Should calculus be taught in high school?

In summary, the conversation discusses the topic of teaching calculus in high school and whether it adequately prepares students for the rigor of college calculus courses. While some argue that it should be taught to develop mathematical maturity and better prepare students, others argue that the fail rates in college suggest otherwise. The conversation also touches on the idea of increasing standards in high school and the role of prerequisites in understanding calculus. Ultimately, the consensus is that while calculus should be taught in high school, it should not be counted for college credit and the curriculum should be reevaluated to better prepare students for higher level mathematics.
  • #71
buffordboy23 said:
Using their critical thinking skills and knowledge of trigonometry, the former student realizes that they can accurately measure the baseline from some position to the tree and the angle from this position to the top of the tree and compute the height of the tree to good accuracy. Thus, the question is answered and learning trigonometry has proved useful to the student. There are many more examples that can convey the value of advanced mathematics, but it requires competency on the part of the teacher to show this to students, and unfortunately, this does not generally happen in our classrooms.

I don't agree that providing real-world examples are likely to improve students' interest. In your example, learning the trigonometry needed to calculate the tree's height is only interesting if the student is actually faced with the problem, takes out a measuring tape to measure the baseline, constructs a device to measure angles, and calculates the tree's height using the collected data. That would be interesting because the answer is a meaningful physical quantity of a real object, not a useless number that happens to be on the answer sheet.

I can't speak for other people, but I absolutely hated the "problem solving" questions in math class, many of which were similar to buffordboy's tree example. I considered them pathetic attempts at demonstrating the simplistic math we used was useful. At the same time, I often used math to calculate physical quantities, like the speed of a falling raindrop or the altitude of the Sun, because actually collecting the data was fun, not because the math was interesting. If a homework question asked me to calculate the speed of a raindrop based on somebody else's data, I would have considered that question as boring as the others.
 
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  • #72
I am very concerned about this image that you have to be doing Differential Equations by age 16 or you will never make it in Math.

If you are taught math from an early age on, you can be sure that you will understand topics like differential equations well before you are 16. It is only because we hardly teach math at all in school does it sound impressive if someone has mastered differential equations before the age of 16.

Then given that our eductional system is severely flawed when it comes to math teaching, the typical math professor is almost always someone who was far ahead with math while in school.

The same is true for other subjects that are not taught in school, like music, sports, etc. etc.
 
  • #73
About real world problems: The fact is that we don't really give "real world problems" to students in school at all. What we do is we give artificially cooked up problems with no relevance at all to practical problems to children.

Real "real world problems" are usually very hard to solve if at all, and require advanced techiques you learn in theoretical physics courses or engineering courses. Giving such real world problems to children could actually make math very interesting. You can then motivate young children to learn calculus and other more advanced topics.

E.g., a high school project could be: "You are given a computer that can only do addition and subtraction. We want to program it so that it can compute all the special functions your calculator can do."
 
  • #74
I'm not sure what level of difficulty of problems you are referring to in the second paragraph. Your example in the last paragraph doesn't seem to coincide very well with the aim in the last sentence of the second paragraph. While I think introducing young students to great unsolved problems could certainly perk their interest, there is still the actual job of teaching these kids, and obviously you can't just give random unsolved problems to them. But again, what you described was kind of vague.
 
  • #75
Count Iblis said:
If you are taught math from an early age on, you can be sure that you will understand topics like differential equations well before you are 16. It is only because we hardly teach math at all in school does it sound impressive if someone has mastered differential equations before the age of 16.

This is not necessarily true. If the students fail to actually pursue this knowledge on their own, then this idea of trying to teach them a bunch of things just so they could understand differential equations or whatever at 16 is probably not going to work out too well.
 
  • #76
Count Iblis said:
If you are taught math from an early age on, you can be sure that you will understand topics like differential equations well before you are 16. It is only because we hardly teach math at all in school does it sound impressive if someone has mastered differential equations before the age of 16.

Then given that our eductional system is severely flawed when it comes to math teaching, the typical math professor is almost always someone who was far ahead with math while in school.

The same is true for other subjects that are not taught in school, like music, sports, etc. etc.
I certainly understand that. However, just because you have talent doesn't mean you always get a head start. The problem is that we give all the attention to the lucky few who got good teachers, the right courses, and parental support.

