NSF grant to enhance understanding of student thinking in mathematics “proof-transition courses”

​The National Science Foundation awarded Professor Rossella Santagata a three-year, $300,000 grant to improve undergraduate instructional teams’ understanding of student mathematical thinking in proof-transition courses.

The project will be conducted in partnership with the UCI Department of Mathematics. Professor Alessandra Pantano and Associate Professor Roberto Pelayo are serving as Co-Principal Investigators.

Proof-transition courses, such as Introduction to Abstract Mathematics, introduce students as freshmen or sophomores to proof-writing for the first time.​

Rossella Santagata

Large percentages of undergraduate students struggle with proof-transition courses and several students consequentially abandon the mathematics major. The notable increase in content difficulty, coupled with the transition from computational to proof-based mathematics, turn these courses into juncture points that determine whether students will pursue studies and careers in STEM. Additionally, the issue affects students from underrepresented groups at a disproportionate rate.

The project will design and investigate the efficacy of a video-annotation curriculum centered on teacher noticing and responsive and equitable mathematics instruction. Teacher noticing entails attending to student mathematical thinking and positioning in the classroom, responding strategically and appropriately, and improving both learning and sense of belonging.

The curriculum for this project will include six components: (1) Mathematical tasks designed to elicit and make visible student mathematical thinking about proof-writing; (2) Frameworks to guide instructional teams’ noticing and reasoning about students’ writing of a complete and consistent mathematical proof; (3) A framework that guides instructional teams’ understanding of responsive and inclusive teaching (4) Video clips of students solving mathematical tasks during one-on-one interactions with an instructor and video clips of whole-class interactions; (5) Video-annotation tasks that support the development of noticing of student thinking and the implementation of responsive, equitable and effective mathematics instruction; and (6) A facilitator guide to support implementation of the curriculum that will allow other colleges and universities to utilize it.

“While teacher noticing has been examined extensively in K-12 mathematics classrooms and has informed the design of successful teacher preparation and professional development programs, it has rarely been applied and studied in higher educational settings,” Santagata said. “I am excited to partner with colleagues in the Mathematics department to design and test this innovative video-based curriculum that has the potential to improve the learning experiences of undergraduate students at UCI and beyond.”

The project team will test the curriculum for its impact on instructional teams’ (including course instructors, teaching and learning assistants) knowledge, noticing competencies, and instructional quality, and on their student learning. Findings will be shared via publications and conference presentations, and the curriculum will be made freely available to other institutions, including those serving large percentages of underrepresented students.

Learn more.