The faculty in the Department of Mathematics at Western Michigan University have a well-funded and active research program that addresses a wide range of research topics in mathematics. See faculty research area groups.

## Active grants

### MOST Research Project

The MOST research project is a National Science Foundation-funded collaboration among researchers at Western Michigan University, Michigan Technological University and Brigham Young University that focuses on improving the teaching of secondary school mathematics by improving teachers' abilities to use student thinking during instruction to develop mathematical concepts. Leveraging MOSTs (2012–17) focused on conceptualizing high-potential instances of student thinking (MOSTs) that, if capitalized on in-the-moment, would support student learning of important mathematics. Building on MOSTs (2017-21) focuses on conceptualizing the teaching practice of building on such high-potential instances.

## Previous grants

### Leveraging MOSTs: Developing a theory of productive use of student mathematical thinking

Leveraging MOSTs (Mathematically Significant Pedagogical Opportunities to build on Student Thinking) is a collaborative project among researchers at Brigham Young University, Michigan Technological University and Western Michigan University that focuses on improving the teaching of secondary school mathematics by improving teachers’ abilities to use student thinking during instruction to develop mathematical concepts. The project is developing a Theory of Productive Use of Student Mathematical Thinking (PUMT Theory) that articulates what the practice of productively using student mathematical thinking looks like, how one develops this practice and how that development can be facilitated.

### Developing principles for mathematics curriculum design and use in the Common Core Era

This project is developing principles for supporting middle school mathematics teachers’ capacity to use curriculum resources to design instruction that addresses the Common Core State Standards for Mathematics. These principles are intended for:

- Curriculum developers to help in the design of curriculum materials.
- Professional development designers and local instructional leaders, to help teachers understand and better utilize curriculum materials with respect to the CCSSM.
- Teachers, so that they can use curriculum resources to design instruction that addresses the CCSSM.

### Assessment for learning research scholars: capacity building in mathematics and science education

This grant is under the direction of Steven W. Ziebarth, with co-directors Chris Coryn. It is intended to support Ph.D. students with an interest in researching AfL principles and developing materials and promoting assessment for learning practices with pre-service teachers in mathematics and science education. It is a cross-disciplinary grant between mathematics, science and evaluation.

### Center for the Study of Mathematics Curriculum

The Center for the Study of Mathematics Curriculum is a national center funded by the National Science Foundation to advance the research base and build leadership capacity supporting school mathematics curriculum design, analysis, implementation and evaluation. CSMC is a collaborative effort with Michigan State University and the University of Missouri and with researchers and educators at Horizon Research, Inc., the University of Chicago and three school districts (two in Michigan and one in Missouri). Major areas of CSMC work include research on the influence and potential of mathematics curriculum materials for student and teacher learning, doctoral program development with an emphasis on curriculum and development of school/district curriculum leadership.

### Discontinuous feedback in nonlinear control

It has been recognized during last two decades that high performance of numerous nonlinear control systems arising in engineering applications can be achieved only by using discontinuous feedback controllers. One example of such a controller is given by sliding mode controllers which are used in important electrical-mechanical systems for stabilization and control. This research project will develop a unified mathematical approach to the design of discontinuous feedback controllers and analysis of their robustness and performance characteristics. Other examples of the need for discontinuous feedback controllers are provided by numerous control and stabilization problems for infinite-dimensional systems such as stabilization problems for fluid flows or quantum-mechanical systems arising in new technological developments. This project will develop geometric control theory for such infinite-dimensional systems to address problems of their feedback control and stabilization by using nonsmooth analysis tools. Such new tools can be used to design feedback controllers in numerous cases when traditional engineering linearization techniques don't work.

### Numerical methods for structured polynomial eigenvalue problems

Polynomial eigenproblems are playing an increasingly important role in contemporary engineering design. Indeed, the computation of resonant frequencies arising from extreme designs presents a real numerical challenge, as these designs can lead to very large eigenproblems with poor conditioning. On the other hand the underlying physics of such problems often leads to algebraically structured polynomial eigenproblems, with concomitant symmetries in the spectrum and special properties of the corresponding subspaces. Existing algorithms, unfortunately, often ignore these structural properties. The types of structured polynomial addressed in this project arise in a variety of applications: T-palindromic (analysis of rail noise from high-speed trains, SAW filters), *-palindromic (discrete-time optimal control), K-palindromic (differential delay equations), alternating (corner singularities, gyroscopic systems, continuous-time optimal control) and hyperbolic (overdamped mechanical systems). Polynomial eigenproblems are usually solved by embedding the system into a larger linear system called a linearization. Until recently, the palette of easily available linearizations has been very limited. Recent work, though, has shown how to systematically construct a continuum of linearizations, from which structure-preserving linearizations and linearizations with nearly optimal conditioning can be chosen. This project aims to further this growing body of work by developing algorithms that exploit these new theories, and in turn, develop new theory and insight for the next generation of algorithms in this critical area of scientific computation.

