Having recently attended the interesting talk by Philip Mani at UNSW on the mathematics of biology, one quote from Alan Turing stuck in my mind: That his biological model was a
"... simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of greatest importance to the present state of knowledge."
I decided to embark on my own journey of simplification, idealization and falsification. Knowing exactly how well students understand MATH1B topics is an impossible task. But I could try to model this by looking at the amount of time spent on them.
Above is a table of data collected from the MATH1241 Online Tutorial exercises. It shows the average number of hours between when a student starts their homework exercise to when they submit their exercise.
Of course, the actual amount of time spent on homework is much less than what is shown. The interesting feature is how this number changes between weeks. Students spent the most time on Algebra during weeks 4 and 6, and on Calculus in week 7. Let's look more closely at what happened in those weeks.
The table above gives us an indication of what problems students spend their time on. There may be many explanations for this. For example, perhaps the questions were vague or difficult (and I'm sorry if this were the case). Some simplified, idealized and (possibly) falsified conclusions can be drawn from this data. On average MATH1241 students:
1. have a good understanding of spans, eigenvectors, eigenvalues, integration, recurrence relations and first order odes.
2. spend more time on questions about linear independence of polynomials, basis, and 2nd order differential equations.
Hopefully this information helps you to direct your study efforts.
-- Daniel Mansfield