This week saw the end of several big units. So, I ended up blogging about each class in other blog posts. Now, this week's post is a little short as it points to my other posts! BTW, this week's YouTube Wednesday was about the 1977 version on the "Powers of 10!" Next week we'll have to do something about PI Day....
I just finished a huge unit in my AP Calculus BC class on Integration Methods (inverse trig, trig sub, by parts and partial fractions) and Differential Equations (variable separable vs. Slope Fields). I've been using the Demana Waits Finney Thomas text since the first edition in 1995. We recently got the 4th edition of Demana Waits Kennedy. These texts are great. However, when teaching Differential Equations, I thought I'd try using the Deborah Hughes-Hallett text that I use in my Summer class at the local college. This text has a lot of nice real world applications in the homework sets and has a very nice approach when presenting Slope Fields and Euler's Method. What follows are some of my ScreenCasts and SmartNotes from class related to the Harvard text, enjoy! BTW, this applies to AB and BC Calculus. If you are only interested in AB Calculus, please skip the parts on Logistics and Partial Fractions as well as Euler's Method.
My Students can't decide when to use: for vs. for each loops, while vs. do while loops, static arrays vs. ArrayLists, static methods vs. object methods
I don't know if this is helpful to anyone. If you find yourself in my shoes, I'm just trying to share a little project I hope you may find useful in your class. BTW, you are in my shoes if most of your students have Senioritis and are taking APCS as their first programming class....
So, I'm doing a review project with them now called Chess960 where we use the Random class to generate 960 Fischer Random chess boards.
Chess960 version 1 uses a static String array to represent the back row of the white pieces on the board. Also, we've been doing Object Oriented Programming all year, so I thought I'd take this opportunity to talk about static methods instead. As you can see in the following links, we used a combination of for loops, while loops and do while loops and made a big deal about when and how to use these different kinds of loops. We even talked about array traversal algorithms and linear searches.
Version 2 of Chess960 will do the same thing. However, I will be talking about refactoring code. In other words, how do we factor out unneeded code.
Version 3 will use an ArrayList to keep track of each randomly generated board until we get all combinations. Along with the ArrayList, I'll use enhanced for loops (aka for each loops) as well. Finally, I'll mention file I/O and have the entire ArrayList copied to a text file to print! That's one large ArrayList as each of the 960 entries consists of 8 Strings for a total of 7680 Strings. At 2 Bytes per String (unicode), that's 15.36KB or 15KiB in one variable holding a 2D matrix! Assuming 60 lines per page when printed and one board per line, that's 16 full pages when printed.
Note, there are only 960 combinations as we follow these rules to generate each board: place a Bishop on a1, c1, e1 or g1, place a Bishop on b1, d1, f1 or h1, place the Queen on one of 6 remaining squares, place a Knight on one of 5 remaining squares, place a Knight on one of 4 remaining squares, place a Rook on the first empty square, place the King on the next empty square and place a Rook on the last remaining square.
So, by the counting principal, we get 4*4*6*5*4*1 = 1920 ways to do this, right? No, it's 1920/2 = 960 because the Knights are considered repeated pieces. Note, the Bishops are distinct as a Bishop placed on a dark square (a1, c1, e1 or g1) will always stay on dark squares and a Bishop placed on a light square (b1, d1, f1 or h1) will always stay on light squares. Also, placing the Rook-King-Rook counts only once as the King has to be between the Rooks for castling!
What follows is an email I recently posted to the AP Computer Science listserv that I thought you'd appreciate:
Flipping the classroom has been a controversial issue for science teachers for some time now as evidenced on the AP Physics listserv. It's only natural that we, as Computer Science teachers, would like to emulate this fad. The idea is this:
(1) if you have sufficient electronic materials such as ppts, pdfs or mp4s, and
(2) if you have sufficiently motivated students ready for said material, then
(3) you can assign most of the traditional class work to be done at home, and
(4) you can focus on the lab work with the students in class!
The problem is that this model is meant to make the most of lab time for lab intensive courses. However, many teachers are flipping their classes even if they teach non-lab based courses. For example, some on the AP Calculus listserv are doing this. I have resisted this trend as I think that the students loose something in the translation. They are there, at least in part, to benefit from your guidance. You can flip a few classes or a unit or two for variety's sake and to see how it works for you. However, if you flip the whole class, you miss interacting with the students and adding your unique perspective on the topic at hand.
