<p>Any subject can be taught well, and any subject can be taught poorly. If a subject is taught poorly, only those students with an affinity for that subject and the willingness to do what is necessary to learn it on their own will succeed. </p>
<p>But if a subject is taught well, every student who is willing to work hard can master it (leaving aside those with true learning disabilities). It takes two: a competent teacher and a motivated learner. And a good teacher can motivate many students to become engaged learners. </p>
<p>Whenever I hear a person say they don’t have a “head” for a subject, I wonder: have they ever REALLY tried? I suspect that in a large number of cases, the completely honest answer would be “no.”
Take foreign languages for example. Learning a foreign language requires a lot of concentrated (and often boring) study. You have to memorize vocabulary, learn conjugations and declensions (in many languages, at least), and so forth. Do some people “get” languages easier than do others? Surely. But unless and until a student has put forth real effort, he or she can’t honestly say they can’t learn languages.</p>
<p>All of the tutoring kids seem to be getting these days has me concerned too. The short term benefits of most tutoring puts kids in levels they are not equipped to handle. If there is a real learning disability or a child missed some crucial concepts and just needs a bit of time to catch up, that is one thing, but to have a child tutored continually or just for higher scores on SAT/ACT, etc. places a child in a level they are not ready to handle down the road.</p>
<p>Math is way too easy in the k -12, that is why all exchange kids are placed ahead and usually do very well, despite of language difficulty. Insufficient background in math results in insufficient prep. in hard sciences like chem. and physics and inability to use analytical skills in these calsses. D. dealt with this while being SI for Chem. prof. in UG. She said that many kids are trying to memorize material when they need to apply math.<br>
SAT/ACT have primarily middle school math with a bit of HS school material. It is shamefully low level. Many advanced kids simply need to refresh it to do well.</p>
<p>Too easy for whom? I disagree. Many many people in this country will have no use for advanced math. If you are talking about college-bound, cc kids, that’s one thing. But there are many more people who dont need to kill themselves over advanced math. Many of the posters here sound like they think all kids should be on the same track, and that higher math is sacrosanct. On my deathbed I will not regret never taking Calculus.</p>
<p>Algebra isn’t advanced math, and is crucial for understanding your personal finances - something, I imagine, we can all agree should be universally taught. It’s also useful simply for building logical faculty, just like history has the side benefit of fostering understanding and memorization.</p>
<p>The actual content you learn isn’t always the end goal, it’s simply a means to an end. If it was, you could make the argument that everything you learn in high school is irrelevant. When does the regular Joe write 5 paragraph essays with introduction, theses, 3 body paragraphs and a conclusion? Toss out English. Or detail the exploits of Alexander the Great? Remove history. Does the typical employee run laps or play basketball during work hours? Let’s cut gym then too. Does the typical employee draw, calculate the number of electrons to balance out chemical compounds, or the force at which two trains collide? No. Cut art and sciences. The rabbit hole is much longer than you think.</p>
<p>IMO a college graduate should be capable of the basics of abstract thought. Algebra is the BASIC level of abstract mathematical thought, not the most difficult. Algebra is not advanced math. </p>
<p>College should not be for everyone. College is supposed to be HIGHER EDUCATION, not basic education. Basic education is what you do in high school. There are certain things a college graduate should be able to do. Every college graduate should be able to read and write at a certain level even if they are engineering or math majors. Every college graduate should be capable of basic abstract reasoning even if they are a liberal arts graduate. Algebra is basic mathematics and nobody should graduate from college without being able to master the basics of abstract mathematics.</p>
<p>Manufacturers in my state are screaming for workers that have a technical education - that is the ability to operates sophisticated manufacturing equipment - and algebra is a part of that. They are not really looking for people with 4-year college degrees; managers are easy to find.</p>
<p>My opinion on teaching math through algebra is that it’s pretty easy to do if you have a parent that’s very comfortable with math with the time, resources and materials to make math a part of the child’s life, starting when they are very young. This means talking about math and math puzzles regularly, keeping a white board around to draw diagrams or explain problems or puzzles, having a variety of handy math puns for entertainment and lots of math books - puzzles, textbooks, biographies, Aha!, etc.</p>
<p>Thanks for that link to “Lockhart’s Lament”. Lockhart does a great job exposing the weaknesses of our ladder-based math curriculum and makes the reader believe that there might be a better way of teaching math. (Although he doesn’t elaborate enough on how to actually implement that type of teaching, in a practical sense.)</p>
<p>I am a degreed engineer, who took more math courses than I ever needed, and for the most part, hated most of them except for speed math techniques I learned as a youngster. I have functioned in the “real world” of engineering just fine for 30 years, having never derived a theorem or created a formula on my own. I am considered an industry expert in a particular sector of the petroleum industry, a sector that utilizes quite a bit of mathematics. </p>
<p>With my two daughters, I have observed math courses and textbooks and teaching methods with keen interest. And I don’t like what I’ve seen, even at their challenging private college prep school.</p>
