Advice Needed for Summer Math Class

My son needs to take Calc Honors next year (sr year of high school).  He took Trig Log Calc Honors as a sophomore, but it was a waste of a year.  Catherine's son had same teacher -- so it was same problems, but then add to that that he was out sick with mono for 6 weeks.

He did not take Calc this year (i.e. Junior Year) because it would have been the same teacher, and we could not live through that again.  Plus, he didn't want to take that risk for  his junior year transcript.

Instead, he took AP Stat - which is fun for him, but not really a math class.

So, I need to get him ready this summer to take Calc in the Fall.  First, I'm not sure if he should take a pre-calc class -- or take a calc class and just audit it, my thought being that he'd  pre-learn the material before school starts.

So that's my first question: Calc class vs Pre-Calc. class

Here are the 3 options I was thinking about:

1) MIT Online math class.  I haven't looked into, but I understand they have High School courses.  He loves this idea.  I wonder whether an online course could work for him.

2) Local community college (Mercy).

3) Local Private school summer course (Horace Man was recommended).  IT needs to be some place he can get to via public transportation, as I can't drive to from every day.


The other thing to add is that he has a summer job lined up (90%) -- so the most time-efficient way for him to do that is a variable too.  i.e MIT sounds appealing because it's on his own schedule.  Horace Mann sounds good because it's only 6 weeks (I think).  I haven't checked into Mercy College schedule.

SAT story & apologies for the disappearing act

Wanted to say quickly that I've got at least 4 meaty emails waiting for me, which I'm not getting to because they're vying for attention with a stack of student papers and so far the student papers are winning.

Hoping to get to emails later today!

I shouldn't be writing posts, either, but I had to pass this along.

C. just came into the kitchen and told me this story.

One of the math kids in his class, a kid so good at math that the calculus teacher (this would be the calculus teacher whose class C. has dropped) told him he could "sleep through every class" and get an A, got a 650 on SAT math.

650.

I say that's a benchmark. A gifted math student who takes the SAT cold gets 650.

C. said, "He doesn't care about the SAT. He's going to X University no matter what."

His folks have free tuition at X U.

update: The last two lines above are ironic.

update update update

Quick note: C., who has left his calculus course for statistics (thank you all for the advice), just told us the calculus teacher is giving his students an essay test. Just to review: this is a calculus class populated by kids who learned next to no precalculus last year. They're in calculus, they don't know any precalculus, and...they're taking an essay test.

Ed said, "You should have stayed in the class. You could have raised your grade."

That was a joke. We both know it's not true. If C. had stayed in the class, he would have done worse on the essay test than he did on the math test, I'll wager.

Must get Allison's Comment about charismatic teachers pulled up front.

C. loves statistics. Loves! First math class he's ever felt that way about.

Courtney James

re: what to do about C. and calculus, Crimson Wife writes:

I have no personal experience with him, but I have heard numerous raves about Courtney James' tutoring from fellow moms in our local homeschool support group. He tutors AP Calculus BC according to his website. 

Exciting!

help desk help desk help desk help desk help desk help help help

arrghh

First of all: once again, I'm sorry to be MIA -- I'm looking forward to becoming a regular on my own blog some time again soon.

Second: help! help!

C's second calculus test came back today: a disappointment, and a Bad Sign. And I am fresh out of enthusiasm for dealing with another year of high school math. Meaning: I am fresh out of enthusiasm for dealing with high school math teaching and high school math grading and high school math hiring of high school math tutors to remediate high school math grading and high school non-learning of high school math and on and on and on and then further on and on some more.

I'm done.

Also: calculus tutors are few and far between. I found only one last year, and the lone session he had with C. didn't help. Other parents have told me they couldn't find calculus tutors, either, and for years I've been hearing things like: "My son did well in BC Calculus. We were lucky because his father can teach it." As I recall, the mom who told me her husband could re-teach BC Calculus at home also told me that her husband's first cousin was an economist who had won the Nobel Prize. I'm pretty sure I'm not making that up.

Nobody in this house can teach calculus. I haven't even finished taking algebra 2, and Ed has forgotten the calculus courses he took in high school and college and doesn't care to revisit them.

So here we are.