### Improving curriculum use for better teaching

iCubit is a his four-year project examining the capacities (knowledge, abilities, ways of understanding and acting) needed by elementary teachers for productive use of mathematics curriculum materials. The project is guided by the assumption that well-designed curriculum programs have the potential to contribute to improvement in mathematics learning opportunities in K-12 classrooms. Yet, minimal research has examined the kind of knowledge and capacities necessary for teachers to use these resources productively. The project investigates these capacities (referred to as pedagogical design capacity or PDC) and develops tools to assess them. A key resource to be developed is a tool to assess elementary teachers' knowledge of mathematics embedded in the representations and tasks in curriculum materials (Curriculum Embedded Mathematics Assessment).

### Core-Plus Mathematics Project

The Core-Plus Mathematics Project, with funding from the National Science Foundation, is completing development and evaluation of the second edition of the Core-Plus Mathematics four-year high school curriculum. Revision of both student and teacher materials has been informed by continuing research on the program’s effectiveness, including a recently completed five-year longitudinal study and by extensive feedback from teachers using the published materials. The revision has also taken into account changes in middle school mathematics programs, the evolving nature of undergraduate mathematics and advances in technology. In addition, CPMP has developed and evaluated support materials for parents.

### Core-Plus Mathematics Project: Phase II

The Core Plus Mathematics Project (CPMP), which was previously funded by NSF to design, develop, and evaluate materials for the first three years of high school mathematics, is developing materials for a fourth year. The fourth-year course builds on the first three and continues the preparation of students for college mathematics, including those who will become professional users of mathematics, and for direct entry to the workplace. Materials for three one-semester courses are being developed. The first semester course is intended for all students, the second course for students who intend to take calculus, and the third for students who do not intend to study calculus. The third course will emphasize discrete mathematics, probability, and statistics. A longitudinal study is being conducted that follows students whose preparation in middle school mathematics is based on one of the NSF-supported, comprehensive middle school curricula and who then study high school mathematics using CPMP or another of the NSF-supported, comprehensive high school curricula. The study also looks at the performance of students during the first year after completing high school.

### Core Math Tools

Core Math Tools is a NSF-funded project that meets the urgent need of providing mathematical tools that students can use as they explore and learn mathematical concepts that are aligned with the Common Core State Standards in Mathematics (CCSSM). The developers have repurposed and modified tools originally designed for an NSF-funded curriculum project (e.g., Core-Plus Mathematics), creating a suite of tools that supports student learning of mathematics regardless of the curriculum choice. The designers provide exemplary lessons illustrating how the software can be used in the spirit of the new CCSSM.

The goal of the project is to provide easy access to core mathematical tools that help students visualize and manipulate mathematical objects. The tools promote mathematical modeling, reasoning with multiple representations of mathematical ideas, decision making, and communicating mathematics related to Algebra, Geometry, and Statistics. The tools are available to all learners and teachers through the website of the National Council of Teachers of Mathematics (NCTM). The website includes feedback loops for teachers to provide information about the tools. By using the NCTM website, the tools can be downloaded for use by teachers and students. The dedicated portal on the NCTM website allows supervisors to use the tools in professional development, teachers to use the tools as an integral part of a lesson, and students to use the tools for exploring, conjecturing and communicating mathematics.

### Core-Plus Mathematics Revision Project

This NSF award supports a major revision of the Core Plus Mathematics Project (CPMP) student materials for high school mathematics, the development of more educative teacher materials, refinement and enhancement of curriculum-embedded software tools, and the development of materials for parents and other community stakeholders in mathematics education. The revision of student and teacher materials will be based on studies of student achievement conducted over eight years; a large collection of suggestions from teachers who have used the materials in their classrooms; results of reviews from expert panels, including the U.S. Department of Education, the American Association for the Advancement of Science; recommendations in the Principals and Standards for School Mathematics and a special review by university mathematicians sponsored by the developers. The development team includes teachers, mathematics education specialists, mathematicians and statisticians.

### Muskegon Area Middle School Mathematics Improvement Project 2

Grades five through eight regular and special education mathematics teachers and administrators from Muskegon City Public Schools, Muskegon Heights Public Schools and Muskegon Technical Academy are partnering with mathematics faculty and staff from Western Michigan University and Muskegon Community College and staff from the MAISD Mathematics and Science Center in an effort to improve the teaching and learning of mathematics within 16 Muskegon elementary and middle schools. The M3IP 2 is a two-year project and is a continuation of the first 2004-06 M3IP Project.