There are plenty of stories of people who pick up a musical instrument as an adult and become very accomplished, why not math? I like the "Lament" where it says the worst thing we have done is to make it madatory!

More and more, to get into the "right" school, Calc is becoming "mandatory."
 
  • #77
I don't think calculus should be "mandatory", but I do think that IF they are offering the class, it should be taught by a well qualified teacher.
 
  • #78
ideasrule said:
In your example, learning the trigonometry needed to calculate the tree's height is only interesting if the student is actually faced with the problem, takes out a measuring tape to measure the baseline, constructs a device to measure angles, and calculates the tree's height using the collected data. That would be interesting because the answer is a meaningful physical quantity of a real object, not a useless number that happens to be on the answer sheet.

After thinking about, I agree with your point. The problem is illustrative but not of current consequence to the student, so it's not really motivational to learning.

ideasrule said:
I can't speak for other people, but I absolutely hated the "problem solving" questions in math class, many of which were similar to buffordboy's tree example. I considered them pathetic attempts at demonstrating the simplistic math we used was useful. At the same time, I often used math to calculate physical quantities, like the speed of a falling raindrop or the altitude of the Sun, because actually collecting the data was fun, not because the math was interesting. If a homework question asked me to calculate the speed of a raindrop based on somebody else's data, I would have considered that question as boring as the others.

I like what you said here. Basically, you like the freedom to choose your own problems. You choose these problems because they apply the content knowledge that you have learned. To ask such relevant questions is a skill. By Lockhart's perspective, we should consider it an art, along with answering the question. My tree example would be better suited as the spring-board to ignite the student's imagination and ask such questions like you have shared with us.
 
  • #79
snipez90 said:
I'm not sure what level of difficulty of problems you are referring to in the second paragraph. Your example in the last paragraph doesn't seem to coincide very well with the aim in the last sentence of the second paragraph. While I think introducing young students to great unsolved problems could certainly perk their interest, there is still the actual job of teaching these kids, and obviously you can't just give random unsolved problems to them. But again, what you described was kind of vague.


We don't need to focus in unsolved problems, simply on realistic problems, instead of artificially cooked up problems that have no relevance at all. Strangely the latter type of problems are often called "real world problems".

Being able to program a computer from scratch to do what you want it to do is certainly a real world problem. It does not have to be the way things are done in practice. What matters is that in the real world you don't have any artificial boundaries. The real world does not care whether or not a solution requires calculus. Since without calculus you can only evaluate rational functions, there are in practice almost no problems you can do without calculus.

Trigonometry without calculus is cheating, because you are then using your calculator to compute the trigonometric functions. I'm not saying that you cannot use your calculator. But I think students should know at least the basic principles about how calculators (can) compute trigonometric, exponential and logarithmic functions.
 
  • #80
snipez90 said:
If a student finds regurgitating material for the AP exam is boring, there is a simple solution: read a more advanced textbook.

As for other students, I very much doubt that they are all memorizing a variety of formulas by rote and whatnot.

I'm not sure what you mean here. Other students meaning ones who don't find regurgitating material boring? Wouldn't they be the most likely to memorize a bunch of formulas by rote?

Anyway, memorizing by rote is still what most of my students try to do*. Why do they do that? Because they shouldn't be in AP Calculus, but schools make them think that if they don't take a lot of AP courses then they'll never get into the school they want. That's my problem with the AP program. If it was filled with kids who really liked math and were able to do it, it would be ten times better. This could all be solved if they didn't get college credit, and then when they entered the school they could try to test out of the class there.

*For example, if you know the quotient, product and chain rules, why memorize d/dx (tan x)? I ask them that, but they still try to memorize it.
 
  • #81
^^^

I agree. Most kids in my class were too worried about memorizing their differentiation and integration tables. As far as trig goes, all I knew by heart entering the test was the product rule, chain rule, and the derivatives of sin u and cos u and I did fine, even with the trig differentiation/integration.

I've asked a few of my friends personally, and they said that the only reason that they were taking AP Calculus was that they want to go to a good school (UCLA, Berkeley, Princeton, etc.).
 
  • #82
Tobias Funke said:
I'm not sure what you mean here. Other students meaning ones who don't find regurgitating material boring? Wouldn't they be the most likely to memorize a bunch of formulas by rote?

