<p>This is something I’ve been thinking about for a while, but I wasn’t really sure who to ask. Parents on CC seem to be pretty knowledgeable, so I thought I’d try here.</p>
<p>I guess the title says it all, why is math so calculus-focused? It seems as if once you start learning Algebra 2, everything taught seems to be focused towards the final goal of learning calculus. The only mathematics AP class offered is calculus. And even when you finish single-variable calculus, there’s multivariable, and then differential equations, and I think a lot of times, even real analysis seems to be brought up before people are exposed to other fields of math.</p>
<p>But I’m not sure what’s so great about Calculus, especially when there’s so much other really interesting math out there. And the impression I get is that teaching Calculus makes it incredibly easy to continue with the idea that math is just about applying various formulas. And things like evaluating limits or the fundamental theorem aren’t taught rigorously at all. I don’t understand how the teaching of a field in high school can be so different from what math actually is. I feel like it would be easier to teach a more accurate representation of math by teaching discrete math, or algebra? At least the ideas in those subjects seem to lend themselves more easily to proofs. And I think students should at least be exposed more thoroughly to those, and other fields of math. But except for computer science and math majors, I don’t think most people are probably even aware of their existence.</p>
<p>I did ask a few people, and the only reason that came up was that calculus is important in engineering. It seems really weird though that engineering could distort the teaching of math this much.</p>
<p>And I guess I might be a bit biased in my own preferences / the fact that I’m a math major, but this is still something I’m really confused about.</p>
<p>I’m not a parent, but I’ll try to answer. Calculus is important because it’s a fundamental branch of mathematics. To have some basic knowledge of and familiarity with math, one must know some algebra, some arithmetic, some geometry, and some calculus. Of these subjects, calculus has the highest prerequisites, so the appropriate time to teach it is at the end of high school (or in early college.) </p>
<p>Calculus is also particularly relevant when it comes to modeling. This is really where most people actually use math, so it’s very important to learn calculus. It’s not just a matter of engineering - calculus is crucial for every scientific field, plus many other areas like economics, etc…</p>
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<p>This isn’t quite true. There is an AP statistics class. </p>
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<p>It depends on what we’re talking about here. Can you give us some examples of the other interesting math branches that you think should be studied in high school? </p>
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<p>To study these concepts in a rigorous way requires a ton of math experience and aptitude. Such classes exist at the college level for the most talented math students - those who will become pure math majors and so on. It doesn’t make sense to teach these concepts rigorously to the majority of the students. It would take too much time and few would find the ideas interesting or useful or necessary.</p>
<p>For math majors like yourself, who are actually very interested in math, these classes definitely do exist. At my college there is an introductory analysis sequence that freshmen and sophomore math majors follow. It’s indeed formal, rigorous, and proof-oriented. But it’s only for a few people - typically a only 15-20 students complete the sequence. The thousands of other freshmen who are going into different areas stick with Calculus 1,2, diff. equations and so on, since those are much more practical classes for them. </p>
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<p>The goal in high school is not to teach students what active research mathematicians really do. It’s just to acquaint students with some useful mathematical notions, that they may need later on in whatever their field of study may be.</p>
<p>I think you have a good point, particularly because the inevitable path (higher math=calculus) probably deters a lot of students from continuing with math studies. </p>
<p>Maybe, especially in this digital age, exploration of different math topics and applications would be beneficial and encourage more students to continue to study math and science.</p>
<p>I agree shravas, having come through a number of the higher-up math courses. There are a lot of other interesting things out there which could be introduced at the high school level. </p>
<p>It seems to me </p>
<p>1) Students have to cover so much in the general sequence of Geometry, Algebra, pre-calculus, calculus, that there isn’t much room for anything seen as “extraneous” to that. </p>
<p>2) the needs of engineering, science, and economics for calculus really do dictate the curriculum to a great extent. Few majors besides mathematics itself need these other things - or at the very least, they survive without them.</p>
<p>3) the high school math teachers probably majored in secondary education. If they majored in math education, they might have taken some junior/senior math courses, but if they struggled through those they might not be comfortable actually trying to teach the material. It’s an unfortunate fact that many teachers are teaching outside their areas of expertise as it is.</p>
