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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) AND ADDRESS(ES) PERFORMING ORGANIZATION REPORT NUMBER SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)U.S. Naval Academy Annapolis, MD 21402 SPONSOR/MONITOR'S REPORT NUMBER(S)Trident Scholar Project Report no. 382 (2009) DISTRIBUTION / AVAILABILITY STATEMENTThis document has been approved for public release; its distribution is UNLIMITED SUPPLEMENTARY NOTES ABSTRACTOur goal was to determine whether expert swing dancers physically optimize their pose for a partnered spin. In a partnered spin, two dancers connect hands and spin around a single vertical axis. We describe the pose of a couple by the angles of their joints in a twodimensional plane. These angles were outputs of an optimization model that gave the ideal pose for a couple. A biomechanical model built in Mathematica allowed comparisons to live dancers with the use of a motion capture system. SUBJECT TERMS AbstractOur goal was to determine whether expert swing dancers physically optimize their pose for a partnered spin. In a partnered spin, two dancers connect hands and spin around a single vertical axis. We describe the pose of a couple by the angles of their joints in a two-dimensional plane. These angles were outputs of an optimization model that gave the ideal pose for a couple. A biomechanical model built in Mathematica allowed comparisons to live dancers with the use of a motion capture system.The optimization objective is to maximize angular acceleration, by minimizing the resistance to spin, but still producing torque. The model considers only external forces and neglects internal forces. It consists of equations derived from physical principles such as Newton's laws and moment of inertia calculations that govern how people move. Using numerical non-linear optimization we found the pose for each couple that maximizes their angular acceleration. Different dancers are differently sized, so every couple has a different optimal pose. Each couple's optimal pose was compared to the pose they actually assumed for the spin.Our motion capture system consisted of four video cameras, reflective balls that could be tracked, and software to integrate the different angles of the cameras. The captured data consisted of the three-dimensional location of each of the marked body joints. We used this data to determine the angles of the joints to calculate the couple's actual pose. The couple's actual pose was used to calculate a predicted angular acceleration. Thi...

A wide range of evidence points to the need for students to have a growth mindset as they approach their learning, but recent critiques of mindset have highlighted the need to change teaching approaches, to transfuse mindset ideas throughout teaching. This shifts the responsibility from students themselves to teachers and schools. This paper shares a mixed methods study conducted across the US, that measured the impact of a “mathematical mindset teaching approach” shown to be effective when taught by the authors, scaled to teachers in 10 US districts. The effectiveness of this novel mathematics approach was measured using pre and post assessments during a summer intervention followed by measures of GPA change when students returned to schools. Both measures showed that a mathematical mindset approach to teaching significantly improves students’ mathematical achievement, and changes students’ beliefs about themselves and their approach to learning. Accompanying analyses of teaching and of teacher interviews give insights into the ways students change, highlighting the need to bring about shifts in students’ mindsets through a changed approach to mathematics teaching and learning.

After experiencing years of procedural teaching in K-12 mathematics classrooms, many students arrive at college with ideas about, and approaches towards, mathematics that are not helpful to their learning. Students’ prior experiences and misconceptions can then negatively impact their experiences in university STEM courses. This paper describes a short course in the “big ideas” of calculus, that offered students an approach of problem-based learning, combined with mindset messages, otherwise known as a “mathematical mindset approach”. The mixed-method study considered how a ‘mathematical mindset’ teaching intervention impacted the learning, achievement, and beliefs of incoming college students, finding that the intervention significantly changed students’ ideas about mathematics, their own potential, and the value of collaboration. At the end of the course students also significantly improved their achievement on assessments of problem solving and collaboration. Importantly the course allowed students to believe in their own potential and to approach mathematics with a growth mindset, suggesting a role for such courses in students’ mathematics pathways.