metacogntive math tutorials - lessons learned and still learning

There are excellent math tutorials online, from Adrienne's Lane-aligned set to Khan Academy and more. Most of them feature algorithms - breaking down an approach to solving a particular category of math problems into a series of steps to follow. There are fewer tutorials demonstrating math thinking in applied problems (aka "story" or "word" problems).

Applied problems challenge students at several levels, requiring:

• translating words to math (requiring skill in reading and language)
• identifying the nature of the problem (what answer is required)
• identifying how to solve the problem (choosing math operations to use and in what order)
• sometimes solving a series of problems using one answer to solve another problem, etc.
• identifying the unit of measurement, beyond a numerical answer (dollars, gallons, meters, etc.

Since I have been gradually shifting to a meta-cognitive, strategic approach to Reading I have been thinking about how to do the same in Math. My goal is to make math thinking more visible to students. I want them to see what strategies I choose from, why I choose different strategies, and how I use the strategies.

Towards this end I recorded three tutorial demonstrations. I wrote out solutions with Notability on the ipad, and then recorded a narration on Screencastomatic. Here is the tutorial on the steps, and here is a sample problem, a 2d sample problem and a 3d sample problem.

I chose difficult, layered problems and narrated the steps I followed and my thinking.

I then showed these test tutorials to students. Based on student feedback and my observations I am now going to adjust my approach:

• break the tutorials into short chunks in a series (whole problems were longer than 5 mins., the best practice for reading thinkalouds is 1-2 mins.)
• use software that allows me to write as I talk (seeing so much text already written out during the narration was visually overwhelming "like a math text")
• show mixed use of strategies instead of one size fits all steps
• make a set of tutorials showing solution of the same problem in different ways, with help from Julie Pfaff and Adrienne Mitchell
• show problems solved at the estimate level - just the thinking without actual number solution