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Sunday, June 19. 2016
Each step of math mastery offers advantages in life, but all of the math steps are steps toward yet another level of mastery and, if you choose and have talent, it can never end.
American colleges these days have been backing off math requirements. Wayne State University Drops Math Requirement and May Replace With Diversity. Brilliant!
There are three reasons for this: 1. Math is hard so I'll go to a school that doesn't make me do it. 2. It is often claimed that, statistically, women are worse with math. So make the curriculum less daunting for women. 3. IQ. Math above the ordinary high school level probably takes more IQ than many modern college students possess.
My view is that a college degree means little unless it includes some proficiency in statistics and calc. The more, the better.
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When I was discussing what classes to take as a chemistry major with my English teacher guidance counselor, she advised me not to take calculus: "because it is too hard." I didn't listen to her, because, although it was hard, it was necessary.
Apparently, your guidance counselor is an idiot who didn't read the catalog.
Self segregation is the best kind. Any professor of engineering or the physical sciences is delighted that his school offers degrees in xyz studies. It gives the loons a safe space, and keeps them out of his cllasses.
There's a structural problem there:
1. Loons stay out of engineering and science classes because they're hard and the problems don't yield to feeling really strongly about them, protesting, chanting, etc.
2. Engineering and science credentials have high status. Loons observe this.
3. Loons insist on participating - on their own terms.
First it's introducing material from a Loon Studies perspective into introductory courses.
Then it's mandatory "Environmental Ethics" courses, electives on "[Group] in [Science]" that satisfy departmental requirements just like an actual science class, and Loon Studies curriculum requirements in every science and engineering class.
Finally Loon Studies takes over and the actual science and engineering becomes a minority interest, hunted by students in various electives which are said to be heavy on the math and light on the required Loon perspectives. The high status disappears and the loons move on to another field that hasn't yet been eaten by locusts.
The value of mathematics to all students regardless of their final proficiency with calculations is the development of formal, structured thinking and abstract thinking. After all, the education is not facts and other gameshow trivia, but rather first and foremost the discipline of the intellect. Mathematics also assists in the establishment of principles and regulation of the heart.
There are many branches of math, and it is at least plausible that you could find something (knot theory?) that didn't require much feel for algebra, that would give the students a good rigorous challenge.
I'm told that some students had no problems with high school (euclidean) geometry but crumpled in algebra, and others had the reverse experience.
If our educational objective is training the person, then a solid course in logic is just as good as a solid course in algebra. (Quadrivium anyone?)
If our objective is to prepare the student to understand the world, we're stuck with the problem that algebraic modeling is the language of many disciplines.
If our educational objective is training the person, then a solid course in logic is just as good as a solid course in algebra.
Which then collides with the omnipresent "I feel."
Both statistics & logic would be good for citizens.
I fail to see how someone should be awarded college degree without having mastered Algebra II, which most of us take in the third year of high school. I am reminded of math exit exams for high school, which require mastery of 8th grade math.
I've argued that a semester's introduction to legal reasoning and an introduction to medicine would also be excellent requirements.
I'm very good at math, and pretty crappy at languages. I'm willing to cut a student some slack if they're crappy at math but superlative at languages. (A's in mickey mouse courses don't count. In fact, I'm not sure what A's mean in a lot of courses anymore...)
College level algebra should be a minimum requirement. A very useful tool, no matter your field of study.
I am reminded of an elementary level schoolteacher who, during a previous oil boom, decided to join the oil field. The training course required 9th grade algebra, which would be subsequently used at the rig site. The schoolteacher had great difficulty with the training modules that required mastery of 9th grade algebra.
I read the syllabi of the classes and do think those topics are very important. I do think students that aren't going to go past geometry should take those in high school.
The lower math requirements are necessary when you have a larger population of students going to college, instead of the elite learners. It's needed when you don't have on the job training any more and employers want certification instead.
I believe that part of the value of learning different courses is that it exercises your mind and thus increases its capacity. You may not need the actual subject matter, but learning how to learn things will be valuable.
There are two issues that I have always had with the way math is taught. First in all but one algebra class and in my statistic classes, there was little if any discussion on how each module related to the others modules. It often seemed that I was being taught facts that had little relation to each other. Not too mention that there might be a semester or two between math classes
The other issue I have that often the was little practical application for the formula given, even an odd history fact would help my retention of the material. But often my classes were taught by math grad students or associates professors who liked theory and cared little for teaching.
Where I went to high school if you had geometry, trigonometry and algebra, you senior year you could take the intro to calculus and analytical geometry course. Calculus isn't too hard for high school. I was an engineering major in college and you freshman year you had to take the calculus course because so many engineering courses required calculus as a prerequisite. If you couldn't pass calculus you weren't going to be an engineer.