<p>Thank you!</p>
<p>Could you comment on my post 79? ^^</p>
<p>again, thank you</p>
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<p>Well, first of all, MIT doesn’t really take your choice of intended major seriously. I bet a third of the people I went to MIT with probably said they were going to major in physics; most ended up in engineering. So declaring as a math major won’t hurt you. </p>
<p>In terms of what will impress Harvard, probably post-AP classes aren’t even enough. You can only really impress them with the math contests. My impression is that people who they select as math people probably have made MOSP. There are probably only 30 of these people graduating every year. However, USAMO winners do well in Harvard admissions–they probably aren’t taken for their math ability, but expectation that their skill in math will help somewhere else like economics or physics. </p>
<p>The ultimate example of a post-AP class not helping in admissions is a kid who got an “A” in Math 55 at Harvard, which I hear is an incredibly hard and advanced class. He got rejected at one or two top places (Harvard and/or MIT, I think.) Later in his senior year he made MOSP, but it wasn’t on his application.</p>
<p>The top schools do placement testing at start of freshman year. They don’t really care what you took in high school.</p>
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<p>This was the philosophy of my son’s private school and in retrospect, I believe they were very right. There were a handful of kids who were on the fast track and did very well. They all finished BC Calculus by 11th grade and the school brought in someone who taught them whatever comes after that math-wise. All of these kids, btw, got into top 10-15 schools.</p>
<p>But there was another group of kids whose parents who pushed the school to let their kids into more advanced classes when the school thought they weren’t ready. A few of those aren’t doing so well in college…one’s majoring in engineering right now and on academic probation.</p>
<p>I look at it this way - if the school has a high pass rate on the AP exam, then they are probably doing a good job screening the kids who are on the fast track as well as doing a good job teaching the college-level material. If, OTOH, kids are taking AP calculus and the school has a low pass rate on the exam, then those kids are being fast-tracked for the wrong reasons. IMHO, everyone who takes an AP class (no matter what it is) and get an A or B in the class should be able to pass the exam with a 3. If not, then the school is either doing a poor job of screening kids or they are doing a poor job of educating them to AP standards. Let’s face it…not * all* kids are ready for college level material in high school. When kids are taking AP classes and can’t pass them, then the school is probably watering down the class.</p>
<p>Other than a handful of kids who are math superstars I don’t see a need to fast track kids just for the sake of doing it. I believe one of the reasons parents push their kids in this area is because they think it will help their chances of getting into more prestigious colleges. Of course, it only helps if they get a good grade in the class and it helps even more if they can pass the AP exam with a 4 or 5.</p>
<p>collegealum314 - too true! My son’s first grade teacher fought for months with the principal before he was finally allowed to jump ahead in math to 3rd grade. Then when he got to second grade it was as if that year had never happened. We ended up gritting our teeth about math in school mostly and letting him explore topics at home. I considered homeschooling him altogether often, but he wanted to be with his friends.</p>
<p>There are very few schools where you apply committed to a particular major - as far as I know even at Harvard you could major in math and start with Math 1. (Beginning Calculus)</p>
<p>I don’t find that the data supports the notion that “many” students are being pushed too far ahead in math. But I would probably agree with the use of the word “more” instead of “many”.</p>
<p>About 250,000 seniors in the class of 2011 took either AB or BC calculus (for context, this is less than 10% of the total senior class, and about 15% of seniors taking the SAT). About 75,000 juniors in the class of 2012 took either AB or BC in 2011 (about 3% of the class).</p>
<p>These fractions are small; however, the total number of students taking AB, for example, is almost double what it was 10 years ago. Quite a few are not prepared: about 33% have failed the AP exam (got a 1) for the last two years in a row.</p>
<p>With all due respect to our math-happy community, teaching Calculus in high school is a waste in my view - Calculus is rarely used by itself but it is more of a tool for other subjects (like most math). At the high school level at least, there’s a lot more useful math that can be taught that would be handy in lots of different majors (statistics, probability, operations research, more / better geometry, numerical analysis, discrete math, and the like).</p>
<p>Just a personal view…</p>