<p>4) Much of our society sees “math” as a subject for geeks. One about which it is perfectly acceptable to say “I’m not good at that.” (When was the last time you heard someone admit they couldn’t read?) There would be plenty of parents who would have s*&^ fits if a school district spent money on courses seen as “egghead classes suitable for only a very few”, when schools are cutting funds for music, art, and so on. Attempting to include such material in the REQUIRED course would lead to even greater outcries.</p>
Not the op, but Abstract Algebra has a lot of interesting topics, many of which could at least be introduced at the level of the high school student.</p>
<p>The thread linked above has tons of discussion from math-sophisticated people of what an alternative bridge between basic math and college math would be. My impression is that math departments are full of people who agree with shravas, and lots of efforts are under way to de-emphasize calculus. But there’s a huge weight of tradition and curriculum design around calculus, and that doesn’t vanish easily. </p>
<p>Calculus definitely has its fans, although some people love it for its usefulness (and I will add that to my mind they do a poor job of explaining just what is useful about it), and others love it for the beauty of its method (a position that tends to draw howls of protest from “usefuls” and math-phobes alike, and does not seem to be reflected in all or most actual calculus courses). There is lots of agreement that introductory calculus courses don’t always serve their students well, whether they are interested in math or not, but a lot less agreement on how they should change to do a better job.</p>
<p>Discrete Math and Lin Alg would be very useful classes for high school students interested in higher math but not necessarily calc. Comp Sci majors have to take both at many colleges.</p>
<p>Great question. I’ve been wondering about that too, as it is practically a requirement now for kids to take Calculus in high school. I suppose it’s not really a requirement, but so many kids feel the pressure to take it in high school.</p>
<p>Calculus can considered as the study of variations. Hardly anything in nature, in the long run, will act in a linear fashion. Therefore, to study these subjects one needs to understand how they vary, ie. calculus. Study includes the ability to model real world situations. </p>
<p>Therefore, calculus is a tool, that’s all for most people who study it. If you are not going to need this tool, don’t study it. Problem comes in that a lot of people will not know (because they don’t always have a full grasp of their intended field of study) whether they will need it or not. Therefore, why limit yourself. Take the calculus. </p>
<p>Differential equations is just putting the calculus you learned to work. Something like doing algebra after learning arithmetic.</p>
<p>I have a friend who is a Mathematician and university Professor who believes no calculus beyond Pre-Calculus should be taught in high school - even for those who want to study Math in college or become engineers. He actually told me that taking calc in high school is a waste of time.</p>
<p>A friend of mine who teaches at a UC said that, for biology division at least (biochem, etc) they are considering replacing the calculus with advanced statistics types of courses. Of course, how long until actual implementation is anyone’s guess. Curriculums do seem to be very calculus-focused, is it now some kind of “bar” for college evaluation and admission?</p>
<p>Coincidentally, my daughter, who is in Grad school just told me yesterday that she wished she had taken a stats class in HS instead of pre-calc. She’s in an International Education program and said that a lot of the information they are learning and some research she is doing has statistics in it. Our school only has AP stats - no regular Stats, and the pre-rec’s are rigorous so generally the students that are eligible for it would go to Calc instead since that seems to be what Colleges want.</p>
<p>Interestingly enough, high school competition math has very little to zero calculus, but does have discrete math topics that aren’t covered in school math curricula at all, like number theory (including modular arithmetic), combinatorics (counting), probability, etc. . .</p>
<p>I don’t believe there is a one size fits all math program for everyone, but I think the typical high school math curriculum, from Algebra through Calculus (with the addition of DE and LA if you get there), is designed to deliver the basic building blocks while being as broadly applicable as possible. Along the line math courses will touch on lots of areas of math in very basic ways. </p>
<p>To a certain extent I think the curriculum is designed to be necessary but not sufficient for the largest number of quantitiative fields.</p>
<p>My degrees were in technical areas other than math, but in almost everything I studied (incldidng courses in physics, EE, computer programming, chemistry, and economics) there was some application for single and multivariable calculus, differential equations,or linear algebra. And that includes the probability and stats courses I took. And I think those are the general courses included in first year college math.</p>