The Flipping Trend is a hard one for me to ignore as I have many of my classes recorded as ScreenCasts and SmartNotes that the students could easily view online at home and still get my perspective on things. I share these files with my students already for those that need to review a difficult concept or need to make up work due to an absence. I post these files as mp4s and pdfs on my ftp, blogspot, youtube, slideshare, pastebin and edmodo sites. I don't think I'd flip a Math class. However, my Computer Science classes could use more lab time....
Here's the rub: most of our students are not as well prepared or dedicated as we would like to think. So, many students probably won't complete the assignment at home. Those students will still be wasting lab time trying to catch up on what they missed at home. Let's face it, today's AP students are way too over booked with other AP courses and activities. Now the student is even farther behind the 8-ball!
Yes, there is life after my AP Calculus BC class! This is by far my favorite time of year. This "season," for want of a better term, starts with LIMACON around the ides of March and ICON around the nones of April. Of course, we also start AP Review around this time followed by AP Exam Week during the calens of May! The AP Calculus exams are usually given early during the 2 AP Weeks, so we have a lot of time to kill after Calculus!
View of my classroom from left rear to left front side.
As a result, Life After Calculus, aka LAC, has evolved into an art form. Right after the AP Exam, we have a Movie Marathon. Traditionally, our Movie Marathon, starts with "Stand and Deliver," but I couldn't bear to watch that movie this year as Jaime Escalante passed away not so long ago. We usually show one or two other movies to do with math, such as "A Beautiful Mind" or "The Proof." In recent years, we've been doing Science Fiction trilogies like "Star Wars" or "Planet of the Apes," etc. I justify this odd behavior by naming each and every TI Graphing Calculator we've ever used after a scifi character.
View of my classroom from right rear to right front side.
TI81 = Obi Wan Kenobi (Star Wars IV)
TI82 = Klaatu (The Day The Earth Stood Still)
TI83 = Ziggie (Quantum Leap TV series)
TI84 = Joshua (Wargames)
TI85 = Johnny5 (Short Circuit)
TI86 = Spock (Star Trek TV series)
TI89 = Hal 9000 (2001: A Space Odysee)
TI92 = Colossus (The Forbin Project)
I use names of characters from these movies and TV series. So, I claim that I'm still looking for a good name for the latest GC, the TI Inspire CAS. For example, last year we saw all 3 versions of "I Am Legend" (Vincent Price, Charleton Heston and Will Smith) and decided to name the Inspire after Dr. Neville! The year before that, I was still looking for a good name for the Inspire, so we viewed "Back to the Future" and chose the name Doc Brown, but it didn't stick. This year, we went crazy and decided to watch all 9 hours of "The Lord of the Rings!" We viewed 2 DVDs worth of LOTR during AP Week and saved the last DVD for these last few days of school. Maybe we'll rename the Inspire as "Nazgul?"
In between these 2 screenings of LOTR, we actually managed to do a lot of math! What follows is a record of some of the topics we covered. We spent some time, LAC Days 1-8, on loose ends in BC Calculus previewing some topics in Calc III and IV. Then I showed my students how to use a bit of SAGE, http://www.sagemath.org
Thanx, Andrew, for a great rendition of "Our Chief Reader, Rosenstein" by Dan Kennedy. I mentioned this Calculus Song, Parody, Filk, or whatever you want to call it, on the AP Calculus ListServ a few months ago as I had lost the words. The song was about the solution to AP Calculus AB Free Response Question 88AB6:
Let f be a differentiable function, defined for all real numbers x, with the following properties (i) f '(x) = ax^2 + bx (ii) f '(1) = 6 and f "(1) = 18 (iii) int(f(x),x,1,2) = 18 Find f(x). Show your work.
I finally found the lyrics sheet I was looking for in my desk, so my students have had the dubious honor of singing this song in class! Since I mentioned it on the ListServ, I have been asked several times for the words, but I haven't had a chance to share them until now. What follows are the long, sought-after lyrics:
