As a former math teacher and current math tutor, I've have seen enough to say that students who fail to learn math fail for the same reason: they were taught badly. By this I mean a faulty method was used. In almost all cases, the faulty method is too abstract.
People, and children in particular, are much better at thinking in concrete terms like time, money, length, etc. instead of pure numbers. For this reason, I strongly believe that theory in math should be kept at an absolute minimum and that most if not all exercises should be word problems.
I say this because I have met many students who can solve complicated arithmetic problems and then get stumped by the simplest word problems. It is though there is a wall in their minds which separates math from everything else. Teachers must remember that math, like language, is a tool for making sense of the world. Just as you can't learn to speak by copying words out of a dictionary, math cannot be learned with just flashcards, formulas, and drills.
I realize there is the old tug-of-war between conceptual vs. procedural understanding. Again, I see language learning as the example to follow. Before children learn about reading, spelling, and grammar, they must first learn how to speak. Intuitive knowledge must proceed deep understanding. If children were taught to speak the same way most are taught math, there would be little speaking and a lot of grunting and pointing.
Math is a fascinating subject, but it is dire need of being taught in a more sensible way. The practice of trying to turn students into little mathematicians needs to die. Instead, they should be taught how to use math with simple, practical examples.
People, and children in particular, are much better at thinking in concrete terms like time, money, length, etc. instead of pure numbers. For this reason, I strongly believe that theory in math should be kept at an absolute minimum and that most if not all exercises should be word problems.
I say this because I have met many students who can solve complicated arithmetic problems and then get stumped by the simplest word problems. It is though there is a wall in their minds which separates math from everything else. Teachers must remember that math, like language, is a tool for making sense of the world. Just as you can't learn to speak by copying words out of a dictionary, math cannot be learned with just flashcards, formulas, and drills.
I realize there is the old tug-of-war between conceptual vs. procedural understanding. Again, I see language learning as the example to follow. Before children learn about reading, spelling, and grammar, they must first learn how to speak. Intuitive knowledge must proceed deep understanding. If children were taught to speak the same way most are taught math, there would be little speaking and a lot of grunting and pointing.
Math is a fascinating subject, but it is dire need of being taught in a more sensible way. The practice of trying to turn students into little mathematicians needs to die. Instead, they should be taught how to use math with simple, practical examples.
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