Wednesday, March 25, 2015

In which I attempt to defend public educators...

I got a new student today.  Today.  Eleven weeks before school lets out for summer.  At the end of class, the kid told me that was the first time she understood what was going on in math class for as long as she could remember.  Her presence, along with some other things I've been thinking about, prompted me to pull out my computer and write what's been on my mind...

I teach in one of the lowest paid states for public education teachers. I work with unbelievably dedicated people who make daily sacrifices to do what they do for a living: to serve other people's kids.

Sadly, I often hear comments like, "I'm just going to go work at Starbucks. I'll make more money there."

Now, let me be clear: there is no question in my mind that we are grossly underpaid.


I understand that we all have frustrating days, where anything sounds better than our current position. But, I also know that--at least for me--the good days far, far outweigh the bad. And if they don't for you, you might want to consider leaving. You're right: we don't get paid enough to be miserable all the time.

But, I imagine most of you became teachers knowing full well the monetary sacrifice you would make. As I recently heard it put so elegantly, you didn't show up for the income, you showed up for the outcomes.

You enlisted because even though we're underpaid and unappreciated by adults, we have kids who adore us and would do just about anything for us.

You kept coming because you knew your kids needed a safe, encouraging, hopeful place. And you are sure as hell going to give that to them. Even if for just one hour a day, a hundred eighty days a year.

You kept reporting for duty because you believe in public education. Who else is going to take the kids who change schools every few months? Who else would take a kid eleven weeks before summer and say, "Hey, we don't know each other yet, but we will. And I will do everything in my power to get you caught up and to be successful in my class."

You continued to show up because you're committed to leveling the playing field. Because you believe every kid should have an opportunity at a quality education--regardless of zip code. Because you're driven by the idea that you want every kid to feel better about themselves leaving your doors than they did entering them. Because you see kids not for who they are, but for who they can be. Because you believe they can make this world a better place. Because you know that they are the hope of the future.  Because you understand that education is key to overcoming poverty, prejudice, and ignorance.  And because you feel this indescribably fulfilling joy every time you're reminded of why you do what you do because of something kind a kid said or did.

Yeah, we don't make a lot financially. But what we do make is not quantifiable.

And so, to all those who recognize this (and that is the vast majority of my fellow teachers), thank you. Thank you for believing in this profession. Thank you for persevering through the bad days, through the media bashing, through the uninformed comments from both loved ones and strangers.

Thank you for choosing to see the positive in public education. For knowing that it's not perfect, but for striving for perfection regardless. Please, keep doing what you're doing. We need you. We need each other.

And your kids need you, more than they'll ever be able to express.

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 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.

Sunday, March 1, 2015

Two more things

Last week, Sam shared two organizational things he does that help keep his classroom running smoothly.  I love reading things like this from real-life teachers as opposed to promotional magazines.  So, I thought I'd share two things I do, too.  They're not life-changing by any means, but they do help me.

#1:  Class Baskets
I give a lot of handouts.  I put all the extra handouts in one of these three baskets:

Baskets labeled "AP Calculus," "Pre-Calculus," and "Algebra"
If students were absent (or if they lost a handout), they know where to look.

#2:  Copy Folders
I, like Sam, try to avoid making too many trips to the copier.  I have a folder labeled "To Copy" that I stick any papers in that need to be copied (revolutionary, I know).  Inside this folder, I also keep a post-it with the total number of students in each course.  After I make copies, I stick them in these folders and then pull them out whenever I need them:

The back folder is my "To Copy" folder;
the rest of the folders hold all my handouts prior to passing them out

Bonus:  Chocolate
I keep a small stash of slightly overpriced chocolate near my desk at all times.  Kids can be awesome.  But they can also be quite terrible.  Sometimes, though, my mind can be cleared with a little bit of sugar.  And, all of a sudden, the kid's words/actions do not seem quite so egregious.  Or the stack of tests to grade doesn't seem too overwhelming.  Or spring break doesn't seem so far away...

Also, my colleagues know I keep chocolate behind my desk and if they've had a bad day, all they have to say is, "Do you have some chocolate...?"

That's my bonus advice for you.  Deep, huh? ;)

Tuesday, February 10, 2015

More Volumes in Calculus {Student Edition}

A couple summers ago, I made some really beautiful (I think) models to represent the kinds of figures we find the volumes of in calculus (post here).  The models worked well last year; I think it made the "formulas" make sense to the kids.  But, I thought it'd be even better if the kids actually got to create some of these in class.  I just couldn't quite figure out how I wanted to do it, without making it a project and without taking up too much class time.  And then, a year late, an idea finally came to me.

First, I bought a package of forty 5.5x8.5" foam sheets that were self-adhesive on one side ($5 at Wal-Mart).  I stacked three sheets together (so I have thirteen "boards") to produce the base of the desired solid.

Then, I graphed two functions (y=2cos(x/2) and y=e^(x/4)) on Desmos, printed them off, and used them as stencils.  So, each foam board has a graph on both sides:

I don't really know why I chose these two graphs other than the fact that I wanted one increasing and one decreasing function, both only in the first quadrant.

Next, I made and printed different kinds of cross sections for the kids to use on cardstock (see file below: squares, rectangles, semi-circles, equilateral triangles, and isosceles right triangles.

And after that, the students did the rest of the work.  They worked in groups of 2-3 to create a solid with either base f(x) or g(x) (I assigned).  Then, they calculated the volume of their solid and put their answer in this table:

Here are some examples of their finished products:

Here's how I told the kids to use the pins:

Finally, here is everything you'll need if you want to do this with your calc kids, too!

The first two pages are the two graphs I used.  The next five pages are the cross sections that I printed off on cardstock.  The graphs/cross sections are sized to fit together.  All you'll need is some foam sheets, pins, and Sharpies. :)

Thursday, January 22, 2015


When we work u-substitution problems in calc, the kids sometimes drop things like powers or a base of e while they're re-writing their integral.  Also, sometimes they don't quite see which parts of the original integral they've taken care of, and which they still need to work on.

So, I had an idea about five minutes before I was to teach u-substitution this year.  I call it the highlight-out method.  I think it's easier just to show a slide with two examples rather than try to explain in words:

I had the kids "highlight out" the du portion so they could focus on what's left.  Alternatively, you could have them highlight u in one color and du in another.

It may help some; it won't help others, but I think it's a step in the right direction for me.


Another thing I get asked a lot is, "What happened to the du?"  This is a way I explain indefinite integrals that I've found helpful:
  • The indefinite integral symbol and the differential dx (or du or d-whatever) TOGETHER are a command that mean "Find the family of antiderivatives."
  • Once you have found an antiderivative, the two symbols disappear because you have completed the command.
  • You cannot have an integral symbol without a differential[1]; they're akin to a capital letter and period.
That has seems to help a little.  Nothing ground-breaking here, but just some thoughts on u-substitution.  Would love to hear other ideas!

Here's a slide that seemed to clear things up a little bit more:

One kid told me the last example actually shed a lot of light.  Hooray!

[1]  Yes, I know, technically you can; I've taken Calculus on Manifolds, but these are Calc AB kids, ok?