Bringing Back Memories

Reminds me of my great days teaching AP calculus at Packemin.

Teaching AP Calculus



JD2718 is one of my favorite bloggers and I agree with most things he writes, but not his post on AP calculus.

I taught AP for more than 15 years and found it to be the best course I ever taught.  I never thought of it as a test prep course as it is impossible to prepare for this exam the way kids prepare for regents.  No two questions are ever the same and memorization and rote repetition don't help.  For the first time kids have to learn to not only read the question, but to carefully analyze what is given and what is being asked.  Much like a detective solving a crime, they must use the evidence to arrive at a conclusion.  A student once told me she felt much better about her calculus AP exam than any of the others she took because here she had a chance to apply her knowledge.  If she forgot a particular fact, it wasn't harmful because she could use other clues to find what she needed.

As for the calculator, I happen to feel this gadget adds another dimension to the problems and allows students to find solutions to problems that are unsolvable by hand.  The calculator alone does nothing.  Each problem requires a tremendous amount of knowledge and thought before the calculator can even be touched.

I never did real test prep when I taught AP.  I gave my students AP caliber questions and let them work them out.  At first the success rate was minimal but it got better as time went on.  The kids told me they were able to apply the skills they learned doing these problems to other aspects of academia and real life.

Getting a 4 or a 5 on an AP exam is like licking the icing out of the bowl after your mom has made a cake.  The cake is great on its own without this little extra treat.  The real benefit is in the knowledge obtained and the confidence these kids gain while taking the class.

I'm sorry JD didn't enjoy his experience.  I bet his students did.  I hope he changes his mind and teaches the course again.  No one gets really good at teaching AP until the third time around.  Even then, its a learning experience for everyone involved.  Teaching AP is something I really miss.

Right Decision?

The AP exam was on Wednesday, but we opted for the late administration this year so our kids won't take it until the 19th.  We need the extra time.  Going to single period cut our class time almost 40% .  Last Friday I finished the curriculum and believe me, these kids need review.  The things they knew in September and October are distant memories now.

I just looked at the free response questions on exam that was given.  (The multiple choice are not released.)  It would have been good for my kids.  I just printed the questions so we can go over them in class this week.  I'm praying the one they take will emphasize the same material and that I didn't make a mistake requesting the later date.

Calculus Rhapsody

Just got this one from a friend.  It might be my all time favorite youtube video, even better than I Will Derive

Facebook Conversation

I'm thrilled that they are studying and helping each other.  The AP test is May 19.

so you guys know how in our calculators POdbaby[what they call me--except with part of my real name instead of POd}  had us store those expressions for when you graph in the y= list thing. it's the derivative and double derivative? well yea. i accidentally deleted those and now i'm lost. can someone tell me what they were?! por favor.

4 hours ago ·  ·  · 

• • 
    

    DS  math 8, vars right y1, comma, x, comma, x, close parenthesis
    

    4 hours ago · 
  • KS  thank you so much :]
    

    4 hours ago · 
  • 
    

    KS  but it's giving me an error..
    

    3 hours ago · 
  • 
    

    DS  you have to put it in one of the other y's like a number you'll never use like y8 or something
    

    3 hours ago · 
  • 
    

    KS  I did
    

    3 hours ago · 
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    JD  whats in your y1 ?
    

    3 hours ago · 
  • 
    

    KS  An expression. I used an equation to check to see if it worked and I gy an error. I tried it with two expressions
    

    3 hours ago · 
  • 
    

    KS  Expression* got* stupid itouch
    

    3 hours ago · 
  • 
    

    CL  Do you have what D  said? "nDeriv (Y1, X, X)"?
    

    37 minutes ago · 

KS oh there are two x's lolol. thank you !

16 hours ago · ·  1 person likes this

Facebook To The Rescue



One of the girls in my calculus class was confused about a question on a "take-home quiz."   These are really just homework assignments I collect and mark.  I do this to encourage them to work together and take homework seriously.  I'm not as good as I should be about checking to see who does it on a regular basis.  It just takes too much time and I still have way too much to cover before the AP exam.  (The single period is killing us.)  The reason I am writing this now is I just checked our class Facebook page and saw the request for help and a dialogue that transpired with 12 comments involving 6 kids, kids I that are not friends outside of school. Membership in the group is up to 70.

