<p>Yes, but thats the point. An introductory statistics course isn’t about teaching you the fundamentals behind a normal distribution, etc. It’s about introducing you to the subject, teaching you how to look at and analyze a series of values, and being able to compare a single value to all of the others. </p>
<p>Introductory physics is nearly the same way. The calc in it can be watered down enough to teach you the general premise of it. For the most part, examples can be simplified down so that calc is not needed at all, even if the fundamentals behind it are based on calc. </p>
<p>The point is you need a certain amount of balance between the amount of math you need to fundamentally understand it and the math needed to simply teach it. If you really want to fundamentally understand physics or statistic, significantly more math than calc 1 is needed, there has to be some amount of balance to differentiate an introductory course to a theoretical course.</p>
<p>The intro stats I’ve had so far was a 1 credit class (that is, linalg and probstat together were 4 credits), and we spent much of our time in probstat on the prob part, so we didn’t spend much time on stat. Despite that, we were using calc in our stats. If you assume that a college student knows mean, median, mode, and standard deviation well, and knows what a normal distribution looks like, pretty soon you end up using calc, or going well out of your way to avoid it.</p>
<p>You can’t fully understand statistics without a good bit of calculus. The “real” statistics course at my university (offered by the math department) has probability as a prerequisite, which has two semesters of calculus as a prerequisite.</p>
<p>I have never seen calculus as a pre-req for any first semester statistics course (nor have I seen statistics paired with LinAlg) so your school is obviously doing something different. Your typical first semester stats class, which is essentially AP Stat, covers descriptive statistics, probability models, random variables, expectation, sampling, the central limit theorem, classical and robust estimation of location, confidence intervals, hypothesis testing, two-sample problems, introductory analysis of variance, and introductory nonparametric methods. All of which can be taught and understood (at a basic level) without calc.</p>
<p>I am well aware of the importance of calc in the fundamentals of statistics but still don’t think it is necessary form a basic knowledge of the subject (which in my opinion is all most humanities majors need). </p>
<p>Like cavalier, the true statistics course at my school requires calc 1, 2, and 3 as well as an advanced probability course.</p>
<p>I wasn’t talking about a first semester stats class. At my school probstat is generally taken sophomore year along with linalg and diffeq, each of which is a 2 credit class. Freshman take integrated course blocks of (first semester) calc for students who have some familiarity with calc bc, mechanics, and engineering of compartment systems, and (second semester) vector calc, e&m, and engineering of distributed systems. </p>
<p>I’m sort of surprised that calc isn’t a part of many intro stats classes, but I’m currently in an environment where the classes I listed above are the minimum that students have had, so all teachers take advantage of the fact that their students know calc.</p>
<p>Unless the college is a techie one, physics and statistics departments offer introductory courses that do not have Calculus as a requisite. Harvard has 4 statistics courses and two physics courses like that. The next level of courses seem to require multivariable calculus.</p>
<p>There’s a lot of applied Stat out there for non-math & science majors which requires no Calc background. Same goes for AP Stats. There’s some value to it, especially if you don’t have to understand the rationale for most of it.</p>
<p>The Calc background would give your appreciation of Stats an extra boost though, that’s for sure.</p>
<p>S said taking AP Calc BC really helped with his year long college calc sequence. Without it, he would have placed in a lower level course and would have had to take Calc courses that required two or three hours per week of additional attendance as a result. He also got elective credit for AP Stat, which was a nice surprise.</p>
<p>My daughter’s high school doesn’t even offer calculus, at least not as a course with a teacher and definitely not as an AP course. There is an option to take the course on-line, but the success rate with that approach is not encouraging. It is small public arts-focused high school, and kids have gone on to Harvard, Yale and other top colleges… obviously without the calculus. Whether they take calc at their chosen colleges or end up as arts/humanities majors I don’t know. I do know that my daughter can opt to take a course in symbolic logic or in statistics in order to satisfy the math/quantitative reasoning requirement at her college. I’m going to encourage her to take the logic course because I feel she will do well in it and that will give her a better foundation if she opts later on to take a more advanced math course. </p>
