What would you recommend for Calculus?

[Guest going42]

I should start by saying that I'm having trouble finding out exactly what is in a pre-calc course, and how it sometimes differs from straight trigonometry depending on who you ask and what text you're talking about, etc. My dh thinks our ds (10th) can go straight to Calculus after Algebra 2 because that's what he did way back when. I'm thinking going 'old-school' and providing ds with a similar plan to what his dad did in high school. As ds's grandpa said, "math doesn't change, the concepts are the same, what changes is the way things are named and the way they present it." Sure enough, his old textbooks from the sixties and seventies are labeled Calculus but include trigonometry.

 

So, which Calculus text have you guys found to your liking and why? I'll be supplementing with Khan academy videos.

 

sorry for typos and sloppy writing...sleepy toddler on lap.

 

Thanks!

[Jann in TX]

Very very few students can go right into Calc...

 

Pre-Calculus is the name for College Algebra (Algebra 3) and Trigonometry-- one semester of each.

 

Pre-Calc (the College Algebra part) goes deeper into functions than Algebra 2... it also explores advanced problem solving...

 

Trigonometry is still pretty much the same thing it used to be...

 

Upper maths HAVE changed with the advent of the graphing calculators... it is great to learn how to solve the equations manually--but when graphing calculators are used as a TOOL--more advanced problems can be worked--and MORE problems can be worked. Also the focus of the problem solving has shifted with the advent of so much technology/science...

 

As a high school Math teacher I strongly suggest NOT skipping Pre-Calc.

[In The Great White North]

Sure enough, his old textbooks from the sixties and seventies are labeled Calculus but include trigonometry.

 

I bet his old algebra II books said trigonometry too. The new ones don't.

[regentrude]

Upper maths HAVE changed with the advent of the graphing calculators... it is great to learn how to solve the equations manually--but when graphing calculators are used as a TOOL--more advanced problems can be worked--and MORE problems can be worked. Also the focus of the problem solving has shifted with the advent of so much technology/science...

 

As a high school Math teacher I strongly suggest NOT skipping Pre-Calc.

 

I definitely second the not skipping pre-calc.

 

However, I would like to comment on the problem solving/graphing calculator issue. Those calculators can be a blessing and a curse.

Many of my college students (engineering and science majors) are unable to solve a quadratic equation that is given symbolically (i.e. without numbers to put in the calculator). Most of them are unable to sketch the basic shape of a function (something a s simple as 1/r^2) and have no idea how you find out about the general behavior of a given function by looking what happens for x going to plus or minus infinity and zero.

These are all skills I remember learning in my high school math. So the old books might actually be a good reminder of skills to learn that are still useful, but fall victim to the calculator use.

[Blue Hen]

My oldest started college a couple days ago and is still not happy that I had him work through a Pre-Calc book in 10th gade. I thought he had to have "Pre-Calc" prior to going into Calculus. We worked through Pre-Calc and he kept saying to me---I know this and I would have him do more problems. ugh....... However, he had worked through one of those old Alg 2 w/ trig books and I had drilled him on trig, and solving quadratic equations and working with functions all prior to Pre-Calc. The one benefit we found was that DS had to use a graphing calculator w/ his Pre-Calc book. Using a calculator, let alone a graphing calculator was new to him.

 

Oh well. DS had a great, strong foundation from really learning and understanding the material. He scored wonderfully on the AP Calc BC exam, scored great on his college's Calculus placement exam and was placed into 2nd year Calc for Engineers. The school awarded him credit for a year of engineering calc so it has worked out well. He, of course, thinks back to the year spent doing Pre-Calc and would like-a-do-over.

 

Interestingly his college's calculus placement exam did NOT permit a calculator. I haven't heard yet whether he is using one in class but a graphing calculator was not on the class' resources required material list.

 

He used Foerster for Pre-Calc and Calc. He used Larson when he took AP Calc BC through PA HS'ers. He liked the Larson text a lot.

Carole

Edited September 2, 2010 by Blue Hen
opps add his calc book

[Jamee]

At the school my mom taught at, after Alegebra II came math analysis, basically a pre-calc course with more advanced trig. I couldn't image going straight to calc from Algebra II. As far as what to do for calc, I'd suggest going to a community college. Good luck!

