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I have taught Engineering Mechanics a number of times. We start out doing 2-dimensional problems using trig, then move to 2-dimensional problems using vectors. There are always those students who protest that vectors are more onerous than just using trigonometry - why make it harder? Then we move on to 3-dimensional problems, which vectors make tractable. But you really need to do some easier 2-d cases so that you can learn how the vector structure works.</p>
<p>Here is the issue (teacher speaking). If a student shows their work…and gets the problem wrong, the teacher (or tutor) then knows where the breakdown in solving came. If its all in the kid’s head, there is no way to know which step was done incorrectly. </p>
<p>Even those very bright students who can do these in their heads make errors…and their teachers should be able to see where they went wrong to help them.</p>
<p>Sikorsky,</p>
<p>As previously mentioned, I hired a retired math teacher to help my S. He referred to my son as a talented mathematician. This helped me convince my son to move to a different math teacher half way through the year. His new teacher and this year’s teacher cut him some slack because they also see he gets it without showing all his work. I should add - my S has ADD - high IQ with a slower than avg processing speed so it is very time consuming for him to show every step. However, if asked he can verbally explain his thought process.</p>
<p>I get that. And I wouldn’t have an issue with your son, as far as I can tell.</p>
<p>As is often the case, there are two strains of teaching-talk in this discussion. One concerns teaching in general and students in general, and the other concerns individual students. A good teacher, of course, tries to teach the subject, and also to teach the students who are actually there in the class.</p>
<p>I’d want to talk with your son (and maybe you) about a reasonable way to cut him some slack in writing while still ending up with a work product I could evaluate, but unless somebody in the discussion were totally unreasonable, we could come to an understanding.</p>