Tuesday, March 3, 2015

Things I'm doing in AP Calculus

I've been asked about things I do routinely in AP Calculus to help get kids ready for the exam throughout the year.  Last year I wrote about a lot of things my colleague and I did to help kids review at the end of the course (post here).  But this post is more about what I do with the kids from August to March (once we get back from spring break, we start reviewing).

#1:  How I structure tests
The AP Exam looks like this: 45 multiple choice questions worth 1.2 points each (=54 points) and 6 free response questions worth 9 points each (=54 points).  So my six unit tests consist of 15 MC questions worth 1.2 points each and 2 FRQs worth 9 points each, for a total of 36 points.  I also typically throw in an attainable bonus question at the end.  My test questions are taken as much as possible from released AP Exams.  If I run out of questions, I'll occasionally pull something out of a study book.  Full disclosure, the previous AB teacher did a lot of work on this end.  I've simply updated her tests a bit and added more multiple choice.

So, the big question--do I curve on an AP curve[1]?

No, not anymore.  When I did, I felt like the kids had a false sense of confidence.  If they got As on all their unit tests they felt they would easily get a 5 on the AP Exam.  Well, a unit test is a lot different from a cumulative exam...

So, I "curve" by (1) putting a bonus question in (typically worth 5 points BEFORE I calculate the percentage...HUGE) and (2) giving them the FRQs beforehand via what I affectionately call "AP Sets"...

#2: AP Sets
AP Sets are released FRQs that deal with what we're learning in class.  The kids have about one due every week.  On the day the Set is due, I randomly call on kids to do one of the parts on the board until all parts are completed.  They may use their AP Set as they explain to the class.  If it's perfect (and I mean I don't have to correct an iota), then they get 11/10 points.  If I have to make a small correction, they get 10/10, and then it goes down from there.  If they're not at all ready, they receive a zero, but they are welcome to come make up the assignment for full credit any time on their own time (before/after school, lunch).  If a kid doesn't get called on for that unit, then they are simply excused from this grade in the gradebook.

Here are the AP Sets I gave this year.  I print them off by unit, but you could very well give them all at the beginning of the year:

I give three to four AP Sets each unit.  Two of those sets show up on their exam pretty much verbatim.  So, the kids have access to half their test weeks in advance.  Are they memorizing answers?  I prefer to think of it as memorizing how to write their answers.  And I'm totally ok with that because in AP Calculus, students must memorize how to write mathematical justifications correctly.  If we don't give them tons and tons of practice with this and teach them how important writing is in mathematics, then we've really missed what I feel is one of the most valuable aspects of the AP curriculum.

#3:  Multiple Choice Packets
For MC practice, I give a packet of about 20 multiple choice questions for the unit we're currently in.  These are either past AP questions or questions I've found in textbooks or study books.  Since the College Board doesn't release MC questions every year, these can be harder to come by.  I can recommend Rogawski's AP prep (at the end of each chapter) for some very good (although maybe sometimes too difficult) MC questions.

In addition to the packet, I print off a slip of paper with numbers 1-20 on it (or however many questions they have).  I put an asterisk by the questions that are calculator active (I use this notation throughout the course).  Their MC questions are "due" two days before test day, at which point we trade and grade their slips at the beginning of class.  They then have two days to correct the questions they missed for all their points back.  They also have access to the questions up until the test this way.  I usually pull a few of these questions word for word on their test.

One thing I think is really important for practicing multiple choice is to force the kids to go back and find their mistakes.  These questions are just written way too well to have the students practice without fixing their errors.  They need to get used to the common distractors and learn not to fall prey!

#4:  Daily Multiple Choice
Nearly every day I pull up one of the secure practice exams from the College Board and ask the kids to discuss a 2-3 MC problems.  Because these are secure exams, it's important that the questions don't leave the classroom so I just project the PDF on the screen instead of printing them out and then I ask kids to toss any paper they might have used to solve the questions.  As they get better, I have them poll in their answers through something like PollEverywhere.com so that I can  better understand what our strengths and weaknesses are as a class.  But, primarily, this is a really good way to get them talking to each other and debating mathematics.

#5:  End-of-Semester Folders
At the end of each semester, we require the kids to submit a three-pronged folder with the following for half a test grade:

  • All quizzes and tests with corrections
  • AP Calculus AB course description from College Board's website
  • Four pages of formulas that I print off for them of colored paper

My kids joke that taking AP Calc with me is like preparing for some kind of war, and I guess I see where they're coming from.  But I want as many of my kids to pass this exam as possible and gain college credit, so--yes--maybe I do go a bit overboard. :)

What are some things you do throughout the year to review the AP Exam?

Update {3/24}

I got an email asking if I keep kids from Googling the FRQs.  I thought I would post my response here also, in case anyone else wondered:

I don't keep the students from Googling the answers; I actually encourage them to do so (attempt first, then Google). If you give past FRQs as homework, I don't think there's any way to keep them from looking up the answers, unless you say it's not for a grade and we're going to check answers together as a class tomorrow (so please don't look these up). I have done that before, but it wasn't super successful. Kids didn't take it seriously enough. 

The truth is, no one is going to get perfect wording on FRQs in the beginning because kids are not used to this type of writing. If students are encouraged to look up the answers, I think it pushes the responsibility back on them--instead of you--and they can also spend time learning the part(s) they need help with. It individualizes the learning process a bit more. 

They do get the problems in advance, so they can always come ask me questions if they can't find a satisfying enough answer on AP Central (or elsewhere). 

[1]  I call an "AP Curve" a curve where students who would have gotten a 5 would get an A; 4s get a B, etc.


  1. Rebecka, do you use the same tests from year to year? If so, do you worry about students taking home their tests for corrections and then sharing them with next year's class?

    1. I modify the tests a bit every year, but the general format is the same. I'm not too worried about them sharing because I already give them so much of what's going to be on the test.

      I don't like the idea of the kids not being able to see what they missed and not correcting their own work...

  2. Since all released multiple choice questions and their solutions are online, do you have problems with the students doing very well on the 20 questions for each unit?

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