Dawn Teuscher, Ph.D. - US grants

The Pathways to Calculus: Disseminating and Scaling a Professional Development Model for Precalculus Level Instruction Phase II MSP involves four Core Partners; Arizona State University, as the lead, and the Mesa, Chandler, and Scottsdale school districts. Supporting partners are: Brigham Young University, the University of Northern Colorado, the University of Georgia, Northern Arizona University, and Scottsdale Community College.

This Phase II project builds on the work of Project Pathways, a targeted MSP that identified attributes of professional development for secondary mathematics and science teachers that resulted in substantive and sustained improvements in student learning, as documented by student performance on district exams, state exams and research-based tools. The Phase II project leverages the research-based processes and tools that emerged in Phase I research to be highly effective for shifting teachers' instruction to be more inquiry-based and conceptually oriented. Phase II builds on Phase I findings in five broad categories that are critical for supporting mathematics teachers to realize significant shifts in their students' learning of key ideas of mathematics. These are teachers': 1) knowledge of the mathematics they teach; 2) beliefs about what constitutes effective mathematics learning and teaching; 3) ability to engage in reflection on student thinking and learning in relation to their teaching; 4) use of curricular support materials that promote inquiry-based and conceptually oriented instruction; and 5) participation in Pathways Professional Learning Communities (PLCs).

Phase I resulted in the development of the Pathways Precalculus Professional Development Model (P3DM), which includes in-class student activities with detailed teacher notes, computer animations and assessments. This supported Precalculus teachers in making instructional transitions that realized significant gains in student learning. Phase II extends this work by scaling the P3DM in three ways: 1) implementation of the P3DM at the community college and university levels, 2) implementation of the model in larger classes; 3) engagement of school administrators, including department chairs, to support all teachers in Core Partner school districts (11 schools) in adopting P3DM in Precalculus. Phase II studies the process of scaling P3DM in each of the three ways, and continues to examine how the P3DM experience affects teachers' instruction in other Precalculus level courses such as algebra II, college algebra and trigonometry.

The Phase II Research Agenda addresses the following:
1. What institutional factors of a school inhibit or support quality implementation of Pathways Precalculus materials? What external resources are needed to mitigate inhibiting factors and capitalize on supportive factors?
2. What is the typical developmental trajectory of teachers understanding and taking ownership of Pathways Precalculus materials? What support do teachers need to enable this development?
3. What is the typical developmental trajectory of teachers' understanding of the core mathematical ideas in the Pathways Precalculus materials and ability to accurately assess students' reasoning about these ideas in the classroom setting? What support do teachers need to understand these concepts and effectively assess student reasoning?
4. What administrative support enables teachers to effectively implement Pathways Precalculus materials?

A minimum of 150 high school mathematics teachers will be involved in addition to university and community college instructors and faculty. The products of this research will contribute knowledge and tools for scaling up the P3DM in the Precalculus strand (precalculus, college algebra, trigonometry and high school algebra II) of mathematics. The investigations will also produce insights about the factors that contribute to a mathematics department's transformation to support students in developing the capacity and confidence to solve novel problems and construct deeper and more connected understanding of the central ideas of a course.

This project focuses on mathematical knowledge for teaching at the secondary level, building upon and extending existing work for elementary mathematics. The project is developing two related assessment instruments: one for assessing teachers' mathematical knowledge for teaching secondary mathematics (MKTsm) and one for assessing the quality of secondary mathematics instruction (IQAsm). Used simultaneously, these instruments are capable of linking secondary teachers' mathematical knowledge with their instruction. The first instrument draws from prior research on teachers' and students' understanding of key mathematical ideas. The second extends the Instructional Quality Assessment (IQA), an existing assessment that focuses on the quality of elementary and middle school mathematics, so that it has a clearer focus on secondary mathematics and on the quality of mathematical ideas that a teacher's instruction fosters. The instruments are being constructed, validated, and tested in three overlapping phases. Development of the MKTsm assessment draws on existing research on teachers' and students' understandings of foundational ideas in algebra and precalculus. The IQAsm extension draws from existing IQA validation studies, from the co-PIs' recent research on transforming secondary teachers' classroom mathematical practices, and from what is learned through the development process in designing the MKTsm instrument. The MKTsm and IQAsm instruments are being piloted in three projects of the Math and Science Partnership (MSP) program, to ensure that the instruments are broadly valuable to MSP projects and mathematics education in general. The instruments are being distributed online, and measures are being taken to ensure valid and appropriate usage by other researchers, or by administrators who might use the instruments for purposes that could include evaluation. In addition to the instruments, the project is developing training videos, scoring guidelines, and an overview for administrators, and also is creating a process by which the publisher will require certification of professional development for use of the instruments when they become commercialized.

