Pandemic Legacy: Quantitative Subjects tips

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Part 1: Moodle forums and asynchronous interactions

We recommend asynchronous interactions which do not require concurrent participation of everyone, as these are best-suited for supporting students across multiple time zones and have low technical requirements (in terms of bandwidth and technical sophistication). Online forums, such as Moodle discussion forums, are a good example of asynchronous forms of interaction.

The School’s Moodle platform implements the MathJax javascript library, which supports the display of typeset mathematics in web browsers using (a large subset of) LaTeX commands. As this is not done through pre-rendered images, typeset mathematics will scale along with normal text when the view is magnified. See here for more details about the Moodle implementation. No additional set up is required in a Moodle course to enable this; in particular, this functionality is present by default in any Moodle Forum.

• For inline mathematics, use $$ … $$, e.g. $$\sin(x)$$.

• For display mode mathematics, use [tex] ... [/tex], e.g. [tex]\begin{pmatrix} 1 & 4 \\ 2 & 3 \end{pmatrix}[/tex]

Sample code

Unfortunately, the parser does not handle line breaks very well, so display mathematics is best written in a single line.

Sample 1

Code:

[tex]\begin{align}\int_0^{\pi/6} \sin^3 \theta d\theta &= \frac{1}{4} \int_0^{\pi/6} \left(3\sin{\theta} - \sin{3\theta}\right) d\theta \notag \\ &= \frac{1}{4} \left[ -3\cos{\theta} + \frac{\cos{3\theta}}{3} \right]_0^{\pi/6} \end{align} [/tex]

Output:

Open

Sample 2

Code:

Consider the vector space $$\mathbb{R}^2$$ where vector addition and scalar multiplication are defined in the usual way and let

[tex]B = \left\{ \mathbf{f}_1, \mathbf{f}_2 \right\} = \left\{\begin{pmatrix} 1 \\ 1 \end{pmatrix}, \begin{pmatrix} 1 \\ 2 \end{pmatrix} \right\} [/tex]

be an ordered basis of $$\mathbb{R}^2$$.

Output:

Open

Sample 3

Code:

Suppose that one observation ,i.e. $$n = 1$$, is taken from the geometric distribution:

[tex]p(x; \pi) = \begin{cases} (1 - \pi)^{x-1} \pi & \text{for}\,x = 1, 2, \ldots \\ 0 & \text{otherwise} \end{cases}[/tex]

to test $$H_0: \pi = 0.3$$ vs $$H_1: \pi > 0.3$$.  The null hypothesis is rejected if $$x \geq 4$$.

Output:

Part 2: Digital writing of mathematics

Producing typeset mathematics is a time-consuming affair, making it cumbersome for asynchronous interactions and perhaps unfeasible for synchronous discussions given the variety of questions you might face.  Physical writing of mathematics may be desirable in such circumstances, raising its own technical challenges.

Tablet devices that support stylus usage, e.g. the Apple iPad and Microsoft Surface/Pro, easily allow mathematics to be written using simple whiteboard applications.  However, these may be prohibitively expensive for many.  A cheaper alternative are graphics tablets, which simple input devices which provide writing/drawing functionality.  Prices vary tremendously, and factors you should consider are:

• Non-Windows support (e.g. Mac, Linux, Android, iOS)

• Size of working area (e.g. while cheap ones start at 4x3”, you may find that a larger size, e.g. 6x4” or even 10x6”, is easier to use for mathematical content).

The table below provides a list of simple recommendations of tablets (with indicative prices) which are reported to work for all major desktop operating systems (Windows, Mac and Linux).

Part 3: Video capture of hand-written content

A popular teaching approach in mathematics teaching is the ‘chalk-and-talk’, where the instructor works through a particular derivation, whilst simultaneously providing a meta-commentary (e.g. not just covering what is being done, but why and perhaps why others things are not tried).

This can be replicated for remote teaching using a combination of writing implements (see above) and video capture software.  While the Echo 360 Universal Capture application allows you to record your entire desktop (along with webcam input), the Zoom client offers more functionality: allowing you to capture individual application windows as well as its bespoke whiteboard, which provides an ideal canvas for writing and annotating mathematics.

Recommendations

• You do not have to reproduce ‘one-hour’ lectures/classes; indeed, it may be easier – for both teachers to produce and students to experience – to aim for shorter pieces of no more than 20 minutes (e.g. covering a single example or topic perhaps).

• You may find it easier to focus on capturing video content first (e.g. of a particularly lengthy derivation or proof) and then use the Echo 360 editing software to overlay audio on top of it.  This can also avoid an issue on tablets where the Zoom capture software will record the sounds made by the pen on the screen along with your commentary.

• While you do not have to produce transcripts of your videos, consider uploading snapshots of each written page alongside the video.  The Zoom whiteboard feature can export each whiteboard as a PNG picture file.

Guide created by Mark Baltovic

[1] Not to be confused with the V2 model (listed separately) which does not boast the same compatibility range.