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

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... e 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 US and international audiences. He is Principal Investigator or co-Principal Investigator of 5 active grants from NSF and the US 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). Abstract There is agreement amongst educators, policy makers and professionals that teaching and learning in STEM areas at the K-12 level must be improved. Concerns about the preparedness of high school students to improve the innovation capacity of the United States are leveled following data showing US students performing below students in other industrialized nations on international math and science tests 1 . To address both the preparedness for and the appeal of engineering, technical education programs have emerged that provide hands-on, project-based curricula that focus on the integration of mathematics and science knowledge with engineering activities. Learning Sciences research emphasizes that integration of new ideas with prior knowledge must be made explicit to learners in order to promote successful transfer to novel problem-solving and design contexts 2 . Thus, integration of mathematics and engineering is important both for mainline (general education) as well as pipeline (career preparation) goals for engineering education 3 . Increasingly, research on high school engineering curricula is focused on the nature of classroom instruction and its impact on student learning. The current study uses actual classroom observations to try to understand how students in the high school classroom learn and integrate mathematics and engineering skills and concepts based on the teacher's actions in a portion of the Project Lead the Way (PLTW) Digital Electronics ™ curriculum. Digital Electronics ™ is a unique course in that it utilizes mathematics concepts such as Boolean algebra that are beyond the scope of most high school mathematics standards. Thus, while students are likely to have little direct prior knowledge, there is a greater need for explicit introduction and integration of the math that is used in this curriculum than is typical for K-12 engineering curricula overall 4,5,6 . To summarize our major findings: The PLTW Digital Electronics ™ (DE) curriculum introduces a great deal of mathematics to students that goes above and beyond the national high school mathematics standards. The mathematics taught in DE is equally skills and conceptually based. Students learn about numbers, Boolean algebra (its notation, transformation and various important theorems), truth tables and Karnaugh maps. These learning opportunities are primarily through project work and tutorials, which constitute 74% of the instruction time in our sample. Process standards of mathematics such as problem solving, reasoning and making connections are also used to complete projects. The engineering skills and concepts used in this curriculum are focused on wiring circuits, and solving (Boolean) logic problems related to circuit design. Explicit connections between mathematics and engineering were observed 78% of the time. This is primarily because the mathematics and engineering in digital electronics work is practically inseparable. That is, in order to achieve the project goals, students must be taught mathematics skills and concepts, which then form the basis for the primary engineering skills and concepts of the lessons.