Also - and this is a repeat - last year's math class was a total, effing disaster. The teacher was and is seriously ill but is still teaching, and the kids were and are dropping like flies. A huge percentage of last year's AP Calculus AB students got 1s on the AP test. Ones. And when I say "huge percentage," I mean eighty-five or ninety percent: the guy broke the bell curve. This was the teacher C. had for pre-calc, so C. is bringing to this year's calculus course an epic level of non-preparedness.

The teacher C. has this year is supposed to be fantastic and in fact told us he was fantastic on Back to School Night (he actually said: "I am it," which was exhilarating at the time), but if the grades are not great then the learning is not great, either. Fantastic is as fantastic does.

Ed is thinking we should just transfer C. to AP Stat (or maybe it wouldn't even be AP Stat - maybe just "Stat Honors," a class in which, according to C., students recently took a test on bar charts after completing a bar chart project) and be done with it.

That's pretty much how I feel, too, but it leaves the problem of algebra 2 and calculus, neither of which C. will have learned in high school -- and neither of which I want him taking in college since he'll likely be attending a school with kids who are a lot better than he is in math. At this point it is crystal clear to me that there is no reason on Earth to take a math course in college, pay for it, get a bad grade in it, and not learn any math. And I'm thinking the same principle holds true for high school. Why spend a single second of your (child's) life in a non-required math course so he can not learn math?

Last data point: C. did fine on the first test in the class and thought he did well on this test, too. He did great on the diagnostic test going in, and is doing well in physics. His mistakes on this test appear to be mostly "careless errors" (I have a whole new take on the nature of careless error thanks to the SAT) and a failure to follow correct notation, etc. In short, he appears to understand the material, not that I would know.

Of course, if that's the case then he needs more practice - but how do we swing that? The teacher doesn't seem to use a textbook, and I'm not going to be able to scrounge useful practice sets this go-round as I did for the 3 years when C. was in middle school.

(Could I talk to the teacher? Why, yes indeed I could talk to the teacher. But seeing as how talking to a math teacher has yielded exactly zero results over lo these many years, talking to the teacher wasn't my first impulse. Writing a help desk post was my first impulse.)

So...any thoughts?

We had a great, great precalculus tutor last spring at the very end of the school year; if we'd hired him at the beginning of last year, C. might have learned pre-calculus. We could hire him again (I assume) and decree that this year C is actually going to learn pre-calculus, which means we could pay tuition for C. to study bar charts at his Jesuit high school and pay tutoring fees for him to study pre-calculus here at home --- who says Americans have to de-leverage?! If you've got kids in school and you want them to learn math, deleveraging is not for you!

Or....or what?

What else is out there?

He could enroll in a community college precalculus course -- when?

Now? While he's in high school? (While he's in high school commuting 15 miles there and back every day?)

Then take calculus over the summer?

Another question: are there solid precalculus and calculus courses online? I took all of the ALEKS geometry course and part of the ALEKS Algebra 1 course, and as much as I want to like ALEKS, as much as I do like the tone and feel of the site, I don't think ALEKS replaces a good teacher or a good textbook. But do others out there think that might be the way to go?

What about online schools and colleges? I know there are universities that offer online math courses that kids take when they've been expelled or can't physically attend their local schools for some reason. Is that a possibility? Any recommendations?

And while we're on the subject, can anyone out there explain to me how in this country does a smart student with no discernible learning, attentional, motivational, or emotional difficulties whose talents and interests lie in history/social science actually learn some damn math?

What does it take?

lsquared on what you must know to take calculus

(lsquared couldn't get this comment to post on Blogger):

Yes, you need to be very good at algebra. Think factoring, equation solving and complex fractions.

You also need to be quite good at trigonometry: knowing right triangle trigonometry is sufficient for almost everything except calculus--for calculus you need to know how to solve equations that have trig functions in them, and you need to know your trig formulas (the double angle formulas are particularly useful). You don't actually do any of the "verify this trig formula" stuff in calculus, but those "verify the trig formula" problems are very useful for teaching the algebraic trigonometry you use in calculus. Oh--and radians. I'm morally convinced that radians were invented to make trig functions work for calculus. Degrees are better for everything else, but in calculus, you have to have radians.

