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.)
Oh, I really like these! Both versions are rich, each in different ways. But I especially appreciate your thoughtful criticism of the Regents questions, and how you propose not just that the sample was too rough, but how to remedy it. This type of analysis helps me as I develop my own questions, too. Thank you!
ReplyDeleteThanks, Jennifer. Including the June 2016 NYS Algebra II Regents questions, we'll continue to see how the tests address these. Mostly, though, teachers will need to borrow and modify questions related to the probability and statistics standards from the AP Stats world.
DeleteThanks for posting this, Amy! I assumed teaching the AP Stats class at my school after the unexpected and unfortunate passing of one of our instructors several weeks before school started and, honestly, I have little experience with statistics (prior to this year, I taught middle school mathematics). I'm absorbing and studying whatever I can. This is a great activity! Is there an answer key available? I like to check my own work before presenting an example to students. Thanks for your help and thanks again for your post!
ReplyDeleteI don't do answer keys. If you have a question, please email me. Also, sign up for the AP Stats community: http://alittlestats.blogspot.com/2014/09/my-advice-for-ap-stats-newbie.html Lots of great questions, answers, and resources.
DeleteI signed up for the AP Stats community last night and just started delving into the message boards/questions/resources. I did the sample question in class today and it went very well! Neither I nor my students ended up needing the answer key either, lol... Thanks for the post and thanks for your time!
ReplyDeleteNo problem! Good luck with the class. It's a fun one to teach.
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