Welcome to the HappyCal Zone

(Honors AP Calculus BC, Period A)
Web address shortcut for this page: www.modd.net/67hapcal

Are you nervous when you see NCWEE? concerned when you see CIRC? perturbed when you see PBC? Visit Mr. Hansen’s fabled abbreviations page to make sense of those cryptic markings you see on your papers.


Schedule at a Glance (see archives for older entries)
Written assignments should follow the HW guidelines.


W 5/23/07

Final Exam, Trapier Theater, 11:00 a.m. Seniors with at least a B average and fewer than 12 absences for the second semester are exempt (assuming there is no senior prank, of course).

Material tested on the exam will be cumulative. However, since you have already taken a difficult cumulative AP exam, this will be a kinder, gentler cumulative exam. The material will be drawn almost exclusively from the IntroCal Saga study guide, a 6-page condensation of the most important material from the course.



Exam statistics:

n = 11
mean = median = 87 (after including 2-point attendance bonus)
s = 9


Sat 6/2/07

Compilation of student course evaluations:

I received the evaluations by e-mail today from Michael V., typed carefully and with all identifying characteristics removed. Per our agreement, he waited until after all the final grades had been submitted.

Many thanks to all of you for your candid and thoughtful comments. Most of the comments were echoed by multiple students. However, I also received some “singleton” comments (comments written by only one student) that are paraphrased below:

Positive singleton comments: Days off, field trip to National Cryptologic Museum, non-mathematical aspects of the course, oral exam in the piano practice room, “no calc” final exam, and presentation of techniques of antidifferentiation (Chapter 9).

Negative singleton comments or suggestions for improvement: One student said that except for the Lagrange error bound, the difficulty of power series (Chapter 12) was overstated. Another comment was ambiguous; the student said that the collaboration “cheating” scandal was unfairly handled, but because of the way the comment was worded, I could not tell whether the student felt that I was too harsh (because all students have collaborated at some time or another) or too lenient (because students are supposed to know that collaboration must avoid outright copying).

The remaining comments, all of which involved two or more students, are grouped below by subject area and summarized within each subject area.

AP preparation: 4 comments, 100% positive.

Fun Friday: 3 comments, 100% positive, although 2 of these 3 indicated that there should have been more playing of the association game.

General assessment of course and Mr. Hansen: 7 comments. Of these, 14% were positive, 29% were negative, and the rest were mixed. The verbal comments were more informative than the raw count, however. The 7 comments may be summarized and paraphrased as follows:


  • A most edifying class, though not the most enjoyable
  • Entertaining, but somewhat confusing, especially concerning the exam
  • Entertaining, but too hard
  • Glad to have taken the class, but it was too intense
  • Great teacher, organized, well prepared, etc.
  • Not very enjoyable and not sufficiently well focused
  • Too teacher-centric; problems should be worked primarily by students


Grading: 6 comments. Of these, 33% were positive, 50% were negative, and the remaining one was mixed (a student who said that the system was helpful overall but that positive points would be better than negative points). One of the negative comments was that there were too many A+ grades. The remaining 4 comments all dealt with bonus points: 2 thought the system was good, and 2 were opposed to it, saying that it unfairly rewarded people for nonacademic reasons.

Hardware: 3 comments, 67% negative. One person stated that the bar code scanner (Necroman) and class randomizer (Smokey) were worse than bad. One person stated that Smokey was a positive and thought that Smokey was not utilized enough.

Helpfulness in class: 7 comments, 86% negative. Almost all of the students who mentioned this topic stated that I need to provide more in-class worked examples and to provide more direct instruction. One student stated that I would be more effective as a teacher if I reached out more, using kindness as a way of closing what he called an intimidation gap. Two students specifically referred to cases in which examples that failed (as a result of numerical errors) wasted days of class time. One student thanked me for my willingness to consider all questions but stated that I sometimes needed to exercise determination to cut off questions and move on.

Response: This is probably the touchiest area and the area I most need to address for next year. I should provide more worked examples, particularly examples that are similar to known categories of AP problems. However, HappyCal cannot be (and probably should not be) a class like some others you may have had, in which each topic is introduced, explained for you, and put to rest with a series of cookbook-like example problems and templates. Calculus AB is not like that, but AB probably lends itself more to that model than BC does. One thing I certainly need to do next year is to set expectations properly, telling the BC students on the first day that if they need a lot of worked examples to feel comfortable and learn, they will probably be happier in the AB class.

Helpfulness outside of class: 1 comment, 100% positive.

Response: Since there were only 6 students who came to see me for help outside of class during the entire year, I am not sure how to interpret this statistic. A positive spin would be that nobody commented negatively on the help I provided outside of class. The negative spin, of course, is that only 6 students sought help from me, and of those, only one of them had anything positive to say about the experience. Next year, I think I will require that every student visit me at least once to ask a question outside of class. After all, there was no one who found all of the homework problems straightforward.