You also need to know logs: solving exponential equations with logs, solving log equations with exponents, and manipulating logarithms.

Back to rational functions. Be able to solve rational equations, simplify rational expressions that are not equations, and graph (by hand, not by calculator) rational functions (using properties of the rational function to graph, not by plotting points) (I may be unusually picky about this).

Sequences and series, including finding sums using the formulas for arithmetic and geometric sequences. Also the binomial theorem.

You don't need matrices, though you do need to be able to solve simultaneous linear equations. If there's a section in the pre-calc book on find partial fraction decompositions, that's directly a calc algorithm.

I think that might be everything you need for pre-calc.

This was an excellent exercise for me. I’m going to have to keep a copy of this to use when counseling students about whether they are ready for calculus or not. Indeed, the homeschooled kid next door wants to get into my calc class in the fall, and I shall be handing this to him I expect. Good luck finding a good class--I think the community college might be a good choice (assuming that they have a pre-calc course).

calculus in prison

from the WSJ article on factories lacking skilled workers:

While community colleges and technical schools struggle to keep up with demand for skilled workers, some prisons are trying to help. At California's San Quentin prison, the machine shop offers training to prepare prisoners to pass exams demonstrating skills in such areas as operating computer-controlled lathes and mills. Some inmates get classes in calculus and trigonometry to help them work with machinery.

MAY 6, 2011
Help Wanted on Factory Floor
by James R. Hagerty

getting ahead of ourselves

from purplemath:

• Given that f(x) = 3 x 2 + 2x, find [f(x + h) – f(x)] / h.

This is actually something you will see again in calculus. I guess they're trying to "prep" you for upcoming courses when they give you exercises like this, but it's not like anybody remembers these by the time they get to calculus, so it's really a lot of work for no real purpose. However, this type of problem is quite popular, so you should expect to need to know how to do it.

I'm a big fan of purplemath.

A view from computer science college professors

I hear from a friend who teaches college computer science that many CS educators agree on the following:

1. There is too much emphasis on calculus, and more focus should be placed on discrete mathematics (graph theory, logic, automata theory, etc) and statistics.
2. K-12 education places too much emphasis on memorization at the expense of conceptual understanding.  This leaves college students ill-prepared for their computer science course work.

Interesting.

Cross posted at Education Quick Takes

Wolfram Alpha

The long-running debate over whether students should be allowed to wield calculators during mathematics examinations may soon seem quaint.

The latest dilemma facing professors is whether to let students turn to a Web site called WolframAlpha, which not only solves complex math problems, but also can spell out the steps leading to those solutions. In other words, it can instantly do most of the homework and test questions found in many calculus textbooks.

The new tool will be a bane to teaching, some professors say—but others see a blessing.

WolframAlpha was created by Stephen Wolfram, an entrepreneur who invented Mathematica, one of the first computer math engines. His new site debuted last month to much media fanfare and, like Google, provides answers to questions typed into a simple search box. It is free and already boasts millions of searches.

A Calculating Web Site Could Ignite a New Campus 'Math War'
by Jeffrey R. Young

I need WolframAlpha for proofs.

A New Online Computation Engine Shakes Up Math

Barry G on learning physics in high school

We had a bit of physics in 8th and 9th grades. My first real course was as a senior in high school. The teacher was very good and I was totally amazed by the subject. Although it was not calculus-based, it did use trig which we were studying at the time, and math and science merged very nicely. I still remember the lecture on the derivation of the formula for distance of a uniformly accelerating body, relating it to the "area under the curve" which in this case was a straight line, and thus was the area of a triangle. I wondered why he called a straight line a "curve", and the next year in freshman calculus, it again all made sense, when we learned integration.

I can't wait to learn calculus.

Or physics.

Speaking of subjects I intend to learn, The Teaching Company has high school courses. I ordered the chemistry course. ^* I'm thinking of asking C. to work through as much of it as he can next summer, before he takes chemistry at Hogwarts. (He's taking AP biology next year, when he'll be a sophomore.)

I have Nature of the Earth, too, and Building Great Sentences, which is fantastic. Building Great Sentences is so fantastic that the other night, when Ed and an attorney friend were discussing the critical importance of writing short sentences, I rolled my eyes.

