ABSTRACT

In order to increase the number and diversity of undergraduate STEM majors in the United States, it is essential to improve students' interest and success in mathematics before they enter their undergraduate studies. The secondary grades are especially important for mathematically preparing students for undergraduate STEM majors, but rigorous and engaging secondary mathematics classrooms require a well-prepared teacher workforce to facilitate these learning environments. This Improving Undergraduate STEM Education Engaged Student Learning Exploration and Design project seeks to transform preservice mathematics teachers' understanding of mathematics early in their undergraduate studies, thus contributing to the transformation of their undergraduate STEM education. More specifically, this project will develop curriculum materials for use in mathematics courses for preservice secondary mathematics teachers as well as develop instructor materials that assist mathematicians and other instructors in using these materials in an active learning environment. The materials will be research-based and focus on targeted, inquiry-based experiences that will develop a deep understanding of functions as they correspond to the high school curriculum and the first two years of the university curriculum. The initial piloting of materials will take place at a research-intensive Hispanic Serving Institution with over 50% of its teacher preparation candidates coming from underrepresented groups. In addition, the project will directly involve the participation of a strong network of teacher preparation programs that use the highly-acclaimed UTeach STEM teacher preparation model. It will also enhance the experiences, both in content and pedagogy, for thousands of preservice secondary mathematics teachers across the country via coordinated dissemination across the UTeach network and other mathematics teacher preparation programs. As a result, the project will impact the mathematical learning experiences of hundreds of thousands of socio-economically disadvantaged students across the country, as 66% of graduates from UTeach programs teach in schools where the majority of students are low-income. That is, diverse groups of preservice teachers and the highly diverse students they teach will benefit from the project's transformation of undergraduate education for preservice secondary mathematics teachers.

Guided by findings from the research literature regarding secondary mathematics teachers' pitfalls in understanding key concepts and ideas about functions, the project will enhance and supplement widely-used resources for preservice secondary mathematics teachers in the first two years of their university mathematics studies. The project will develop research-based tasks and explorations that will address key concepts and ideas about functions that are typically problematic for secondary mathematics teachers, to include functions versus equations, graphical connections to function patterns, and other important function concepts. Curriculum widely-used in the UTeach program will be augmented with an instructor's guide to scaffold the lessons and explorations for mathematicians and other instructors teaching the course. As part of the cyclic design process, the project will collect evidence on whether and how these materials adequately close gaps in understanding of critical problematic concepts identified in the research literature and therefore, will contribute to the knowledge base in the specific areas of design and implementation of inquiry-based materials for preservice secondary mathematics teachers. The project will generate knowledge about the key characteristics of such mathematical tasks and about what instructional and pedagogical supports mathematicians need to implement inquiry-based materials for preservice secondary mathematics teachers. The project will also provide evidence on how the curriculum materials and implementation of these materials address conceptual difficulties that teachers encounter with functions. Thus, the project will generate evidence for curriculum and instruction that could transform the education of preservice secondary mathematics teachers. A distinguishing feature of this project will be the purposeful integration of the mathematics education research literature on the key mathematical pitfalls or misconceptions held by preservice and inservice mathematics teachers into the design and redesign of mathematical experiences and explorations for secondary mathematics teachers in the first two years of their mathematics studies.

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