Anyway, memorizing by rote is still what most of my students try to do*. Why do they do that? Because they shouldn't be in AP Calculus, but schools make them think that if they don't take a lot of AP courses then they'll never get into the school they want. That's my problem with the AP program. If it was filled with kids who really liked math and were able to do it, it would be ten times better. This could all be solved if they didn't get college credit, and then when they entered the school they could try to test out of the class there.

*For example, if you know the quotient, product and chain rules, why memorize d/dx (tan x)? I ask them that, but they still try to memorize it.

Well the way I see it, you are regurgitating material either way. My calculus teacher was not particularly inspiring, but he still made sure many people got 4's and 5's. The easiest way of doing that is spending the couple of months before may assigning every Free Response packet from 1970 to the 2000's. Perhaps I spoke imprecisely, but what I meant was that if people are able to do the calculus problems assigned - well actually we never actually had to do our homework, but let's say the AP FRQ's - they probably don't have that much to be critical of. Many of the classmates I mentioned who went into engineering do not particularly care much for theoretical calculus, but they have the intuition and the computational fortitude. I guess I was responding to earlier posts that complained that the AP Calculus Exam is "not to be trusted" and those who had a theoretical leaning but do not understand how difficult it is to reform the current curriculum anyways.

As for your main point, shouldn't it be the job of the teacher and other administrators to try to persuade those who aren't doing well to reconsider taking the course in the first place? I still think that if one is able to do 80% of the AP Calc Exam correctly, then credit should be given. I don't think that college placement tests are really going to be much more precise in determining the right placement. I can give you two examples. The school that I attend has a very rigorous undergraduate math curriculum (very pure), but the computational portion of the exam was basically the AP Calc BC exam, perhaps easier. Although the free response portion was more theoretical (those who did particularly well on this portion placed into a very difficult analysis course), anyone who could do the computational part will get placement for calculus, or entry into our theoretical calculus course. My friend at MIT found their placement test to be of similar difficulty to the AP Exam as well. If people can do better than 80% on the AP Calc exam, they probably have a good intuitive and computational grasp on calculus, and there is no reason for them to have to do the same thing over again. But instead, you have people who essentially barely passed a math exam getting 5's and thinking they know calculus.

As for memorization, it would be terrible if someone approached everything in calc through memorization, but sometimes it's not a big deal. For instance, no one would really bother deriving the derivative of tan(x) all the time. I mean as long as know how to do it, I honestly don't see how hard it is to just memorize it. I mean if you use something like the derivative of tan(x) often, it really isn't something that's particularly hard to understand that you just all of a sudden forget that it's sec^2(x)?
 
  • #83
I've asked a few of my friends personally, and they said that the only reason that they were taking AP Calculus was that they want to go to a good school (UCLA, Berkeley, Princeton, etc.).

Why does this bother you? I don't see anything wrong with being competitive and demonstrating high achievement.
 
  • #84
Just got back from an AP Calculus teacher's workshop. You'd think that we would talk about pedagogy, maybe whether or not to introduce the epsilon-delta definition of a limit, how to prove MVT, etc.

No, we spent almost all of the time doing standard AP problems because the teachers needed it. Think about that if you're entering AP Calc next year. Your teacher may very well have learned the material only a few months before (or possibly still not learned it). Think your teacher can do a straightforward, although tedious, derivative with 3 chains and an ln or tan thrown in? If you're lucky. Think they'll remember to change the limits of integration in a u substitution? Not many did. Think they can determine

[tex]\frac{d}{dx}\left(\int_0^{x^2}\sin(t^3)\,dt\right)[/tex] ?

Don't be so sure. Not once did we discuss how to find a limit algebraically. We plugged points into the good old calculator and were encouraged to have our students do the same. When going over old tests, we noticed how lenient the grading is. A student who wrote "=V(x)" instead of the correct "=V(25)" was given full credit. Someone who defined a function O and then used O to mean two clearly different things in a formula was given full credit. None of the other teachers even noticed this either.

I liked the story about the official grader who started crying during a problem because she finally got it. And this was a simple problem about using the derivative curve to gain information about the function itself! Even the graders don't have to know what they're doing because they have everything laid out for them. If they see V=2,000, give one point, etc.

We discussed in class how to get more enrollment in the program. Well, dumbing down the math for the students is the only way*, and it's quite obvious that that's what's happening.

