Thread: Math Books...Questions Not Explained

I notice that most math books include questions at the end of each chapter that are never explained by the author(s) of the books or the classroom teacher.

Why is that the case? This is a mystery to me.

The questions that I post here are given by the teacher without an explanation.

He said that all students should be able to answer questions at the end of each chapter based on the basic ideas taught in class.

This does not make sense.

Take for example, the two questions I posted today:

(1) Parabolic Arch Bridge

(2) Find Rectangle Dimensions

Those two questions were never explained in class nor are they explained in the textbook but according to our teacher, we should be able to answer these and other questions.

He went over the basics of the parabola but nothing more.

I want your advice.

Your thoughts?

1) Part of the teaching of mathematics is to train your brain to think in such a manner as to be able to solve problems not previously encountered. It is a common misconception that the teaching of mathematics is only to force you to memorize formulas and techniques that you never will need. A strong background in mathematics WILL defend you throughout your life. It always amazes me what lies can be exposed simply by following the logic and mathematics behind the statements made.

2) Part of the purpose of the problem sections is to differentiate the students between various classifications. I'll try a very loose definition:
----- a) In the wrong class, consider transferring out, (How did they manage to get past the placement exam?)
----- b) Absolutely not getting it, but with help may come along,
----- c) Starting to understand, needs consistent encouragement,
----- d) Grasping nicely, don't let this one slip away,
----- e) Leader in the classroom, consider a formal appointment,
----- f) Get out of this student's way and allow to move on quickly.
If sorting is for permanent labels only, it is wrong. If it is for more effective teaching, it is good. There is no law against classification jumping. Like my letter d), I have a warning against jumping to a lower classification. Normally, we don’t like that. Nothing says one cannot jump to a higher classification, otherwise, what would be the point of making an effort, for the student or for the teacher? This differentiation should be an ongoing process, not a life-altering (or life-limiting) assignment.

3) What would be the shape of our society if there were NONE among us who could solve problems not previously encountered? Wouldn't you like to be one of these who actually advances knowledge?

4) If you will pardon a mistranslation of an old saying, credited to many, "No problem set is so difficult that whining about it won't make it even worse."

My views. I welcome others'.

I am thankful for your recent reply.