The future already exists, you just have to look for it.
Teacher: *Hands out homework*
Me: I don't... Like being handed things.
I often notice that teachers will just give their students some examples, and send them on their way to do their homework. That doesn’t sit right with me. That teaches the students to follow rigid guidelines, and does not allow them to use their own judgement.
I’ve had a few great teachers and they all have one thing in common, they explain the concepts. They tell you the background of the knowledge, why the equations and the process makes sense. They will explain the concepts to you, and then give you the problems a different day so that those concepts can work their way into your brain.
Teaching concepts rather than teaching steps allows the students to find their own way to solving a problem. I think that allowing the student to think independently, rather than forcing them into a specific process, promotes more growth and understanding.
I wish all teachers were like those. Teach a student to think analytically, let a student find their own way after teaching them the concepts. Let the students realize that a lot of the concepts are interconnected, and as a result they aren’t learning anything that’s new, but rather an extension of their own knowledge. Don’t force them to memorize equations. Don’t force them to memorize rules. Don’t teach them to memorize things, teach them to use those concepts in order to derive the idea of the problem. Teach them to connect one idea to another.
That’s the way I learn the best.
If you don’t know calculus, sorry for the rant. This is a visual idea.
*if f ’ is above the x axis from one point to another, then f will be increasing from that point to that other point.
*If f ’ is below the x axis from one point to another, then f will be decreasing from
that point to that other point.
*If f’ is above the x axis before it crosses the x-axis at a point (that is on the x-axis)— then you will have a local maximum, and you will have a concave downward.
*If f’ is below the x axis before it crosses the x-axis at a point (that is on the x-axis)— then you will have a local minimum, and you will have a concave upward.
—The second derivative can also determine concavity… But I like this idea better. ^
I thought I would share my ideas.
IF I’M WRONG, PLEASE CORRECT ME. IF YOU HAVE BETTER WAYS OF PERCEIVING IT, PLEASE TELL ME TOO.
On Khan Academy, my username is Astronomy93.
If you want, we could say we’re each others coaches, then you can see my activity and I can see yours.