Vilma Mesa - US grants

This research program seeks to study how standards recommendations regarding a student-centered approach to mathematics instruction can be actualized so that systematic investigations of its impact on students? learning can be carried out. I propose (1) sensitizing studies: to understand the contexts in which mathematics faculty in community colleges teach; and (2) probing studies: to test conditions under which teaching strategies designed to influence planning, classroom interaction, and verification practices affect instruction. I use a combination of qualitative and quantitative methods for data collection, analysis, and interpretation. This work will develop our understanding of artifacts in teaching, how planning is affected and how classroom interaction can be changed in undergraduate classrooms. The results will highlight the critical conditions under which mathematics is delivered in community colleges and contribute to raise awareness of the need to support them as they strive to improve their practices.

This study to be conducted under the auspices of the Mathematical Association of America (MAA) undertakes a national investigation of Calculus I to identify the factors that contribute to student success, to understand how these factors are leveraged within successful programs and to use the publications, committees, and public fora of the MAA to disseminate the information and help mathematics departments build on its insights.

The study uses both quantitative and qualitative methods. During the study's first phase, a large-scale national survey of Calculus I instruction will be conducted through mathematics departments. The study builds on the Conference Board on the Mathematical Sciences (CBMS) studies to link the survey data with student success. Using the epidemiological model developed by Sadler and Tai, the PIs will examine factors such as instructor attributes, departmental focus, classroom variables, and out of class expectations as likely explanatory factors. A web-based student survey will also be conducted. Data will be studied through HLM analyses and institutions, course-level characteristics, and student characteristics will all be examined.

Phase II of the project will develop a preliminary theoretical framework for institutional models that produce successful calculus students. This informs the selection of eight cases to be conducted in different kinds of institutions. The cases will be analyzed using the approaches of pattern matching, explanation building, and cross-case syntheses.

The study is significant because the number of calculus students has been steadily decreasing in spite of the fact that more high school students are taking higher level mathematics courses. The PIs state that many students leave STEM fields as undergraduates because of poor calculus instruction. Identifying what works in college calculus instruction and why it works and widely disseminating the information will improve student success in calculus courses.

Improving student outcomes in mathematics courses in community colleges is important in meeting the nation's demand for college graduates in STEM (science, technology, engineering and mathematics). Entitled "Transitioning Learners to Calculus in Community Colleges" (TLC3), the project will gather a team of higher education researchers, mathematicians, and mathematics educators to transform institutional approaches to identifying and remedying barriers that impede student progress to and through Calculus II in community colleges. A significant impact of TLC3 will involve supporting instructional improvements aimed at increasing the success of historically undeserved students, particularly underrepresented racial minority (URM) students, thus contributing ultimately to the diversity of the nation's STEM workforce.

The broader goal of TLC3 is to build and test theoretical models that predict STEM URM student success in the Developmental to Pre-calculus to Calculus II (DPC2) sequence, based on programs, structures, and instructional strategies in successful programs. The project uses a mixed-methods approach, including a census survey of 948 community colleges and case studies focused on minority-serving institutions. The models will inform the development of a change tool (i.e., the institutional self-assessment), that examines institutional readiness to facilitate successful outcomes for URM students in the DPC2 sequence. Five institutions selected from a TLC3 networked community (with a minimum of 50 institutions) will test the models and self-assessment tool. The institutional self-assessment tool will help identify a professional development approach that departments and institutions can use to remedy barriers that inhibit student success in the DPC2 sequence. This project is supported by NSF's Improving Undergraduate STEM Education Program (IUSE) and the EHR Core Research (ECR) Program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.

The UTMOST 2.0 project will design, develop and study innovative approaches to the teaching and learning of undergraduate mathematics using open software and electronic textbooks. This project will study students' use of electronic textbooks when these are made freely available in a variety of formats and on a variety of devices. These textbooks will support interactive computation through a seamless integration of Sage, the leading open-source computing system for mathematics. The main vehicles for this integration will be SageMathCloud, a rich online environment for computation and collaboration between students and their course instructor, and Sage cells, self-contained interactive calculation modules that can be embedded in any web page while requiring no software installation or prior knowledge of Sage, because the commands are pre-loaded. Additionally, UTMOST 2.0 will support the further adoption of MathBook XML, an authoring platform that enables the creation of highly functional, open-source textbooks--in particular, textbooks which can exist both in print and in an online format that contains Sage cells. The project includes technical improvements to Sage cells which will make it easier for instructors to create their own Sage cells for their particular course needs. A catalog of Sage cells will be curated, which will further lower the barrier to widespread adoption.

