Calc without precalc?

[Wildcat]

There is a thread on the hs2coll yahoo list discussing heading into calculus right after alegbra 2/trig due to the fact that much of precalc is 'review'.

 

Providing a student fills in any gaps as they are found, what do you all think about that school of thought?

 

:bigear:

[Jane in NC]

I would say that it depends on the strength of the Algebra II/Trig course. Unfortunately some students see more Algebra II than Trig. Usually a pre-calc course is split between additional polynomial algebra; some work with exponentials and logarithms; and trig. A good pre-calc course will also include sequence and series work. If the Algebra II curriculum has little coverage of transcendental functions, then skipping pre-calc might be problematic.

[regentrude]

Trigonometry is usually part of precalculus and about a semester's worth of material. If this were squeezed into an algebra 2 course, I would be concerned about the coverage of the algebra 2 material.

 

Our precalculus course was far from review. Geometry had introduced some basic trig, but precalc spent several chapters on trig identities and geometry applications. Algebra 2 had introduced polynomials; precalculus went much deeper. Vectors and matrices that we covered in precalc were not covered in algebra 2 at all. Polar, spherical and cylindrical coordinates had neither been covered in algebra 2 nor in geometry.

[kiana]

I could see it happening with a bright student who got a solid A in an honors alg 2/trig class that followed an honors alg 1 and an honors geometry class. For a specific example, I think Foerster's alg 2/trig would be enough if thoroughly understood.

 

But I wouldn't do it if the student got anything but a solid A in the alg 2/trig class. Why hurry up just to struggle in calculus?

[Jane in NC]

Why hurry up just to struggle in calculus?

:iagree:

 

So many students struggle in Calculus not because of Calculus concepts but because of algebraic problems or lack of connection between trig concepts. Solid understanding is indeed needed to make the transition.

[Dana]

 

So many students struggle in Calculus not because of Calculus concepts but because of algebraic problems or lack of connection between trig concepts. Solid understanding is indeed needed to make the transition.

 

Fractions, unit circle, trig identities, exponential rules (especially when using fractional and negative exponents), anything with logarithms.

 

When I've taught calc, students flunk because of these main issues (and not doing homework, but that's kind of separate).

[Wildcat]

I'm glad to know I'm not alone in the thought that it's not wise to skip precalc. 

[Gwen in VA]

I would never skip precalculus.

 

My own kids did Dolciani for algebra 1 and algebra 2, so they had a strong algebra foundation. For precalculus we used Brown's Advanced Math, which applies the math learned to all kinds of new and interesting situations.

 

For them, precalculus was not really about learning new topics; precalculus was not only about getting super-comfortable with the math they new but also learning to apply the math in new situations. For them, precalculus was a relatively "easy" class, but it was necessary -- it cemented their math foundation.

 

I did consider skipping precalculus with my first, and I am very very grateful to the friend who talked me out of skipping it!

[Wildcat]

They are coming from the viewpoint that the PreCalc offered to their child is mostly review. I see it here with my sons's courses -- they oculd easily have spent a few weeks to learn the new material over the summer and taken Calc instead. the main problem is that algebra1 is watered down, and that shoves material that used to be covered in a1 back to a2. a2 is a busy busy course, and weaker students don't master it, necessitating a second chance in precalc. So, precalc omits units such as matrices, vectors, prob/stats. I would guess these parents have had their children do those units in summer enrichment or with their tutor or math club.

 

Now that I have read all of the replies on that thread, I can see what they (and you) are saying. Thanks for explaining it.

 

 

[EKS]

Speaking as a person who took the first two semesters of calculus in college after having gotten a D in Algebra II in high school (with zero retention and little understanding) and before that having had to retake Algebra I during the summer between the 8th and 9th grades (and still not understanding it), I can say with certainty that it is possible to get a C in calculus with a prealgebra-level understanding of math. But I wouldn't recommend it.

[Jann in TX]

Another -- not suggested vote.

 

Pre-Calc is all about USING the Algebra skills taught in Algebra 1 and Algebra 2.

 

Skipping Pre-Calc would be similar to assigning an essay without teaching paragraph development! SOME students can learn as they go (we are talking cream of the crop natural math students)--but the majority of average and above average students need Pre-Calc.

