Over a four-year time span, several departments at North Carolina State University offered experimental sections of courses taken by freshman engineering students. The acronym IMPEC ͑Integrated Math, Physics, Engineering, and Chemistry curriculum͒ describes which classes were involved. This paper discusses the physics component of the curriculum and describes the impact of the highly collaborative, technology-rich, activity-based learning environment on a variety of conceptual and problem-solving assessments and attitude measures. Qualitative and quantitative research results indicate that students in the experimental courses outperformed their cohorts in demographically matched traditional classes, often by a wide margin. Student satisfaction and confidence rates were remarkably high. We also noted substantial increases in retention and success rates for groups underrepresented in science, math, and engineering. Placing students in the same teams across multiple courses appears to have been the most beneficial aspect of the learning environment.

A method of finding explicit expressions for the roots of a certain class of transcendental equations is discussed. In particular it is shown by determining a canonical solution of an associated Riemann boundary-value problem that expressions for the roots may be derived in closed form. The explicit solutions to two transcendental equations, tan β = ωβ and β tan β = ω, are discussed in detail, and additional specific results are given.

As college students experience the challenges of their classes and extracurricular activities, they undergo a developmental progression in which they gradually relinquish their belief in the certainty of knowledge and the omniscience of authorities and take increasing responsibility for their own learning. At the highest developmental level normally seen in college students (which few attain before graduation), they display attitudes and thinking patterns resembling those of expert scientists and engineers, including habitually and skillfully gathering and analyzing evidence to support their judgments. This paper proposes an instructional model designed to provide a suitable balance of challenge and support to advance students to that level. The model components are (1) variety and choice of learning tasks; (2) explicit communication and explanation of expectations; (3) modeling, practice, and constructive feedback on high-level tasks; (4) a student-centered instructional environment; and (5) respect for students at all levels of development.

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