Last year when I started working on Dead Bunny, I realized very quickly that part of why my students struggle with new math concepts is because they often have to learn not just the new concept but a skill they probably should have been taught earlier.
In some cases, a teacher just failed to introduce the earlier skill at all. In others, it’s been a curriculum issue. At any rate, the poor student needs to understand something new to learn the new skill you’re teaching them, which introduces a small overload.
When I noticed that there were skills I was perpetually teaching my students so they could work through a new skill, I grabbed a stack of index cards, wrote the skill at the top, and all the skills the student probably needed to know before successfully being able to learn the current one. Then, I attempted to sequence the cards based on this list of prerequisite skills.
It was an eye-opening experience. I’m pretty sure I’ve blogged about the need to re-order fraction skills (an experiment that met with mixed results in my learning center due to less than ideal conditions), but there are other skills that could benefit from being presented in a different sequence.
For example, I’ve found that if I approach the number line as an example of the x-axis with students just starting with integers or early algebraic reasoning skills, they’re less likely to confuse the x-axis and y-axis when they start learning about coordinate geometry.
Another example (and one I’d love to hear more about how it aids later learning) showed up when I was catching up on my “to read” links the other day. Denise over at Let’s Play Math uses the distributive property to help students better understand their nines facts in multiplication. My high schoolers struggle with the distributive property, so this is pretty interesting to me.
What’s funny is that reading about Denise’s use of the distributive property came right on the heels of a discussion at work about whether it was reasonable or necessary for a second grader to understand the concepts behind the associative and commutative properties as well as their proper names. But if we encourage that understanding in our younger students, would I have fewer high schoolers struggling with the same skills at a more advanced level?
Again, it’s a question of how to best scaffold these skills to really help students not only learn, but retain these skills through their math education and beyond.
