4 ms·

Hence has its place, as do the holes left in theorems that our betters leave for us. These gaps leave ups to leaps of faith at our beginnings and thorough proof

Hence has its place, as do the holes left in theorems that our betters leave for us. These gaps leave ups to leaps of faith at our beginnings and thorough proofs as we mature. When I was a green tutor I would attempt to make every single last step as obvious as possible, but I later recognized the value of making the the pupil do the work. It builds their confidence and character to have faith in themselves or, if failing, their ability to find the answer that they could not bridge themself.

xg15 6y ago
As long as you guide them doing so and help them out if they get stuck - which is your job as a tutor. No one is helped if the gaps make it impossible for students to understand the concepts.
xg15 6y ago
As long as you guide them doing so and help them out if they get stuck - which is your job as a tutor. No one is helped if the gaps make it impossible for students to understand the concepts. > These gaps leave ups to leaps of faith at our beginnings and thorough proofs as we mature. As a student who had been in such a situation, I can say that both of those seriously impacted my and my colleagues' understanding of the subject. I've had professors who didn't explain their reasoning for certain steps at all and others who "explained" it by simply reading through the mathematical proof. That was about as helpful as getting thrown into vi without any help documents vs getting thrown into vi with just a copy of the full source code next to you: Neither helps you understand how to actually work with vi. I believe the goal of, say, a mathematical lecture should be to explain the basic idea of a mathematical tool and the reasoning why it is there and how one can use it. I believe if students have understood that, they will have less need to dive into some hairy details of the actual proofs as well.

xg15 6y ago

As long as you guide them doing so and help them out if they get stuck - which is your job as a tutor. No one is helped if the gaps make it impossible for students to understand the concepts.

xg15 6y ago

As long as you guide them doing so and help them out if they get stuck - which is your job as a tutor. No one is helped if the gaps make it impossible for students to understand the concepts. > These gaps leave ups to leaps of faith at our beginnings and thorough proofs as we mature. As a student who had been in such a situation, I can say that both of those seriously impacted my and my colleagues' understanding of the subject. I've had professors who didn't explain their reasoning for certain steps at all and others who "explained" it by simply reading through the mathematical proof. That was about as helpful as getting thrown into vi without any help documents vs getting thrown into vi with just a copy of the full source code next to you: Neither helps you understand how to actually work with vi. I believe the goal of, say, a mathematical lecture should be to explain the basic idea of a mathematical tool and the reasoning why it is there and how one can use it. I believe if students have understood that, they will have less need to dive into some hairy details of the actual proofs as well.