I am way behind on posting materials for AP Calculus, but better late than never, I suppose. Here is a Tarsia puzzle for practicing techniques of integration (specifically for AB). The puzzle includes both definite and indefinite integrals. I used this as an end-of-the-year review before the AP Exam.

PDF Version is here. Word document of problems only is here. The word document can be used as its own assignment or only for the students who were absent for the puzzle.

# EPSILON-DELTA

## Monday, May 1, 2017

## Monday, August 8, 2016

### Get Them into Calc: A Defense of Calculus Education

I recently applied to be an AP Calculus Reader for (hopefully) next summer. This has been a dream of mine for the past three years, so I was excited to finally be allowed to submit an application.

The application questions really got me thinking. I realized (not for the first time) how passionate I am about calculus education.

A few months ago, I applied to begin a PhD in Mathematics Education, and I put these thoughts on paper for the first time. (I was accepted but deferred as I realized I couldn't stay away from teaching.) Here's part of my essay for admission:

Yes, calculus allows students to navigate both abstract and applied mathematics. If done right, it teaches them how to see the world through derivatives and integrals. It teaches them about the physics of motion and about the science of change.

But, it teaches them in many other ways...

For better or for worse, calculus is seen to many as the pinnacle of mathematics education, maybe even the pinnacle of all high school education.

I'm not saying this is right. But I

When the majority of my students start calculus class, they come in with a mixture of anxiety and excitement. They've reached a point many do not reach. They are both proud of themselves and also scared of failure. If they fail, what does that say about them?

What I believe is vital is that--if they show up and if they try--they will not fail.

In fact, they will succeed.

And when they succeed, they soar. Sure, they've done well in other classes before, but something unique happens when they do well in calculus. Again, part of this is due to the way our culture glorifies calculus; but part of this is due to the fact that you really cannot BS your way through calc. You have to

Hence, when students achieve that passing grade (ethically), they know they earned it. They know they mastered the material.

My point is: I believe we have to do more to (1) get more students

It's our job as educators to push our kids to greatness. We have to believe they are capable of more than they believe they're capable of. We have to demand more of them than they would demand of themselves. We have to give them the tools to conquer their goals and their fears.

Get them into calculus. It will accomplish all of this.

The application questions really got me thinking. I realized (not for the first time) how passionate I am about calculus education.

A few months ago, I applied to begin a PhD in Mathematics Education, and I put these thoughts on paper for the first time. (I was accepted but deferred as I realized I couldn't stay away from teaching.) Here's part of my essay for admission:

I fell in love with school from the moment I was first introduced to it. I was the kid who would come home from school only to make her little sister pretend-play classroom until it was dinnertime. Never was my sister allowed to be the teacher, by the way. Being a teacher was all I ever remember wanting to be when I grew up. [...]

Not unexpectedly, one of the highlights of graduate school for me was teaching my own sections of College Algebra. Because of this, I searched primarily for college teaching positions upon graduation. I was pleased to accept a position at Tulsa Community College, teaching mostly for their EXCELerate program. This meant that I had the privilege of teaching high school students at Union who were taking college classes for dual credit. What I did not expect when I accepted this position was just how much I would love teaching high school students. It should be noted that I attended only private school or homeschool through my childhood; hence, teaching at a large public school like Union High School was never on my radar. Little did I know that I had just found one of my utmost passions in life.The following year, a position at UHS opened, and the administration asked me to apply. With some trepidation, but mostly excitement, I accepted the position and began my journey as a high school teacher. The past few years at UHS have been nothing short of incredible. I accepted this job because I thought I could make a difference in the lives of young adults. What I did not realize was what a profound impact these young adults would have on my life. They have taught me the importance of kindness, vulnerability, patience, persistence, and love. I adore my kids more than words can say, and I am forever in their debt for giving me a career about which I am truly passionate. My favorite class to teach is AP Calculus. I feel this is a wonderful course that teaches so much more than mathematics. Last year, I had an eighty-two percent pass rate on the AP Exam (one hundred percent pass rate for the students who had also had my PreCalculus course); the national pass rate was fifty-seven percent. [This year I had an eighty-seven percent pass rate; national pass rate was fifty-nine percent.] Calculus education is a field that is somewhat under-researched, and I am excited to learn more about what can be done to promote calculus literacy and fluency at both the high school and the college level. My goal in pursuing a PhD in Education is to one day be a teacher-leader at the district or state level to help schools vertically align their mathematics courses so that as many students who want to take calculus can do so and can experience success. I have seen what experiencing this success can do for a child’s confidence. I want as many students as possible to encounter this joy, and I want to help as many teachers as possible witness this.That is my passion: open access to calculus for all students who want to take it and who have taken the appropriate steps to acquire the necessary background knowledge. I believe that access to calculus is vital for a school's success because a school's primary goal should be to see its students grow. My claim is that advanced mathematics allows students this opportunity. When students experience success in calculus, their view of themselves blossoms. They start to see themselves as young adults who are capable of basically anything...if they will work and

*stick with it*. I've seen it time and time again in just a few years--calculus gives kids confidence they never had before.Yes, calculus allows students to navigate both abstract and applied mathematics. If done right, it teaches them how to see the world through derivatives and integrals. It teaches them about the physics of motion and about the science of change.

