Andrew Izsák, a professor in the College of Education, conducts research on the mathematical reasoning of middle grades teachers and has developed several innovative courses for pre-service teachers, like one that takes them to the UGA physical plant to see Euclidean geometry applied to sheet metal work.
Where did you earn degrees and what are your current responsibilities at UGA?
I earned a bachelor’s degree in mathematics from U.C. Berkeley, a Master of Science degree in mathematics from M.I.T., a Master of Education degree from Harvard, and a Ph.D. in science and mathematics education from U.C. Berkeley. I am currently a professor of mathematics education in the department of mathematics and science education. I conduct research on the teaching and learning of mathematics, primarily upper elementary and middle grades content including fractions, proportional relationships and linear functions. I teach mathematics content courses for undergraduate pre-service mathematics teachers and mathematics education research courses for doctoral students. I also serve as the graduate coordinator for my department.
When did you come to UGA and what brought you here?
I came to UGA as a new assistant professor in August 2001 after completing a two-year post-doc at Northwestern University. I was attracted by the opportunity to join one of the leading mathematics education faculties in the country and the world. I felt confident that I would receive strong mentorship and support during the critical early years as a new faculty member, and I did!
What are your favorite courses and why?
I love teaching mathematics content and have developed several courses for pre-service teachers that you would not find in the offerings of traditional mathematics departments. One course that I developed examines conic sections (circles, parabolas, ellipses and hyperbolas) and their applications to astronomy, including the design of telescopes and orbits. A second course looks at mathematics in workplace settings. I take students on several field trips, my favorite of which is the UGA physical plant. There are great applications of Euclidean geometry in sheet metal work that make ingenious use of basic ideas like parallel and perpendicular lines and subdividing line segments and arc-lengths into equal-sized pieces. One of the things that makes these courses fun is that, as I have developed them, I have learned new things about mathematics.
What interests you about your field?
When I was an undergraduate, I had no idea that there was a field of research about the teaching and learning of mathematics. After I completed college, I worked for one year as a tutor in an urban junior high school that tracked students. I worked with a variety of students and saw examples where students placed in the regular mathematics track were better at solving non-routine problems than students in the more advanced algebra track. The lesson I drew was that achievement in school did not necessarily correspond with the thinking I had learned to value as a mathematics major. These experiences led to my interest in mathematical cognition, how people think and reason when solving mathematics problems. Mathematical cognition is subtle and complex; gaining insight into how it works poses significant challenges that can support a lifetime of research, and progress often involves inventing new research methods.
What are some highlights of your career at UGA?
With respect to teaching, a main highlight is email I get from former students telling me how helpful a particular course or lesson was for their work as teachers. With respect to research, a main highlight has been the development of collaborative research. I have been very fortunate to work with some of the psychometricians at UGA, including Al Cohen, Jonathan Templin and Laine Bradshaw. Psychometrics is about statistics for testing. In a series of projects funded by the National Science Foundation, we have examined new applications of psychometric models to mathematics education research. A main goal has been to develop methods that leverage insights gained from the detailed study of cognition in small samples to study cognition in large samples. Another collaboration with Sybilla Beckmann is described below.
How does your research or scholarship inspire your teaching, and vice versa?
My research and teaching have become increasingly integrated in the past few years. With my colleague Sybilla Beckmann in the department of mathematics, I am conducting research on pre-service teachers’ multiplicative reasoning. Multiplicative reasoning includes reasoning about whole-number multiplication and division, fractions, ratios and proportional relationships, linear functions and other topics. This is core content in the upper elementary and middle grades that presents persistent challenges for children and adults. Beckmann and I are collaborating on a research study supported by the Spencer Foundation in which we are interviewing each other’s students to find out what is easier and harder for them to learn, and we are using results to refine our courses intended to help pre-service middle and secondary grades teachers develop their ability to think about and explain multiplicative relationships. We have just received a new four-year grant from the National Science Foundation to continue this research.
What do you hope students gain from their classroom experience with you?
The main thing I hope pre-service teachers gain from my courses is a new perspective on how to teach mathematics. Figuring out how to solve problems is at the core of mathematics, but many of my students have only experienced a sterile version of mathematics and mathematics instruction in which they are first shown a method determined by the teacher and/or textbook for solving a problem and then asked to complete exercises to practice that demonstrated solution method. Such instruction often only requires that students remember what to do, not understand why a solution method is logical and reasonable. During a typical lesson, I give students a set of problems to work on in groups. I do not tell them how to solve the problems. Rather, students have opportunities to develop their own methods for solving the problems and explaining their methods to each other. I use my students’ thinking to work toward my goals for the lessons. My hope is that students will experience my teaching methods as beneficial to their own learning of mathematics and that this experience will help them envision how to teach mathematics through solving problems to their own students in the future.
Describe your ideal student.
Mathematics can be an intimidating subject, even for future school mathematics teachers. My ideal student is one who is willing to tackle new problems when the way forward is not clear and who is willing to explain what he or she is thinking even when unsure if that thinking is productive or correct. Students who make this effort help themselves, other students and me. Students’ partially correct thinking helps me understand what is challenging, and I am always very grateful when students are willing to place themselves in what can be the vulnerable position of possibly being wrong in front of their professor and classmates.
Favorite place to be/thing to do on campus is…
When I am not in my office, the classroom or the swimming pool, I enjoy the turtle pond in front of the School of Ecology.
Beyond the UGA campus, I like to…
My hobbies are traveling, hiking and photography. I am also interested in a wide range of music including classical, jazz, blues and other genres with roots in Louisiana.
Favorite book/movie (and why)?
One of my favorite books is actually a pair of books by James Welch, a member of the Blackfeet Nation. “Fools Crow” is historical fiction set in the northern plains as Europeans are beginning to arrive in the 19th century and traditional Native American society is under assault. “Killing Custer” is a non-fictional account, from a Native American point of view, of the events leading to the battle of Little Bighorn, the same history as in “Fools Crow.” In both books, Welch crafts compelling prose to recount grim history for Plains Indians.
Proudest moment at UGA?
Like many other faculty, some of my proudest moments are when students from our programs in mathematics education notch their own significant professional accomplishments, such as presenting at conferences, publishing and receiving awards for research or teaching.
Originally published on Sept. 14, 2014