<p>Some of you “old timers” on CC have heard this. Our MS, like many others, offers an accelerated math track to 8th graders. This was offered to our daughter. My husband and I declined the offer. We were the first parents EVER to do so. DH is an engineer and felt very strongly that a good foundation for math was essential and felt that accelerating was not necessary.</p>
<p>Just FYI…our daughter graduated from college with two bachelors degrees…one in engineering and one in biology. Clearly…her lack of acceleration in math made NO difference. Oh…and yes…she did this on the four year plan.</p>
<p>Turbo…my husband completely agrees with you (he’s an engineer). He says…colleges will likely want you to take calculus…and do it their way!</p>
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<p>So you can learn calculus and you can learn applications of calculus. Right now, the AP curriculum covers both, though the applications might seem a bit theoretical - for example, calculating extrema using derivatives, or the volume of some object using integrals. Now, maybe you think this covers too much, that there needs to be more depth - you’re going to have to eliminate the applications, because it’s kind of hard to use applications without knowing the calculus behind them. But if you want to cover more applications, then you’ll have to sacrifice some depth.</p>
<p>My D attended a GT magnet for middle school. All students took algebra in 7th grade. About a fifth of the students were invited to take geometry in 8th grade. The rest took “advanced” algebra. At the time I was surprised D was not offered a spot in the geometry class, but just went along with school recommendation.</p>
<p>It ended up to be a good decision. The strong algebra background served as a great foundation for high school math and science classes. She could focus on the higher level concepts in those classes because her algebra skills had become second nature.</p>
<p>D’s final class in high school was calc AB. She did fine on the AP test, but is starting with Calc I in college. Her dad and I figure that a strong calculus foundation is as important for her engineering studies as a strong algebra background was for her high school courses.</p>
<p>Starting off in Calc I in college – as most students do – is not going to hold her back from academic opportunities.</p>
<p>See, I’ve worked as a Civil, Computer, and Human Factors engineer (with degrees in all three) surrounded by Electricals and Mechanicals also. Never ONCE has anyone been stumped in Real Life ™ because they forgot how to integrate by parts. At the same time, Statistics comes up on a regular basis, and my arsenal of Operations Research methods (anything from Integer and Linear Programming, Traveling Salesman, MinMax, etc) also make frequent appearances at work. </p>
<p>Teaching raw Calculus is like the US Naval Academy teaching Midshipmen how to navigate by the stars. Sounds like a great idea, except… In practice, an Engineer using Calculus to solve a problem is wasting valuable company time (why did we get a site license for Mathematica again?), and a ship without functioning GPS has more things to worry about than where they are :-)</p>
<p>My personal theory (or conspiracy theory) on why Calculus is such a pain is simple. Calculus, more than any other subject, is a profit center for any university. Everybody needs it, let’s just make it a wee bit too difficult, chi-ching…</p>
<p>Turbo…our daughter really didn’t love Calculus but she LOVED (and did better in) Differential Equations.</p>
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<p>But then isn’t statistics one of the things that uses calculus as a tool?</p>
<p>Also, understanding what a derivative and integral mean conceptually is certainly useful in a lot of contexts. For example, people get confused all the time about claims that some type of job will grow in the future, without realizing that the number of jobs is small and will still be small after the growth.</p>
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I think the Prof was probably talking about “great mathematicians” rather than the rest of us mere mortals. I have an MA in math and a PhD in physics, but I am in no way a “great mathematician”, in fact, I don’t even consider myself a mathematician in any sense. Lots of people can learn to sing, far fewer can be Celine Dion.</p>
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<p>The biggest problem with not doing calc in high school is that you will take it in college with people who already took it and are in it to get an easy “A.”</p>
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Perhaps your sample is too small. S spent a lot of painstaking time doing large problem sets for Calc AB. He didn’t do all that well on the in-class exams, but he aced the mid-term and passed the AP with a 5. When I took Calculus I and II in college, I spent many, many hours doing problems so that I would understand what I was doing. </p>
<p>Frankly, you don’t know what you are talking about.</p>