Teachers and parents complain that the kids spend too much time on the Internet.  Well, here is a group using it for something positive.  Funds may have been cut to schools, our class time has decreased but Facebook has provided a way for my kids to get the extra help some so desperately need.

More Important Than Stats

Too bad everyone is so hung up on stats. I'm old fashioned and this e-mail means more to me than the grade. I wish people like Obama and Bloomberg would realize that as well.

Hi Mrs. POd!
This is J :)
I hope you are enjoying your summer with your family !
Hmm, I just got your email about R sending her AP score to you.
well, I only got a 2 :( But, I'm still really glad. At least, I will still be ahead in calculus when I learn in college this year.
You've taught me calculus as if it was the easiest thing in the world.
You were really awesome and you were the best teacher out of all my four years of high school.
There aren't a lot of teachers who really cared and encouraged their students as much as you did. :)
I'll really visit you one day :)
Until then, take care!
- J.

I thanked her for her letter, told her that I am glad she is not stressing about the grade and that the grade did not matter to me at all.

I'm sure, come September, or sooner, Mr. AP will have some comments about these grades as well. I'll just have to learn to live with them.

Open Night Mic

Friday night was Open Mic Night at my school. I challenged the kids to do a rap or something else calculus (or any math in my other class) related. I promised five extra points for anyone willing to do it. One student promised to oblige. Because of this, I was forced to attend. I'm not sorry I did. I had a great time. Not only were there top kids there, but there were kids from all walks of school. My friend sent me her poem, which I share now. I wish I could put up her video for everyone to see and enjoy.

MY rap about Calculus :)

This one goes out to you Ms. POd

When I decided to take AP Calculus,
Most of my friends thought it was ridiculous,
I was persistent cuz i wanted them to see,
That the derivative of position equals velocity,
Then they asked about acceleration,
and I told them to find the slope of the velocity equation,
They were amazed they stared in awe,
Then I told them about the trigonometry law,
Sine, cosine, tan of theta
Plug them all into your graphin calculator,
This rap is so fly, but I'm almost done,
But I gota discuss local min and maximums,
Find them by doing f prime
so that 9x+5 becomes nine,
Rate of change-Mean Value Theorem---MAKE THE connECTION
CAN I GET A WA WA from the AP Calculus Section!

:)
I luv u Ms.Pod

Basic Training

I don't give too many big tests in calculus, mainly because I have trouble keeping quiet for two periods in a row. But, I also don't like to over stress the kids. I feel if they made it to AP calculus, they paid their dues. Now, it is their turn to learn without stressing about grades. So, instead of 100 point major tests, I give quite a few little exams (one period) and take-home exams. Each short answer question is worth 1 point and the long questions are worth 9 points. I try to keep AP standards when I mark and, when I am in doubt, I just mark the question wrong. At the end of the marking period, I add up all the points and figure out some sort of curve. No one who is working gets under an 85 and almost all the grades are between 85 and 95. The kids don't really know how they are doing until they get their report cards. The only thing I tell them when I go over an exam is the class average so they can see how they did compared to everyone else. The AP exam is marked on a big curve. To get a 5, they can score 70 out of 108 points (sometimes more, sometimes less.) These kids are not used to not being able to complete an exam and they are certainly not used to not knowing everything on it, so calculus is a new experience for them.

The most important thing I try to teach my students is how to think. They learn the basic skills but the application of these skills is a killer. No two problems are the same. In the past, they memorized materials taught in class and regurgitated it all on an exam without real understanding. They hate thinking.

Our midterm is coming up. It will be a double period exam. During the first period, they will be given calculator problems and during the second no calculator is permitted. I know the test is hard and long. Most won't finish. But, they have to learn to budget their time and they have to know that skipping a few 1-point questions won't harm their scores.

I've been spending this week reviewing. I even stayed two hours after school helping them yesterday and today. They are upset because I won't tell them exactly what is on the exam. I won't give them review sheets.