### Kalamazoo Area Algebra Project

The Kalamazoo Area Algebra Project was a cooperative effort between Western Michigan University, the Kalamazoo Area Mathematics and Science Center and southwest Michigan schools funded by the Michigan Department of Education Mathematics Science Partnership Program. The project was designed to help sixth- through 12th-grade teachers improve the teaching and learning of algebra and pre-algebra concepts.

The KA^{2}P staff, along with faculty from the Western Michigan University and Miami University mathematics departments, created interactive instructional modules to be utilized during professional development dinner/dialog sessions. Module content was built around state and national standards along with the needs of participating teachers, school districts and students. Additionally, the emphasis of the instructional materials was developed around the concepts of fostering algebraic thinking and mathematical modeling. Differentiated instruction, a constructivist approach and a compilation of diverse resources were incorporated into each of the modules.

KA^{2}P launched Feb. 1, 2010, with the release of its first DVD. By Jan. 2011, four DVDs were created to house 37 mathematical instructional modules.

### Michigan Mathematics Rural Area Project

The Michigan Mathematics Rural Area Project was a cooperative effort between Western Michigan University and rural schools in Michgan's northern lower peninsula funded by the Herbert H. and Grace A. Dow Foundation. The project was designed to assist rural area school districts in improving the teaching and learning of mathematics in grades four through six.

The M^{a}RAP staff, along with faculty from the Western Michigan University Department of Mathematics, created interactive instructional modules to be utilized during professional development Dinner/Dialog sessions. Module content was built around state and national standards along with the needs of participating teachers, school districts and students. Differentiated instruction, a constructivist approach and a compilation of diverse resources were incorporated into each of the modules.

M^{a}RAP launched March 5, 2011, with the release of its first DVD. The project created 17 mathematical instructional modules geared toward fourth- through sixth-grade teachers by the close of the project in Aug. 2013.

### Michigan Mathematics Rural Initiative Project

The primary objectives of the five-year (2005-10) Michigan Mathematics Rural Initiative were to:

- Build the mathematics content knowledge and knowledge for teaching of its participating teachers.
- Establish and sustain professional learning communities.
- Investigate effectiveness of the project's professional intervention model.

The expectation was that accomplishing these objectives would lead to improved mathematics achievement within the grades sixth through 12 classrooms of the project's 20 participating school districts. The participating schools were rural area, primarily low-income schools in Michigan's central and northeastern Lower Peninsula. As a continuation of M2RI, DVD modules focused on various algebra-related concepts were developed. Two of these modules are:

### Michigan Middle School Mathematics Reform Project

Building Michigan's Capacity for Middle School Mathematics Curriculum Reform, commonly known as the Michigan Middle School Mathematics Reform Project or M3RP, was a statewide four-year mathematics improvement effort coordinated by a team from Western Michigan University. The purpose of the 1999 to 2004 mathematics projects was to improve the teaching and learning of mathematics within the middle school classrooms of 90 school districts across Michigan.

### Renewing Mathematics Teaching Through Curriculum

RMTC is a collaborative of 15 high schools in southwestern Michigan that have recently adopted the Core-Plus mathematics Project instructional materials in their quest to improve mathematics teaching so that all students can develop mathematical power.

### Transition to College Mathematics and Statistics Project

With funding from the National Science Foundation, the three-year (2010-13) Transition to College Mathematics and Statistics Project is developing, field-testing, and evaluating a fourth year high school mathematics course. This course is intended for the large number of students planning to major in college programs that do not require calculus. The course is being designed for students who have completed three years of a conventional or integrated college preparatory mathematics program. This course is intended to provide an effective way of helping schools meet the new Common Core State Standards for Mathematics and better ensure college and career readiness of their graduates.

### Mathematical Sciences Sequential Summer Institute for High School Mathematics Teachers

The Mathematical Sciences Sequential Summer Institute for High School Mathematics Teachers, funded by the National Science Foundation, provides a three-year master's degree program for 30 well-prepared high school teachers (selected state-wide) builds on a current, Michigan state-supported project: Making Mathematics Accessible to All (MMAA). The program includes three sequential summers of mathematics courses in such areas as: discrete mathematics, statistics and probability, dynamical systems, transformational geometry, matrix algebra, etc. All courses in the program stress: applications and mathematical modeling, the uses of computers and graphing calculators, long-term projects requiring cooperative group efforts, and writing about mathematics. To complement the sequential summer program, in each of the three academic years, participants take an additional course, including two mathematics education courses that focus on issues of curriculum; pedagogy; assessment; and the teacher as a thoughtful practitioner, researcher, and mentor. These year-long courses include six two-day meetings on campus and a staff site-visit to each participant's school, but more frequent interaction between participants and staff will be facilitated by MichNet. A post-program evaluation study will document the participants' professional activities and the kinds of leadership roles they assume.