Online dynamic textbooks provide a unique opportunity to directly measure all aspects of how they are used. UTMOST 2.0 is designed to leverage technology to enhance the quality and breadth of the mathematical education research into how students and teachers use electronic textbooks and modern online tools for communication about technical subjects in real classrooms. UTMOST 2.0 will work with instructors at multiple institutions, all of whom will use MathBook XML textbooks, some in the online version and some in the printed version. The online version will be hosted in the cloud, on a server that will be configured to record all user activity at an extremely fine-grained level. The automatic online data collection will be combined with classroom data collection methods, providing a means to validate the information collected that can later be correlated with student gains in course content knowledge. UTMOST 2.0 will also assist authors of undergraduate mathematics textbooks that have already converted to the Mathbook XML format in the next steps of incorporating interactive features such as Sage cells and WeBWorK exercises. This will greatly increase the number of books with those advanced features and simultaneously expand the areas in which the UTMOST project can perform its research investigations.

This Improving Undergraduate STEM Education (IUSE) Development and Implementation project aims to address challenges in the undergraduate STEM curriculum, particularly the need to promote student learning and the development of mathematical and computational skills. Specifically, this project focuses on open source mathematics textbooks that are available in free online versions. It seeks to understand two interrelated questions: "How do instructors and students use textbooks?" and "How can we develop textbooks that better support teaching and learning?" To answer these questions, the project will complete a comprehensive educational research study that includes gathering data from multiple classrooms in a variety of settings, and subsequent analysis of that data. The development portion of the project will focus on PreTeXt, a publishing system designed to encourage the creation of free, open source textbooks. The project will examine the use of existing books created with PreTeXt, and from these observations further develop the PreTeXt platform, so that open source textbooks can have increased effectiveness. The integration of research and development activities is designed to create a continuous cycle of innovation between the research and development activities.

The education research component of this project will study 49 courses taught at two-year colleges, and four-year colleges and universities. These courses include first-year calculus, second-year linear algebra, and upper-division abstract algebra. The research study will investigate the work of instructors in planning and teaching lessons drawn from an online textbook and the work of students as they use the same textbooks to learn the material. In addition, the study will contrast such work with the work that instructors and students do when using less dynamic resources, e.g., a PDF or bound copy of the same material. PreTeXt is a new authoring platform that enables authors to easily fashion a textbook for both print (static) and online (dynamic) formats, including both computational and interactive components in the online version. The project will continue the development of PreTeXt and the technical underpinnings to create high quality online versions of textbooks, while only requiring authors to concentrate on their content. The accessibility features for readers with disabilities will be further improved. The inherent technical structure of online PreTeXt books will allow automated collection of student textbook usage data, organized by individual reader, with resolution to the minute and at the level of individual components, such as viewing a video. This interplay between research and development activities will produce large amounts of high-quality data about students' use of their textbooks. The Open Textbook Initiative at the American Institute of Mathematics will continue and expand its leadership in vetting and recommending quality free and low-cost textbooks, and help other STEM disciplines to adopt its successful evaluation criteria. Workshops for instructors, authors, and software developers will blend dissemination, professional development, editorial review, and software development. A novel feature of these workshops will be teaching test-site instructors how to contribute to the improvement of the open source textbooks that they are using in their courses.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

This STEM Learning and Learning Environments project seeks to advance understanding of algebra education at community colleges. It will build on prior work to explore further the relationship between the quality of instruction in college algebra classes and teachers? mathematical knowledge for teaching. This ?knowledge for teaching? is the mathematical understanding that teachers need in order to be effective teachers of mathematics. For example, this knowledge enables teachers to explore and diagnose why students are struggling with a mathematical concept and provide targeted help. Despite its critical role in US higher education, instruction at community colleges is a neglected sector of instructional capacity in the United States. To advance mathematics education research related to the first two years of college, this project will develop the Mathematical Knowledge for Teaching Community College Algebra assessment. This assessment will identify the specialized knowledge that teachers need for teaching community college algebra in a way that supports student growth in thinking about fundamental mathematical concepts. The project will also advance previous work by refining the Evaluating the Quality of Instruction of Post-secondary Mathematics instrument, which assesses characteristics of high-quality instruction in community college algebra courses. These efforts will enhance the research tools available for studying post-secondary teaching at community colleges, specifically in College Algebra. Since college algebra is often a gateway course to STEM degrees, this project has the potential to improve the recruitment into and success of students in STEM fields and, thus, support STEM workforce development.

The project involves four primary institutions: University of Michigan, University of Minnesota, Maricopa Community College District, and Oregon State University. The primary goals of the proposed research are to: (1) develop, pilot, field test, validate, and disseminate the Mathematical Knowledge for Teaching Community College Algebra assessment; (2) refine items in the Evaluating the Quality of Instruction of Post-secondary Mathematics video-coding instrument to address aspects of instruction that support diversity, equity, and inclusion in mathematics classrooms; and (3) theoretically and empirically explore the connection between the constructs that underlie both instruments. The project will use a mixed methods design that involves qualitative analysis of artifacts, item development, and psychometric testing, with the input of community college faculty in all the phases of the study, including integrating community college faculty as research associates, and thus building capacity for future research collaborations. At the conclusion of this project, two instruments will be available to support multiple efforts to advance the quality of instruction in postsecondary settings and the professional development of instructors. This project is supported by the EHR Core Research program, which supports work that advances fundamental research on STEM learning and learning environments, broadening participation in STEM, and STEM workforce development.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.