# Patricio Herbst

### Professor, School of Education; Professor, Department of Mathematics, College of Literature, Science, and the Arts

Pat Herbst is a mathematics educator whose research focuses on the nature of the mathematical work that students do in secondary classrooms and on the work teachers do to manage knowledge development. He has studied mathematical work, student thinking, and teacher decision-making in geometry classrooms with particular attention to the use of reasoning and proof to solve problems and develop new ideas. Herbst’s research aims at describing and explaining the work that teachers do to create and sustain mathematical activity and knowing in classrooms; his research also includes identifying and measuring the sources of justification for teachers’ decisions, including knowledge, situational norms, and professional obligations. Herbst has pioneered the use of animated depictions of classroom stories to prompt conversations about instruction among teachers, and using these conversations to understand teachers’ reasoning and decision-making. He teaches courses on mathematics instruction, curriculum, and research in the doctoral specialization in mathematics education, and a course on secondary mathematics instruction for the teacher education program. He received his doctorate from the University of Georgia in 1998.

His research includes Thought Experiments in Mathematics Teaching II (ThEMaT II, a National Science Foundation-funded research and development program directed by Herbst and codirected by Dan Chazan at the University of Maryland. The project is developing scenario-based instruments to assess teachers’ decision-making, recognition of instructional norms and obligations, and mathematical knowledge for teaching in high school geometry and algebra. These instruments are being included, along with other resources (instructional modules, software tools) in an online environment (www.lessonsketch.org) for teacher development that supports the learning of mathematics teaching in, and from, practice.

Herbst teaches courses in the following program(s):

W.K. Kellogg Foundation's Woodrow Wilson Michigan Teaching Fellowship

Mathematics Education

Teaching and Learning

Secondary Teacher Education

Secondary Teacher Education (Secondary MAC)

## Selected Publications

### Book chapters

Herbst, P. and Balacheff, N. (2009). Proving and Knowing in Public: What Counts as Proof in a Classroom In M. Blanton, D. Stylianou, and E. Knuth (Eds.), *Teaching and learning of proof across the grades: A K-16 perspective* (pp. 40-63). New York: Routledge.

Silver, E. and Herbst, P. (2007). The role of theory in mathematics education scholarship. In F. Lester (Ed.), *Second Handbook of Research in Mathematics Teaching and Learning* (pp. 39-67). New York: Information Age.

### Articles

Herbst, P. and Chazan, D. (2011). Research on Practical Rationality: Studying the Justification of Actions in Mathematics Teaching. *The Mathematics Enthusiast*, 8(3), 405-462

Herbst, P., Nachlieli, T., and Chazan, D. (2011). Studying the practical rationality of mathematics teaching: What goes into “installing” a theorem in geometry? *Cognition and Instruction, 29*(2), 1–38.

Herbst, P., Chazan, D., Chen, C., Chieu, V.M., and Weiss, M. (2011). Using comics-based representations of teaching, and technology, to bring practice to teacher education courses. *ZDM—The International Journal of Mathematics Education*, 43(1), 91–103.

Chazan, D. and Herbst, P. (2012). Animations of Classroom Interaction: Expanding the Boundaries of Video Records of Practice. *Teachers’ College Record*, 114(3)

Kosko, K. and Herbst, P. (2012). A deeper look at how teachers say what they say: A quantitative modality analysis of teacher-to-teacher talk. *Teaching and Teacher Education*, 28, 589-598

Chieu, V.M., Herbst, P., and Weiss, M. (2011). Effect of an Animated Classroom Story Embedded in Online Discussion on Helping Mathematics Teachers Learn to Notice. *Journal of the Learning Sciences 20*(4), 589-624.

Nachlieli, T. and Herbst, P. with González, G. (2009). Seeing a colleague encourage a student to make an assumption while proving: What teachers put to play in casting an episode of geometry instruction. *Journal for Research in Mathematics Education, 40*(4), 427-459.

Herbst, P. (2006). Teaching geometry with problems: Negotiating instructional situations and mathematical tasks. *Journal for Research in Mathematics Education, 37*, 313-347.