Second semester physics for us includes topics like waves, optics, electricity and magnetism. With this in mind, I’ve been trying to organize my thinking about how the content is different through a lens that isn’t focused on topics, but rather on the shifts in thinking and skills required.
1. 2nd semester has more and more varied non-linear relationships, including more relationships that have non-monotonic or asymptotic behavior. These include, sinusoidal behavior, exponential behavior, Inverse square laws, and whatever the heck the Thin lens equation is.
2. 2nd semester has more focus on describing how behavior changes over space (potential or fields), whereas first semester has more focus on behavior changing in time. Thinking in wavelengths also becomes crucial. We more strongly employ a landscape metaphor for talking about concepts like potential and potential energy. We shift from vectors to vector fields.
3. 2nd semester has more of a focus on properties of media (index of refraction) and space (permittivity of free space) rather than particles (mass) and objects (density, volume, moment of inertia).
4. 2nd semester has a focus on energy flow (transport) across systems, whereas first semester is more focused on energy transformations within a system. This is reflected in need for concepts like wave speed and intensity. Even how we think about power subtly shifts from the rate of energy changes to rates of energy arrivals and departures.
5. 2nd semester has a focus on local conservation laws, whereas first semester relies more on global conservation. This is a result of focusing on flow.
6. 2nd semester has shifts from single variable functions to multi-variable functions. This is most obvious to me with waves. There also just seem to be more interdependent things going on–circuits.
7. 2nd semester has shift from 1D and 2D geometries to 3D, with examples including spherical waves, Coulomb’s law, magnetic fields and flux. The more complex geometries and focus on behavior over space are at heart of interference. Visualization becomes critical.
8. 2nd semester has a shift in scale requiring more fluency with SI prefixes and scientific notation. Nanometers, TerraHertz, fundamental charge values, etc. I’ve tried over the last year to spend time explicitly getting students to start thinking of SI prefixes as adjectives rather than wholly different units, and to become fluent at using adjectives that allow us to talk in whole numbers as much as possible. 180 mJ, 90 nC, 600 microns, 500 THz,
9. There is a proliferation of new units and unit combinations: Watts (J/s), Coulomb, Volts (J/C), Ampere (C/s), Tesla, Weber, V/m = N/c, eV, Ohms (V/A). Last semester I really noticed how much cognitive demand this placed on students and designed more activities to help us build fluency, familiarity, and connectivity.
10. There’s also a ratcheting up of the instrumentation needed to conduct investigations, diffraction gratings, multi-meters, oscilloscopes, etc.
this is incomplete, but I wanted to start getting a record of some of my thinking.