I like to connect what I do in my math teaching to my job, and since my job is all about building students’ conceptual understanding in math, I like to think about where else we look for conceptual understanding.
There’s this movement in the math field where we push conceptual understanding (for great reason) because we know memorization can only get students so far and that we need to build critical thinking skills. When we see a math test, say, a scantron or even just a SAT score, we might have the question of “Yeah, they did score well, but do they *really* understand math or are they just good memorizers or they just know how to ‘plug and chug’”?
Then I think about conceptual understanding in my hobbies: piano and gymnastics. When I play a song on the piano, sometimes I’m on autopilot, sometimes I’m sight-reading and paying really close attention, but I don’t think I’m really doing a lot of conceptual understanding when I’m actually playing. When I think of conceptual understanding for the piano, I would imagine it being about music theory: Oh, I’m playing a G major chord, this is a D major chord in 1st inversion, a major 5th sounds good because…, etc. I honestly do not do any of that when I’m playing. Am I a bad pianist because I don’t? I know that in math, the process is just as important as the final answer, but could this be applied to music too? When you hear a pianist play, does the question come to your mind saying “Yeah, she plays beautifully, but does she have music theory down too? Does she understand why the music she plays is beautiful?” Berkeley Everett mentioned that jazz musicians use their conceptual understanding all the time and I agree. Most of the time they are just given chords and they need to improvise with only those chords. But what about other musicians? High school marching bands? Do audience members or judges in competitions wonder about the performers conceptual understanding?
In gymnastics, most if not all gymnasts know basic physics concepts, such as being in a tucked position gives you a faster rotation than being in a laid out position, and to always jump first before twisting, but we can definitely get more conceptual. But when we see them perform, I’m not sure if we really say “Yeah, they stuck that landing, but did they *really* know the physics behind how they stuck that landing?” It seems like gymnastics isn’t the place that we ask for conceptual understanding and that even if they do it on muscle memory, it’s still great.
Some ideas that might seem a little “out there” to ask of these people for conceptual understanding include: people tying ties (or shoelaces) and if they know why what they did created a knot, or asking bakers if they really know the chemical reactions in baking cookies, or asking a clarinetist why playing with the register key takes their notes up an octave. All of these examples are ideas of conceptual understanding of what they are doing. Yes, it would be cool if people know the reason behind the things I previously mentioned, but we don’t really find ourselves pushing everyone to understand the whys behind it.
For math, conceptual understanding is the forefront of what we teach students. This isn’t a blog post bashing that. This blog post is centered around the question of “Where else should we ask for conceptual understanding?” A lot of athletes and musicians practice and practice until their difficult routines are muscle memory so they do not have to think about it when they perform. For me, when I play piano, I often mess up when I think about what I’m playing a little too much. I just tell myself to just rely on muscle memory.
This might even be the most ridiculous blog post I’ve written (so far), but it’s something that has been in my mind. So I ask you, what subjects (not just school subjects, but ANYTHING) should we ask for conceptual understanding and what subjects do we allow people being okay to just not think about it and just do it? I can imagine asking doctors, lawyers, historians, and scientists for their conceptual understanding (and I am positive they have great conceptual understanding in their field) but I’m having trouble finding where else to ask for conceptual understanding.
Thanks for reading.