# Gas station without pumps

## 2011 February 2

### Trig and Anal Geo

Filed under: Uncategorized — gasstationwithoutpumps @ 07:35
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I have never really understood parents’ objections to math homework, nor teachers’ objections to textbooks, until now.  My son has always delighted in math, and math homework was always the least difficult to get him to do, nothing like the meltdowns over writing homework.  He has always chosen math or computer programming for science fair projects, because they are fun for him, and he has done fairly well in contest math (winning county math competitions in 5th through 8th grades, for example) without really studying.

Doing 20–30 minutes of algebra or geometry was no big deal, and while books like Foerster’s Algebra and Trigonometry were not riveting reading, they were easy to learn math from. He did self study from Ruscyk’s Introduction to Geometry when he was in 6th grade (before taking a more formal 2-column-proof class in 7th grade) and he raced through Ruscyk’s Introduction to Algebra in the summer between 7th and 8th grade, before taking Algebra 2 Honors using Foerster’s book in 8th.  The Art of Problem Solving books were good, with just the right level of explanation for him and challenging problems.

His study approach was to read the section, then tackle the hardest problems Ruscyk presented.  If they stymied him, he’d drop back to the more straightforward ones to get more practice before tackling the tough ones again.  When he got one of the tough ones, he almost sparkled with delight at having done it.

This semester he  has just started a course titled “Trigonometry and Analytic Geometry” as the filling between Algebra 2 last year (at a different school) and calculus next year, since he hasn’t had any trig (other than SOHCAHTOA and $e^{i\theta}=\cos \theta + i \sin \theta$, which he learned for doing phasors in sinusoidal circuit analysis).  They are using Larson and Hostetler’s Precalculus 6th edition (Houghton Miffilin, 2004).  He was disappointed to find out that they don’t get to trig for over a month, doing a review of algebra instead.

One week into the course, and he is already ground down by mountains of mindless drill.  The teacher assigns 30–40 problems a night—all very, very boring routine work. Word problems are very rare, and the few there are look like

The cost of sending an overnight package from Los Angeles to Miami is $10.75 for a package weighing up to but not including 1 pound and$3.95 for each additional pound or portion of a pound.  A model for the total cost $C$ (in dollars) of sending the package is $C = 10.75 + 3.95 \lfloor x \rfloor,~x>0$ where $x$ is the weight in pounds.

a) Sketch a graph of the model.

b) Determine the cost of sending a package that weighs 10.33 pounds.

This isn’t even the pseudocontext that Dan Meyer rails against, but complete destruction of the whole idea of a word problem—the students don’t have to read the English, since they are handed a formula and asked to graph it. One or two such drill problems would be ok, but 30 a night, every night, with no end in sight?

I can see now why none of the other students in math club are interested in doing recreational math or preparing for math contests—they need to spend all their time grinding away at the mountains of math homework.  I can’t think of a better way to kill all the joy of math and send students screaming away from entering STEM courses in college.  (The teacher has expressed a belief that this amount of homework is the bare minimum for the students to learn the material, and she’d rather be assigning much more, so asking for a reduction in homework seems futile.)

We looked at skipping him up to the next level course (“Introduction to Calculus”) but that seems to have the same structure of 30–40 drill problems every night, and he’d miss learning trig, which has some very pretty and very useful math in it.  I’m thinking that the lifeline may be the Art of Problem Solving on-line Precalculus class.  We know that the books from AoPS are good, and one class meeting a week with self-study in between is probably about the right ratio for him.  I have enough math education to help through any spots he gets stuck in for at least a couple more years, so there really isn’t much need for daily classroom instruction, and certainly no need for hours of mind-numbing drill.

In the time freed up, he might even be able to work on his science fair project!

We met with a high-school counselor today to see if there is a way out for him that will let him learn the math without losing his love for math. An online course doesn’t count toward the school’s Average Daily Attendance, so they required him to replace the course, not just drop it. Result: he dropped the trig class and added a video production class.  There weren’t many options open, since almost every class at the school is full, but the video production is synergistic with his interest in theater, so it may even be fun for him.

The AoPS course is not accredited (so it can’t be put on his high school transcript), and so he’ll have to find out if he can do credit-by-exam for the trig class.

1. This is an incredibly common problem, which is very sad. Seems like teachers don’t realize there is any other way to learn math than rote repetition, of the same thing for 30 problems. I used Saxon math when I was that age, which gives a set of problems per day that continually mixes the types of problems (mostly old, some new concepts). Much less likely to get boring.

