Active learning in mathematics for STEM: real-life engineering applications

An opinion piece in Scientific American [1] discusses how a fraction of students ultimately complete a STEM degree and cites research [2] that disengagement with traditional calculus courses as one of the causes. It goes on to highlight examples of several promising calculus reforms and recommends that STEM faculty take the lead in introducing changes by collaborating and co-creating across disciplines to make mathematics more relevant and interesting to students. Feedback from module surveys indicate that students learn much better when the link between theoretical and practical knowledge is captured and echoes pedagogical literature. The author introduces past experiences of active learning approaches to enhance the teaching of mathematics to first-year engineering students. Class discussions incorporate real-life engineering applications highlighting example problems from a wide variety of core engineering modules such as Fluid Mechanics, Vibration, and Mechanics of Materials. The impact of this approach has not been directly measured and documented for the module being discussed here and is motivated by encouraging student feedback where they shared that they find the teaching interesting, fun, engaging, and interactive. The present concept paper therefore outlines how past pedagogical practice have influenced the enhancements in the delivery of engineering mathematics with a particular focus on interdisciplinary approach. It then goes own to demonstrate some examples of implementation and offers initial reflections based on student feedback. Finally, the author proposes future steps of detailing the effect on student learning experience via class surveys, interviews and making comparisons to comparably taught modules

A universal, turbulence-regulated star formation law: from Milky Way clouds to high-redshift disk and starburst galaxies

Whilst the star formation rate (SFR) of molecular clouds and galaxies is key in understanding galaxy evolution, the physical processes which determine the SFR remain unclear. This uncertainty about the underlying physics has resulted in various different star formation laws, all having substantial intrinsic scatter. Extending upon previous works that define the column density of star formation (Sigma_SFR) by the gas column density (Sigma_gas), we develop a new universal star formation (SF) law based on the multi-freefall prescription of gas. This new SF law relies predominantly on the probability density function (PDF) and on the sonic Mach number of the turbulence in the star-forming clouds. By doing so we derive a relation where the star formation rate (SFR) correlates with the molecular gas mass per multi-freefall time, whereas previous models had used the average, single-freefall time. We define a new quantity called maximum (multi-freefall) gas consumption rate (MGCR) and show that the actual SFR is only about 0.4% of this maximum possible SFR, confirming the observed low efficiency of star formation. We show that placing observations in this new framework (Sigma_SFR vs. MGCR) yields a significantly improved correlation with 3-4 times reduced scatter compared to previous SF laws and a goodness-of-fit parameter R^2=0.97. By inverting our new relationship, we provide sonic Mach number predictions for kpc-scale observations of Local Group galaxies as well as unresolved observations of local and high-redshift disk and starburst galaxies that do not have independent, reliable estimates for the turbulent cloud Mach number.Comment: 6 pages, 2 figures, Accepted for publication in ApJ Letters, Movie available here: http://www.mso.anu.edu.au/~chfeder/pubs/universal_sf_law/universal_sf_law.htm