Nicole Rigelman
“When students recognize there are lots of different ways to do math, and those ways are okay and welcomed, that’s when we learn.”
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
Nicole Rigelman, EdD, is a professor of mathematics education in the Department of Curriculum and Instruction at Portland State University, where she teaches math education courses for preservice and in-service teachers. She also serves as an Education Program Officer at The Math Learning Center, a nonprofit curriculum development organization. Rigelman began her career as a middle school math teacher and later worked as a K–12 mathematics curriculum specialist. She has been recognized by AMTE with its Excellence in Teaching in Mathematics Teacher Education Award.
Can you discuss the progression of your research interests and the driving factors behind that?
When I was in my teacher preparation program, I had my first opportunity to think about mathematics in a different way.
When I was in school, mathematics classes were very much focused on following a procedure that the teacher had presented and then mimicking that process. And when I was in teacher training, I discovered that math was a lot more than algorithms to follow and could be a lot more interesting and fun. I actually was a student at Portland State University, which is where I work now.
The professors in the math department were doing some really innovative things with visual models and math manipulatives. We were using things like tiles, cubes, and geoboards to convey meaning behind the math concepts. I would say that over time, I became a person who thinks about mathematics visually. Now, whenever I go to solve a problem, I will draw a quick sketch of what is happening.
I started my career as a middle school math teacher. And fairly early in my career, I became a math curriculum specialist in my district. I was interested in making changes to how math was being taught in the district by supporting teachers to learn some of the things I learned in my preparation program.
And so that's what really set me off on my research agenda. I had the opportunity as a college student to change my thinking about what mathematics was and how it should be taught. For people who are teachers, when they learn these ways, they have to not only let go of how they learned mathematics, but also let go maybe of how they taught mathematics, and what they perceive it means to be a mathematics teacher. I recognized that all the changes were really hard for people, which is why the change process is so slow and needs so much support.
For my dissertation research, I studied what middle school math teachers do to promote mathematical thinking and problem-solving in their classrooms. From there, I developed cases to use in professional development. They were meant to help teachers develop an image of what it might look like to teach in a more student-centered way and include problem-solving and reasoning as regular parts of their teaching.
What are some of the main findings that you've had with your research on math modeling?
One thing that I have learned through my work is that when students are conveying their mathematical thinking—whether that be with a model or numbers and math symbols—it is an opportunity to make sense of math and talk about it with others. When they get to do this, it leads to a much deeper understanding for them.
That has been really echoed not only in my research, but also in the research of others. Now, in my work with math coaches and teacher leaders, I try to help them think about how they might work alongside their colleagues so that they can all be learning about math more deeply, trying out things with their students, and coming back together to talk about how that experience went, what kids are thinking and doing, and what they might do next to build on their students’ thinking. So it's a much more responsive way of teaching than what I experienced as a student.
A lot of things I do in my teaching and research are really focused on high-level mathematical thinking, problem-solving, and reasoning. And is there a common theme in some of the advice that you give to math coaches and teachers? I think the big thing I would say is adopt something like the Nike slogan of “Just Do It.” So, “Just Try It.”
Try it out with your students. See what happens. See what works and how you might morph the new teaching approach to work for your style. But also really work in ways that are responsive to your students, because that's what helps everyone feel like they are capable of learning and doing mathematics. When students recognize that there are lots of different ways to do math. And those ways are okay and welcomed, that’s when we learn. We learn from people who have different ideas from ours.
And in modeling, what are some of the different ways to approach modeling tasks or assign modeling tasks to students?
I was actually just recently designing a modeling task that's centered around making friendship bracelets. The reason I wanted to use that particular context is that there are different ways of thinking about fractions that don't always come up naturally as students solve problems. Many people think of fractions only as part of a whole, but fractions are division.
Some people don’t know that fractions are division until they move into math that includes more abstract symbols, variables, and whatnot. I wanted to think about a context where you wouldn't be tempted to take a quantity and chop it into little bits and divvy it out, because you wouldn't want a friendship bracelet made of all these little pieces of cording. So, seeing fractions as division is recognizing that I'm going to deal with the whole length and then divide that length into equivalent parts. For example, if the length were five feet divided into four equal parts, each of those parts is five-fourths, which is one and one-fourth.
The real-world context is really important in making sense of this other way of thinking about fractions. Being clear about your mathematical goal as you're designing the task is important because it influences the questions you'll ask related to that context.
What are some studies you would build on to develop concrete teaching methodologies based on your modeling research?
The National Council of Teachers of Mathematics recently published a book that I've been using with teachers. It's called “Becoming a Teacher of Mathematical Modeling.”
The authors have been working together for quite some time. Across the grade levels, they’re thinking about how to give kids experiences with mathematical modeling. When learning in these ways, students are both doing and learning math through applying math in these real-world modeling contexts. They are learning to mathematize their world.
Once they’ve built their model of the situation, posed and answered questions, they need to go full-cycle and connect back to the real world again. It's been a really powerful resource for the teachers that I work with.
Similarly, there's a project called EQSTEMM that has a lot of culturally responsive community-based mathematical modeling situations teachers can use as well. The leaders work alongside their teachers to design modeling tasks and resources they share. It's so powerful for teachers to see the different ways that you might work on ideas with students that make math really relevant to them. They get much more excited about math, and they feel like it is useful in the real world.
What are some of your current and upcoming projects and initiatives?
Well, I mentioned earlier that I do a lot of work with people who are becoming math coaches and teacher leaders. I am engaged in some work now where we're looking at how we are preparing math teacher leaders and thinking about how those different preparation models and contexts influence their work, not only with students in the classroom, but also with their colleagues.
And so that work has been keeping me busy. While we're in some upheaval right now with regard to grant funding, I am always looking for those next opportunities to get some grant funding to support teachers in their ongoing mathematics professional learning, especially at the elementary level. Because their attention is split to all the different subject areas, they don't always have the opportunity to do things that will help them learn more math and improve and deepen their math instruction.
And so I would say that those are the things that are on my mind now, how can we support some more teachers?