<p>I guess I see it kind of like CGM – I think a course that my d. enjoys is more likely to lead to her continuing to study more complex math than a course that kind of puts the nail in the coffin in terms of convincing her that math is something painful to be avoided. </p>
<p>We all take different paths. I think it’s silly to argue whether students should take calc in high school when it is not an option at many US high schools, or if it is, the teaching is substandard. It is a valuable course for students who are strong in math or interested in scientific careers to get early; for those who have more difficulty with the concepts, it might be better to teach alternate math courses that will help them get a better grasp of underlying concepts or which seem more directly relevant to their primary interests.</p>
<p>The problem with teaching a course to someone who finds it extremely difficult is that the person is unlikely to use and apply the concepts outside of class, and they will tend not to retain whatever it is they have learned once they are past the final exam. So it’s not much better than rote memorization - they “learn” but they don’t become utilizers of that learning.</p>
<p>Because I know my daughter and I know her history with math, and I know how she thinks. Calculus is out of the question for her when it comes down to it, without a lot more prep - she hasn’t even had trig. The choice I was referring to was between the logic course and stats – I think that she will benefit from the stats, but I think she will do better in the long run if she takes the logic course first.</p>
<p>Some colleges require calculus (or equivalent math) at college of all students as part of the core requirements, but this does not necessarily mean it has to be taken in high school in order to be successful at it. As for logic courses it would be nice if there was one that was offered in middle school, I believe that is about the time logic in discussions begins to seem impossible.</p>
<p>If you want to take Calculus during high school, my suggestion is a college calculus course at a local college/univerisity. First off, since it’s not part of your high school GPA, if you fail, you’re fine, and on the flip side, the harshness in a college math class is good preparation for what to expect in college. This (senior) year I took Calculus 1-2 at San Diego MESA community college, incredible experience, with a B first semester and C second semester (just FYI, second semester of calculus is going to kick your ass for those who will, be ready). In contrast to AP Calculus BC (since it’s the only comparable class), the college variation will be far harder than AP where the teacher may award credit for items that would be considered frivolous in a college environment. Calculus in the AP system IS too much for high school, only in the sense that AP Calculus is NOT adequate preparation for college math IMO, unless you’re incredibly smart, because a 5 on the AP Calculus BC test can be done with relative ease compared to getting an A in college calculus.</p>
<p>If it is taught propery AP Calc is definately adequate prep for college and in some cases can be more beneficial to a student than taking it in college. It is very dependent on the program, which is the ultimate problem since many of the HS programs are not very good.</p>
<p>I’d still say that the best math teacher/class I’ve had in terms of being taught/learning the material was my AP calc class, hands down. It is really case specific, and very difficult to make broad generalizations.</p>
So what’s your point, Cavalier? I’ve a kid who hasn’t taken any high school math beyond algebra II. “More complex” math at this point means trigonometry and precalc. She was accepted at Berkeley, U of Chicago, & Barnard with that academic profile, so it clearly didn’t trouble the ad coms at those colleges. </p>
<p>I personally think she should probably take the logic course and then take one of the stats courses geared to students in the social sciences. I think my daughter’s strengths lie in understanding language, and symbolic logic is a good bridge between language-based thinking and mathematical representation. I think her weakness in math is because she has been able to memorize a lot of formulaes, but she doesn’t really see the connections – more math courses would simply be more formulaes that she would commit to memory - she’d get decent grades but she would not develop an intuitive understanding or be able to apply the concepts outside of the classroom. </p>
<p>I happen to know something about the cognitive/neurological processes that go on with math, so I know that some mathematical operations are based on language-based thought (left brain), and others stem from spatial understanding (right brain). Learning your multiplication tables is left-brained; understanding the concept of “larger than” is right-brained. Lots of studies on this- for example, experiments show that if students who are fluent in 2 languages are taught in one language, they will have to be re-taught the language-rooted concept in the 2d language, but will transfer the spatically-rooted concepts from one language to the other without further teaching. </p>
