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<p>I don’t think the students are expected to figure the math concepts totally on their own. Eventually, the teacher has to step in and say: “Okay, here is how you should do it, and here is the solution.” This is true even if the students have figured it out already. As I mentioned in a post, this step is important to reinforce learning.</p>
<p>I agree completely that teachers are key, no matter what the curriculum is. A big problem in k-8 education is that teachers are generalists, and very often, they focus on reading rather than math pedagogy. By the time the kids get to the point were they encounter specialists, they have been taught math and science badly and have huge holes in their knowledge. It does not matter which method is used. </p>
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<p>In my 11+ exam (right after 5th grade), we were handed blank sheets of paper in which we would be writing our essays, do our math, science, etc… So the first step was to draw straight lines. Even with a ruler it was a nerve-racking experience, as it was a race against time. Focusing on drawing neat, parallel lines took time away from actually doing the exams. But penmanship was also a component of the exam. I can still have nightmares about it!</p>