But, it teaches them in many other ways...

For better or for worse, calculus is seen to many as the pinnacle of mathematics education, maybe even the pinnacle of all high school education.

I'm not saying this is right. But I

*have*taken advantage of this.When the majority of my students start calculus class, they come in with a mixture of anxiety and excitement. They've reached a point many do not reach. They are both proud of themselves and also scared of failure. If they fail, what does that say about them?

What I believe is vital is that--if they show up and if they try--they will not fail.

In fact, they will succeed.

And when they succeed, they soar. Sure, they've done well in other classes before, but something unique happens when they do well in calculus. Again, part of this is due to the way our culture glorifies calculus; but part of this is due to the fact that you really cannot BS your way through calc. You have to

*know*it. You have to understand it; to apply it.Hence, when students achieve that passing grade (ethically), they know they earned it. They know they mastered the material.

My point is: I believe we have to do more to (1) get more students

*into*a high school calculus course and (2) get those students to succeed in calculus. Because when these kids succeed in calculus, they decide they are capable of just about anything.It's our job as educators to push our kids to greatness. We have to believe they are capable of more than they believe they're capable of. We have to demand more of them than they would demand of themselves. We have to give them the tools to conquer their goals and their fears.

Get them into calculus. It will accomplish all of this.

## Sunday, May 8, 2016

### Rate In/Rate Out Review

The AP Exam is over! This year, I reviewed my kids very similarly as I did last year (each week we focused on a new multiple choice and free response topic, with a review quiz each Friday that the students helped write).

One free response topic that was certainly lacking in my review last year was Rate In/Rate Out questions. These have intimidated my students in the past, which is not great as they seem to be becoming a popular first question (including this year). Not a great way to start the free response section.

So, this year we spent a whole day on these types of questions. However, instead of just throwing several past AP questions at my kids, I gave them ten different questions they may be asked to answer for these free responses. Of course, the College Board can ask whatever they want, but these are questions that seem to arise frequently.

We answered these ten questions for two arbitrary functions, I(t) (the rate IN) and O(t), the rate OUT. This seemed to really help my students. I'm relieved that I finally found a way to make these questions easier to digest because these really can be fabulous questions that model real-world situations beautifully.

Below are the ten questions with answers:

And here is the student handout (the ten questions, two past AP FRQs, and two FRQs I wrote).

A great follow-up to this is to have kids create their own Rate In/Rate Out problems. Unfortunately, I don't have time for this project until after the AP Exam, but it's still one of my favorites.

So, this year we spent a whole day on these types of questions. However, instead of just throwing several past AP questions at my kids, I gave them ten different questions they may be asked to answer for these free responses. Of course, the College Board can ask whatever they want, but these are questions that seem to arise frequently.

We answered these ten questions for two arbitrary functions, I(t) (the rate IN) and O(t), the rate OUT. This seemed to really help my students. I'm relieved that I finally found a way to make these questions easier to digest because these really can be fabulous questions that model real-world situations beautifully.

Below are the ten questions with answers:

And here is the student handout (the ten questions, two past AP FRQs, and two FRQs I wrote).

A great follow-up to this is to have kids create their own Rate In/Rate Out problems. Unfortunately, I don't have time for this project until after the AP Exam, but it's still one of my favorites.

## Wednesday, May 4, 2016

### Dear Legislator

Dear Oklahoma Legislator,

Last week, one of my seniors told me he's thinking about becoming a math teacher. I've taught this kid for two years--in PreCalculus and AP Calculus--and he's always told me he wanted to be a pediatrician. I'll tell you this: a bunch of my kids say they want to be doctors. You know what's different about this one? He would actually do the work necessary to become one.

But now this boy--this smart, competent, enthusiastic young man--is considering becoming a public educator instead. He has only one concern: Will he be able to support a family on an Oklahoma teacher's salary?

I ask you, how am I to answer that?

Some of your colleagues have answered my question with, "You knew what you were going to make when you entered this profession."

My students are starting to listen. And now a whole generation is terrified of pursuing an education degree out of fear that they will not be able to make it financially.

I'd like to paint you a picture. Let me tell you what my student's classroom would look like, if he decides to pursue a career in education.

His classroom door would be open to anyone, at all times. He would treat his students as if they were his own children. He would teach with passion and enthusiasm, researching ways to make sure every kid had the best possible learning environment. He would never give up on his students, even if they gave up on themselves. No child would ever feel left out or lonely, because this young man is a champion of the underdog. His students would learn elegant mathematics, and they all would be stretched in their thinking. They would leave his class with more confidence than when they entered.

His students would feel connected to their school, because this boy has more school spirit than anyone I've ever known. He would sit in the front row at their plays, games, and concerts. He'd be their biggest cheerleader. Those kids would feel so loved. His would be the class that would brighten their day--even when the demands of high school tugged at them.

