News: Thoughts about maths thinking
The unexpected fear of statistics
Statistics is the cause of a lot of fear. There are thousands of students studying psychology, sociology, economics, biology, medicine, animal science and education who thought they would be free of mathematics and suddenly discover they have to deal with statistics. In the case of psychology it is absolutely everywhere: both in whole courses about statistics, but also embedded in almost every other course they do. For most of these students, their fear of statistics carries over from their existing fear of mathematics, and so as sad as it is that they are afraid, it's not wholly unexpected.
Remainders remain a puzzle
My first post of 2018 is a record of some rambling thoughts about remainders. I may or may not come to a final moral here, so consider yourself warned.
The Arts student's maths brain
Yesterday I talked about one of the common responses to people finding out I am a mathematician/maths teacher, that of saying, "I'm not a maths person." The other common response I get is, "I don't have a maths brain." (John Rowe mentioned this in his comment on the previous post.)
Actually, I am a maths person
I am a mathematician and a maths teacher. Therefore it is an occupational hazard that any random person who finds out what my job is will respond with "I'm not a maths person." The most frustrating people are my own students who I am trying to tell that my actual job is to help them learn maths. I used to tell them that there was no such thing as a "maths person", but I have recently come to the conclusion that this is a lie. There is definitely such a thing as a maths person because I am a maths person.
Childhood memories
Two books I've read recently have encouraged me to investigate my memories from childhood. In Tracy Zager's "Becoming the Math Teacher You Wish You'd Had", she urged me to think about my maths autobiography to see what influenced my current feelings about maths. In Stuart Brown's "Play", he urged me to think about my play history to see what influenced my current feelings and tendencies about play. In the spirit of those two, here are some of my earliest memories about maths and play.
Money and me
In the online resources for Becoming the Math Teacher You Wish You'd Had, Tracy Zager provides information about the benefits of writing a "math autobiography". I really have tried to do this, but I am having a lot of trouble organising my thoughs and memories. However, I reckon I can track some of my memories about one particular application of maths: money.
Finding an inverse function
There is a procedure that people use and teach students to use for finding the inverse of a function. My problem with it is that it doesn't make any sense, in two ways.
How I choose which trig substitution to do
Trig substitution is a fancy kind of substitution used to help find the integral of a particular family of fancy functions. These fancy functions involve things like a2 + x2 or a2 - x2 or x2 - a2 , usually under root signs or inside half-powers, and the purpose of trig substitution is to use the magic of trig identities to make the roots and half-powers go away, thus making the integral easier. One particular thing the students struggle with is choosing which trig substitution to do.Â
[Read more about How I choose which trig substitution to do]
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.
Problem strings and using the chain rule with functions defined as integrals
In Maths 1A here at the ×îÐÂÌÇÐÄVlog 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]
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