Math is not linear, so why do we teach it like that?

Most of my school's funding is and was not dependent on their student's skills, schools get funding for attendance. When I went to school they checked attendance 6 times every day (once for every class), and gave you 3 bathroom breaks/year/class. Taking attendance took about 5 mins/ class, every time you went to the bathroom a teacher had to sign a form verifying you had permission. This comes out to about* 340,000 HOURS of wasted time in ONE YEAR FOR ONE HIGHSCHOOL. This isn't even considering many, many fundamentally wrong things with how grades and classes are structured and credit is awarded. For every competent teacher teaching a useful subject there are 3-4 incompetents wasting people's time with sophistry and selectively blind adherence to stated rules.<p>Public high school education in this country is a net negative. High school "education" has nothing to do with teaching students skills, its there first to benefit the people running the school, and second to make people obedient for factory jobs.<p>Math &#38; science people tend to be humble &#38; introverted because they're usually wrong about the solution to whatever problem they're trying to solve, and they spend all their time doing math/science and not talking to people. This is a bad thing. Every hour spent on spiffy presentations is an hour not spent on telling people public school's are doing it wrong. The author wasted his/her time on this* * , it's not going to change anything. Math/Science people who want to improve the state of math/science education should spend their time politicking, not science'ing.<p>* (5mins/attendance * 6 classes * 10 mins bathroom break form filling/a day * 2000 students * 34 weeks/year / 60mins/hour = 340K)<p>* * It is pretty cool, though.

An interesting quote I came across today from Edward Tufte:<p><i>One more example. If you are teaching math, hand out the proofs on paper at the beginning of class to all the students; then work through the written-out proofs aloud in class, following the proofs on paper.<p>That way your students aren't merely making notes and recording your words; instead they are thinking. I believe that students should THINK in class, not take notes. So give the students your lecture notes and go through them carefully in class, trying to insure understanding of each part as you go. Your voice in effect annotates and explains the material on paper.<p>(Of course, these ideas apply widely, not just to teaching math.)</i><p><a href="http://www.edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=00001B&#38;topic_id=1&#38;topic=Ask+E.T" rel="nofollow">http://www.edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=0...</a>. -- It's the last paragraph under "E.T. ON TECHNOLOGIES FOR MAKING PRESENTATIONS".

We teach it like that because we learned it like that.<p>We also teach it like that because states have various standards with pretentious names and acronyms ("Essential Academic Learning Requirements" = EALRs [1]) that require students to have specific bits of knowledge at specific ages. This means that, instead of students exploring various mathematical subjects in parallel, they're stuck going through them in exactly the order presented.<p>I remember being in a room full of math profs and TAs discussing how to get more students interested in becoming math majors. I suggested a 100-level number theory course, with the rationale that it's simple, accessible, mathematically interesting, and makes it clear that there's more to mathematics than the "progressively-harder calculus-based classes" (up to DiffEq) most hard-science majors end up taking.<p>[1] 252 page, 8+ meg pdf: <a href="http://www.k12.wa.us/Mathematics/Standards/K-12MathematicsStandards-July2008.pdf" rel="nofollow">http://www.k12.wa.us/Mathematics/Standards/K-12MathematicsSt...</a>

It's time for a favorite quotation about mathematics again:<p>"What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus; and the calculus now taught is, sadly, much less than it used to be. Little by little, calculus has been deprived of the algebra, geometry, and logic it needs to sustain it, until many institutions have had to put it on high-tech life-support systems. A subject struggling to survive is hardly a good introduction to the vigor of real mathematics.<p>". . . . In the current situation, we need to revive not only calculus, but also algebra, geometry, and the whole idea that mathematics is a rigorous, cumulative discipline in which each mathematician stands on the shoulders of giants.<p>"The best way to teach real mathematics, I believe, is to start deeper down, with the elementary ideas of number and space. Everyone concedes that these are fundamental, but they have been scandalously neglected, perhaps in the naive belief that anyone learning calculus has outgrown them. In fact, arithmetic, algebra, and geometry can never be outgrown, and the most rewarding path to higher mathematics sustains their development alongside the 'advanced' branches such as calculus. Also, by maintaining ties between these disciplines, it is possible to present a more unified view of mathematics, yet at the same time to include more spice and variety."<p>Stillwell demonstrates what he means about the interconnectedness and depth of "elementary" topics in the rest of his book, which is a delight to read and full of thought-provoking problems.<p><a href="http://www.amazon.com/gp/product/0387982892/" rel="nofollow">http://www.amazon.com/gp/product/0387982892/</a>

