Erin Krupa
“When I saw students succeed after getting the chance to think for themselves and bring their own ideas into math, I wanted to help make that more widespread.”
About the article:
This post is a part of an ongoing series in which I interview educators and education researchers to supplement the articles on AJ’s Takes on Why. All speakers have my sincerest gratitude and are acknowledged below.
Speaker Bio
Erin Krupa, a former high school mathematics teacher, is an Associate Professor of Mathematics Education in the Department of Science, Technology, Engineering, and Mathematics Education at North Carolina State University. She is the founder of Exploring Mathematics Curricula Creatively (EMC2), which seeks to design and evaluate engaging materials for grades 6-12 mathematics learning. Her research focuses on improving the quality of mathematics teaching and learning through innovative curricular materials and professional development. She has been awarded more than $8.5 million in external funding over the last seven years to support her research.
How did your experience teaching high school math help shape the ideas that you were interested in or that you worked on?
I got my PhD so that I could design, test, and evaluate instructional materials. I thought that if I could learn more, I could help more teachers understand how to use interesting curricular materials. When I saw students succeed after getting the chance to think for themselves and bring their own ideas into math, I wanted to help make that more widespread. That’s what led me to pursue my PhD and then work toward that through teaching undergraduates how to teach math, as well as through the research I do. Seeing it happen in real life, where you give kids a task, and they think about it, problem-solve, use their reasoning skills, and present their ideas, that’s what sparked me.
Then, when I got into my dissertation, there was this really cool textbook called Core Plus Mathematics, and it’s all investigation-based. You open it up, and it doesn’t even really look like a math book. It’s all text and narrative. It’s not the same “here’s a warmup, here’s a definition, here are some problems to solve that are exactly like the example right before it,” where students have no autonomy and don’t get to think at all. It was through watching that be successful in high-poverty schools in North Carolina, that I was like, “Oh wow, this is really cool.”
Could you describe some of your findings on the entrepreneurial pitch papers and what inspired them?
I’m sure you’ve seen the show, Shark Tank. I call these “Shark Tank for math,” but the Design-and-Pitch Challenges in STEM have a targeted math goal, a really important social context, and an entrepreneurial pitch competition. Students are given a challenge in a one-minute video, often by a young kid, an entrepreneur or somebody on the edge of technology. Since I love geometry, one of my favorites is Flashy Fashion. We have a fashion designer who infuses LED light technology into dresses and sometimes does underwater photo shoots, and she’s the challenge champion for Flashy Fashion. She talks about fashion and this technology, and then launches the task, which is for kids to create a wearable product that infuses LED light technology. That’s really fun and exciting because the kids get to decide what they want to do for their product.
One of the most exciting examples I’ve seen was when kids went back to school after COVID and were upset that they couldn’t show their facial expressions. Through Flashy Fashion, they designed a face mask where they could program their mood so it could smile, look astonished, laugh or cry. That’s a small example, but it shows how the challenges engage students in math through their lived experiences and what they want to bring in. We’ve had students create wheelchairs to help their grandfathers with Parkinson’s golf, and we’ve had students create environmental projects to reduce waste around issues that matter to them.
I think that’s a good example of how I’m trying to engage students with things they find meaningful. Sometimes it’s YouTube, sometimes it’s restaurants, but they’re bringing their own culture and interests into the math class. Along the way, as they build their product, they’re learning targeted math. My research team is really confident that they’re learning whatever instructional goal we identified in that unit. For Flashy Fashion, it’s transformations. For Keep It Real, which is about phubbing—when you’re trying to have a conversation and someone is too busy on their phone—it’s a graphical representation. So students are trying to reduce their phubbing over time, which means they’re graphing and collecting data. All of the challenges hit targeted math. They have a technology component, and they have a challenge champion to show how math is used in the real world and make it relevant.
How exactly are these entrepreneurial challenges designed?
Yeah, so my team—the first founder was actually my advisor, Dr. Jere Confrey—has had two NSF grants. In one, we created nine challenges aligned to middle school content, and then in the second, which I led, we created nine more challenges related to high school content. We’ve graciously gotten funding from the National Science Foundation, and that’s paid for it. My research team—graduate students, a research scholar, and faculty members—works to come up with compelling ideas for kids. We talk to students, we talk to teachers, and we run summer camps just to test ideas and see if they have any viability. It takes a while just to get the idea right.
You have to balance what makes a good context. There’s this cool new technology where you can create edible pods that enclose liquid, and we heard about that on NPR and thought, “How can we turn that into a math challenge?” So you’re thinking about contexts in the world that matter, but then you also have to have the right math, and it has to be entrepreneurial. It’s this big balance, and then you have to test out writing the challenge and getting all the supporting resources together.
Another project that I wanted to ask about was the V²MED project. Was there anything that sparked it? And did you get any feedback from people who use the database?
Yeah, I call this my service project to the field because it’s not as flashy or exciting as some of my other work. I love making curricular resources because it’s fun and immediately applicable to students—teachers can pick up the materials and use them. But this project comes from the fact that anytime you do research—and in my case, it’s usually around instructional materials—you want to test the quality of those resources on something. It could be student engagement, student beliefs, or content knowledge. But if you want to measure something, you need an assessment or an instrument.
And when the federal government gives you money, they want to know that they’re funding good work. So almost every federally funded research project relies on assessments. There are a lot of really good assessments that have been thoughtfully developed, and there are others that were developed for one purpose and maybe don’t have as strong a research backing.
If the weatherman tells you it’s going to be 75 tomorrow, you want some validity behind that 75—you want to believe it. If I tell you that you got a 75 on your math test, we want to know what that means and what we should do about that score. When you go to college and take an entrance exam, that score should tell you something about where you should be placed in your college math class. So the scores you get on an instrument are really important. The V²MED project—the Validity of Measurement in Mathematics Education Project—came from the fact that there are tons of instruments being developed all across the world, but we don’t always know the validity evidence behind what those scores mean. So we tried to catalog every instrument used in math education research from 2000 to 2020 and identify the validity evidence for the claims made about that instrument. That’s what the repository is. Hopefully, future researchers can go there and say, “Oh, look at this instrument. It’s really robust. I trust that the score I get is going to measure what I intend for it to measure.” So really, the goal is to help the field build stronger research that can also build on itself.
What are some projects that you're currently working on?
I have another curricular project called Animated Contrasting Cases in Geometry, which I call Acing Geometry. There’s a cognitive psychology idea that if you have two contrasting cases, you can make deeper insights into each of them. I have little kids, so when we’re walking around the lake, we’ll see ducks. We’ll say, “Oh, look at that pretty duck,” and then keep walking, and one of the kids will say, “Look, there’s a duck.” And I’m like, “Ooh, that one’s a goose.” But if you see a duck and a goose next to each other, you can look at their characteristics and you’re more likely to be able to distinguish the two. This is a duck, this is a goose.
Take that idea and put it in math class. If you have one student solve a problem and another student solve a problem, and you directly compare the different ways they solved it, you can come to a richer and deeper mathematical understanding. So my team created animated web-based materials where students can go through this process and look line by line at different strategies to make sense of the nuances and differences between them. So that’s fun, too.