 

Lial's Algebra 2 is a strong text but it does not include Trig. Lial's Pre-Calc picks up where the Algebra 2 left off ( analytic geometry --circles and such.) and has an emphasis on problem solving and application. It also covers some 'Algebra 3' concepts rarely found in Algebra 2 and has a semester's worth of Trig.

 

I think of Pre-Calc as a maturity class-- it forces the students to THINK about algebraic relationships--it is more than following a pattern.

 

Solid Algebra skills are vital to success in Calculus.

[In The Great White North]

They are coming from the viewpoint that the PreCalc offered to their child is mostly review. I see it here with my sons's courses -- they oculd easily have spent a few weeks to learn the new material over the summer and taken Calc instead. the main problem is that algebra1 is watered down, and that shoves material that used to be covered in a1 back to a2. a2 is a busy busy course, and weaker students don't master it, necessitating a second chance in precalc. So, precalc omits units such as matrices, vectors, prob/stats. I would guess these parents have had their children do those units in summer enrichment or with their tutor or math club. The high schools in this area that do have honors courses have a pathway for the top students that skips precalc.

 

:iagree: And you can tell by looking at the table of contents in your alg I and alg II books. Ds did alg I in a school with a 90's Dolciani and redid it homeschooling in 9th with an older Foerster. The Dolciani ended with the quadratic formula, which was only half way through the Foerster text.

[flyingiguana]

I wouldn't skip it unless the earlier courses were really good and intensive. And if the student had mastered the material *extremely* well. Even then, I wouldn't skip it.

 

Even though my older one was a math whiz and it looked tempting to skip, we did it anyway. And I'm really glad we went through the pre-calc. The repetition is really good before moving onto calculus. By the time a student gets to calculus, they really need to be able to do algebra in their sleep, or they get bogged down with that and miss the concepts that are being taught.

 

And just about every student, even if they do very well in a class, will forget a good chunk of the material by the time they need it again if they've only seen it once. Repetition is essential.

[Julie in MN]

I asked my youngest about this. He was strong in algebra but last semester he took Algebra3/College Algebra (through a college) and now he's in Precalc through the same college (very different teacher), so he's taking both of those in between Algebra 2 and Calculus (plus he did a bit of AOPS after Alg2 but didn't like it).

 

Ds's thoughts are similar to these:

Pre-Calc is all about USING the Algebra skills taught in Algebra 1 and Algebra 2.

 

Repetition is essential.

 

 

For example, ds said that yes, he had the quadratic again. But it was jumping right in, and it was mixed in with everything but the kitchen sink (imaginary numbers etc.). So it was the same topic, but a totally different pace, without being spelled out, and done while jumping in and out of various topics he had done separately in the past.

 

I suppose it might depend on what you plan to use. For instance, jumping into a 1 semester college course might be impossible, while jumping into a full year course meant for high schoolers might be more do-able?. Or, a student could do one semester of precalc, at the "college pace," and then feel ready for calculus, itself?

 

Of course every family is different, but we like getting things solid here. My eldest started Calculus three times -- at his public school, at the community college, and at his final university. He got A's all 3 times, but he wanted the foundation. He graduated as an engineer in 4 years, while others tended to take 5-6, and maybe some of that was that he had a strong foundation?

 

Julie

P.S, The more college-prep high school in my area adds even ANOTHER year before calculus. They do algebra 2, FST (functions, stats, trig), then precalc, then calc.

[vonfirmath]

There is a thread on the hs2coll yahoo list discussing heading into calculus right after alegbra 2/trig due to the fact that much of precalc is 'review'.

 

Providing a student fills in any gaps as they are found, what do you all think about that school of thought?

 

:bigear:

 

I went from Algebra 2 to Trigometry/Analytic Geometry to Calculus BC. No sweat

 

The next year they called the Trig/Anal Geometry class Precalculus instead. I don't know what changed in the class and how it was taught.

 

But yes, depending on the information in the Trig class, going from Trig to Calculus makes sense.

[kiana]

 

I went from Algebra 2 to Trigometry/Analytic Geometry to Calculus BC. No sweat

 

The next year they called the Trig/Anal Geometry class Precalculus instead. I don't know what changed in the class and how it was taught.