Is the US high school mathematics curriculum really as linear as described here? Do you really work through, say, "geometry" in one go, and never revisit it?<p>My mathematical education was a bit more like advancing on several fronts at once. A chapter on geometry, then a chapter on basic algebra, then some more advanced geometry, then some more advanced algebra, then some basic trigonometry, which enabled you to understand some more advanced geometry, then...

Sorry, I couldn't finish the presentation because of that stupid animation.

The most useful part of this link was finding prezi, which is awesome, and I hadn't heard of it before.

A delightful misuse of Prezi for zooming around with needless effects from place to place rather than moving within content.

Alison Blank (the author) should write a math book instead of making this presentation. I think that would be a great way to prove her point (which I agree with).

I hope my (little) daughter gets a math teacher with A. Blank's sense.<p>A similar point is true of all parts of knowledge, of course: I was convinced to send my daughter to a local hippy dippy lab school when I saw the teachers facing the "But what if my child is Gifted?" question from yuppie parents. The teachers vehemently rejecting separate 'tracks' for the 'gifted' in favor of the Blank plan: if some students master something early, you needn't move them on to the 'next' thing, since this is in some respects an illusion. Rather you get them working on something cool that is 'off to the side' from the point of view of the curriculum sequence, whereby <i>inter alia</i> they learn the unlimited character of possible knowledge and might strike something that would really get them absorbed.<p>--This horrified the linearize-their-way-to-Yale yuppies in the audience, but it seemed like genuine wisdom to me. (That they were really losing people with this also attracted me.)<p>We'll see how it works in practice. I have a feeling Blank's utopia would be too expensive given the significance attached to education in the present age.

Because high school curriculums are much easier to plan when they are linear. At my high school the curriculums for English and Social Studies were also linear. Only in science did we get to choose which order we took Chemistry, Biology and Physics in.

We teach math linearly, because we follow the child's brain development.<p>numbers are quite an abstract things, and proportion is even more so. the next step, the percentage, add relative point of views too. you just can't teach that to a child that literally can't tell his right from his left.<p>Well, you can, but he won't really understand it and it is effort down the drain.<p>So I know that here we all are CS/EE/whatever, and probably knew more math then our elementary school teachers, but there is a reason to these steps, even if the said teacher never know about it.

Doesn't just apply to math. Applies to education in general. It's like someone one day decided that it's ludicrous someone might actually <i>want</i> to learn something to <i>do something cool</i> and decided to take the safer systematic approach to education. Only problem is that this systematic approach actually disadvantages those who want to learn, especially the ones with ADHD ('cause it's harder for them to shift focus to something they aren't immediately interested in).

Because time is linear?

Her rectangle problem is wrong. Here are four rectangles with the same area and perimeter:<p>x = 3, y = 6; x = 4, y = 4; x = 5, y = 10/3; x = 7, y = 14/5<p>The formula is fix x &#62; 2 (one side), let y = 2x / (x-2) (other side). Derived from xy = 2x + 2y.

I got dizzy reading that and gave up half way through. Stick to math and let someone else design your presentations :)

the root of the problems in the education system lie in its prussian derived methodology.<p><a href="http://www.johntaylorgatto.com/underground/" rel="nofollow">http://www.johntaylorgatto.com/underground/</a><p>compulsory schooling is stupid and wasteful, just like compulsory anything.

I love everything about it. The message, the presentation. Ugh if only I was taught this way, makes me jealous. This is how my calculus teacher in college taught. It was incredible compared to anything before that.