My students are smart but, they are kids. They are not as energetic as they ought to be. They won't work too hard if they think they can cram it all at the last minute. I have to toughen them up now, so they can succeed in May. I know my methods work. Last year, I had over 90% of my class pass with grades primarily of 4's and 5's. They walk out of the exam and tell me how much easier it was than anything I gave them to do all semester. I know its not easy. I've just gotten them to do the unthinkable. I've gotten them to think.

I know the grades on the midterm will not be good, but that is okay. It is only January. By May, they will be ready. I have a good group this term. I know they will succeed.

You've Come A Long Way Baby

We graphed a third degree polynomial equation today. We used minimum and maximum points. We used concavity and inflection points. When we finished, we compared our results to the results on the graphing calculator. The kids were amazed at how accurate our picture was. The teacher who entered the room as my class was ending was impressed.

I told the class to remember when graphing straight lines was a challenge. One boy took the picture above. They've come a long way, baby!

I Can't Win With This Guy

The AP scores are in. Here are a few comments that I have received from my students.

I got a 5 on my AP Exam.Either the Test was extremely easy or you were one
heck of a teacher, and im gonna have to go with the second option obviously.
Thanks for making the experience of calaculus fun and easy for a guy like me to
understand. You truly are a great teacher.

I hope you are enjoying your summer, and missing us tremendously. Well you
might have been notified that we received out AP scores. Before I tell you,
I want to thank you for everything and let you know that this would not have
happened i without you and your confidence for us. Your support wasa great
deal, and we all appreciate it. You were more than a teacher, you are a great
friend. I just wanna hug you right now. Well here it goes. Drum Roll
please................I got a 5. Haha thank you so much, hehe. Well have a great
summer, and talk to you later.

i gota 4 on the AP !!!!! woohooooooooooo
this is Patty btw .. im so
proud of myself.. o man you were right about me ms.
THANKU FOR
EVERYTHING

i didn't forget, i jus got mine yesterday. Now brace yourself...i got a ...
five. I know, i can't believe it either. But its true. There must be a big
curve. Thank you, its also because you are a great teacher. Thank you
again

I got an e-mail from Mr. AP today. He told me that over 90% of my class passes. It is a new record for our school.

I will mail them [the grades] to you. Your students did exceedingly well. Maybe we should put more students into BC.

No," good job", no "congratulations", no "keep up the good work", just the implication that they did well because they were too smart for the class. It seems he is unhappy if they don't do well and he is unhappy when they do well. He should only know where the kids were all term and how poorly some of them were doing. And, if it had been up to him, he would not have let some of them take the exam because their grades were so low all semester. It's the e-mails from my students that keep me going.

The AP Exam

Wednesday was the AP Calculus exam. My kids were psyched and ready. They were nervous. But, they were well prepared. All semester I tested them brutally. They never knew what to expect from a POd teacher test and they usually walked out of them feeling like they had been run over by a truck. No matter how many times I told them not to worry, they worried.

I stressed all term that training for the AP exam was like training for the Olympics. Their endurance was pushed to the limit. For the first time in their young lives, they were forced to think. No longer could they memorize processes and blindly spit back meaningless material.

Today I proctored the English regents, an exam the majority of my English speaking students took. They told me that calculus was a piece of cake, compared to English. The questions on the AP exam were far easier than the ones I had been making them suffer through all semester.

I feel good right now. I know I did my job well. There will be kids who only get ones and twos and will have to retake the course in college. That, does not matter. I told them all to feel proud. My 67 students accomplished more than almost every other student in the building. My 67 students know more math than many of the teachers in the building. Learning calculus is the fresh cake their mom has just baked. Getting a 5 is the added treat of licking the icing bowl.

While I am on the topic of AP exams I have three major complaints:

1. Teachers that are too lazy to do the work necessary to prepare kids for the exams.

Year after year, the kids complain about one teacher who does nothing to
prepare them for the exam. A few weeks ago, she had them playing "dress up" at a mock wedding. Although this might have been nice, it did not help with the exam.

Another teacher never introduced the tape recorder and CD player the kids needed to use on the exam. There were problems with the machines malfunctioning and the kids had difficulties they should not have had.

