I have a rising 12th grader who took calculus at the community college, earning an A and a B, respectively each semester. He did struggle a lot in the second semester. Also, he was weak on trig.

I'm not a math person (in fact, I enrolled him in the wrong calculus class initially). Any suggestions for what I should have him study this year? Would it be better for him to go back over weak areas in trig? What comes after calculus?

I am open to any option, not just having him dual enroll again.

thanks for any ideas!

margaret7

## Beyond calculus?

**Moderators:** Bob Hazen, Theodore, elliemaejune

### Re: Beyond calculus?

Calculus 2 comes next, then calculus 3. If he's not a math person, though, chances are his major won't require math beyond calculus. Check with the college he's going to and find out what level of math they require. If he's already done everything necessary, have him go back over the trig.

### It depends

As Theodore said, it depends on what he wants/going to study in college. If he is going to study non-math related subjects, than studying more math would not really serve him. In general, except for engineering school, Advanced Trig is quite useless. If he is going to a science discipline, often Linear Algebra is required, but again, it would depend.

Therefore, check with the college what are the requirements for his intended major and get him to study those.

As for not doing well on Trig - it doesn't matter

Therefore, check with the college what are the requirements for his intended major and get him to study those.

As for not doing well on Trig - it doesn't matter

Moti Levi

www.LearningByYourself.com

www.LearningByYourself.com

### Re: Beyond calculus?

margaret7 wrote:I have a rising 12th grader who took calculus at the community college, earning an A and a B, respectively each semester. He did struggle a lot in the second semester. Also, he was weak on trig.

I'm not a math person (in fact, I enrolled him in the wrong calculus class initially). Any suggestions for what I should have him study this year? Would it be better for him to go back over weak areas in trig? What comes after calculus?

I am open to any option, not just having him dual enroll again.

thanks for any ideas!

margaret7

Calculus by itself (at least at this level) is an extremely easy subject. The majority of the failures could be attributed to a simple lack of fundamentals in properties of functions (basically the "mechanics" of functions--which is not really difficult) and very often such a simple things as basic factoring, numerical sequences--especially so geometric ones with quotients less than 1 (which is the path to Limits) and the problems "with calculus" usually are not the problems with it at all and occur and accumulate much earlier. This could be relatively easily addressed. There are number of effective ways of "pulling" even below average student into all this calculus business.

Warmest Regards

### Calculus is not easy

I found Calculus I rather difficult, but I suppose that was partly because I was learning it from a textbook and jumped straight to it from Algebra II (the Calculus book covered all the necessary trig in the first chapter or so). I'm finally giving up and taking Calculus III in a class, since Calculus II sure didn't get any easier, and I'd like to minimize my pain and suffering

The main difficulty, though, is just the volume of material. The only other subject I've done which came close to being as difficult was Discrete Math, which was practically a whole new course in each chapter. Not for the faint of heart.

The main difficulty, though, is just the volume of material. The only other subject I've done which came close to being as difficult was Discrete Math, which was practically a whole new course in each chapter. Not for the faint of heart.

### Hard vs. difficult

Theodore,

Applied calculus can be difficult, but not hard. Proving theorems and such in calculus [the theory of it] is hard. The difference I put between difficult and hard is that the former means you need to know (remember) much and practice quite a bit before you can do it well. The latter (hard) means even such might not do the trick. But often calculus becomes difficult and even hard because it is not taught correctly, and often the underlying ideas are not being made really clear in a way a student can understand those intuitively. I have seen many students change their opintion once the three ingredients (intuition, facts, and practice) are present. Proving calculus theorems can be hard since quite a number of those require a real deep understanding of the underlying theory and structures, as well as being well trained in methods of mathematical proofs, which not all are easy to master and apply in new situations.

I have not seen a REALLY GOOD textbook for calculus yet

As for discrete math - this can be and is hard, even when it is only the applied part. The reason being that even having the three ingridients does not ensure the ability to solve a new problem. It requires having the structure of the problem in one's mind (and that can be hard for some problems) and often having some creativity in changing the problem structure/repersentation to make it solvable. In fact, set theory (which is one of the subjects within discrete math) was taken out as a required course just when I finished my undergrad [where I come from we only study one thing, no general studies and such] because it was deemed as generally too difficult for students.

So take solace, you are not alone

Applied calculus can be difficult, but not hard. Proving theorems and such in calculus [the theory of it] is hard. The difference I put between difficult and hard is that the former means you need to know (remember) much and practice quite a bit before you can do it well. The latter (hard) means even such might not do the trick. But often calculus becomes difficult and even hard because it is not taught correctly, and often the underlying ideas are not being made really clear in a way a student can understand those intuitively. I have seen many students change their opintion once the three ingredients (intuition, facts, and practice) are present. Proving calculus theorems can be hard since quite a number of those require a real deep understanding of the underlying theory and structures, as well as being well trained in methods of mathematical proofs, which not all are easy to master and apply in new situations.

I have not seen a REALLY GOOD textbook for calculus yet

As for discrete math - this can be and is hard, even when it is only the applied part. The reason being that even having the three ingridients does not ensure the ability to solve a new problem. It requires having the structure of the problem in one's mind (and that can be hard for some problems) and often having some creativity in changing the problem structure/repersentation to make it solvable. In fact, set theory (which is one of the subjects within discrete math) was taken out as a required course just when I finished my undergrad [where I come from we only study one thing, no general studies and such] because it was deemed as generally too difficult for students.

So take solace, you are not alone

### Re: Hard vs. difficult

Moti wrote:Theodore,

I have not seen a REALLY GOOD textbook for calculus yet

So take solace, you are not alone

SHENK Calculus And Analytic Geometry (not today's watered down and confusing REissues) but Second Edition of 1977, 1979 is, probably, one of the greatest calc textbooks written in any language. Combined with classic edition of Flemming's Algebra (Hamline University) this is a powerful couple of math books--for those, who really want to progress far. Yes, it will require a tedious and hard work but presentation of the material is unquestionable in both. There are, however, some other classic sources on calc and triginometry, which could be also extremely helpful. As for trigonometry--Flemming's Algebra is excellent, as well as classic edition C.L. Johnston's Plane Trigonometry.

Warmest Regards

Theodore wrote:I'm using Calculus: Early Trascendental Functions (Third Edition, Larson, Hostetler, Edwards).

This is an excellent book too, even in its Fourth Edition of 1990. (Heath and Company). Although there are other excellent supplements out there, one of them (sadly--not sure about precise title) 1970-s Calculus in Economics--a superb narrative on practical applications of calc. As well as simply OUTstanding book by Richard Paul and Leonard Shaevel Essentials Of The Technical Mathematics With Calculus (Prentice Hall 1989 Edition)--beautifully compiled superb review of fundamental algebra with transition into calc/ NO gimmicks, no baloney--outstanding book. In many respects this is an exemplary book insofar as the balance and volume of the material (albeit still 1300 pages goes.

Warmest Regards

The university I will be attending in the fall suggests that one take analysis after a year of calculus, so that is an option, too. Or, your son might want to review trig and calculus during his senior year to become more firmly grounded - and possibly to pass out of college math requirements.

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