Among many dimensions of improving STEM education in the U.S., this research addresses two of particular urgency: (1) improving mathematics learning for undergraduate students in developmental (remedial) mathematics and (2) improving the preparation of secondary mathematics teachers. These two populations – undergraduates who are inadequately prepared for college mathematics and prospective secondary mathematics teachers (PSTs) – have complementary needs. The undergraduates need intensive attention to go beyond a focus on procedural knowledge to develop *conceptual understanding*, *strategic competence*, *adaptive reasoning*, and *productive dispositions, *the other strands of mathematical proficiency (Kilpatrick, et al., 2001). The PSTs need supervised, authentic mathematics teaching experiences that focus on helping learners build mathematical proficiency. This project brings these two populations together for their mutual benefit, with the PSTs serving as teachers for developmental mathematics under the supervision of mathematics and mathematics education faculty.

In many institutions across the U.S., students of color make up a large percentage of the population enrolled in developmental mathematics, prerequisite for college algebra and calculus. These students are under-represented in STEM majors. MSU is no exception: over 35% of students in developmental mathematics are students of color, and the failure rate (drops and grades of D or lower) for all students in developmental mathematics is about 30%. Targeting this population can improve the likelihood that more of these students will continue in STEM majors.

The intervention uses research-based instructional methods to help students develop mathematical proficiency, engaging them in problem solving with materials designed to provide multiple entry levels, link to prior knowledge and support collaborative learning through instruction and discussions that focus on students finding and justifying solutions. PSTs enrolled in a year-long course in methods of teaching mathematics will learn to teach with these materials, will develop lesson plans based on them, and will use teaching techniques that promote mathematical proficiency. Every PST will teach and observe peers teaching. This “approximation of practice” (Grossman et al., 2009) will provide PSTs with an authentic teaching experience and at the same time help the developmental mathematics students learn the mathematics they need.

## Intellectual Merit

This project will test the hypothesis that students in developmental mathematics taught using research-based materials and methods to promote mathematical proficiency perform better on measures of mathematical proficiency, including procedural fluency, than students who do not receive such instruction. Well-prepared PSTs under close supervision of faculty are used as instructors for developmental mathematics students. This research provides evidence-based support for improving outcomes in developmental mathematics and also addresses the problem of finding appropriate, authentic and educative field experiences for PSTs. The project provides teaching materials that can be used in other developmental mathematics courses and an innovative approach for improving the mathematical performance of students in developmental mathematics and for improving the preparation of future mathematics teachers. The project personnel include faculty from mathematics with a long history of work in developmental mathematics and experienced mathematics education faculty associated with the top teacher preparation program in the U.S.

## Broader Impacts

This project promotes teaching and learning by improving outcomes for students with historically low participation in STEM majors and providing more authentic experiences for PSTs. The research is conducted in 2 sections (50 students) of developmental mathematics with students targeted as likely to need extra support. The teaching approach and materials can be expanded to additional sections in subsequent years and adopted in whole or in part by other universities. The model for combining these two populations – PSTs and developmental mathematics students – can be used by others. The research improves outcomes for underrepresented groups, increases STEM participation overall, and contributes to a teaching force better prepared to teach a diverse population of students and to teach mathematics that has historically been difficult for many high school students.

Slides for the November 2013 presentation at PME-NA, Chicago, IL

Slides for AAC&U presentation, November 2014, Atlanta, GA

NSF Proposal, TUES 2012

Funded by Michigan State University and the National Science Foundation DUE-124540

Updated November 2014