[z3phyr]

> Ask why do I need to determine similarity of two vectors

Simple:

Start with

a) Suppose you are making a video game..

b) Suppose you are determining ballistic trajectory of your missile system based on model rockets

c) Suppose you are running a fighter robot group..

Or any of the stuff children are supposed to *actually* do and then take these classes with determination to do the actual creative things that they wanna do all life.

There is an aspect of jest in the above comment, but it also contains some likely truth. Children love doing stuff, and these are the things that may enable them.

[kyykky]

Take a random group of students from the general population and one of those examples (Edit: or any single given example whatsoeve). Turns out 95% are not really interested.

Edit 2: The teacher probably gave some example from biology or something that you didn't care about and therefore forgot about it.

[z3phyr]

The core skill of the teacher lies in recognizing the interests of the pupil and then working on refining those skills so that the pupil can use those skills for at least their betterment, if not the society.

And that is one of the toughest things to get right. Children are extremely curious, that's how they learn and master absolutely anything including arts, dancing, music, history, skating, catching insects, street smarts etc. It's on us as teachers to not let that curiosity wither into nothingness.

[xandrius]

This is exactly how I would teach SO many subjects in school: take what kids are actually interested about and make them see the connection.

The worst thing was to learn something just because the teacher said so. If I hadn't had the motivation not to fail, I would definitely not have gone this far in my studies and in life.

[slowmovintarget]

If I'm writing an instruction manual for a lathe, I'm probably not going to run through all the varying things you produce with the lathe. I'm going to talk about correct use of the lathe. It won't help you understand what a lathe is for, but it will help you use the lathe correctly.

I think the same goes for mathematics instruction. The thinking is that you will soon take courses that will make specific application of these tools that have broad application.

[z3phyr]

You will be correct for the most part. However, there is a question of motivation as well. Kids can make very cool toys with a lathe.

I am not from the west, but I watched Band of Brothers. From most of the ww2 media there is always a term being used. "Why we fight?"