To summarize, if you or someone you care about enjoys math and wants to enter a career where you may use it, take AP calc at your own risk. DON'T assume your teacher knows what he or she is doing, and please don't skip calculus in college. Wait one year and you'll get a much better teacher. If you're a student who has to take every AP class and join every club to get into Harvard, then take AP calc. Nobody likes you anyway :). And if you respond with "well, my teacher was great!", then good for you. You got lucky. There were 3 or 4 other good teachers with me in the workshop and they were as shocked as I.

*Well, of course the only real way is to fix math education from the bottom up, but nobody, at least no teacher or education "expert", wants to talk about that issue because it's difficult and worthwhile.

Edit: Another scary thing is that courses like this count towards grad credit(in education, not math I hope) and are the basis for teachers to be called "highly qualified". What a joke.
 
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  • #85
Tobias Funke said:
No, we spent almost all of the time doing standard AP problems because the teachers needed it.

Wow! What qualifications does one need to become a maths teacher in the US?
 
  • #86
cristo said:
Wow! What qualifications does one need to become a maths teacher in the US?

Well, a common complaint among teachers is that students keep getting passed along from grade to grade even though they don't know the math. When these people in turn become teachers, this is what happens. I'm apparently one of the minority who is crazy enough to believe that one should be pretty damn good at a subject before teaching it. I'm no PhD, but I majored in math. I don't know about some of these other people...

But you can't say anything. It's like a blind guy trying to be an art critic, but it's somehow rude of you to suggest that he should find another job. I got death stares in class for bluntly saying that we need more qualified elementary and middle school teachers.
 
  • #87
When I have to grade, I don't focus that much on whether the student got the correct answer. What matters is if the student understands the problem and understands the techniques needed to solve the problem. Then a student who makes a few errors can get an answer that it totally wrong, while a student who you can tell doesn't really understand much, can sometimes get a correct answer simply by using a correct formula by chance.
 
  • #88
Count Iblis said:
When I have to grade, I don't focus that much on whether the student got the correct answer. What matters is if the student understands the problem and understands the techniques needed to solve the problem. Then a student who makes a few errors can get an answer that it totally wrong, while a student who you can tell doesn't really understand much, can sometimes get a correct answer simply by using a correct formula by chance.

Makes sense, but it's not really the main complaint I have. It was just one more thing i didn't like. I would subtract a few points, but when there are 3 points to give for the subproblem, it's a choice between giving a 100 or a 67. There's no real freedom when grading, which isn't a good thing.

The main issue is teacher knowledge. It's scary.
 
  • #89
Tobias Funke said:
Well, a common complaint among teachers is that students keep getting passed along from grade to grade even though they don't know the math.

Yes, but university is the place that rectifies this. I find it amazing that there are maths teachers teaching AP calculus who haven't got a degree in maths! Over here (in the UK) if you want to teach maths at the highest high school level, you need a degree in maths. Thus, I completely agree with you when you say that one should be good at something before teaching it!

But you can't say anything. It's like a blind guy trying to be an art critic, but it's somehow rude of you to suggest that he should find another job.

Not really: a blind man can't help being blind!


Out of interest, do you need teaching qualifications to teach in the US? Do people study education at university then go into teaching a subject, or do they study a subject at university then obtain a separate teaching qualification?
 
  • #90
cristo said:
Out of interest, do you need teaching qualifications to teach in the US? Do people study education at university then go into teaching a subject, or do they study a subject at university then obtain a separate teaching qualification?

Yes, you need qualifications. They vary from state to state. I only needed a degree in anything and a passing grade on the (extremely easy) math test to get a preliminary license. But if a school needs a math teacher, even an AP teacher, and they're shorthanded, guess who gets asked? A Chemistry teacher, or a Biology teacher.

So while you need a certificate to teach in most schools, nobody is really checking. As to your remark about universities fixing the problems students have, maybe for math majors that's true. But from what I've seen, majoring in education is a complete joke. Just look at our education system and this makes sense. I think most math teachers have some kind of education with math degree and not an actual math degree, but I'm not too sure about this.

It's becoming more and more clear to me that AP is just a business like any other. How else can you explain the fact that underqualified students are let, and even encouraged, into the program? Our workshop leader was completely fine with saying that most of her students have trouble with precalculus topics like logs and exponentials. Why is this acceptable? Oh yeah, money.

And then when you say anything about the program, it's always your fault for "not seeing" the goals or somehow not understanding a great new way of teaching lol. People in education are wonderful because they're always right, even when nobody knows math!
 
