AC 2009-1790: INTEGRATION OF MATHEMATICS IN PRE-COLLEGE ENGINEERING: THE SEARCH FOR EXPLICIT CONNECTIONS

Educational leaders and researchers have mandated that technical education and academic subject areas be integrated so students can develop both academic and occupational competency. Mathematics, in particular, is recognized for its singular importance for modeling and generalization. In response to this clarion call, engineering and K-12 pre-engineering curricula are being developed and redesigned to invigorate the engineering pipeline and to provide an integrated program of STEM education. Explicit integration also enhances the likelihood that learners will be able to transfer new knowledge to novel situations. An important research aim, then, is to document the extent to which these objectives are being achieved. In conducting the current study, our goal was to identify all instances of explicit integration of mathematics concepts in three pre-engineering curricula that make up the 3-year foundations sequence for a widely adopted high school technical education program, Project Lead the Way (PLTW). Explicit integration is defined as any instance wherein the materials specifically point to a mathematics principle, law, or formula, and depict how it is used to carry out or understand an engineering concept, task or skill. We used the Standards as adopted by the National Council of Teachers of Mathematics to determine the target math concepts. For each of the three foundations courses, we analyzed the content of: (a) the intended curricula, including planning materials, performance objectives and classroom activities; (b) the assessed curricula, including student projects and presentations, and written examinations; and (c) and the teacher training materials. In addition to the structure of each course, we looked for alignment between the intended and assessed curricula and for the longitudinal progression as one advances through the 3-year program of courses. Overall, we found that the explicit integration of math concepts with regards to engineering concepts in all three PLTW courses was apparent, but weakly so, and showed many areas of potential improvement. While there are many implicitly embedded opportunities for creating connections between the math concepts and the engineering activities and topics, many of these opportunities were not explicitly stated, and are likely to go unaddressed in the classroom. We found that the two later courses integrated mathematics concepts better than the entry course. We also found many areas in each of the courses where the intended and assessed curricula were misaligned, so that topics emphasized in the course were not tested, while concepts and skills on tests were not always supported by the course materials. While these findings may seem at odds with claims by the curriculum developers, we attribute the different interpretations to Expert Blind Spot, the psychological phenomenon that those highly knowledgeable in their own fields more readily see the deep conceptual underpinnings than novices do. We then use the results of these analyses to illustrate how mathematics concepts can be explicitly integrated with preengineering activities, and thereby enhance the likelihood that learning will be deep and foster transfer to new tasks and settings.