2. Teachers being removed from their classes the day before their exams to proctor a different exam.

I proctored the English exam today which was no problem as AP Math was given yesterday. The other calculus teacher had to proctor the day before his exam was given. His students missed valuable review and confidence building time.

3. Administrators that don't know how to follow directions.

The memories of the TI 83, 84 or 89 calculators do not have to be cleared before the exam. However, no one told Mr. AP and he sent someone to the room to clear the calculators. Teachers that teach the course are not allowed near the room so we had no idea that this was going on.

At least it is all over. Here is an e-mail from one of my kids. His grammar and writing skills are really quite good, so don't let this writing sway your opinion of him. Next week he is taking the AP physics exam.

Hi Ms POd, just letting you know, the AP Exam went well for me.
The test was overall fair.The Multiple choice with no calculator I didnt know a few of them and i omitted 4. Worse case scenario I get 6 wrong for section 1 plus 4 omits(28 questions).For section 2 multiplechoice with calculator, it was a breeze, worse case scenario 2 wrong(17 questions).For the short answer portion of the exam, it was fair. The hardest question would probably be the slope field one which for 2 parts i couldnt answer. I think for all of the short answer portions I wasnt sure of the answer for about 4 of the parts (6 questions, approx. 3 or 4 parts each = around 20 parts) but i think i did good, im not too worried.What sucked the most was that Ms. H walked around clearing the memory from all of the calculators, which deleted all notes and programs when she should have only cleared ram. Mr. G was talking about this today in his BC class.

THREE

Calculus is by definition a hard substance and the study of calculus is also hard. My tests are even harder because they emphasize applications of knowledge, not just rote reiteration of problems that were taught in class. Studying is not enough to pass a test in my class. You really have to be able to use what you have been taught.

I know this is a difficult thing for kids to do. I don't expect them to do well on my exams at this point of the term. (All grades are curved so they don't have to worry about averages being ruined.) I do expect them to know certain things and I have no tolerance when they don't.

1. The use of the word IT is strictly forbidden. They must be specific in all their justifications. Yet, as I mark midterm exams, I find this word on more than one paper.

2. All answers must be expressed to a minimum of three decimal places. This is mentioned every single day. Yet, as I mark midterms, I am constantly taking off points for answered expressed as only a one or two place decimal.

These kids are bright kids. I know they understand THREE. I don't understand why they fight using three places for their answers. Maybe when they get the exams back, with the -1's for decimals and "ITs" they will learn to do what is required of them.

AP Calculus

Professor Posamentier, the dean of education at City College recently wrote an article in Newsday saying that AP calculus should not be taught in high school, that school's should emphasize algebra skills instead. He said kids are coming into the colleges with AP credit, yet their skills are severely lacking.

I know Professor Posamentier quite well. He was my main math education teacher as an under graduate, graduate and post graduate student. He is a brilliant teacher and I credit him with my skills as a teacher. I completely and whole-heartedly disagree with the premise of this article. Kids might come into college ill prepared but, it is not the fault of AP calculus. Instead I would blame the poor curriculum of Math A and Math B. I would blame the early emphasis of calculator use. I would blame the use of manipulatives, instead of memorization (multiplication tables) in elementary school.

I have been teaching AP calculus for over ten years. The students I have must qualify for the class by taking pre-calculus and doing well in that class. By taking away AP calculus from these kids we are dummying down the curriculum and once again teaching to the lowest level possible. We should not assume that all kids are not capable. The kids in my school are. Sometimes I do end up with students who "sneak in." They don't have the prerequisites. When I find out, I try to "hide" them in the class. The five on the AP exam is not that important. The skills they learn in my class are. AP calculus is a class that teaches kids how to think, how to apply their knowledge to problem solving. They are able to solve problems numerically, analytically, algebraically, and graphically. They must be able to support or confirm answers through written exercises. They must understand that technology is used to support results. Students are taught that mathematics provides the foundation that allows technology to solve problems. No other math class does this.

Calculus taught on the college level does not delve as deeply into the subject as it is on the high school level. There simply is not enough time. Rather than remove AP calculus from the high school curriculum, we should be doing more to insure more students get to take it.