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Matthew Daly
Matthew Daly
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My son is in high school (France, 2nde) and I was watching how he solves math exercices. This led me to the following question: when are students expected to plug in actual values in their calculations?

As a background, I am a physicist by education and was always of the opinion that the symbolic calculations should be dragged as far as possible. The actual numbers are used at the very end and it is not the most important part.

It seems that the way math is taught today is different.

I will take a concrete example:

We have three points $M(7;-2)$, $N(O;t)$$N(0;t)$, $P(3;1)$. Find $t$ so that they are aligned.

I would have done it by generalizing the points ($M(x_M;y_M)$, $N(x_N;y_N)$, ...) and finding co-linear vectors with the calculations being done on those generalized points. It is only at the very end, having a general formula, that I would have used the actual values of $M(7;-2)$, etc.

My son is telling me that they do the calculations directly.

Which approach is expected at a high school level? The example below is a simple "training" exercise, but when the problems get longer I see that he is still using the numbers early on, without any generalization.

My son is in high school (France, 2nde) and I was watching how he solves math exercices. This led me to the following question: when are students expected to plug in actual values in their calculations?

As a background, I am a physicist by education and was always of the opinion that the symbolic calculations should be dragged as far as possible. The actual numbers are used at the very end and it is not the most important part.

It seems that the way math is taught today is different.

I will take a concrete example:

We have three points $M(7;-2)$, $N(O;t)$, $P(3;1)$. Find $t$ so that they are aligned.

I would have done it by generalizing the points ($M(x_M;y_M)$, $N(x_N;y_N)$, ...) and finding co-linear vectors with the calculations being done on those generalized points. It is only at the very end, having a general formula, that I would have used the actual values of $M(7;-2)$, etc.

My son is telling me that they do the calculations directly.

Which approach is expected at a high school level? The example below is a simple "training" exercise, but when the problems get longer I see that he is still using the numbers early on, without any generalization.

My son is in high school (France, 2nde) and I was watching how he solves math exercices. This led me to the following question: when are students expected to plug in actual values in their calculations?

As a background, I am a physicist by education and was always of the opinion that the symbolic calculations should be dragged as far as possible. The actual numbers are used at the very end and it is not the most important part.

It seems that the way math is taught today is different.

I will take a concrete example:

We have three points $M(7;-2)$, $N(0;t)$, $P(3;1)$. Find $t$ so that they are aligned.

I would have done it by generalizing the points ($M(x_M;y_M)$, $N(x_N;y_N)$, ...) and finding co-linear vectors with the calculations being done on those generalized points. It is only at the very end, having a general formula, that I would have used the actual values of $M(7;-2)$, etc.

My son is telling me that they do the calculations directly.

Which approach is expected at a high school level? The example below is a simple "training" exercise, but when the problems get longer I see that he is still using the numbers early on, without any generalization.

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WoJ
WoJ
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How much symbolic calculations before plugging in actual values?

My son is in high school (France, 2nde) and I was watching how he solves math exercices. This led me to the following question: when are students expected to plug in actual values in their calculations?

As a background, I am a physicist by education and was always of the opinion that the symbolic calculations should be dragged as far as possible. The actual numbers are used at the very end and it is not the most important part.

It seems that the way math is taught today is different.

I will take a concrete example:

We have three points $M(7;-2)$, $N(O;t)$, $P(3;1)$. Find $t$ so that they are aligned.

I would have done it by generalizing the points ($M(x_M;y_M)$, $N(x_N;y_N)$, ...) and finding co-linear vectors with the calculations being done on those generalized points. It is only at the very end, having a general formula, that I would have used the actual values of $M(7;-2)$, etc.

My son is telling me that they do the calculations directly.

Which approach is expected at a high school level? The example below is a simple "training" exercise, but when the problems get longer I see that he is still using the numbers early on, without any generalization.