I’ve just had an idea I may use in my teaching, and since I’m trying to use this blog for collecting my thoughts… here goes:

Set a homework task for students to add 3 (or whatever amount is appropriate) examples of a certain skill to a class wiki. For example, suppose we are studying logarithms. Students are given the task of typing up 3 examples of solving equations that involve logarithms, giving clear explanations at each step.

Issues

Of course, we would need a wiki with an easy-to-use equation editor. Or perhaps a blog would be suitable – I have just installed the WP LaTeX plugin for WordPress and it seems to work well:

x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

This is not a WYSIWYG editor – some knowledge of LaTeX (or should that be TeX?) input is required. To enter some maths you just put it between tags. The process is described on the WP LaTeX FAQ page.

I only have a basic knowledge of TeX input, and although a bit daunting at first I feel reasonably comfortable with it now. So it would require students to learn some basic TeX. I don’t know how successful this would be.

To help learn TeX I have been using the CodeCogs Online Equation Editor. This has been very useful in learning the TeX language.

Here’s an example of what I hope the students could come up with:

Solve to find x:

\log_2 x=32

Write both sides of this equation as power of 2. I have chosen 2 because it is the base of the logarithm and will allow us to do some simplifying in the next step:

2^{\log_2 x}=2^{32}

The identity a^{\log_a x}\equiv x means we have:

x=2^{32}=4,294,967,296

Pros

  1. If the students are creating their own questions then it is likely they will not get ‘nice answers’. For example, I often hear students saying “this answer can’t be right”. When I ask why, their reply is along the lines of “it’s a decimal” or “it’s negative”. Therefore, this activity would require good subject knowledge from the students (or rather it could develop understanding?)
  2. Also, assuming all students complete the task successfully, they will then have access to a number of annotated examples.

Cons

  1. Students need some understanding of TeX and to be fairly comfortable writing to a wiki/webpage. [I think only by trying this activity a few times will I get an idea of the size of this obstacle.]
  2. Students may cheat (i.e. by just copying an example from the web or a textbook). [I always try to explain to students why I set homework and point out it's for their development. So if students are going to cheat then it's their loss! I wonder if it would be the same students who copy each others' paper-based homework?]
<pre><code>&#x5b;latex]e^{\i \pi} + 1 = 0&#x5b;/latex]
</code></pre>