But I applaud you for finding a solution! (Despite the silly regulations on attendance…) Sounds like the new situation will be much better for all involved.

Comment by Miss Outlier — 2011 February 2 @ 08:17

2. Ah, it’s too bad that he couldn’t take it independent study.

You might consider University of Missouri’s high school math courses if you want an accredited course. They are less expensive in some cases than the talent search courses. They use Larson for online Trig and Brown for distance PreCalc. We haven’t used them yet, but that’s the plan when we exhaust the free courses at our high school since we don’t want the gen ed Community College versions of the classes above Alg II.

Comment by D — 2011 February 2 @ 12:32

• We’ve used the AoPS books for self-study before and are very happy with the approach used in them. The online course here is mainly a way to keep focused on going through the whole book. I don’t really care as much about the accreditation as about keeping him interested in math. I mean, accreditation would be nice, but it probably would not reduce the hoops we have to jump through to get the credit on the transcript. The credit-by-exam method is probably simpler than transfer credit.

Comment by gasstationwithoutpumps — 2011 February 2 @ 22:05

• I hope so.
For us, transfer is easier as it just takes the principal’s signature.
Credit by exam here means the dept final plus a project. After doing the work at the honors level where the dept only offers reg ed, I just don’t want the boy to waste more time on a project. I have my doubts about the current dept writing a fair exam also, especially since they don’t offer the courses on campus any more.
I”m tempted to not do anything official after Integrated Alg. II which means ds would follow his college’s placement and test out policy.

Comment by D — 2011 February 4 @ 07:28

• Our high school does not provide mechanisms for transfer of unaccredited classes. They routinely transfer credit from other high schools, from the community college, and from the university.

The mechanism we are planning to use is called “challenging a course,” and provides credit for the course being challenged. Usually the challenge consists of the final exam in the course (at least for math courses, where such an evaluation is a reasonable assessment method). We have already used the mechanism once—my son challenged the 9th grade “core” health course, since he had just had a similar course in 8th grade and didn’t think he could sit through another one. He only got a B on the test (they asked some questions that indicated that they had not updated their curriculum in a while, like the ratio of breaths to compressions in CPR), but he was willing to take the hit on his GPA to avoid the tedium.

Comment by gasstationwithoutpumps — 2011 February 4 @ 10:45

3. FWIW, this is precisely what we encountered with my elder, a mathy kid. She ended up replacing precalc with AoPS trig and complex numbers (since renamed Precalculus) and officially taking a study hall for the first class of the day (with “late arrival” so she could arrive for second period instead of 1st). We did have to work out a way for her to still graduate had she remained in that school, even though we knew she was transferring at that point. There was only 6 weeks in an entire year that she hadn’t already mastered.

Her sister will be in the exact same position next year, but she is not a mathy kid. We’ll see how it turns out.

Comment by MJ — 2011 February 2 @ 12:35

4. Is this type of drill appropriate for some children? Then, I guess we’re stuck finding the appropriate accomdation for our children, who don’t need that amount of drill. But, I’m struck by the idea that anyone would benefit from doing 30 problems that are basically the same problem over and over again (and, I share the particular annoyance of “word” problems that are of the form “blah blah blah blah 7x+3 blah blah blah blah blah x=2” and their variants).

But maybe I’m wrong, and some children do need to practice the same problem with minor variants for a long time to get the concept (or alternatively need enough examples to build a big enough look-up table to do the problems expected of them on texts?)

Comment by bj — 2011 February 2 @ 14:05

5. Welcome to the occasional absurdity of education. I know you’ve managed to mostly dodge this bullet until now. I’m sorry you’ve had to learn firsthand that these teachers do exist. I’m even sorrier that I’m sure they think they are “doing right” by their students.

Comment by Kelly Sorensen — 2011 February 2 @ 17:53

6. […] in algebra, with 30 rather mindless problems a night, every night. (I posted on this at the time in Trig and Anal Geo).  We needed a course that covered trigonometry at a reasonably fast pace and provided challenging […]

Pingback by Good online math classes « Gas station without pumps — 2011 April 19 @ 17:59

7. […] recommendation from freshman bio to honors physiology), but the math course was a disaster (see Trig and Anal Geo) and English was worse (not the teacher’s fault, just a mismatch between my son and the […]

Pingback by Debate about how schools treat gifted students « Gas station without pumps — 2011 October 8 @ 18:50

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