What makes mathematics difficult for some students to learn? Two College of Education researchers believe the answer may lie in the way mathematical reasoning is communicated in classrooms.

Assistant professors Jessica Bishop and AnnaMarie Conner, both in the mathematics and science education department, are working on separate five-year studies documenting student-teacher interactions and assessing other classroom factors that may influence mathematics learning. Two CAREER Awards from the National Science Foundation that total $1,207,853 will fund the studies.

As a former high school mathematics teacher, Bishop often wondered what aspects of her teaching made a real difference in student learning. Much of the time in math classrooms was spent talking, she noticed, but not all of the talk was “mathematically productive.”

“What elements of mathematics conversations encourage students to generate, explain and defend mathematical ideas and to make connections between concepts?” asked Bishop. “We need to be able to identify what it is that teachers and students are doing in productive mathematics conversations so we can better support practicing and prospective teachers.”

Over the next five years, Bishop will use an NSF CAREER Award of $672,846 to systematically document the details of student-teacher exchanges in elementary and middle school math classes. She will analyze shifts in student-teacher interactions across different curricular topics, grade levels, school periods and teachers, and in schools with student populations from a variety of backgrounds.

Conner will use NSF funding of $535,007 over five years to observe and document how college mathematics education majors and new teachers help students create and critique mathematical arguments, or proofs. Conner will study a learning process known as collective argumentation, whereby students-with teacher guidance-discover ways to answer particular mathematical questions.

“Prospective teachers often come to class believing that math involves memorizing rules and the teacher’s role is to communicate those rules,” Conner said. “If a teacher can foster student involvement in creating mathematical arguments and proofs, however, students learn something more valuable: reasoning skills.

“Creating and critiquing mathematical arguments is an increasingly important part of mathematics classes,” Conner also said. “This will lead to students having better mathematical preparation for college.”

Conner’s research team will follow college mathematics education majors through their coursework and into their first two years of teaching. The team will record how novice educators’ support for collective argumentation evolves. In addition, the research team and educators will use the data they collect to develop more effective ways to support this learning method.