To become an effective student of mathematics, it takes more than just memorizing procedures and recalling facts. Understanding the “why” through reasoning and proving is vital for deep learning of mathematics but is often the most challenging aspect to instill in learners.
To better understand how new teachers utilize reasoning and proving in their classrooms, Orly Buchbinder, assistant professor of mathematics education, was awarded a prestigious National Science Foundation Early CAREER Award. The five-year grant is for $903,581.
“I am happy that this project will allow me to support our teachers and answer a lot of research questions identified as interesting and critical,” says Buchbinder. “This is an area we don’t know enough about in our field and I am excited to contribute to that.”
The project aims to address a knowledge gap, specifically how sociocultural environments, school norms and professional support affect the development of teachers’ proof-related expertise. It will do so by following UNH graduates of the secondary teacher preparation program over a three-plus year period that includes their first two years of teaching in a school district. The graduates will first participate in a capstone course focused on implementing reasoning and proof into classrooms.
“We want secondary students to justify what they are doing and to be able to understand why they are doing it,” says Buchbinder. “We want to take away shortcuts and understand why properties work the way they do, where formulas come from and why they act in those particular ways.”
The goal is for participants to connect high-level mathematics learned through their graduate work with the world of a secondary classroom.
“Bridging those two realities in not an easy task for anybody,” says Buchbinder. “We want the graduate students to take classroom curriculum and transform it in a way that will highlight the why and give students the opportunity to reason mathematically -- not just practice raw skills.”
The teachers’ progress will be evaluated in a variety of ways including interviews, bi-annual classroom evaluations and presentations at a conference in the education community.
The program will also provide professional development to participants through feedback and quarterly check-ins with the professional teaching community, including annual attendance at a regional conference.
Buchbinder says she is most excited to continue to work with UNH students beyond graduation.
“I think our mathematics education preparation at UNH is so strong and I am constantly impressed by our graduates,” she says. “I am looking forward to seeing how they spread their wings and fly on their own in the classrooms.”
The CAREER grant is a follow-up on an existing NSF Improving Undergraduate STEM Education grant that developed the capstone course, led by Buchbinder and Sharon McCrone, professor of mathematics and associate dean of the College of Engineering and Physical Sciences.
Buchbinder expects the projects to advance scientific knowledge with theoretical and practical benefits to the field and society beyond its scope. Educators will be better prepared to implement proof-related practices that will positively impact a diverse body of students who will be more prepared to pursue careers in science, technology, engineering and mathematics. The results of the research are also likely to benefit the UNH teacher preparation program and impact teacher preparation and professional development programs nationwide.
The research is aligned with educational reform and national standards initiatives and contributes to the NSF Discovery Research PreK-12 program goal of enhancing the theoretical and empirical knowledge base about the nature of teacher knowledge and improvement of teachers’ instructional practices that advance STEM learning.
The funding will also support a post-doctoral position for four years and UNH graduate students that assist in the research process.
“I am thankful to the department of mathematics and statistics and the Office of Research, Engagement and Innovation for their enormous support and professional development that allowed me to secure a CAREER proposal,” says Buchbinder.