Teaching Numeracy - Working Answer Keys

I am partaking in a book study over at the Math Coach’s Corner on the book Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking by Margie Pearse and K.M. Walton.   So far we have read the Foreword (by Arthur Hyde), Preface, Introduction and this week we are discussing the first two Critical Habits.  Below are my thoughts for the week.  If you want to join in, all you need to do is start reading and post comments on her blog posts for the book study:

Reading through this week, I was particularly intrigued by the Working Answer Keys.  Working Answer Keys are not just giving kids a sheet with the answers, but also showing a process (because there could be multiple ways to do it) on how to get to the answer.  The idea is to carefully choose 5-10 homework problems for the students to work on but give them the solution paths and answers, expecting the students to use the Working Answer Key as just that…to help them as they are working the problem.  As I was reading about them, Dan Meyer’s video about Khan Academy doing Angry Birds, popped into my head and so I went back and watched it again to gather my thoughts about why it came to mind.  

It is a very short video, so I encourage you to check it out but here are two important pictures and a bit of quoted text:

I’m not saying lectures and explanations are never necessary in math and science — or in Angry Birds, for that matter. When I couldn’t get past that one really tricky level, I went online and found a walkthrough. But the walkthrough — the explanation — wasn’t the first thing I did when I experienced Angry Birds. So why does Khan Academy make an explanation the very first thing a student experiences with a new topic in math. When we put the explanation first, we get lousy learning and bored students.

I am interested in trying out the Working Answer Keys, but my fear is that it will become like Dan’s list for Khan Academy instead of his list for Angry Birds.  I want the students to see math tasks like they see Angry Birds: just jump in and play with the math, experiment and try out solution paths, get feedback by looking at their calculated answer versus their estimated answer as well as my Working Answer Keys, and then get an explanation from their peers and me in class, thus building their learning.  But my fear is that the students will see it more like Khan Academy: get an explanation from the Working Answer Key, play around with the math to see if they can figure out what I did to get the answer, experiment a little to see if they can discover a different solution path than mine, get feedback based on whether or not they got the same solution path as me, and learn that math is just about doing the same steps as the teacher.

Now, I’m being a bit dramatic here for effect…the authors do caution us that there needs to be a lot of discussion, oversight, and modeling when you first start using Working Answer Keys.  So, for those of us that plan on trying it out I think we need to contemplate a lot more about how it will play out and be watching for those kids who are using it like Khan Academy instead of like Angry Birds.