  • #91
Tobias Funke said:
But from what I've seen, majoring in education is a complete joke. Just look at our education system and this makes sense. I think most math teachers have some kind of education with math degree and not an actual math degree, but I'm not too sure about this.

I agree that it is not ideal for a teacher holding a degree in education should be teaching higher maths! From what I gather of the system over here, degrees in education are incredibly useful for people wanting to teach primary, or lower secondary school (elementary or middle school, in your terminology), since for the former, one needs to teach most subjects, and for the latter, one teaches at least a few subjects. But.. the more complicated stuff should be taught by mathematicians.
 
  • #92
Most of the teachers just obtain a degree in general education and test for a specific subject credential (say math). But that test is like a joke, really.
 
  • #93
cristo said:
I agree that it is not ideal for a teacher holding a degree in education should be teaching higher maths! From what I gather of the system over here, degrees in education are incredibly useful for people wanting to teach primary, or lower secondary school (elementary or middle school, in your terminology), since for the former, one needs to teach most subjects, and for the latter, one teaches at least a few subjects. But.. the more complicated stuff should be taught by mathematicians.

Unfortunately, "mathematicians" here won't go to teaching secondary schools because the pay is low. Of course they would rather work in a university or in a private sector because the pay is much, much higher.
 
  • #94
thrill3rnit3 said:
Unfortunately, "mathematicians" here won't go to teaching secondary schools because the pay is low. Of course they would rather work in a university or in a private sector because the pay is much, much higher.

By "mathematician" I meant someone with a degree in maths (or maths major, as you lot would say). Some people don't just judge their job on income! Anyway, how much is "pretty low"?
 
  • #95
The pay isn't great, but teachers do tend to exaggerate how incredibly poor they are. If you factor in all the vacation time, most veteran teachers make quite a bit of money, at least in MA. The main problem for some is huge, unruly classes and just a general lack of respect from society. Teachers do have to put up with a lot of crap that just gets in the way of actual teaching, and our system doesn't place them correctly or asks too much of them, especially elementary school teachers. So many of them are bad at math and I'd imagine they really want to change this, so we need to do a better job at helping them.

So even though I was shocked that we spent an hour doing a left Riemann sum, I guess that's what teachers need. I'd just feel more comfortable if every AP teacher had to pass the test with a 5. For some reason, I bet that would be fiercely resisted by a lot of teachers.
 
  • #96
Snipez90, what you describe in your post #82 is ridiculous. What happened to Praxis? What about CSET? What about the meaning of "highly qualified teacher" including possession of minimum of 32 nonremedial units of Mathematics? Saying that teachers do not get misassigned is not for me to say, since I really do know better than that; but the way you described misassignments for teaching of Calculus - ... If that is true, then it is really very disappointing.
 
  • #97
Um, exactly what part of my post are you responding to? Since when did I imply anything about teacher misassignments? Much of this thread has been on the focus of the student and I was mainly addressing issues brought up in that regard. The only statement I made about teachers in general was that they should share the responsibility in deciding who should stay in the course. Even if I am wrong on this, I still don't see how this is an extremely pertinent point. In light of Tobias Funke's description, I could see how I could have had a worse teacher. But still, my teacher knew the material, he was just not very good at teaching. Asking students to work through every FRQ and MC test in existence and telling them to discuss the solutions among themselves without further guidance is pretty terrible, but if you learned enough to pass a calculus test, you could probably get a 5, or at least a 4. Of course, Tobias Funke's description of the graders is rather troubling.
 
  • #98
In clearer wording, misassignment of a teacher is putting a teacher into a situation to teach something which that teacher is technically not authorized to teach; mainly because that teacher does not have the fitting subject knowledge to teach a particular course. Check back again to post #82. Teachers do actually get assigned to jobs which they should not be, but we seem to understand that this is a bad thing. Students hoping to learn Calculus need both a good textbook and a very knowledgeable Calculus teacher. A teacher without sufficient knowledge of Calculus can simply not give effective guidance on the Calculus topics. Even some highly motivated students need guidance from well qualified teachers.

I really can not say how frequent is the misassigning of teachers to courses. At the very least, I know that it happens. Misassigning teachers for Calculus seems to be worse than other courses for misassignment.
 