<p>Higher math likes calculus relies more on spatial thinking abilitities. It’s largely about the study of shapes & movement, but it can be very difficult for many students to see the relationship between the numbers on a page and the shapes they represent. </p>
<p>Introductory math, including math taught through the level of algebra, is more language/numbers based. So it is fairly common for someone to be relatively good at math and then hit a wall at geometry or trig, when they can’t make the transition from thinking primarily with the left side of their brain to thinking primarily with right brain. If they are lucky enough to have a very patient and capable teacher - then they will be o.k. – but unfortunately teachers like that are rare. </p>
<p>I’d like to point out that not too long ago NASA lost a $125 million spacecraft because engineers delivered navigation information in English rather than metric units. See <a href=“http://www.space.com/news/mco_report-b_991110.html[/url]”>Space News - Latest Space and Astronomy News | Space;
That demonstrates the problem with too much math education and not enough common sense education --these were highly trained people who could do the math but not really think in terms of the practical implications of what the numbers represent. That’s why I think it’s important not to essentially commit the educational equivalent of the Peter Principle – pushing good students beyond their level of competency.</p>
<p>The point of this whole discussion, calmom, is that colleges look for rigorous and diverse courseloads, and calculus is the most rigorous math course offered in most high schools. Not only that, but calculus is a “gateway” course to other higher level classes. Your daughter may have done well in admissions with a weak math background, but most of her peers at the schools she got into will have gotten in with substantially more math under their belts. Her unique profile certainly not the rule, just like an unhooked applicant with a 1200 SAT getting into Harvard is not the rule.</p>
<p>Yes, but many of those peers will have substantially less foreign language and arts instruction. My d. took a rigorous curriculum, she just didn’t take a rigorous <em>math</em> curriculum. Her chosen college actually does not offer very much in the way of higher math – I’ve noticed that my daughter’s math SAT score is way below median for her school, but her writing SAT is above median, and I figure that her success in her college courses is going to depend more on her writing ability than her math ability. I didn’t take any difficult math courses in college - though I did take courses such as introductory computer programming – and my son didn’t take any math during his 2 years at a LAC, depite the fact that he did take calculus in high school. I assume that if he does want to continue math in college now he’d need a refresher course - so the high school calculus has essentially become irrelevant. </p>
<p>The point of this thread isn’t whether some students should take calculus – it seems to be one focused on whether all students should take calculus. Dadguy opened the thread with the opinion, “It saddens me to see students holding themselves back”, essentially criticizing those students who choose not to take the most difficult math track in high school. </p>
<p>I’m saying that, given the fact that many students are not going to become mathemeticians or scientists, there is no reason for them to “challenge” themselves in a subject that will be of little direct value to them when they can choose to challenge themselves in other ways.</p>
<p>Clearly, not all students should take calculus. Many tens of thousands of students don’t even go to college, and the vast majority who do go to college go to schools that are vastly less competitive than the 40-50 schools regularly discussed on CC. Applicants applying to top schools should, in my opinion, take calculus, along with the most rigorous courses available in all disciplines. Ever person I’ve know who has gotten into a top 25 school has done something closely resembling that.</p>
<p>As I noted before, my d’s high school doesn’t offer calculus and students have been admitted to top schools. This includes Harvard, Yale, Columbia, Swarthmore, Williams, etc. – and my d. was admitted to U. of Chicago (#15 on the US News list). Of course Calculus looks good on a college app – but so does AP Stats – and so does another demanding course of study for a student who chooses that. If anything, lack of individuation in course selection hurts students competing for elite colleges, not because there is anything bad about taking the same set of AP courses everyone else agrees is de rigour for the top colleges, but simply because it is hard to stand out that way. And when it comes down to it, a kid who gets A’s in other challenging, AP & Honors level courses probably is at an advantage over the kid who isn’t ready for calculus at age 17 and ends up with a C. </p>
<p>So basically, of all the reasons that a student might take calculus in high school, the claim that it is needed to get into the top colleges seems to me to be the least convincing. Obviously a prospective math major or matriculant to MIT would want that – but that simply isn’t the case for all students.</p>