[Matryoshka]

At my school, the sequence was:

 

Alg I

Geometry

Alg II/Trig

Calculus OR

 

Geometry

AlgII/Trig

Trig/Analytic Geometry

Calculus

 

I was on the latter track, but junior year I wanted to take Creative Writing and it conflicted with the Trig/Analytic Geometry, so I took Probability (a class aimed at less mathy students) instead, since I figured that since some people were going right from Alg II/Trig into Calc, the other course must be filler to stall people so they didn't run out of math courses (my school required 4 years of math and didn't go any higher than the Calculus course). There was no course called Pre-Calculus, so I've always kind of wondered exactly what that was (I have been somewhat enlightened by reading this board).

 

When I got to Calculus senior year, I floundered for the first time ever in a math class - don't know if it was that I'd missed something in the Trig/Analytic Geometry course after all, or if it was just a really bad idea to take a whole year off from rigorous math right before Calculus...

[asta]

I don't know if this helps or not, but if you're not looking for your kid to have "tested out" of classes prior to going to college, the majority of colleges I've been looking at (and they have all been for physics programs) all just want a kid to have a solid background in pre-calc. They want to teach the kid calculus - their way.

 

I've been focusing on going very slowly through Alg II (Systematic Mathematics - which allows no calculator use), and will then switch over to R.E.A.L. Mathematics for College Algebra (advanced Alg II, of which we've already done about a 1/4). REAL has a trig program, too, but I also have a "trig for physics" class that I found in an obscure student guide to the CalTech Mechanical Universe Physics course he'll be taking (thank god for old, obscure libraries...).

 

Personally, I think the best thing we can do is get them older texts with either the problems worked out in the back, or some type of teacher's edition to show the longer problems so that they can see where something went wrong, and then a calculator supplement to teach them how to utilize the new fandangled technology (which tests like the SAT assume, but profs don't, necessarily). Boy, that was a long sentence. I think it was even grammatically correct...

 

 

a

[creekland]

As a slight difference from Asta's experience, colleges we've talked with for our oldest didn't want to see kids who had Calculus because they'd found those coming in with it didn't really know it enough. Their high school, or perhaps community college, course wasn't really up to snuff even though they were given credit for it. Many colleges WILL accept AP credit, but shy away at anything else in majors where it matters. Some no longer even accept AP credit. Pretty much all give some sort of placement test of their own to see where a student should start.

 

Edited to add: Colleges like to see that a student has ATTEMPTED Calculus, they just don't trust that Calc course without proof. It didn't come out right the way I worded it above - that appears to imply they don't want to see Calc on a transcript - not so - they do like to see it there. They just don't trust it without more proof.

 

My oldest used Chalkdust for Calc. I don't have it right here, but I think it used Larson's text. He tested out of needing math in college, but is not in a math heavy major (doing business or economics as one of his degrees).

 

I, personally, wouldn't skip Pre-Calc. However, I would let a student move at their own pace through it. If their previous books have covered the same material, move on. Different books do have different scopes. If a student doesn't do well with Pre-Calc topics they are unlikely to do well in Calc. It doesn't really matter what name the book with those topics has.

 

I'm another that prefers the student learn the math, then add the calculator. I see way too many students that can use a calculator, but have no clue how to do the math without one. Everyone I've seen that can do the math can fairly easily adjust to using the calculator.

 

Some math profs in college no longer allow the graphing calculator to be used in class, or don't allow it on certain parts.

Edited September 2, 2010 by creekland

[memphispeg]

We are using Foerster for Pre-calc. There was no way that my daughter was ready for Calc. after her ps Alg. 2 course. She likes the book v. much. I think a year of confidence building is due b4 Calc. If I remember correctly, having a good pre-calc./trig. class made calculus much easier. Foerster is good for both calculator and non-calculator based problem solving. It is easier to do some of his problems w/o the calculator....you sketch and think....good for the brain. The calculator is good for confirmation tho'. His tests have calculator and non-calculator problems.

[flyingiguana]

 

Personally, I think the best thing we can do is get them older texts with either the problems worked out in the back, or some type of teacher's edition to show the longer problems so that they can see where something went wrong, and then a calculator supplement to teach them how to utilize the new fandangled technology (which tests like the SAT assume, but profs don't, necessarily). Boy, that was a long sentence. I think it was even grammatically correct...

