iI figured out that the values simplify to the same four numbers in a pattern.

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