About my teaching
One of my main aims in teaching is to get students to see the connections between various parts of mathematics, thereby glimpsing the Big Picture which represents a mathematicianís view of the world. I also encourage students to think of mathematics both symbolically and visually, as these two modes of thought often support one another. Examples of this can be found in some of the resources below.
- MATLAB experiments in linear algebra (2010) to help students explore the meaning of basic terms from linear algebra, and to develop a feeling for typical behaviour of vectors and matrices.
- MAPLE experiments in advanced calculus (2001-2007). The following MAPLE worksheets are modelled on similar resources from the Connected Curriculum Project.
- intro.mw An introduction to basic MAPLE commands.
- lab2.mw Critical points for f(x,y) and how to classify them.
- lab3.mw Line integrals: how to picture them, how they depend on the choice of path.
- lab4.mw Second order ODEs: how solutions depend on initial values, and interpretations for spring systems and simple AC circuits.
- lab5.mw Second order ODEs and Laplace transforms: how solutions respond to different forcing terms.
- lab6.mw Rates of convergence for Fourier series.
- J. Hannah (2003). Maple labs: Calculus from all angles, Remarkable Delta:03 Communications (Queenstown, 2003) 122-128. (A conference paper reporting on some aspects of my use of the above resources.)
- J. Hannah (1997). A context for introducing vector spaces. International Journal of Mathematical Education in Science and Technology, 28 893-902. Version prepared for an accelerated first year class (1999)
- J. Hannah (1996). A geometric approach to determinants. Amer. Math. Monthly, 103 401-409. Version prepared for an accelerated first year class (1999)
- I received a University of Canterbury teaching award in 2001. The citation is here.
- As the histograms below show, most students in recent years have liked my teaching but a few are not so happy.
- Some student comments about my teaching in EMTH 211 (2011).
- As part of my sabbatical year in 2012, I spent a month at Quest University in Canada teaching a mathematics course for liberal arts students. Quest students do just one course at a time, with each course squeezed into a three and half week block, so I had the whole course to myself. This style and the actual course content was all new to me, so it was an exhausting experience. Quest recently topped all five categories in Canada's national student engagement survey, so the generally positive student comments about my teaching were quite pleasing. A fascinating learning experience for all of us.
- Student comments about my teaching in EMTH 118 (2013).
- Student comments about my teaching in MATH 103 (Semester 1, 2014).
- Student comments about my teaching in EMTH 210 (Semester 1, 2015).