You know that excitement and softness that people use when they talk to a new baby? That's the kind of enthusiasm and kindness with which he would treat his own students. Imagine a world where we all learned to treat each other in that way. We could start a revolution.

His students would learn the importance of serving each other and working together. He would model what it looks like to put others' needs above your own. He would serve and teach with generosity, humility, and compassion. He would be every kid's favorite teacher.

But he'd also make a great doctor.

So I ask you, what am I to tell him?

How would you answer him?

You and I both know we need people like him in the classroom. A high school teacher impacts thousands of young lives over his career. Think of the lives he could change for the better.

I've done my part: I've lit the fire. I've sparked his interest.

Now it's up to you. What will you do to keep this young man--and many others like him--in our schools?

I hope you choose to

**go light the world**.
Sincerely,

Rebecka Peterson

Union High School

Tulsa

## Thursday, February 18, 2016

### Five

Lisa, my friend, mentor, and boss, challenged me to answer five questions about this school year. We'll see how far I get before baby awakes. Also, I apologize in advance if my writing is sub-par. Sleep deprivation, folks. I suggest we all go treat our moms and dads to a steak dinner for all the sleep they sacrificed for us.

Without further ado...

Or maybe more accurately: FOMO (fear of missing out).

I fear I'm missing out on my students' lives while I'm on maternity leave. I know there are milestones in their learning (of math and of life) that I won't get to witness. And then, when I return to school, I fear missing milestones in my son's life. He's only two weeks old. I get that he won't remember any of this. But--as exhausted as I am--it kills me to leave him. I can't win either way. I want both worlds. But I can't have them simultaneously.

Without further ado...

**What has been your ONE biggest struggle during this school year?****Fear.**

Or maybe more accurately: FOMO (fear of missing out).

I fear I'm missing out on my students' lives while I'm on maternity leave. I know there are milestones in their learning (of math and of life) that I won't get to witness. And then, when I return to school, I fear missing milestones in my son's life. He's only two weeks old. I get that he won't remember any of this. But--as exhausted as I am--it kills me to leave him. I can't win either way. I want both worlds. But I can't have them simultaneously.

**Share TWO accomplishments that you are proud of this school year.**

- I made it to four hundred posts on the One Good Thing blog. The blog honestly changed my life. Every day, I--along with several other educators around the country--post one good thing that happened at school. Our mantra is, "Every day may not be good, but there's at least one good thing in every day." I recognize that life is hard and that some days are...not good. But searching for the good regardless has been incredibly therapeutic.
- I've had four students this year tell me they want to be a math teacher because of me. (I know it's not
*only*because of me, but I'll take it anyway.) Each of these students is bright, compassionate, and fun-loving. I know they will all make amazing teachers, should they continue on that route. But, even if they don't, I'm so humbled that they think enough of me and of my career choice to want to emulate it. In a~~world~~state where teachers are often undervalued and certainly underpaid, I'm proud to say that I'm helping the next generation see our worth. I'm hoping they'll join us in making a positive difference in Oklahoma public education.

**What are THREE things you wish to accomplish before the end of the school year?**

- I'd like to make it to five hundred posts on the One Good Thing blog.
- I want to have at least as high of a pass rate on the AP Calculus Exam as I did last year.
- When the school year is over, I don't need my kids to remember me. But I would like for them to remember how they felt being in math class: I hope that they leave knowing that their teacher will always love them, respect them, fight for them, and be there for them. I hope they feel that on a daily basis. And I hope I act in such a way as to never cast any doubt.

**Give FOUR reasons why you remain in education in today's rough culture.**

- I love being around teenagers. I think they're funny, vulnerable, smart, and completely inspiring. I know I learn more from them then they could ever learn from me. They challenge me to be the best version of myself every day. It's an impossible challenge, but one that I'm thankful for regardless.
- I love mathematics. I would be hard-pressed to find a job where I get to do this much math every day.
- I'm stealing this one from Lisa:
*If not us, then who?* - I believe we're called to repair the brokenness that exists in the world. I'm a Christian. And while I openly apologize for the insensitivity, the irrelevance, and the complete asinine behavior that often accompanies the church, I won't apologize for what I believe. What I believe is that God created this world to be perfect and whole, but when He created human beings He abdicated His right to control (this is where some Christians may disagree with me). That abdication was necessary for humans to be able to love...but that must mean we are also capable of hatred. And, hence, we've created a "brutiful"--a brutal and beautiful--world. But, God entered the world again through Jesus, and Jesus called us to continue bringing heaven to earth--to continue to repair what has been broken. For me, this reconciliation means teaching. It means helping students discover their worth. It means letting them know that they are kind, important, valuable, and smart. It means showing them that they, too, have a role to play in the repairing of the world.

**Which FIVE people do you hope will take the challenge of answering these questions?****I'm going to just ask two other women who also teach math in Oklahoma public schools. I challenge @druinok and @mathequalslove. Both of these ladies are incredible math educators and fight for the rights of their students on a daily basis. I admire them deeply and hope to hear their answers.**

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