Are The Students THINKING?

I am a fan of Robert Kaplinsky who has some great blog posts on Depth of Knowledge (DOK). Check out his new post ”
Is Problem Solving Complex or Complicated?” We sometimes give students strategies to tackle problems, but then we risk the students focusing on the tricks/tips/strategy rather than really thinking about what they are doing.

In reference to a math problem strategy Kaplinksy noted:

“While these steps did work for some problems, there were many problems where they completely fell apart. Fortunately I had the perfect solution for this issue: I stopped using math problems where this method did not work!”

Real life is messy. [tweet]Rarely will students encounter problems exactly like the sample problems.[/tweet] If students can not adapt and apply what they’ve learned to a dissimilar problem, did they really learn the concept?

I make no secret of my fangirl love for Dr. Jo Boaler. In her book Mathematical Mindsets she states that giving students a page of the same problem is not the way to go. Giving a bunch of similar problems is not the student thinking but rather practicing following steps. Instead of a page of similar problems, try giving students fewer problems that are dissimilar or exceptions. Analyze, contrast, explain, dissect… focusing more on demonstrating thinking rather than following steps.

[tweet]Do students actually UNDERSTAND what they are doing or just able to follow procedures?[/tweet] If given problems that deviate from the example are they able to use conceptual understanding to figure out what to do or do they give up? In his post, Robert Kaplinsky provides a problem solving framework for students to strategize and think about the problem they are solving.

Google Slides Template

As I’m prone to do, I recreated the problem solving framework into a Google Slides template. I like to use Slides because it allows students to present their ideas.