 

 

a

 

I agree -- a calc book with worked out answers is the way to go. The publisher and author is less important than having those worked out problems.

 

Don't skip trig. It can be covered on its own, in the algebra 2 year, or in the precalc year. But don't skip it and assume the student will pick it up in the calculus year.

 

Pre calc may also cover some topics that are nice to know but aren't necessary for calculus. Sometimes it seems to be a grab bag of things that just didn't get done in all the years previous. Just because they may not be needed for calc doesn't mean a student shouldn't do them. There's more to math than calculus. Pre-calc usually also includes algebra review. Even with kids who did well in algebra the first couple times, this review is very important. You need to be able to do algebra in your sleep, or calculus will bowl you over.

 

Calculus books do include chapters on trigonometric functions (they should, anyway, or you're not getting a full calc book), but the basic trig is generally assumed at that stage. The trig in a calc book is a further embellishment on what students are supposed to already know. And as the students have already learned it by the time they get to calc, a calc book won't usually cover the topic adequately. The trig chapters in calc books may do a quickie review of basic trig before launching into the calculus of trig functions. For an extremely bright kid, that review *might* be enough, but I kind of doubt it. FWIW, my older one is extremely good at math. She blasted through alg/geometry/trig years before the average college bound kid, but she slowed down for pre-calc and did a thorough review. She just wasn't ready for calculus yet. Calculus assumes a facility with all the previous math that is difficult to attain with only one pass through. We started calc and realized it just wasn't going to work (at least not to the level I expected out of her), so we went back and did the review and picked up those other things in precalc. When she came back to calc,she was ready. She still managed to finish all her math requirements for the physics major before she ever got to college.

 

We used this book:Calculus: Graphical, Numerical, Algebraic (Finney, Demana, Waits, Kennedy)

It had a lot of graphing calculator problems, as I recall. If the plan is to take the AP test, it's really essential to know how to use a graphing calculator. If the student is going to take a test with the calculator, they really need to learn it early. Adding it on later is a big mistake. There's a sizable learning curve. (Don't ask me how I know...)

Edited September 2, 2010 by flyingiguana

[Jane in NC]

My oldest started college a couple days ago and is still not happy that I had him work through a Pre-Calc book in 10th gade. I thought he had to have "Pre-Calc" prior to going into Calculus. We worked through Pre-Calc and he kept saying to me---I know this and I would have him do more problems. ugh....... However, he had worked through one of those old Alg 2 w/ trig books and I had drilled him on trig, and solving quadratic equations and working with functions all prior to Pre-Calc. The one benefit we found was that DS had to use a graphing calculator w/ his Pre-Calc book. Using a calculator, let alone a graphing calculator was new to him.

 

 

 

For clarification, let me add that Blue Hen's son used an old Dolciani Algebra II/Trig text which has material that is equivalent to a modern Precalc text. The old Dolciani series did not have a Precalculus text. Rather, students would move on to a book called Introductory Analysis which is more focused on proof than modern Precalc books.

 

I will argue that not all math texts are created equal. Consequently, some students would be able to move from Algebra II/Trig to Calculus; many will not be able to attempt a rigorous Calculus course after Alg II/Trig without subjecting themselves to great pain and significant gap filling.

Edited September 2, 2010 by Jane in NC
clarity

[MomsintheGarden]

I agree that colleges want proof of Calculus knowledge. Ds goes to engineering school. He used Chalkdust, which uses a Larson book, to study for the Calculus AB AP exam, and got credit for Calc I. The school required all students who had gotten AP Calculus credit to take a validation exam before starting their classes.

 

I think it's common practice for schools to double-check, no matter how high a student's score is on their AP Calc exam. They don't want students floundering in upper-level math.

 

GardenMom

[Guest Barb B]

DS(12th) and I are doing calculus now (we started last semester). There is no way we could have done it without precalc! In fact, we are watching TTC dvd on calculus and the professor emphasizes (more then once!) how important pre calc. is. Just remind dh that his alg. textbook must have had alot of precalc in it. Also - your son is only in 10th - why the rush? Pre calc is very important.

 

Also, doesn't the ACT math test have pre calc in it. I also think the SAT subject math tests do to. It would be worth your ds's time to cover that info well.

 

Barb