<br>
<br>
<p>Some of us have taught it too.</p>
<p>Give kids a love for it when they’re really young and it’s far less work when they are older.</p>
<p>Redpoint:</p>
<p>I don’t think people are forgetting about those who cannot pass a particular course. I think that what people are saying is that if a person cannot pass Algebra then perhaps they are not college material. Our country is the only country which insists that anyone can go to college. This is affecting our ability to be competitive in the world because our brightest students are not being challenged out of some misguided notion of fairness.</p>
<p>What does it mean for a subject to be difficult anyway? One kid will spend 20 minutes working through a concept and think, “That was easy.” Another kid will give up after 10 minutes, thinking “This is too hard, I’ll never get it.” </p>
<p>There’s something to be said about perseverance. Creating a cultural attitude labeling an essential subject as difficult doesn’t help anybody.</p>
<p>
</p>
<p>What if that person was a fine arts major, or a theater major? Or are you one of those STEM-uber-alles types?</p>
<p>Proud patriot: I think the problem is when Algebra is a barrier to passing high school. That is an important part of the article we are discussing. Not having a high school degree is a tremendous liability. Although that is not important for those on cc, it is a huge social problem. (Im not saying everyone should just pass high school without standards. What is important is giving those whose formal education stops in high school the education they need) College and the college-bound are another related subject. And I completely agree with pizzagirl. One can have trouble with math and still be quite good in other subjects. My h has a phd in Physics and can do advanced math in his sleep, but still doesn’t know the difference between were and where when he writes. Some of you are being myopic. (especially the bit about trigonometry in sixth grade. I’m still not over that one)</p>
<p>
Would you let a math major go to college without basic writing skills? Don’t need to be able to write in complete sentences or coherent paragraphs to do a problem set. </p>
<p>I think every educated person should be able to do algebra. If you don’t understand algebra, you don’t understand arithmetic. Feel free to disagree with me, but I think that most people should be able to solve everyday arithmetic/algebra questions. (I would not say the same for trigonometry.)</p>
<p>Again, there are two different subjects. What is expected of high school graduates vs what is expected of those that are college bound.</p>
<p>
</p>
<p>This does not mean that someone not going to college for a bachelor’s degree has no use for what is ordinarily high school level math in the US (algebra, geometry, trigonometry), or other high school subjects. Consider the carpenter determining the correct lengths of wood to build an A-frame, or someone measuring the correct length of rope or band to wrap around a cylindrical object.</p>
<p>A slightly more advanced problem involving physics would be to understand why a small person who cannot deadlift much has trouble loosening the wheel nuts/bolts on his/her car to change a flat tire. Of course, once the problem is understood, the solution involves another subject commonly taught in high school, physical education.</p>
<p>Here’s the problem. If children in other nations can learn higher level mathematics at a younger age, and learn it well, mind you, then why can’t our children? There is no inherent intellectual barrier between children of different races - any such barrier erected is simply a construct for an excuse. If you say that it is harder for most of our children to learn algebra at an early age, then why can children in other nations do it? </p>
<p>But, transcending algebra, calculus has been watered down in our schools - this is a fact. It’s no longer as rigorous as it used to be. If our parents and grandparents could learn calculus with the delta-epsilon concept of a limit, understand continuity, etc. then why can’t we? We are not becoming less intellectually ept over the generations. It’s just that our societal attitude has changed. We seek to educate the lower quintile instead of focusing on the average. So teachers water down versions of their classes so the lower quintile children can “get” the material. What about the other four quintiles? They sit bored in class and do not cover the more advanced concepts they need for higher level classes. Everybody suffers. Why not just educate at the level of the average child? You ask, who defines average? Well, nobody does. Grade inflation runs rampant in our high schools today. This is an era when most of the class is not satisfied unless they get an “A.” Do you know what an “A” was conceived for? “A” means that the student demonstrated an outstanding mastery of the material. “B” means a good mastery. And “C,” well, “C” means satisfactory performance - your average joe. Thus, you know you’ll have achieved your goal of making a fair class when your average test grades are a C and you have a bell curve. You’re probably shocked by this statement, but that was how it should have been from the outset. Today, the bell curve is heavily skewed towards the “A,” where teachers hand out A’s liberally. </p>
<p>And @redpoint, I do not consider myself to be “brilliant” at math. I understand calculus enough to where I fairly deserve a “B” in the class. But the tests were so simple (read: plug the numbers in and crank the answer out) that almost everybody - even those who knew the material minimally compared to me - got an A. Very rarely in the real life will you just have a problem in front of you where you just have to plug the numbers in. </p>
<p>Also, I have Spivak’s Calculus book right now and am going through it. It’s supposed to be an introductory calculus book, but for exceptionally bright math students (which I am not), so I think it is rather thick. The language is easily understandable, but some of the concepts are more difficult to grasp. It’s proof-based and really should be named “An Introduction to Real Analysis,” as the author even said.</p>
<p>I am not one of those STEM at all costs people. I am a very pro arts person. However, I think that in order to graduate from college a person should be both literate and numerate. Expecting someone to pass algebra is not expecting them to discover new mathematical truths. It is algebra, the very lowest level of abstract mathematics. People who cannot pass algebra are not college material. They are not bad people. They are not useless people. They are simply people who are not college material.</p>
<p>For those that oppose a minimum requirement for math: what is that minimum requirement to graduate from high-school?</p>
<p>I think being able to understand unit prices in grocery stores is useful. To understand the interest charged for credit cards, car loans, mortgages is useful. To understand compound interest - a professor that I used to work for routinely lamented that his students had little to no understanding of compound interest - and he was teaching math and science majors.</p>
<p>How about conversions in measurement systems? Minimizing shipping costs (some shippers charge by weight and linear dimensions). Computing costs for rental cars where some charge by time and others charge by time and mileage.</p>
<p>I wish everyone knew algebra so that we wouldn’t have to fill out those really stupid tax forms that assume that you don’t know algebra. Yeah, I know - software will do all that stuff now but it is nice to be able to understand what is going on so that you can plan.</p>
<p>How about calculating what you will need for retirement? Figuring out the NPV of an asset? Determining whether it’s worth it to buy a washer/dryer or go to the Laundromat? Changing the size of a recipe?</p>
<p>There are times when someone asks me a question and I have to figure out their level of understanding. On TV, the usual reply is “It’s complicated.” - maybe I should start doing that. It takes some effort to dumb things down. Some things shouldn’t be dumbed down.</p>
<p>High school is basic. All people who graduate from high school should be able to read, write and do basic mathematics. Algebra is basic mathematics.</p>
<p>b@r!um - Have you ever read a high level math paper? It highly depends on the author’s writing ability and general communication skills.</p>
<p>Concerning the original topic I would guess that we as a country need to recognize that:
- Not all kids will go to college. Nor should they. Neither the existing economy nor the aptitude of all kids will allow for that.