 

But yes, depending on the information in the Trig class, going from Trig to Calculus makes sense.

 

I think you are thinking of a different sequence than they are. The sequence that they are talking about is:

Algebra 1

Geometry

Algebra 2/Trig (one course)

Precalculus

Calculus

 

Whereas you seem to be talking about:

Algebra 1

Geometry

Algebra 2

Trig

Calculus

 

Both of these sequences have the same number of courses in them, and contain the same amount of material -- it's just divided differently.

[In The Great White North]

FWIW, back in the day, I did:

 

9th gr - Alg I

10th gr - Geom

11th gr - Alg II/Trig

12th gr - Calc BC

 

So there were definitely schools that skipped pre-calc.

[zenjenn]

Ditto the above post. I never even heard of Pre-Calc until recently.

[kiana]

The alg 1/geometry/alg2trig/calculus sequence was a lot more common when it was nearly unheard of for students to take algebra before 9th grade. Postponing algebra until 9th grade or later allowed for more breadth and depth of coverage in the high school courses, so that calculus could legitimately follow algebra 2/trig.

 

In most cases now, the algebra courses do not cover what they did then (foerster's is an exception, but many places do not use the whole book) and so needed information may be missed.

[Kristie4]

We are moving into Calculus after doing the whole Foerster's book. My dd is taking it at the local University. We looked through all of the topics (they call of the courses here in Manitoba pre-calc if you are in the non 'applied math' stream) in the Grade 12 math course and Foerster's has them covered. I would still like my dd to do some review of topics over the late spring and summer and she is eager. Does anyone have any suggestions for a refresher for some of those need to be fresh topics??

[AngieW in Texas]

Since I'm a curious creature ( :D ), how would I know whether or not precalc would be a review for my child and she should/could move right into calc? For instance, dd had Jacob's Alg, Prentice Hall geometry (did all the problems in the book except for those that required a 'class' setting, and is currently in a Lial's Alg 2 class. Admittedly, I haven't looked to see if there is trig in the Lial's book. So, if, say, dd, spent the summer doing trig (to learn or just reinforce), how would I know if skipping precalc would be the right choice here?

 

FWIW, I'm not asking because I would have dd skip precalc, I'm asking because I'm truely interested as I hadn't seen this come up before.

 

I am tutoring a student through Lial's Intermediate Algebra right now. A student would NOT be ready for Calculus after this text. It's a solid Algebra II text, but it doesn't go any further than that.

 

My two older girls both used Kinetic Books Algebra II. It covered everything in Lial's Intermediate Algebra and also covered almost everything in Lial's Precalculus. I think it is certainly possible to move straight into Calculus after KB Algebra II. I still had both of my girls go through precalculus though. It's better to have a solid foundation.

[caroljenn]

What text did you use for precalculus? My dd, who went to a private school through 8th, used Pearson/Prentice Hall math books and she likes them. I am going to have her do precalculus next year because she is going to be an engineering major and needs a good foundation.

 

Thanks ahead of time!

[Wildcat]

I wanted to say "thanks" to everyone who participated in this discussion. It has been most interesting!!

 

[regentrude]

Anyway, I wonder if the 'invention' (for lack of a better word) of a precalc class was necessary due to the many math books covering different topics/not moving at the same speed. A dumbing down of math? I don't know.

 

I find that there really is no such thing as "precalculus", in the same sense that there is no such thing as "prealgebra". It is all math, and some topics must be covered before others because they are a prerequisite. How the course is labeled is immaterial; the packaging of math into neat portions with labels such as "algebra" and "precalculus" is an idiosynchrasy of the US school system.

It would be much more sensible to compare actual content instead of course names.

[Kristie4]

My dd is finishing up Foerster's Algebra and Trig- she is going straight to the U. for calculus. I looked at our school systems topics and she will have covered them all.

 

On a side note, she was at an engineering fair yesterday and answered almost every math question from the prof., including ones from the second year engineering math class that the students were having a time with. I would love to take credit, but she is pretty much self taught at this point. It was a nice break from the anxiety of transcripts right now...