# Gas station without pumps

## 2016 September 6

### Step drills

Filed under: Uncategorized — gasstationwithoutpumps @ 12:06
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I tried a new (to me) tool yesterday—a step drill bit:

This step drill is for drilling holes from ⅛” to ½”, in increments of 1/32″.

The purpose of a step drill is to drill large holes in thin material (like sheet metal) neatly. Yesterday, I needed to drill ½” holes in a plastic project box for the USB-to-DMX adapter that my son and I are working on (him much more than me). Because the holes had to be very precisely placed, I decided to try using the step drills I’d bought earlier this summer, though I could have also used a ½” Forstner bit for such a soft material.

To use the step drill, I first drilled a starter hole (3/32″) smaller than the smallest size on the bit (1/8″), then I changed bits on the drill press and carefully aligned the bit to be centered on the starter hole. Because I was going all the way to the largest size on this drill bit, I did not have to set the stop on the drill press—if I’d wanted a ⅜” hole, I would have needed to make sure not to drill too deep. Because I was drilling plastic, I did not need oil for cooling and lubricating the bit, as I would have if I were drilling sheet metal. Drilling the hole was very fast, and the hole was quite clean.

It may not have been necessary to drill the starter hole, but the tip of the step drill did not look that sharp to me, so I figured that the extra step of making a starter hole was worth the time. Some of the bigger starter bits really do need a starter hole to enlarge.

I have several step drill bits now, because I bought two sets from Harbor Freight when they had a coupon sale on them earlier this summer:

These five bits normally cost about $34 from Harbor Freight, but I paid$24 on sale. The bit I used is the rightmost one, which provides 13 different hole sizes up to ½”. Other bits in the set let me drill thicker material or go up to 1-⅜”.

The bits are cheap and probably not likely to last long drilling hard materials (like stainless steel), but I’ll mainly use them for plastic and aluminum, and I don’t need to drill very many holes with them to justify the price.

## 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.