"You don't try to write short sentences?" Ed asked.

"No," I said curtly, leaving the men to wonder why.

While it is true that I personally have not read Strunk & White, I have listened to two lectures from Building Great Sentences, and thus feel confirmed in my view that short sentences are neither here nor there.


^*"This course was an absolute joy."

Richard on Physics First

I have a quote on my teaching room along the lines of .......

"There are three physics courses taught at most universities: physics with calculus, physics without calculus and physics without physics."

It sounds like Physics First could be a prerequisite for "physics without physics."

Speaking of physics without calculus, is this calculus without calculus?

I've been cruising this course for a long time....

I will derive

Math Program Reviews

Yes, occasionally I have some non-phonics thoughts.

The Well-Trained Mind has an excellent review of several math programs, here's a short excerpt:

Which method is better? In my opinion, the one which the student understands most clearly. In both cases, it is possible for the student to learn the mental trick without thoroughly understanding why it works, although the sheer amount of repetition in the Saxon method makes it easier for this lack of understanding to escape detection. But the strongest mathematical training of all would come from a combination of programs – in which the student is taught to do a mathematical process using several different methods and mental procedures.

Currently, Singapore and Math-U-See are “thought-oriented” math programs available to home school parents; Saxon and A Beka are “skill-oriented” programs. A combination of Saxon + Singapore, or Saxon + Math-U-See, or Singapore + A Beka, or A Beka + Math-U-See, may come closest to fulfilling the goals of classical education. Math-U-See + Singapore would also be an excellent combination, as long as you use MUS’s supplementary drill sheets. Treat one program as primary and the other as secondary; when you cover a concept in the primary program, look it up in the secondary program and see whether it is explained and illustrated differently.

I like her idea of using 2 programs. I do that all the time with phonics--I know what is best about each program and pick and choose accordingly, I have dozens of phonics programs from my tutoring. Also, if a student is struggling with a certain area, it's good to have a few books that explain it in slightly different ways. I hadn't thought to do the same with math.

There is also an interesting review at Sonlight, a basic review of their math choices from grade school through calculus, and then, they explain their choice for algebra and geometry--teaching textbooks:

• CD-ROM-based "whiteboard" lectures and step-by-step explanation of how to solve every practice problem taught by a tutor who has been teaching homeschoolers for years...since the days he tutored probability and statistics at Harvard . . . and . . .
• CD-ROM-based "whiteboard" solutions guide that works every step in every homework problem, so you see exactly how to solve each problem . . . and why you want to use the methods the instructor (or, more accurately, personal tutor) uses.

Their calculus choice, thinkwell math, also includes CD-ROM video tutorials.

We're currently using Math-U-See with our daughter for Kindergarten math. I personally like Singapore or Saxon better, but this is what is working for her. The good thing about Math-U-See is that they have a DVD with each lesson so that if you get that "blank stare," (yes, it is even possible with kindergarten level math!), you can just plop in the DVD and have an actual math teacher explain it in field tested verbage.

Math-U-See's approach to fractions is also interesting, I'm not sure what I think about it. The rectangles do make more sense to me than the traditional circle/pie method. From their downloads page, in sample lesson pages, click on Epsilon.

For an even more interesting and thought-provoking review, read Wild About Math!'s Calculus in 4th grade? I'm really not sure what I think about that one. Luckily, we're still doing kindergarten math so I have time to figure it all out.

calculus textbook recommendation

from anonymous:

You might want to try the Larson 8th ed or the Finney books. Much more "user friendly" [than Foerster] so to speak. I use Larson in my AP Calc (both AB and BC) but supplement from several others. Foerster has a supplement that goes with it called calculus explorations (and one for precal also) that are excellent.

Pre-calculus and Calculus at Key Curriculum Press

Thanks!

Information about Foerster's Calculus book

I'd appreciate any information about Paul A. Foerster's Calculus Concepts and Applications book.

Thanks.


Catherine here - dropping into ec's post

Here's a link to calculus text recommendations at ktm-1. (This may be all of them, but if not I'll try to post the other links later.)

bonus: calculus advice from Rudbeckia Hirta.

Barry's calculus text recommendation.

Elementary Calculus by Jerome Keisler

here

H. Jerome Keisler's home page