A while back I read through this blog post that has been circulating the math ‘sphere. If you have a few minutes, you should definitely check out the videos within the post showing students’ problem solving. This sums it up the main idea pretty well:
In the days that followed I reflected upon what happened and I decided that my students primarily had procedural skill and fluency but very limited conceptual understanding or the ability to apply mathematics. I realized that for my students to “understand mathematics” they would have to have a more balanced understanding that included all three. This experience provided the foundation for why I value using real-world applications whenever possible. They provide a context for building the conceptual understanding and procedural skill needed for rigorous mathematical understandings.
I find that this directly applies to science (especially chemistry) as well, and could become something of a personal challenge:
“I realized that for my students to ‘understand [chemistry]’ they would have to have a more balanced understanding of [procedural skill, concepts, and applications]. Using real-world applications provides a context for building the conceptual understanding and procedural skill needed for rigorous [scientific] understandings.”
Problem-based learning anyone? I know Shawn Cornally knows what I’m sayin’.
I think a further issue is the order in which these three pillars are addressed. What might seem like a logical progression (skill -> concept -> application) might cause students to focus so much on the first or second part that they miss the last piece. What would it look like to reverse this in the classroom (application -> concept -> skill)? Not sure yet. Sounds like a topic for another day.