Is Your Math Class More Like an English Class or a Food Science Class?
"Oh, so you just..."
I cannot stand hearing students say this as it is a major indicator that a student does not understand why, and understands mathematics as a procedure. I'm going to attempt to fit this into other subject areas in an attempt to understand why it happens so frequently in mathematics. My initial feelings
English - "Oh, so you just write"...too general. "Oh, so you just write the theme?"...Why don't students say this in English? Writing the theme in English is meaningless without any context around it. The theme of "Betrayal" manifests itself much differently in the book 1984 than in Julius Caesar.
Social Studies - "Oh, so you just memorize"..."Oh, so you just figure out the type of government"..."Oh, so you just compare and contrast the interactions between Islamic and non-Islamic nations". I don't think I need to belabor the point about a relevant context, but Social Studies is all around a kid and they interact with the content of the course constantly. Kids must study social phenomena to remain relevant in the world.
Science - "Oh, so you just add the two chemicals together"..."Oh, so you just cut the frog here"...Science provides the great purpose that is so elusive to students these days. Yes, you are following the procedures, but with the purpose of learning something greater when the procedure is done. Most frequently, our end result in mathematics is what value makes a statement true. Scientific procedures often have a more relevant purpose than this.
Food Science - "Oh, so you just add the milk after the eggs?"...if you add them before, your meal will come out wrong
Context, relevance, purpose all generate much higher outcomes than the procedures we follow in Mathematics. Our outcomes in Mathematics are the answers and never the "why and how". Many of our mathematics classes follow the instructional models of Food Science where if you don't follow the right procedure, you wind up with something that tastes bad. Couldn't mathematics be enriched by delving deeper into the why's and how's, instead of just placing caution signs for what you should be careful not to do?
So many of the great math educators whose blogs I've been reading (dy/dan, Point of Inflection, and f(t)) instruct from the perspective of having their students understand the rules before they even begin to follow them.
This post is in no way meant to belittle any of the subjects listed.