  • #99
All right, I am still not sure what gave you the impression that I made any general comment about the misassignment of teachers. Yes, I know what it means, but you expressed great incredulity at my earlier post for some reason. Highly motivated students will know when they require resources that the teacher won't provide. One of my best friends despised the calc teacher, claiming that the only reason I did well in calculus was because I studied it on my own. Students hoping to learn calculus can do it themselves, but many are lazy. Now any reasonably intelligent student probably knows what the current education system in America is like. But there are students in this category who still refuse to do the work or resort to whining. I've seen this attitude even in my honors calculus course this past year as a freshman in college.

I agree that highly motivated students need guidance, but if the teacher is not up to the task, it is the responsibility of the student to find outside resources. Motivated students will make their efforts worthwhile. Many students have access to an internet connection and a library, but if they continue to rely on an incompetent teacher, then I would not call them motivated at all. Now obviously, I am not proud of the fact teachers are missassgined, nor am I refusing to believe this is often the case. I simply hold the view that one solution to such failures largely depends on exactly how motivated a student is. Most people will never use calculus, but if some student wants to learn it, then he or she had better utilize other resources.
 
  • #100
Should calculus be taught in MY high school?

Should calculus be taught in MY high school?

In the school where I teach (private, Catholic high school for girls) we do offer an AP Calculus AB course. (We also offer an AP Calculus BC course, but it is offered only sporadically and students usually take it as an independent study.) Despite having taken both tests myself when I was in high school, I have been lately becoming anti-AP, and I wonder if they do more harm than good to our students. The students who take our AP Calculus AB class come in with not-so-strong algebra skills. I teach Pre-calculus (designated an honors course), and I've b**ched-and moaned more than once here about the incredible Algebra mistakes my Pre-calculus students make.

I should mention that not all of juniors who take PreCalc proceed to AP Calc. Those who really struggle in PreCalc are placed into Stats (non-AP) their senior year. Those with A's and B's in PreCalc junior year go to AP Calc as a senior -- and many of these students still have not-so-strong algebra (and now trig) skills.

And it's not just the Precalculus students. Pretty much most of the school body enter our school with weak math skills. We give an entrance exam to 8th graders that tests English and Math, but Administration/Admissions admits students they shouldn't, because many of the ones we initially offer admission to will end up going to one of our competing schools for whatever reason. As we are a small school (and especially with the financial troubles that all of our area private schools are facing), we have no choice but to admit students who may not have done well on the math portion of the entrance exam. And for the foreseeable future, I don't think this is going to change.

With all of this as a preface, if you were in my shoes would you make a proposal to Admin that we drop AP Calc? Maybe in its place, we can make Pre-calculus a two-year course. A number of schools offer Pre-calculus as two year-long courses -- in fact, the public school system in the district where I live offers separate "College Algebra" and "Trigonometry/Analytic Geometry" courses. Or, would you just suck it up and keep the honors track in place (Algebra 2 - Geometry - PreCalc - AP Calc), because we don't have many graduates who will major in math/science anyway? Or do you have any other ideas?


01
 
  • #101
Well the simple solution is to cut AP Calculus. If not that many students demonstrate interest or commitment, then many probably won't pursue math/science as a major. In this case, they should take stats instead of calculus.

On the other hand, the syllabus of a precalculus course should be fairly flexible, so maybe varying the emphasis of the topics covered may help. I felt that in my precalculus class, we covered a few topics that were not particularly helpful for the subsequent AP Calc course. For instance, there was no need to cover trigonometry in great depth. The basic identities and reasoning with the unit circle should suffice. We also covered vectors, conic sections, and applications of complex arithmetic (up to DeMoivre). Although these topics may be of interest, they should not take the place of more direct ways of building algebraic manipulation skills if the students need it. I think a good precalculus curriculum should emphasize on reinforcing algebra skills, introducing basic trig, and then move straight into limits and derivatives.

Or yet another way is to teach geometry before algebra 2. My high school did not have an honors algebra 2 course, and that might be why algebra 2 was taught first. The more motivated students took algebra 2 in 8th grade, so when I moved to my new high school, I took honors geometry with them freshman year. Then I took algebra 2 and then precalc. I think it makes a lot more sense to teach precalculus right after algebra 2. The algebraic manipulation skills in typically encountered in algebra 2 are crucial.
 
  • #102
I was reading the thread "Who wants to be a mathematician" by the good ol' mathwonk (I wish he'd come back), and he asserts that the focus of the high school math program (and AP) should be linear algebra instead of calculus.

