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> I find both of these easier and faster using other methods. Maybe just because I've been doing them since childhood. Sure. It's just another tool. > I disag

> I find both of these easier and faster using other methods. Maybe just because I've been doing them since childhood. Sure. It's just another tool. > I disagree entirely with "Memorizing building blocks", mostly because I see the huge dichotomy among students between those who try to memorize and those who attempt to learn concepts. Do you find the best students are fluent with the techniques and have an understanding? It would seem to me, spending time pondering meaning also has the benefits of remembering 'building blocks'; because they're the primitives involved in the struggle for understanding.

cgriswald 10y ago
There are three components: facts, techniques, concepts. Being fluent with techniques is not strictly necessary, but is generally important and can aid in helping to understand concepts by demonstrating relationships. But a student who prioritizes concepts is probably better off than one who only understands techniques.[0] My objection to the article is that it is advocating memorizing facts. Figuring out that 3/5 == 0.6 is trivial if you already understand the concepts and knowing that 3/5 == 0.6 is pointless if you don't know what it means. [0] - Anecdotally, I breezed through calc 1 in high school. First done with every test, always aced those tests, never studied. Had no idea what I was doing, because I was just memorizing and applying rules. Knowing just the techniques was equivalent to knowing nothing.
- discombobulate 10y ago
  > Had no idea what I was doing, because I was just memorizing and applying rules. Knowing just the techniques was equivalent to knowing nothing. I suppose so. If you wrote some code to carry out the rules, you wouldn't say the computer knows anything.
- dwringer 10y ago
  If you were always first done and aced your tests, but think you had no idea what you were doing, then think how everyone else must have felt.

cgriswald 10y ago

There are three components: facts, techniques, concepts. Being fluent with techniques is not strictly necessary, but is generally important and can aid in helping to understand concepts by demonstrating relationships. But a student who prioritizes concepts is probably better off than one who only understands techniques.[0] My objection to the article is that it is advocating memorizing facts. Figuring out that 3/5 == 0.6 is trivial if you already understand the concepts and knowing that 3/5 == 0.6 is pointless if you don't know what it means. [0] - Anecdotally, I breezed through calc 1 in high school. First done with every test, always aced those tests, never studied. Had no idea what I was doing, because I was just memorizing and applying rules. Knowing just the techniques was equivalent to knowing nothing.

discombobulate 10y ago
> Had no idea what I was doing, because I was just memorizing and applying rules. Knowing just the techniques was equivalent to knowing nothing. I suppose so. If you wrote some code to carry out the rules, you wouldn't say the computer knows anything.
dwringer 10y ago
If you were always first done and aced your tests, but think you had no idea what you were doing, then think how everyone else must have felt.