Mitchell J. Nathan - US grants

The focus of this engineering education design project is two-fold: 1) to assess the epistemic frame of practicing engineers to identify the skills, knowledge, values, and ways of thinking that engineers in industry need; and 2) to assess the knowledge and skills that instructors, curricula, and guidance counselors communicate to students as prerequisites for pursuing engineering studies and for becoming successful engineers.

The PIs will collect and analysis data from practicing engineers from two groups: the 1994 cohort of undergraduates who completed the first design course as freshmen at UW-Madison and participants in professional development courses sponsored by the Department of Engineering Professional Development (EPD). The proposed data collection methodologies for the practicing engineers provides a systematic approach, a large interdisciplinary sample, a specific longitudinal cohort from undergraduate to practicing engineer, and a thorough analysis and meta-analysis that lacking in the current literature. Second, having first-year engineering students conduct, reflect on, and analyze the interviews is a novel approach with potential benefits to student researchers that can easily be scaled up nationally.

At the conclusion of the data collection with practicing professionals the PIs expect to have a robust profile of practicing professionals including the knowledge, skills, values, identity, and ways of knowing that make them engineers. They will evaluate the utility of having undergraduate engineers\ interview practicing professionals and analyze the resulting data as a means to develop the engineering epistemic frame of undergraduate engineers. They will produce a manuscript documenting those findings, as well as curricula and professional development materials to disseminate the technique.

Regarding the second thrust of the project the PIs plan to study high school instructors' beliefs and curricula and use classroom observations to identify how engineering-related subject matter is presented to pre-engineering high school students and document how the science and mathematics education of high school students relates to engineering principles and practices. In addition, they will compare and contrast practices at the high school level to those in the first year of an engineering curriculum.

The results of these studies will contribute to basic theory about the nature of pre-engineering education, the curriculum structure for pre-engineering, and the beliefs that high school teachers, guidance counselors, and first-year college instructors have about the developmental trajectories of potential engineers. They will design and facilitate a professional development workshop to help instructors integrate positive experiences into STEM curricula and develop a learning module to help career development facilitators understand engineering and promote it as a career based on accurate understandings about what an engineer does.

Mathematical reasoning requires understanding connections between different representations of mathematical information. The way mathematical representations are linked in the classroom may determine whether students come to understand important mathematical principles and procedures. Our past research showed that teachers use various forms of visual scaffolding to link different mathematical representations. The purpose of this project is to understand how variations in teachers' visual scaffolding affect students' learning. Our specific focus is on the nonverbal supports that teachers produce in instructional episodes that link related representations of mathematical information. In particular, we examine those nonverbal supports that serve to ground ideas in the physical environment or in familiar actions, experiences or representations. The research has three aims: (1) to investigate whether students' learning is facilitated if teachers ground the to-be-linked ideas with hand gestures (as opposed to using speech alone); (2) to examine whether certain types of nonverbal supports are especially beneficial for learning (specifically, redundant vs. complementary gestures, and pointing vs. representational gestures); and (3) to examine whether gestures offer a "special" way to visually scaffold ideas, in the sense that they are more effective at doing so than other, non-gestural methods of visual scaffolding. We will address these aims in experiments with middle school students learning about linear equations. The experiments will involve video lessons that vary the teachers' gestures or the medium used to highlight aspects of the linked representations (hand gestures or digital icons). We will assess students' conceptual and procedural knowledge of linear equations before and after the lessons, so that we can evaluate how variations in teachers' visual scaffolding affect students' learning. We will also conduct a pilot study to prepare us to extend this line of inquiry to college students learning about statistics. This pilot study will investigate how teachers link representations using speech and gesture in instruction about confidence intervals.

This work will contribute to our scientific understanding of learning and instruction from an embodied cognition perspective. By experimentally manipulating the ways in which relations between mathematical ideas are conveyed, and exploring the consequences for learning, we will gain a deeper understanding of the cognitive processes involved in acquiring mathematical understanding. This work will provide an empirical basis for recommendations about how teachers can use visual scaffolding effectively.

The next generation of digital learning environments for science, technology, engineering, and mathematics (STEM) content will be more interactive, more personalized yet more collaborative; provide developers and teachers with rich, real time data from users to track engagement and support formative assessment; and target both conscious and unconscious learning processes. Embodied cognition research provides promising findings that show how body movement contributes to STEM education by allowing learners to physically engage with ideas, and by describing how teachers naturally use their bodies in ways such as gestures to enhance their instructional effectiveness. Mathematics education, in particular, can benefit from such innovation in embodied cognition because it serves as the connective representational "language" across the STEM fields. Technologies exist now that can track people's movement in real time and provide feedback. Yet there is no current consensus on the best ways to design educational technology for supporting embodied cognition for mathematics education. The timing for motion capture technology, theories of embodied cognition, and interest among teachers for movement based educational innovations is ideal for bringing scholars and classroom practitioners together for a workshop on embodied design for mathematics education. During a 3-day workshop at the University of Wisconsin-Madison in the spring of 2019, teachers and research scholars will gather to discuss ways in which new computer technologies support embodied approaches for improved math education. The workshop participants examine learning in and out of school, but with a focus on the design of systems for promoting embodied ways of learning and teaching in classroom settings.

Embodied design for mathematics education, a research-oriented pedagogical design framework rooted in theories of embodiment and design-based research as practiced within the learning sciences, supports the improvement of instructional methodology for students' mathematical proficiency in the classroom. Currently there is a convergence of theoretical, technological, and methodological developments in formation that make this a particularly promising time to support advancements in embodied design for mathematics education. The workshop will bring research scholars and classroom teachers together in order to achieve four central objectives: (1) synthesize current research into a coherent theory of embodied mathematical imagination and cognition, (2) identify the most promising opportunities for conceptual and methodological integration, (3) curate a set of evidence-based design principles for enhancing mathematics education and broadening participation in all STEM fields, and (4) articulate a future research agenda in the growing area of embodied cognition. This workshop will assemble an interdisciplinary set of scholars from education research, cognitive science, the learning sciences, developmental psychology, movement science, linguistics, computer science, and mathematics. Presentations and discussions will span grades K through 16 on topics in arithmetic and algebra, proportional reasoning and fractions, geometry, complex numbers, statistics, and calculus. The workshop will bring together an intellectually and ethnically diverse group of scholars to synthesize the evidence for embodied design as a means to enhance mathematical reasoning and thereby promote STEM education and participation. The workshop organization will promote interdisciplinary research and theory building in the learning sciences and identify current challenges and future research efforts. The approach is tightly connected to the societal need to foster an educated and technically competent workforce. A particular emphasis on mathematics is intended to broaden participation in math and STEM by creating new entry points for historically underserved ethnic, racial, economic, and gender groups.

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.