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Catching Elephant is a theme by Andy Taylor
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.
You don’t need to be in school to improve your education. Check out Coursera!One of the biggest issues that I continue to see pop up for people, especially within the young adult generation[s], is the problem of being at a loss for readily available, and seemingly ‘affordable’ educational sources, information, and courses. I recently reblogged a post with a brilliant list of 500 FREE online courses from top universities, which was pretty popular. Then I received a suggestion from a lovely follower of mine to check out Courseera, as I might be interested. So, in addition to the previous online free courses post, I present you with yet another amazing and FREE resource for personal mind expansion. Courseera offers dozens of free online courses from various universities such as Princeton, Stanford, University of Michigan, and University of Pennsylvania.Below you can view the different types of courses offered on this useful site:
- Mathematics and Statistics
- Healthcare, Medicine, and Biology
- Society, Networks, and Information
- Computer Science
- Economics, Finance, and Business
- Humanities and Social Sciences
Knowledge is power. Educate yourself, explore, and expand!
The Importance of Continuing Education and How to Achieve It (via ashouttothevoid)
That’s the way I learn the best.
Trig substitution in integration.
I just think it’s amazing that something so complicated can become something so simple.
As a lady scientist of color, I have felt like the impostor in the room many many times. Here are two specific things that made me want to switch out of the hard sciences when I was in college. I want to mention them because I suspect they play a part in the lack-of-women-and-minorities-in-STEM-fields issue:
#1 - Being met with incredulity when I said I didn’t know something in a science class. Nothing made me doubt my own abilities more than this. I was so shocked by this behavior when I first started taking math and science courses in college that I straight-up stopped asking questions for about two years. Ask me how much that set me back.
#2 - Asking someone about their class or their research, and they explained it in jargon that was obviously not part of my lexicon. This always made me feel like I just didn’t have the brains or background necessary to pursue the higher-level science classes that I wanted to. Also, it’s a dick move. Also also, there is no slicker way to bore someone, so just don’t do it. My advisor at Stanford, who was totally brilliant, always argued that it takes a really really smart scientist to communicate science in a way that is understandable to nonscientists. That guy publishes like it’s his job (disclaimer: it is), so take heed friends!
The real point here is that most girls are less likely to do the
- “what, you don’t know…?!?”
thing, or the
- “I’m just researching the implications for three dimensional homology jargon and filtration of jargon jargon, it’s pretty simple”
act. So when I first heard people talking like this about classes I was interested in, it was new and scary and made me feel like I was not cut out for science or math.
It wasn’t until many years later that it hit me that everyone has to learn something for the first time at some point, and asking ridiculous questions usually aids and abets this learning process.
However, I’m not one to rant about a problem without proffering a possible solution, so here is my recommendation:
Gentlemen (and ladies too!) in STEM fields, please, check your rhetorical behaviors, before you wreck the excitement and eagerness of women entering the field. Additionally, people will like talking to you better if you dispense with the jargon. I like you better already!
(also shout-out to jtotheizzoe for posting this comic. Love yr blog dude.)
Reblogging for the above comment. ^
I have met people that make fun of you for making small mistakes, and it is just incredibly rude and it gets people nowhere. Accepting that you might not know everything is when you really learn.
We live in an age of increasing specialization, and for good reason. Humanity keeps learning more about each field of study; and as every specialty grows, it tends to split into subspecialities. That process happens over and over again, and it is necessary and desirable. However, there is also a growing need for specialization to be supplemented by integration. The reason is thatno complex, nonlinear system can be adequately described by dividing it up into subsystems or into various aspects, defined beforehand. If those subsystems or those aspects, all in strong interaction with one another, are studied separately, even with great care, the results, when put together, do not give a useful picture of the whole. In that sense, there is profound truth in the old adage, “The whole is more than the sum of its parts.”
People must therefore get away from the idea that serious work is restricted to beating to death a well-defined problem in a narrow discipline, while broadly integrative thinking is relegated to cocktail parties.In academic life, in bureaucracies, and elsewhere, the task of integration is insufficiently respected.
— Murray Gell-Mann,The Quark and the Jaguar, 345
Oh my god. ^
This is what I think, summed up.
If you don’t know calculus, sorry for the rant. This is a visual idea.
But,
*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.
Dan Meyer is a high school math teacher in California. He explains that modern-day math textbooks scuttle inquiry and analysis in favor of teaching kids rote ways to solve problems—without actually learning anything.
Another part of the problem is that kids don’t seem to care about math, an issue that sometimes continues into an adulthood. ” Math makes sense of the world, math is the vocabulary for your own intuition.”
In teaching remedial math at his high school in Santa Cruz County, Meyer rewrites state-approved math word problems to obscure information until students think to ask for it. He also adds multimedia, like video, to his lessons to show his kids how math underlies just about everything they observe and do.
The way math is taught in the U.S. creates:
I’ve seen this in my friends, in my family, and even in myself growing up until I got to calculus and I opened up my mind.
Brilliant way to remember some of the basic trig identities. Full explanation here.
I THINK I CAN FINALLY MEMORIZE MY TRIG . IDENTITIES with this.
This is amazing, you have no idea. I could never memorize them.