<p>I believe that the basics of Algebra, Geometry, Trig, and Calculus are important to learn. But our ladder-based curricula blow past the basics so fast that the average student never really does grasp the basics. Many of the dedicated ones still do OK with their grades, but don’t actually learn the basics well enough to use them in a practical manner later in life.</p>
<p>I am in the group that would like to see math education overhauled, such that the basics are emphasized more than simply taking “higher” level math courses. I am also very much in favor of teaching math courses with more real world applications.</p>
<p>Coming from a recently graduated high school senior, The math is easy if you have the will to learn it. I’ve seen it my entire four years of schooling. People fail all the time because they think it doesn’t matter. If the math is coming easy to your child then why complain? Congratulate and move on. It just means your child is smart.</p>
<p>I think I’m on one side of this argument when we’re talking about algebra, but I’d be on the other side if we were talking about calculus.</p>
<p>I had a thought sparked by this:
I think this is all true, but it also suggests that one student might have to put in a substantially higher investment than another in order to get the same return (i.e., fluency in the language). Obviously, this is true for all subjects, but my belief is that it is more true for some subjects than others–my observation is that some people have a clear “knack” foreign languages, and I think the same is true for math. So, you might reach a point at which the return (mastery of the topic) is not worth the investment. Personally, I hit this wall for both math and French my first year of college–so after that, I took other courses that I like better and that were “easier” for me to master.</p>
<p>“Too easy for whom?”
-At every level, in every grade 1 thru 12. It does not prepare kids for college at all. Many, including top students from private schools have to seek tutoring.
Also, many top kids are simply bored and become not interested in class that should be very exciting if taught properly.<br>
Algebra should beging in 5th grade and geometry, trig. should start in 6th, all taught as separate subject. I am talking about math for all as a general program, not for selective group of advanced kids. This group can seek more advanced math privately if desired.</p>
<p>To me, the main problem in the US is that the best way to teach math doesn’t fit with our culture. The best way to learn math is by rote. The US is opposed to rote; we value creativity and understanding of concepts. Our system pays off for the people who are capable of understanding math well, as seen in the success of our people in the actual sciences that use math. But it is terrible for teaching most people because most people can’t understand the material very well. </p>
<p>One could also say the US problem is stubborn adherence to a belief system in which each person is deemed capable of understanding and which believes each person should be taught to a level of understanding. But then the US is a country of believers. </p>
<p>A typical US exam will test kids on applications of the material they’ve learned but in a new and different way. Many tests, particularly as you move higher, focus on what you don’t know to see if you understand well enough to apply your learning in a new way. Other countries teach you material and test you on your ability to recite back that material. </p>
<p>My kid saw this in a top Chinese high school - where she went for a semester; the math classes functioned at our BC Calculus level but all of the learning was memorizing material which was then tested. They learned specific problems and how to solve them and were tested on those problems. That system generates a lot of people who are good at doing the raw processes of math. It also creates people who know how they are supposed to learn: if a new problem comes up, someone generates a solution and that solution is then spread widely and copied by rote. Their system assumes most people are capable of learning but not necessarily of understanding and that a few creative people will drive the entire mass forward as long as the mass has the basic tools.</p>
<p>^yes, some immigrant communities have thier own schools to primarily fullfill gaps in k - 12 math and science education ans they realize ridiculously low level of this classes in comparison to their respective countries. They also realize that math is not just a knowledge of fe math facts, it is a tool to develop analytical thinking.</p>
I think what Lergnom just posted suggests the opposite of this–that rote approaches to education don’t really promote analytical thinking. We certainly saw this with some kids in my D’s class, who had piles of rote knowledge (about history, for example), but couldn’t really apply it in an analytical way. Generally, these were Asian kids who had acquired the rote knowledge in an outside program. Perhaps there is some happy medium, or perhaps different approaches are needed for different kids.</p>
<p>^is not supported by at least one known to me fact that Asians are way overrepresented in Med. Schools accpetance, more so in the top ones. They need excellent science background to accomplisht that. It is not possible without usage of math and superior analytical skills.</p>
<p>In addition to this two memories have stuck with me in the years since I read this book. During one of the American lessons the PA system comes on and interrupts the class. The Japanese teachers listening to the video were horrified, classroom time is sacrosanct and would never have been interrupted except for an emergency. The other thing I remember was that the Japanese classroom had a long blackboard and at the end of the time the entire day’s lesson was on the board. In contrast, the Americans were using overhead projectors so that they could only see a piece of the lesson at a time. (They are probably using SmartBoards now with the same problem, though presumably you can backtrack if necessary.)</p>
<p>Some medical schools do not even require calculus as a pre-med prerequisite (and calculus-based physics is not generally required either). But that could perhaps lead to things like this:</p>