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The advent calendar function
In a previous post I discussed how we need ways to think about functions that are not curves on an x-y-plane. Well I have a seasonally-appropriate one for you: the Advent Calendar.
The Fear of Mollycoddling
Recently I was a guest at a planning meeting for a certain school and ended up in a session where we discussed how we can better support students in terms of their wellbeing. We were shown a news report highlighting the fact that the suicide rate in professionals of this particular discipline is four times higher than the general population. One of the major factors mentioned in the news report was that professionals in this discipline are very unlikely to seek support from anyone when they are struggling, having been trained too well to be self-sufficient while they were students.
A function is not a graph
When students learn about functions at school, we spend a lot of time forging the connection between functions and graphs. We plot individual points, and we find x-intercepts and y-intercepts. We use graphing software to investigate what the coefficients do to the graph, and discuss shifting along the x-axis and y-axis. We make reference to the graph to define derivatives and integrals. Some teachers help students to recognise from the formula of a function what general shape its graph ought to have, such as recognising that a quadratic function must have a parabola-shaped graph. (I wish this last point was much more strongly pushed, actually.)
Research reading can of worms
Today's blog post is about my experience attempting to become better read in the area of education research, and I'm sorry to say I'm not going to be glowingly positive about it. As the title suggests, it just seems to get out of hand so quickly.
Give good teaching a go
It was the Uni of Adelaide Festival of Learning and Teaching last week, and as always there was a string of people telling us about the great things they're doing with their teaching. As much as it can get a bit weary sitting through presentations all day, I really do love seeing that there are people excited about doing their best for student learning.
Splitting logs
In our bridging course (and indeed in Maths 1M and Maths 1A and several other courses) there is a section on differentiating logarithmic functions. One of the classic questions that we ask in such a section is to differentiate the log of some horrifying function, with the intention that the students use the log laws to simplify the original function first and then differentiate. There is something about this particular type of question has long bothered me and I only just figured out how to resolve my issue with it. I'm so excited I need to share it somewhere!
Jamie Oliver's teaching lesson
[This is a guest post by MLC lecturer Nicholas Crouch]
Rotation confusion
I had a long chat with one of the students the other day about rotation matrices. They had come up in the Engineering Physics course called Dynamics as a way of finding the components of vectors relative to rotated axes. He had some notes scrawled on a piece of paper from one of my MLC tutors, which regrettably were not actually correct for his situation. I know precisely why this happened: rotation matrices are used in both Dynamics and Maths 1B, but they are used in different ways (in fact, there are two different uses just within Maths 1B!). It's high time I made an attempt to clear up this confusion, especially since three more students have asked me about this very issue in the last week!
Contrapositive grammar
We had students the other day from Maths for Information Technology and their task was to form the contrapositive of a several statements. Given a particular statement of the form "If A, then B", the contrapositive is "If not B, then not A", so mathematically the problem is not actually very difficult. However grammatically the problem is much harder than it looks.
Archimedes's Integrals
One of my staff (thanks Fergus) told me ages ago about Archimedes' proof that the volume of a sphere is 4/3 π R3 (where R is the radius of the sphere). It is a very very cool proof and it's high time I shared it! One of the reasons it is so cool is that it uses the concept that a volume can be produced by stacking up a whole lot of thin slices. This is the idea behind integration, and Archimedes used this idea thousands of years before Newton or Leibniz.