- For the kids who don’t (or shouldn’t) go to college, there still needs to be a set of standards so they can still be functioning members of society. A non-college track doesn’t mean jettisoning them. It means preparing them for a post high school life that likely will still require many of the subjects they still teach today.
- It is irrelevant that certain subjects don’t have a direct application in the real world. What school really does is to teach the student HOW to learn and how to approach new subjects. This is what the real world will demand regardless of educational attainment.
- It seems to me that US education is not broken at the top. It is broken at the bottom. And I place the blame squarely on parents of those kids who refuse to take education seriously.</p>
<br>
<br>
<p>Parents don’t have the tools.</p>
<p>If I were in control, I think that it would be just as important to teach the parents so that they could help teach the kids.</p>
<p>In our household, I talked about all kinds of ideas when the kids were young. Math, physics, chemistry, literature, music, news, politics, business, etc. They might not understand but they could ask if they wanted to know more or go look for information by themselves. I’m sure that the vast majority of parents here do similar things - perhaps with a different selection of topics but in a way that exposes children to the real world.</p>
<p>There were many, many times where the kids didn’t get it. I asked questions too - would you do this or that, why did this person do this - questions to see what their level of understanding was or if they could take an educated guess. This stuff isn’t that hard to do in a family dinner setting but I can’t imagine doing this in a classroom with a huge variety of experiences unless the classroom was somewhat uniform.</p>
<p>I’ve slacked off in every Math class till Calc III and gotten As and Bs. I think it’s too easy if anything…</p>
<p>
This is a much too general statement.</p>
<p>Most colleges offer remedial courses for those who did not “get it” very well in high school. Plenty of students who apparently were not “college material” survive the remedial courses and go on to survive college as well.</p>
<p>I agree that colleges offer remedial classes and those are available to students who did not pass algebra in HS. However, if they cannot pass algebra in college, even after remedial classes, they are not college material. Algebra is not advanced math.</p>
<p>Even to the average math student, there is nothing earth-shattering about algebra. Concepts are logical, if you take the time and effort to learn. Algebra is something you should have mastered by the end of high school. We start learning basic algebraic concepts in middle school, for crying out loud!</p>
<p>I’m not trying to be arrogant and rude and I apologize if I offended anyone by saying that trig or math isn’t hard. I am sincerely sorry for that. </p>
<p>My stance is the same as ptontiger’s : if the rest of the world can do it, why can’t America? I sincerely believe that America does a terrific job underestimating its children. Obviously people with genuine disabilities are an exception and there should be alternative programs for students like that: different tracks that give such kids other options.</p>
<p>But for ‘normal’ kids, instead of having a knee jerk reaction and saying that stuf is too hard, we need to determine the norm- what kids are actually capable of if they apply themselves. Kids do poorly now for many reasons, some which are legitimate and some that aren’t. Most kids my age care more for Facebook and their social life than they do school. Are low test scores then a reflection of student’s true abilities? I don’t think so. </p>
<p>Someone should do an experiment where they enforce strict but reasonable standards for passing/graduation at a school and provide students with lots of helpful resources and then see if kids do better or not. I think that would be very interesting. </p>
<p>OT- aren’t Nys requirements for graduating: Apgebra 1, Geo and Algebra 2 + bio and another science and 4 years of English/history and electives ? </p>
<p>I think that’s a bit excessive, especially because the curriculum gets watered down and trig isn’t for everyone.</p>
<p>Normal math sequence at the high school level does vary.<br>
In my area, most students took Algebra 1 in eighth grade, and so, the normal high school math curriculum is:
9th Geometry
10th Advanced Algebra
11th Precalculus and Statistics
12th Precalculus with Discrete Mathematics</p>
<p>The difference with Honors level math is that they do Precalculus in one year and take Calculus. </p>
<p>I took Calculus 1 and I have never used it since. Most college grads don’t use much beyond Advanced Algebra, trigonometry, and statistics.</p>