Thoughts?
 
  • #103
If I had to pick one of the most utility to high school students in general, I would pick linear algebra, despite that fact that I have more affinity for calculus. I mean just on the surface, vectors and matrices and their underlying theory seem far more applicable in a general scope than derivatives and integrals. I don't think specific examples would be that hard to find.
 
  • #104
I just wanted to add my personal experience to the mix here. I took BC calc in high school as well as some other AP courses. The courses were challenging but most of my class did well. My first semester in college I started in calc3 (multivariate) and the second semester of the introductory calculus based physics series.

My GPA would have been higher if I hadn't skipped those initial courses, but I ended up with Bs anyways. I'm very glad that I took the AP courses and got a jump on college. I was able to double major with honors in both mechanical engineering and philosophy. Without my AP credits that would have been impossible. I feel that I learned a lot more in college and am much better off now because of the jump I was able to get. It opened up a lot of doors that would have been closed otherwise. The only downside was that I bit off slightly more than I could chew early on, but I would much rather see students have the opportunity to be challenged and face their limits than be held back.
 
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  • #105
Well Calculus was a compulsary part of your Math courses in the last two years of my high school. I think most people found it easy and had more problems with co-ordinate geometry where a lot of algebraic manipulaion was involved.
 
<h2>1. Should calculus be taught in high school?</h2><p>This is a common question among educators and parents. The answer is not a simple yes or no, as it depends on various factors such as the curriculum, resources, and student population. However, many experts argue that calculus is an important subject that can benefit high school students in their academic and professional pursuits.</p><h2>2. What are the benefits of teaching calculus in high school?</h2><p>One of the main benefits of teaching calculus in high school is that it prepares students for college-level math courses. It also helps develop critical thinking, problem-solving, and analytical skills that are essential in various fields such as science, engineering, and economics. Additionally, calculus can open up career opportunities in these fields.</p><h2>3. Is calculus too difficult for high school students?</h2><p>Many people believe that calculus is a challenging subject, and some argue that it may be too difficult for high school students. However, with proper instruction and support, high school students can grasp the fundamental concepts of calculus and even excel in the subject. It is important to provide students with a strong foundation in algebra and geometry before introducing calculus.</p><h2>4. Are there any alternatives to teaching calculus in high school?</h2><p>Some educators propose alternative math courses, such as statistics or data analysis, instead of calculus in high school. While these courses may also be beneficial, they do not cover the same concepts and skills as calculus. Therefore, it is important to offer a variety of math courses to cater to the diverse interests and abilities of students.</p><h2>5. How can we make calculus more accessible to high school students?</h2><p>One way to make calculus more accessible is by incorporating real-world applications and examples in the curriculum. This can help students see the practical applications of calculus and make it more relatable. Additionally, providing extra support and resources, such as tutoring and online resources, can also help students who may struggle with the subject.</p>

1. Should calculus be taught in high school?

This is a common question among educators and parents. The answer is not a simple yes or no, as it depends on various factors such as the curriculum, resources, and student population. However, many experts argue that calculus is an important subject that can benefit high school students in their academic and professional pursuits.

2. What are the benefits of teaching calculus in high school?

One of the main benefits of teaching calculus in high school is that it prepares students for college-level math courses. It also helps develop critical thinking, problem-solving, and analytical skills that are essential in various fields such as science, engineering, and economics. Additionally, calculus can open up career opportunities in these fields.

3. Is calculus too difficult for high school students?

Many people believe that calculus is a challenging subject, and some argue that it may be too difficult for high school students. However, with proper instruction and support, high school students can grasp the fundamental concepts of calculus and even excel in the subject. It is important to provide students with a strong foundation in algebra and geometry before introducing calculus.

4. Are there any alternatives to teaching calculus in high school?

Some educators propose alternative math courses, such as statistics or data analysis, instead of calculus in high school. While these courses may also be beneficial, they do not cover the same concepts and skills as calculus. Therefore, it is important to offer a variety of math courses to cater to the diverse interests and abilities of students.

5. How can we make calculus more accessible to high school students?

One way to make calculus more accessible is by incorporating real-world applications and examples in the curriculum. This can help students see the practical applications of calculus and make it more relatable. Additionally, providing extra support and resources, such as tutoring and online resources, can also help students who may struggle with the subject.

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