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17

Speaking from an American perspective, your son's approach strikes me as much more natural. For instance, to solve your problem We have three points $M(7;-2)$, $N(0;t)$, $P(3;1)$. Find $t$ so that they are aligned. my students would start by observing that the slope (gradient) of $\overline{MN}$ would have to be the same as that of $\overline{MP}$ and ...

11

Calculate when you want an answer. Solve algebraically when you seek patterns. If the problem was "show that for any two points, you can find a third point along the y-axis that is collinear with them," then symbolic logic is the right way to go. But if you have the points, just plugging them in simplifies the problem dramatically and makes it easier to ...

6

I don't think this is a nationalistic difference (I'm in the US), but I also don't think your example is optimal. As an example where the correct technique is more well defined, let's say we have a physics problem like this: A bug starts from rest and accelerates with constant acceleration for 0.53 s, traveling 1.37 m. Find the bug's acceleration. I would ...

3

You can't generalize a single, isolated question, which is what your high school question about collinear points is. Of course you can invent a set of similar problems, create a general solution for the whole set, and then solve the particular problem given - but why do all that unnecessary work? If your child's homework set contains several similar ...

2

My own experience in math classes (as a student in Germany) and tutoring my peers would lead me to the following conclusion regarding your question: Many students have problems with the generalized formulas, because they find it rather unintuitive to calculate with "letters" rather than numbers and they would frequently ask for real world examples and ...

2

I think the difference between the two approaches is the goals. Your solution is exactly what I would do, but I'm an engineer. In high school, the goal of learning is usually more about understanding the general concept and gaining some practice with the mechanics. I would think that plugging in the values early on is "easier" to grasp the ideas than ...

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