Asee peer logo

Modal Engagements in Pre-College Engineering: Tracking Math and Science Concepts Across Symbols, Sketches, Software, Silicone, and Wood

Download Paper |


2011 ASEE Annual Conference & Exposition


Vancouver, BC

Publication Date

June 26, 2011

Start Date

June 26, 2011

End Date

June 29, 2011



Conference Session

Engineering as the STEM Glue

Tagged Division

K-12 & Pre-College Engineering

Page Count


Page Numbers

22.1070.1 - 22.1070.32



Permanent URL

Download Count


Request a correction

Paper Authors


Mitchell J. Nathan University of Wisconsin, Madison

visit author page

Mitchell J. Nathan, BSEE, Ph.D., is Professor of Educational Psychology, with affiliate appointments in Curriculum & Instruction and Psychology at the University of Wisconsin - Madison, and a faculty fellow at the Wisconsin Center for Education Research (WCER) and the Center on Education and Work. Dr. Nathan studies the cognitive, embodied, and social processes involved in STEM reasoning, learning and teaching, especially in mathematics and engineering classrooms and in laboratory settings, using both quantitative and qualitative research methods. Dr. Nathan has secured over $20M in external research funds and has over 80 peer-reviewed publications in education and Learning Sciences research, as well as over 100 scholarly presentations to U.S. and international audiences. He is Principal Investigator or co-Principal Investigator of 5 active grants from NSF and the U.S. Dept. of Education, including the AWAKEN Project (funded by NSF-EEP), which examines learning, instruction, teacher beliefs and engineering practices in order to foster a more diverse and more able pool of engineering students and practitioners, and the Tangibility for the Teaching, Learning, and Communicating of Mathematics Project (NSF-REESE), which explores the role of materiality and action in representing mathematical concepts in engineering and geometry. Dr. Nathan is on the editorial board for several journals, including The Journal of Pre-College Engineering Education Research (J-Peer).

visit author page


Candace Walkington University of Wisconsin, Madison

visit author page

Candace Walkington is a post-doctoral fellow in Mathematics Education and Learning Science at the University of Wisconsin, Madison.

visit author page

author page

Rachaya Srisurichan University of Wisconsin, Madison

author page

Martha W. Alibali

Download Paper |


Modal engagements in precollege engineering: Tracking math and science across symbols, sketches, software, silicone and woodMotivationEngineering education at the K-12 level is often a collaborative, project-based experience forstudents where ideas and activities include encounters with a broad range of modalities: abstractmathematical equations; 2D designs, CAD and simulations; material construction of devices inwood, metal, wire and silicone; and a range of physical settings and participation structures,including lectures, individualized work and small group collaboration as they occur in theclassroom, laboratory, wood and metal shop, and out in the field. Encountering a range of modalengagements are assumed to be beneficial, since they provide students with a varied set ofcontextualized encounters with ideas, representations, tools and skills that foster a rich andgrounded engineering education. Yet K-12 students also struggle to see the interrelatedness thatis apparent to curriculum developers and instructors and fail to transfer their learning to othertasks and settings. Research is needed to better understand the challenges students face inestablishing and maintaining coherence across the range of modal engagements in theengineering classroom.Theory and MethodWe have conducted a comparative analysis of PLTW lessons that focus on two multi-day units:mechanical engineering (ballistic devices) from the Principles of Engineering course (the secondcourse in the PLTW sequence); and digital circuit design (a voting booth privacy monitoringsystem) in the Digital Electronics course (third in the PLTW sequence). • Ecological shifts reorient the activity context to include new modal engagements (e.g., when students move from a math-oriented lecture in the classroom to construction activity in the woodshop). • Projections are moves performed in speech, gesture and written or drawn representations that connect current modal engagements to past and future contexts (e.g., advice that students will need “clean” circuit wiring to help them with the inevitable debugging task later). • Coordination makes links between modalities (e.g., asking students to identify in a catapult sketch the angle of release of the projectile to match the trigonometry and kinematics equations). • Projection and coordination are methods of threading the mathematics through the various modal engagements in order to established and maintain coherence of the central math and sciences concepts.Results and ConclusionsThreading the math and science concepts through a range of modal engagements is the hallmarkof STEM integration and central to engineering practice. To the students in both digitalelectronics and kinematics units, the locally salient qualities of a particular modality oftenremained unconnected to the many modalities that came before and after it. Analyses of speechand gesture reveal that students often failed to see how the math and science were threadedthrough these modal engagements. Consequently they made few of the connections that wouldhelp ground abstract ideas to the engineering activities or that reveal the general scientificprinciples that are widely applicable to many engineering projects.It appears that, for many students, the coherence of math and science concepts has to beexplicitly produced and continually enforced by the participants through the methods ofcoordination and projection. When this is not done, students come away experiencing theselearning experiences as a sequence of loosely connected activities, rather than as a coherentthread of STEM integration that mutually reinforces their understanding of the science,technology, math, and engineering.SignificanceMany aspects of engineering curriculum and instruction seem to assume that students willspontaneously build coherence across modalities. The process of threading the mathematics andscience through these modal engagements is a demanding one, but, once identified, can besupported through effective instruction and curriculum design. Effectively threading ideasthrough the range of material forms, representations, tools, settings and participant structures isnecessary to provide the deep and integrative understanding that Learning Scientists call forwhen prescribing reform in support of the transfer of learning.

Nathan, M. J., & Walkington, C., & Srisurichan, R., & Alibali, M. W. (2011, June), Modal Engagements in Pre-College Engineering: Tracking Math and Science Concepts Across Symbols, Sketches, Software, Silicone, and Wood Paper presented at 2011 ASEE Annual Conference & Exposition, Vancouver, BC. 10.18260/1-2--18760

ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2011 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015