<p>Are many middle/high school students being pushed too far ahead in math?</p>
<p>I believe the wrong question is being asked. Math and most of the STEM fields are ones which one might call building block fields. What you learned yesterday becomes the block upon which you must stand to learn todays lesson. Many other fields are not this way to the extent the STEM fields are. In history, it doesnt matter how well you understood the feudal system to understand what happened during World War 2. However, you need a thorough understanding of addition to understand algebra. And you need an understanding of algebra to understand calculus. And you need calculus to understand differential equations.</p>
<p>I believe we are letting students progress without requiring them to have the depth of understanding to move to the next level. Learning the subject just enough to pass the next test is a sure road to ultimate failure in math. The same issue exists with passing students with middling grades in the subject (i.e. B or lower grades given that most high school classes include homework grades that are usually somewhat inflated). They lack a thorough enough understanding to move on.</p>
<p>So the real question should be Are focusing enough on making sure the students really learn the subject matter? I believe the answer to that question is NO. </p>
<p>My son would help some of his classmates with the math. Listening to them, it was obvious that they were not prepared to understand the lesson of the day as they didnt sufficiently learn yesterdays and the day before thats lessons. A couple of those kids dropped out of the calculus class as to not jeopardize their high GPAs as they were looking to go to top tier schools (including one who ended up going to Harvard).</p>
<p>I also believe that a good math education begins in early elementary school. My sons second grade teacher blew me away when she said that math at that grade level (i.e. Addition and subtraction) was just a matter of memorization. I doubt she knew much more about math than what you needed for her class. You need to know what I like to call how to build up numbers and how to break them down. Without going into this subject in depth (which is a pet peeve of mine) lets just say that good mathematicians get their start early, and so do poor mathematicians.</p>
<p>Another pet peeve of mine is those students that stop at calculus. Why take calculus? The whole point of learning calculus is to use it; and you use it in differential equations (DEs). If you dont need to understand DEs, then you dont need calculus. However, engineering (and many of the sciences) is built on understanding and using DEs. Some learn DEs enough to see where the formulas used in engineering are derived and then never use DEs again, only the formulas. But they need to understand how the formula was derived to know when to use it correctly. However, in my engineering career I used both the cookbook formulas as well as going back to the basic formulations to derive specific solutions to the problems I faced. So, IMHO, having a good understanding of calculus and differential equations is critical for an STEM type major. Pushing ahead without totally understanding the lesson of the day is useless in the long run.</p>
<p>So, lets push our students to UNDERSTAND the math we are trying to teach them.</p>
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<p>You hardly need calculus to understand that concept!</p>
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<p>Some stuff requiring formula work (continuous distributions) there’s a bit of calc there, but nothing heavy. Maybe a bit in multivariate analysis, but again, nothing heavy. Mostly formula work and evaluating integrals, but again, this is in college. </p>
<p>In practice (as Mrs. Turbo’s former statistician career is any indication) the majority of non-research work involves using stuff, not coming up with new stuff. </p>
<p>My ‘beef’ so far has always been with Calculus. I took Calculus in my home country in HS, in college, and some here. Back home, Calc was taught largely at the ‘Jeopardy’ level, meaning, 3 hour exam for 3 problems, and if you knew the answer you were out in 30 minutes, if you did not, 30 days would not help you. In the US, tests are more ‘breadth’ than ‘depth’ (which is good) but there is not as much good teaching as I would have expected. Some profs are very good, some are very nasty, and some are very easy. This wide variation in skills tells me that not a few of the people who teach Calc in college should not be teaching, but that’s tenure for the rest of us. </p>
<p>In my humble view, the only practical use for Calculus is either as a profit center or as a weed-out.</p>
<p>OK, it looks like we have closure. The OP asked if HS students are being pushed ahead too quickly re: preparation for college Calculus … and posters respond that Calculus isn’t required in “real life.” So the answer to the OP’s question is obviously “No, because one can’t be pushed ahead too quickly in coursework that has no application.” Wait, that doesn’t sound right.</p>