Areas of Interest

Exploration of mathematical modeling, problem-solving, and teamwork in mathematics/engineering education

Research Interests

Teaching and research interests

My research and teaching interests are centered on the integration of STEM (Science, Technology, Engineering, and Mathematics) concepts in mathematics, science, and engineering classrooms. Getting students interested in STEM fields while at the same time providing them with rich learning experiences is challenging. In order to address this challenge, my research agenda has been focused on learning and teaching problem solving and modeling through the context of engineering. I believe that providing students with realistic contexts in which to learn mathematics and science furthers their interest in these subjects. Because of my belief that teaching mathematics should be tied to a context, I have been developing curricular tools and researching professional development in this area. I am currently working on three National Science Foundation supported projects related to my research interests: the Engineering through STEM Integration project, the MEDIA Project and the Reach For the Sky Project.

Implementing K-12 Engineering Standards through STEM Integration

(Engineering through STEM Integration Project) – NSF EEC CAREER award

I am the Principal Investigator on the Engineering through STEM Integration project, which is a Faculty Early Career Development (CAREER) Program award from the National Science Foundation. Currently, there is a movement in K-12 education to include engineering academic standards in the science curriculum. In 2009, Minnesota was one of the first states to implement such standards. Integration of engineering into science and mathematics requires a shift in current educational practices; therefore, teacher training on the implementation of these standards is offered through grants from the Minnesota Department of Education. This research project builds on the STEM Integration research paradigm, defined as the merging of the disciplines of STEM. There are two main types of STEM Integration: Content Integration and Context Integration. Content Integration focuses on the merging of the content fields into a single curriculum in order to highlight "big ideas" from multiple content areas. Whereas Context Integration focuses on the content of one discipline and uses contexts from others to make the content more relevant. The purpose of this research is to understand and identify the ways in which teachers implement engineering standards in their classrooms. The research questions are:

1. How are K-12 engineering standards being implemented in mathematics and science classrooms?
2. How are teachers using STEM Content Integration and Context Integration to address the engineering standards? And what are the advantages/disadvantages of each?
3. What are teachers’ perceptions of the individual STEM disciplines and the integration of these disciplines during their implementation of the standards? How do the perceptions change over time?
4. How do teacher professional development modules and professional learning communities affect the implementation of the K-12 engineering standards? How do they affect the STEM learning of all students, as well as underrepresented students, in those schools?

This project utilizes a mixed methods, multiple-case, embedded case study design that employs a variety of data sources in order to fully understand teachers’ implementation strategies and obstacles as they work to address the engineering standards in the K-12 classroom. The work here advances pedagogical understanding about how to teach STEM content in an interdisciplinary manner. It will enhance the theoretical models of Context and Content Integration across STEM and models of student learning in these context-rich interdisciplinary problem spaces. By researching the implementation of K-12 engineering standards, this project will add to the theoretical basis for student learning in STEM integration environments.

Improving engineering students' learning strategies through models and modeling

(MEDIA Project) – NSF DUE CCLI Phase 3

For the MEDIA (Model Eliciting, Developing, and Integrating Activities) project, I am the principal investigator, along with Gillian Roehrig as co-PI, at the University of Minnesota. This is a large-scale, four-year collaborative research project between six major universities: University of Pittsburgh, University of Minnesota, US Air Force Academy, Colorado School of Mines, Purdue University, and California Polytechnic State University.

The purpose of the research is for the implementation of models and modeling as a foundation for undergraduate STEM curriculum and assessment, especially within engineering domains. To do this, we are building upon and extending Model-Eliciting Activities (MEAs), a proven methodology originally developed by mathematics education researchers, and which has been recently introduced to engineering education. These authentic assessment tasks are complex, open-ended problems set in a realistic context with a client. Solutions to MEAs require generalizable procedures, which reveal the thought processes of the students. The activities are such that the students work in teams of three to four to express their model, test it using sample data, and revise their procedure to meet the needs of their client. MEA theory and practice was developed to observe the development of student problem-solving competencies and the growth of mathematical and conceptual cognition. However, it has been increasingly documented as a methodology to help students become better problem solvers, as a tool to help both instructors and researchers better design situations to engage learners in productive conceptual thinking, and as a vehicle for interest and engagement for underrepresented student populations. For this research, we are extending the MEA construct to help repair misconceptions by creating concept MEAs (C-MEAs), to ethical situations by creating ethics MEAs (E-MEAs), and to innovation by creating innovation MEAs (I-MEAs) in order to better understand the various strategies student teams use in approaching these respective concerns.

Successful completion of this project will provide engineering and STEM educators with an understanding of how students learn to become better problem-solvers including resolving ethical dilemmas, how misconceptions enter into the process (and how they can be repaired) and how to enhance the creative process to produce more innovative engineers. Faculty will be able to better identify areas for learning enhancements and introduce informed curriculum improvements. This should be particularly useful in classroom settings where instructors could determine students’ abilities at various points during the course, intervening when appropriate and enabling students to better understand their areas of weakness. In addition, students will learn to become better problem-solvers and more innovative. Clearly, such results could be extended beyond engineering to other STEM disciplines.

My research team has four main roles in this study: (1) research the development and change in beliefs of faculty writing and implementing MEAs, (2) lead the MEA writing team across all six universities, (3) research the implementation of MEAs within Electrical and Computer Engineering domain and within all domains that are heavy users of thermodynamics, and (4) re-write MEAs for application in K-12 settings.

Discover more at Science of Shakespeare

Reach for the Sky: Integrating technology into STEM outcomes for American Indian youth

(RFTS Project) – NSF

Selected Publications