Cryptography to Calculus: Teacher Dr. Pena-Lopez 

From inspiring a love for mathematics to guiding students through the toughest concepts, Dr. Pena-Lopez has developed a talent for making calculus not just approachable, but genuinely enjoyable. With her engaging teaching style and ability to break down complex ideas, she has turned Advanced Placement Calculus AB and BC into a subject that students look forward to. This Tuesday, Nicholas and I had the chance to sit down with Dr. Pena-Lopez and learn more about the journey, motivations and experiences that shaped her career.

Q: What inspired you to pursue your career?

A: As a little kid, I always helped people with mathematics. It came very easily to me. I understood patterns right away. My friends had a hard time with mathematics. Females tend to have a little bit harder time than males with mathematics, so I was always helping my female friends out. As I pursued high school, I questioned whether I should do pure mathematics or accounting, because I like math but also accounting and business. When it was time to decide, I was like, no, I really like getting to understand the complexities of mathematics. So that's what I decided. I really wanted to go into mathematics in college.

Q: And you also went into physics too, right? Where did that come from?

A: Physics was more my ambition to open the doors for mastery level. I wanted to show that I could complete more. For physics, I only needed to do six more classes because math and physics had similar classes, so I was like, let me do it. 

Physics during my time was all boys. There were no girls. It's a boy's world. Even mathematics was, back then, a very boys’ world. Physics was even worse. I never saw a female in my class. And I noticed males somehow in my class, I don't know how, but, in class, the professor used to ask a question and they would answer it without doing any mathematical work.

And I just couldn't see it that way. But when it came to assessments where you have to prove things, I would kill them. I just, because I understand math, see the patterns. So for me, patterns happen more on paper and proving things like that. I can't see it visually as much as some of the males could, but I could prove anything on paper and tell you why mathematics is correct. So I did like that about physics. Like I was able to prove why it works. Why, you know, why did you get that answer? And the males kind of knew what the answer was, but could never prove it. They couldn't prove it mathematically or through physics, you know. So I did enjoy that. I felt bad for them. They hated me. But I did like seeing physics come alive through mathematics a lot. That I did love. And I loved physics experiments because I could see the mathematical concepts coming alive in real life.”

Q: Did you do research with math?

A: Yeah. So when you do your dissertation, your PhD, you do a lot of research.

Q: What was your thesis for your PhD?

A: So my thesis was in visual cryptography, which is pretty much a mathematics equation using matrices, which are pixels, like black dots. In real life, it would be like black dots, which are a lot like the QR codes you see. So it's like black pixels like that right and all those black pixels have a lot of math in it. So what visual cryptography is like, think of transparency — a clear paper, kind of like laminating paper — and then you put the pixels in it on top of that. We call that paper a ‘share,’ so when you stack the shares, it's called visual cryptography because it has a hidden message in it. Back then, it was especially used for when you’re in a war and you have a message, say for example, hey we're in a war and we'll send Nicholas to this camp and we'll send Doreen to this camp and me to this camp and then we'll meet in another camp. So if they stop Nicholas and they see his paper, it just looks like little black dots everywhere. These are secret messages they can't read, but once the three of us get together and put those papers on top of each other, it tells us, oh you need to kill so and so or something. Visual cryptography is coding and decoding messages visually and we would put mathematical equations together to get the pixels.

Q: How did family values shape your decision to pursue being a teacher?

A: Yeah so a lot of decisions, especially once I met my husband, it was—and we both knew we wanted kids — that was part of what we wanted and we always talk about if we didn't have kids, our life would have been so much different — I wouldn't be here, that's for sure. But yeah, I wanted to be a mom but not a house mom. I didn't want to stay home because I still wanted to have something but yeah that made the decision.

Q: What do you find most fulfilling about being a math teacher here?

A: Oh what I love about is seeing the growth of the students. Even like this year, a lot of the students came very, very weak. Like they came like they shouldn't have been in this class, and I could tell right away. But I’m not one of those teachers who discourage those students, you know, I’m always like I’ll put them aside, hey let's meet or you know, come and I’ll help you or let's go over what you did wrong. So being a teacher, my satisfaction is seeing them grow and get stronger, and then I like hearing emails from them when they go to college. I get a lot of kids from Ivy League come back and they're like, ‘Our class is so easy because of you.’ My goal as a teacher is to see them grow and become better than me. I want them to succeed much more than I did. You know what I’m saying, like because you built them as far as you could go, now you’re hoping that there's a professor that will pull them even farther than you could. You want them to succeed, you want them to do the new science, the new math to make our world better. So that's the satisfaction and I'm always thinking hopefully in the future I’ll see them.

Q: What challenges have you had to overcome to get to where you are now?

A: Challenges… um... I have four siblings, and two of them are gifted. When I say gifted, I mean they are skyrocketing geniuses. One is a lawyer and one has her PhD in human aid, and I'm the oldest, so I wasn't gifted like them. I have to work super, super hard to be number one, or number two or number three. Like, them, they never study. Do you get what I’m saying? They come in and they're like one two three. I always have to, since little, even in fourth grade, I would stay up to one o'clock making sure I understood the material. So, I think I just had to work so hard— that I had to overcome it. You know, I wasn't strong in reading, I wasn't strong in writing, I had to work triple hard. My sisters could write an essay in five minutes, you know, a whole college essay. I just had to work so much harder than them, but it's okay, I went far.

Q: If you were to go back in time to when you were a freshman in high school what would you tell your younger self?

A: My younger self… I think I would tell my younger self to enjoy it a little bit more because I was just so dedicated to schoolwork. I was the first generation to go to college and I came from a very poor, when I say poor, I mean a poor background and environment— not my family, but the city I lived in. I would never take my boys there. But um yeah, I think I would tell myself to enjoy life a little more, you're going to get there where you want, but do enjoy it, and don't be so hard on yourself.

Q: Who did you think you were going to be when you were a kid?

A: I think teaching— when I was a really small kid it was always teaching. And then when I went to high school, I said I never wanted to teach high school. That was my thing, I said, ‘God, please don't let me teach high school, I want to be a professor.’ So as I got older, I knew I wanted to go into the teaching world, but I always thought it would be as a professor, never as a high school teacher.

Q: Why are you a high school teacher now?

A: So the high school teacher is mostly for my kids, partially because of the tuition, but the main reason was I was a full-time faculty at Palm Beach State College. I had tenure, which is very hard to get. Tenure is pretty much your job is secured, they cannot fire you for any little thing. You have to do a major criminal act to get fired, you are top-notch. So I had tenure. I loved my job, but I did travel. I had to leave at five o'clock to travel an hour and 30 minutes to make it to my job. If I do not leave at five o'clock, it'll be almost a three-hour drive, just one way. I lived in Pembroke Pines, the west side, and it was all the way in Lake Worth. So, towards the end, I think I was 13 years there. I loved my job. I loved it. And by that time, I already had two boys and they were really small, and I got into an accident with a semi-truck and I survived it. And it was really my husband who said, ‘Look, either you could stay with the job you love, or you quit and get something closer to home, and your kids will have a mom.’ It was a hard decision, but in the end, I chose my kids over my job.

Talking with Dr. Pena Lopez was nothing short of inspiring. Her passion for teaching and love for math shines through in everything she does, reminding us that learning is as much about the journey as it is about the destination. We are so grateful for educators like her who not only teach but also ignite curiosity and confidence in their students. Whether it is solving derivatives or inspiring the next generation of problem-solvers, Dr. Pena Lopez is truly making a difference in her student's lives — one calculus lesson at a time.