<p>For me, in my electrical engineering program for example, I ended up having to take courses in z-transforms and difference equations, as well as numerical methods. Somewhere in my high school curriculum they saw fit to teach me series and sequences which came in very handy. But to actually specifically know how to solve a difference equation? In all likelihood many engineers went through their entire couse of study not even really knowing what one was.</p>
<p>On the flip side, and fully admitting I know very little about these subjects, I don’t think I ever had a need for topology, set theory or group theory, except in a very simple or abstract way that I didn’t even recognize. Not so if I was a math major, I’m assuming. But I still think all math majors need to know calculus. At least I’m sure they all do.</p>
<p>My first gut reaction was remarkedly similar to tetrahedr0n’s. Calculus (i.e. analysis) is one of the fundamental branches of mathematics and all of the other branches have made it into the high school curriculum as well. In fact, calculus is the only glimpse of modern mathematics we see in high school - everything else we learn dates back to the Greeks. Calculus captures the idea that we are living in a continuous world, more so than any other branch of mathematics. Why would you want to remove this idea from the high school curriculum?</p>
<p>Calculus is essential both within and outside of mathematics. Outside mathematics it is used extensively as a tool in sciences and engineering. But it is fundamental even within mathematics. Modern number theory, topology and probability would not be possible without calculus.</p>
<p>Given its significance in so many different areas, I think that the standard college math sequence should start out with a few semesters of calculus. Let’s not forget that most of the students taking these classes need it for applications. There are plenty of lower-level math classes in other branches of mathematics that curious minds can take concurrently with or instead of the usual calculus sequence.</p>
<p>For what it’s worth, I would probably not be a math major if it had not been for my high school calculus class. The concept of a limit was mind-blowing yet so basic that I was surprised that it had never crossed my mind. The concept of an integral is a very intuitive extension of basic high school geometry and I was excited to see it work out to nice formulas. Formal proofs would have only distracted from the main ideas. The beauty of the concepts spoke for itself. Calculus was the first time that I saw mathematics as an entire theory and not just a collection of recipes for formal computations (how to solve for x, or how to compute the area of a triangle given three random pieces of information).</p>
<p>It’s simple–that’s what college admissions want. If they valued other types of math that is what the high schools would be teaching. </p>
<p>As a high school math teacher (Statistics major) I can tell you that my colleagues (who were all math majors–our state does not allow a secondary education degree and I don’t know what that is) agree that the majority of the students will not need calculus (at least trig based) for their intended majors. The students also all agree that AP Statistics is much more interesting and something they see as applicable to so many fields. BUT–they need both if they are to get into a selective college. </p>
<p>I suspect that colleges are just interested in whether or not kids can organize and synthesize large amounts of information. I think it is possible to do this with a lower level math course but they are so watered down these days since now nearly everyone takes alg II to be college eligible (notice I didn’t say college ready). In order for the top students to get sufficiently challenged they need a calculus class.</p>
<p>If the lower tier colleges would “hold the line” and make sure that students who have completed algebra II actually know algebra II (instead of being remediated back to algebra I) high schools would be forced to make these classes more rigorous. As long as these colleges keep taking unprepared students the cycle will continue.</p>
<p>Calculus has a lot of applications in real life which many high school students can understand, appreciate and use later on. That is more the applied calculus where you focus on problem solving rather than intricacies of concepts. So many colleges in fact have applied calculus and proof based calculus as separate classes. I think HS curriculum try and combine both (some practical applications and some theory) which does not address either issue. AP statistics as per S’ assessment was a lot more applied.</p>
<p>That could be the problem i.e. the way calculus is taught. If HS can offer two options in calculus, students can decide which to take. May not be economically feasible in many schools though.</p>
<p>There can be variations to this model. My S is currently a frehsman at Northwestern U, in their competitive entry and rigorous Integrated Science Program. He took AP Calc BC as a sophomore and then had to decide what would come next. His AP Calc teacher, seeing his performance and understanding what S might want to study, waived him away from the AP Stats class, saying it wouldn’t provide as well what S needed. If he needed to pick up statistics, the AP Calc teacher said he could find a better class in college. </p>
<p>So, S went on to take online classes in linear algebra (junior year) and mv calculus (senior year.) Online classes at that level are a little rough, and he didn’t particularly enjoy the linear algebra one (thus confirming what he’d already decided, that he didn’t desire to major in engineering.)</p>