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In math, algebra, geometry, and trig are easier to visualize when you're studying them. As for calculus, one just has to "hang on for the ride." It's challenging trying to visualize what a derivative or an integral is going to look like, as you're doing the calculation(s).
In science, the same is true of biology. You've got this visual road map going, whether it's what is diagrammed in the book or your very own fetal pig. Chemistry becomes more elusive. Then, with physics, the mechanics part of it is easier to grasp, because you can sort of visualize torque and whatnot. The second part, having to do with electricity, light and sound, is harder to grasp.
All other subjects are easier. If you're studying history, you can "direct your own movie" while you're reading the book. In psychology, you can make up your own role plays, or draw from life experiences.
I really think that's why math and science have always fetched fewer students, and lower grades.
It's challenging trying to visualize what a derivative or an integral is going to look like, as you're doing the calculation(s).
Honestly this part is not that hard.
As the textbooks usually show, derivative represents how fast a function/curve changes, and integral represents how much a function/curve accumulates... The basic level knowledge can be graphically represented with ease.
Actually I think linear algebra is harder. What is an eigenvalue? It is harder to visualize.
As the textbooks usually show, derivative represents how fast a function/curve changes, and integral represents how much a function/curve accumulates... The basic level knowledge can be graphically represented with ease.
I am aware of that. However, as you are calculating a first and a second derivative, it's not as if you can see it while you are doing your homework. As you read the chapter that precedes the homework, then it is described graphically.
The other thing is that a lot of things which hinge on calculus are then distilled to tabular form or algebraic equations, or neither.
One of my friends who was in pre-med, and doing well at one of the UCs, spoke of calculus as it applies to the everyday practice of medicine and said "It's not like I'm going to be dealing with a patient and say 'Ok, let me take your derivative'."
I think for adults, it's a question of "use it or lose it." If the last time you did a math problem was 20 years ago in high school or college, then you are not going to be adept at it now. You need to keep refreshing your knowledge of these areas. There are many free resources on-line for doing that for all levels, from grade school to post-graduate. Right now I'm taking Algebra through the Saylor Foundation:
and others. These courses are taught by professors from top universities around the world, including MIT, Harvard, Stanford, and are 100% free to anyone! At many of these sites you can work at the course at your own pace, others have a time limit of a few months. There are online lectures, readings, and discussion forums for your discourse with students of all ages from all around the world.
If you have a kid who is struggling with Math, sit down at the computer a few nights a week, and work through a few Math exercises. It will benefit both of you.
The other thing is that Math is hard, (but that doesn't mean it's not fun.) There's this misconception that some find it easy, so people feel stupid when they don't get it, and they give up. There's a very small minority, probably < 1 % of the population who find Math easy, but most people do not. That is one of the most valuable things a teacher can do, acknowledge that Math is not easy. It involves learning things step by step, and then lots of practice.
The other thing that Math and Science teachers need to impart is just how exciting and fascinating these fields are. Luckily the web courses on sites like Coursera and Udacity do just that.
Okay so I see this article today about how only a third of PA 8th Graders are proficient in science. What is the deal with people learning science and math? Out of all the subjects I've taken throughout my career it's the science and math courses that seem to confuse people and I'm not sure why. And I'm not talking high level math or science either. And I'm not really talking about 8th grade students either, but just in general when it comes to high school students and most adults. I've said it before and I'll say it again, when it comes to math and science the general public is so unbelievably dumb it's quite embarrassing.
For some odd reason people just don't understand basic basic science, and I'm not kidding when I say this either. I always found it interesting when I see large amounts of freshmen entering schools like Bloomsburg University as biology majors and then seeing that number literally cut in half by the end of the first year, if not the end of the first semester. They must see the course requirements and the lab requirements and say 'hell no' and switch majors and go into something else like business, which I'm not saying is a bad thing. In general, do most people find basic biology and physical science tough to understand? And if so, what exactly is it that they don't understand? Maybe it's the way it's being taught, maybe it's their homelife or their upbringing, not sure but it's quite alarming to see so many people unable to understand basic basic science and math. How do we as a society help change the way most people think about everyday science and math?
I never really liked science and math.
I suspect that those biology majors who switch were probably planning on being "pre-med" and found out that they really didn't have what it takes for medical school. I know that some colleges intentionally make some of the "pre-med" classes difficult for this very reason -- to weed out those students that would never have a chance at medical school. It is better to find out in freshman year that you can't cut it.
For someone like me who cannot do numbers, that triangle would be easy as long as you gave me a formula to follow. That's not the kind of math that is hard when we say math is hard. That's not even math to me. x + y = ? Now that is math, the kind of math that is incomprehensible to me.
Okay so I see this article today about how only a third of PA 8th Graders are proficient in science. What is the deal with people learning science and math? Out of all the subjects I've taken throughout my career it's the science and math courses that seem to confuse people and I'm not sure why. And I'm not talking high level math or science either. And I'm not really talking about 8th grade students either, but just in general when it comes to high school students and most adults. I've said it before and I'll say it again, when it comes to math and science the general public is so unbelievably dumb it's quite embarrassing.
For some odd reason people just don't understand basic basic science, and I'm not kidding when I say this either. I always found it interesting when I see large amounts of freshmen entering schools like Bloomsburg University as biology majors and then seeing that number literally cut in half by the end of the first year, if not the end of the first semester. They must see the course requirements and the lab requirements and say 'hell no' and switch majors and go into something else like business, which I'm not saying is a bad thing. In general, do most people find basic biology and physical science tough to understand? And if so, what exactly is it that they don't understand? Maybe it's the way it's being taught, maybe it's their homelife or their upbringing, not sure but it's quite alarming to see so many people unable to understand basic basic science and math. How do we as a society help change the way most people think about everyday science and math?
Everyone has strengths and weaknesses but I'm telling you many people today don't get a chance to develop full potential due to: ***** ty teachers, bad educational structure and various social and family issues, all of which can and WILL adversely affect ability and will to stick. I've seen many underprivileged kids or kids in less than ideal situations give up. Poor schools don't get opportunities that they should whilst prestigious schools with kids who don't need them get all sorts of perks. Some teachers think because they work for a regular or lower class school they don't need to put in the effort. Then you have parents and their attitudes. Sometimes it's just plain laziness and disregard but you're right that upbringing and homelife greatly affect the minds of youth and the paths they take. Teachers I think need to start teaching again and reevaluate their methods instead of relying too much on the internet and giving students way too much projects (which really equates to teaching themselves as the teacher is too lazy to do their part) when they're still at a young stage.
When you have all those things against you as an underprivileged child, deciphering your teacher's vague explanations just become too much. With science and math, you need very lengthy and practical explanations of concepts with real life examples. I've had my share of moronic teachers but I've still done very well, mostly I guess out of luck. I recall I once asked a college math major the logic behind a certain equation and how to know if it was true or not in a situation and he couldn't give a sufficient explanation, he just repeated the textbook. He confused me even more and left me wondering if he really understood it himself.
Math can be really, really boring. Whenever we studied math in school I was longing to get back to reading, spelling, and social studies.
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I recall I once asked a college math major the logic behind a certain equation and how to know if it was true or not in a situation and he couldn't give a sufficient explanation, he just repeated the textbook. He confused me even more and left me wondering if he really understood it himself.
