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Holding the other parts constant
It seems like ages ago – but it was only yesterday – that I wrote about differentiating functions with the variable in both the base and the power. Back there, I had learned that the derivative of a function like f(x)g(x) is the sum of the derivative when you pretend f(x) is constant and the derivative when you pretend g(x) is constant.
The Zumbo (hypothesis) Test
Here in Australia, we are at the tail end of a reality cooking competition called "Zumbo's Just Desserts". In the show, a group of hopefuls compete in challenges where they produce desserts, hosted by patissier Adriano Zumbo. There are two types of challenges. In the "Sweet Sensations" challenge, they have to create a dessert from scratch that matches a criterion such as "gravity-defying", "showcasing one colour" or "based on an Arnott's biscuit". The two lowest-scoring desserts from the Sweet Sensations challenge have to complete the second challenge, called the "Zumbo Test". In this test, Zumbo reveals a dessert he has designed and the two contestants try to recreate it. Whoever does the worst job is eliminated.
Problem strings and using the chain rule with functions defined as integrals
In Maths 1A here at the University of Adelaide, they learn that says that, given a function of x defined as the integral of an original function from a constant to x, when you differentiate it you get the original function back again. In short, differentiation undoes integration. And then they get questions on their assignments and they don't know what to do. They always say something like "I would know what to do if that was an x, but it's not just an x, so I don't know what to do".
[Read more about Problem strings and using the chain rule with functions defined as integrals]
SQWIGLES: a guide for action and reflection in one-on-one teaching
It's university holidays again (aka "non-lecture time"), which means I'm back on the blog trying to process everything that's happened this term. Mostly this has been me spending time with students in the Drop-In Centre, since I made a commitment to do more of what I love, which is spending time with students in the Drop-In Centre. When trying to decide what to write about first, I realised that a lot of what I wanted to say wouldn't make much sense without talking about SQWIGLES first. So that's what this post is about.
[Read more about SQWIGLES: a guide for action and reflection in one-on-one teaching]
(Holding it together)
Last week, I helped quite a few students from International Financial Institutions and Markets with their annuity calculations, which involve quite detailed stuff. One of the more important problems was about how the calculator interprets what they type into it, which is really in essence about the order of operations.