Teachers are crucial to improving mathematics instruction in the US. Improvements in understanding teachers' knowledge about mathematics for teaching have led to improvements in teacher education and professional development. However, there are gaps in the understanding of mathematics knowledge for teaching, including how teachers reason about curriculum. Because curricular resources, including textbooks, continue to be important resources and tools for teachers, understanding how teachers reason about curriculum are important to improve teachers' knowledge and instructional practice. This collaborative project with the University of Nevada Las Vegas, Brigham Young University, University of Arkansas, and Grand Valley State University, will study middle grade mathematics teachers' curricular reasoning and develop a taxonomy that can be used by curriculum developers, teacher educators and professional developers to help in the development of productive curricular reasoning for teachers. This research is funded by the EHR Core Research Program, which emphasizes fundamental STEM education research that will generate foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development.

This three stage study will begin with adaptation, development, and pilots of the interview and observation protocols with eight teachers to verify that these instruments are valid and reliable. The second stage focuses on developing the curricular reasoning taxonomy by collecting analyzing interview and observation data from 12 grade 8 mathematics teachers in four states. These teachers will be using novel curriculum materials to teach geometry transformations during their regular classroom instruction. During this stage, the project will develop an initial taxonomy of teachers' curricular reasoning as they plan and enact these lessons. In the third stage, the researchers will verify and refine the curricular reasoning taxonomy by collecting interview and observation data from 20-40 grade 8 mathematics teachers in four states with a variety of teaching backgrounds.

Teachers of mathematics engage in curricular reasoning as they design and interact with their students, choose curricular materials, and implement curriculum standards in the service of high-quality instruction. Currently, there is no shared measure of curricular reasoning of middle school teacher classroom decision making in mathematics. In this research project, the team develops and validates two measures of middle school teachers’ curricular reasoning in mathematics as practiced. The first measure looks at curriculum reasoning from the perspective of the teacher, the second measure attends to the perspectives of the mathematics education research community. The research examines teacher self-assessment compared and aligned with those of professional observers (e.g., coaches, school leaders, and researchers) to establish the validity of the teacher self-report measure. The research establishes benchmark scores of teachers curricular reasoning in middle school mathematics, supporting increased interpretability and utility of the curricular reasoning score to improve classroom practice.<br/><br/>The researchers carefully examine four research questions: [1] To what extent does validity evidence support use of the Curricular Reasoning Self-Assessment Survey Suite for middle school mathematics teachers to measure their own curricular reasoning? [2] To what extent does validity evidence support use of the Curricular Reasoning Observation Assessment to measure middle school mathematics teachers’ curricular reasoning? [3] Is there a significant relationship between middle school mathematics teachers’ curricular reasoning when measured by the new curricular reasoning tools? [4] What benchmarks define different curricular reasoning levels on each of the two measures? The research team gathers validity data based on shared standards held by the American Psychological Association, the National Council on Measurement in Education, and the American Educational Research Association. The research advances our understanding of teacher curricular reasoning through the development of the two measures. The work bridges research and practice as the researchers use self-report and observational evidence to support and improve teachers’ practice of curricular reasoning. The team uses Rasch psychometric tools for standard setting to improve the usability of the measures for classroom usage. <br/><br/>The Discovery Research preK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering, and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models, and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. <br/><br/>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.