Homework: 9 comments, 67% negative. One student said that there should be more reading assignments, including reading that went beyond the textbook. Four students said that homework was not scanned frequently enough. Two said that it was scanned too frequently. Of those who mentioned the volume of homework, one said that it was too much and the other said that it was about right (60-90 minutes per night). Hmmm. Perhaps that was meant sarcastically, since I certainly consider 60-90 minutes per night to be excessive.

Response: It is not the case, as one student apparently felt, that college-level calculus courses require problems to be worked only on a weekly cycle. Although it might be more comfortable to have problems due only once per week, the calculus is a cumulative subject, and if you miss a day or two you can quickly get too far behind to participate meaningfully in class. Unlike history, for example, in which you can almost always participate if you at least know the most recent day’s assignment, the calculus requires daily effort. Occasional exceptions can be tolerated (hence my dropping of a few low HW scores each quarter), but they need to be kept to a minimum.

Quizzes: 2 comments, 50% negative.

Strictness: 9 comments, 44% negative, 33% mixed. There were 2 students who thought the strictness was good, with one citing academic rigor and the other saying that he liked the stubble checks.

Response: For next year, I am planning to change the point system so that each student can choose which plan he wishes to be on. “Plan A” will be 10 bonus points at the beginning of the semester but with the usual deductions for minor infractions: 1 point for each minute of tardiness, 2 points for talking while another student has the floor, 3 points for yawning or disrespect, etc. “Plan B” will involve no point bonuses and no point deductions, but repeat offenders (after a few warnings, that is) will get 7 o’clocks instead. Or, maybe I will just forget the whole thing and make life easy on myself.

Tangents and digressions: 8 comments, 25% positive, 12.5% negative. The rest all said something to the effect of enjoying the tangents but wanting them to be limited in scope, especially on days near an upcoming test.

Tests: 9 comments, 55% negative. Most people stated that the tests were too difficult. The Feb. 14 take-home test was cited 3 times by its nickname, and 2 of those people felt that it was a disaster. However, 2 people (including one who seemed to have a positive impression of the St. Valentine’s Day Massacre) recommended that it become a rite of passage for future HappyCal classes. One person liked the inclusion of essay questions on tests. One person had a mixed report on test corrections, saying that they were worthwhile but created too much stress when due the day following a test.


Essential Links:
STA School Handbook
-- College Board: AP Calculus BC Course Description
-- Eric Weisstein’s World of Mathematics, the Web’s most extensive mathematics resource (no kidding!)

Extra Help:
-- Karl’s Calculus Tutor for first-year students
-- Calc101.com, a site I really shouldn’t tell you about (click it and you’ll see why)
-- Temple University: Calculus on the Web (COW)

Links Based on Class Discussions:
-- Troy’s Integral Approximation Thingy: a neat JavaScript application for Midpoint Rule, Trapezoid Rule, Simpson’s Rule, etc.
-- Another integral approximator tool found by John S. (actually shows you the rectangles or trapezoids)
-- Chris and Andrew’s proof that Simpson’s Rule is a weighted average of the Midpoint and Trapezoid Rules
-- Braxton’s direct proof of FTC2
-- Proof that FTC1 implies FTC2 and conversely
-- Related rates tutorial and practice problems
-- Partial fraction decomposition with sample problems and solutions, courtesy of the University of California at Davis

Links for AP Preparation:
-- Real sample AP questions from the College Board
-- AB Calculus Cram Sheet (courtesy of Will Felder and Mr. Hansen)
-- BC Calculus Cram Sheet from previous years
-- “Stuff you MUST know cold” (link to another AP calculus teacher’s site; requires Adobe Acrobat reader)
-- Review question logsheet (requires Microsoft Excel)
-- Permitted features for graphing calculators on the AP examination: you’ll definitely want to print this one out
-- Actual college calculus tests from Mr. Hansen’s alma mater (great practice!)
-- Multiple choice practice #1 with answer key
-- Multiple choice practice #2 with answer key

Fun Links:
-- Homemade “Segway”-like balancing scooter uses a fair amount of calculus!
-- Mathematicians as depicted in the movies (Good Will Hunting, etc.)
-- An Algebra II problem that has a calculus flavor to it. (This is problem #26 from §11-7 of Foerster’s Algebra and Trigonometry: Functions and Applications.) The problem is to determine which sweepstakes prize is better: a $20,000 lump sum or $100 a month for life. Assume 4% annual interest compounded monthly. In part (d), the challenge is to determine how the answer changes if the interest rate changes to 7%.
-- The Mt. Sinai problem and two variations
-- The astonishing Bailey-Borwein-Plouffe algorithm for calculating pi to any desired decimal place
-- Sound wave analysis (harmonics, Doppler shift, etc.) / excellent site developed by students at TJHSST in Virginia
-- Good problems (some calculus, some not)
-- More fun links on Mr. Hansen’s home page

Serious Links:
-- Summer math camps for talented high school students
-- Click here for other serious links

Return to Mr. Hansen’s home page

Return to Mathematics Department home page

Return to St. Albans home page

Last updated: 03 Jun 2007