Friday, May 20, 2016
Common Core Algebra II: Music and Gender
In Fall 2015, NYS released a set of sample questions for the new Common Core Algebra II Regents. They included this question regarding independence. I've done similar questions like this with my AP Statistics students. Here, I outline how I would improve and present this question to Algebra II students. In fact, I've created two enhanced versions of this problem.
The Algebra II Regents Fall Sampler questions were released with lots of caveats about the questions not being fully developed. Even taking that into consideration, I think this is a really challenging question and one that deserves more than 2 points indicated in the rubric. This problem reminds me a lot of an AP Exam question that I use in class, 2003B #2, regarding independence of age and income. Keep in mind, students are expected to take 10-12 minutes doing these types of free-response AP problems, rather than just a couple of minutes like on the Regents. In fact, despite the fact that the table is larger and the question is intended to take longer than a Regents question, I think the AP question is easier.
Yes, I think the AP Statistics exam question is easier than the Regents sampler question.
First, the AP Stats question has a table with the marginal totals provided. While those sums are not hard for an Algebra II student to do, it's a step that requires time and a step in which a student can easily make a mistake (that is not at all part of the intent of the question). Secondly, the AP Stats question is scaffolded nicely. There are three parts. The first part asks a relatively easy question about a marginal probability. The second asks a more intermediate question about a conditional probability. The last part asks a more advanced question regarding independence, but directs students to use their work from the previous two parts for the justification. This is a smart strategy in that it both guides students about how they might provide evidence (without giving away the answer) and streamlines standardized grading of the question.
Using the Regents sampler and the AP question as an inspiration, I've provided my own versions of this question. The first is a short version that can be used as a Regents practice question, but includes the entry points like the AP question. I would grade this on a 4-point scale instead of two and suggest 15 minutes for students to complete the question. The second version is longer and can be used as an in-class activity.
Preferred Music Style and Gender 1.0 (short version)
Preferred Music Style and Gender 2.0 (long version)
(Problem from the Fall 2015 NYS Common Core Algebra II Regents Sampler on EngageNY.)