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Category: How people learn (or don’t)
Anything about how people learn — mostly how they learn maths — or how they get blocked from learning
There is only one kind of function that distributes over plus
There is a very common thing that students do that causes pain, distress, confusion and depression in any maths educator who witnesses it. Both the error itself and the educator’s response to it are very clearly described by this excellent picture from the blog “Math with Bad Drawings”:
Every single one of the statements in that […]
Sleeping through Miss Marple
My wife and I like to watch mystery shows together like Poirot, Midsomer Murders and Miss Marple. Unfortunately I have a slight problem: when watching television in a comfortable position, I tend to drift in and out of sleep, no matter how interesting the show might be. This can be quite disasterous for mystery shows, […]
Inspiration, not instructions
We have a big problem-solving poster on the MLC wall that gives students advice for solving problems. One of those pieces of advice is that to decide what to do for your current problem, you could look at other problems for inspiration. Yesterday I saw the dangerous results of what happens if you look at […]
Jack Frost’s centre
On the weekend I watched the film “Rise of the Guardians” by Dreamworks Pictures, and it is a very enjoyable film. In it, Jack Frost is enlisted by the Man in the Moon to join the Guardians of Childhood–who already have Santa Claus, the Easter Bunny, the Sandman and the Tooth Fairy in their ranks–and […]
Complex is not the same as complicated
The Complex Numbers are unfortunately named. Most people take the word complex to mean “difficult to understand”, so the very name we give this family of numbers sets students up to think it’s going to be a lot of hard work to understand them. This is sad, because they really are very very cool and […]
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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 […]
Past Exam Vision
Students have just been told their exam results for Semester 1, and some of them are facing replacement exams. So we’ll be trotting out our standard suite of exam advice again, which will be all the more poignant now because these people tried to do it last time and failed!
One piece of advice we give […]
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Numbers don’t change the situation
The coordinator of first year Chemistry had a chat to me the other day about how to support students in solving word problems. The issue is that students have trouble using the words to help them decide what sorts of calculations need to be done in order to solve the problem. This issue is not […]
Two wrongs make a right
Students make a lot of mistakes when doing their maths, but sometimes they will make two mistakes in such a way that their final answer is still correct. This happened last week with one student quite spectacularly, because his doubly wrong method of doing a particular problem always produces the correct answer.
Let me explain: the […]
Assignments don’t teach people
It is a well-known truth that assessment drives learning. Students will often not learn a particular topic or concept unless it is assessed by an assignment or exam. Fair enough — often students are not choosing to do a particular course for the sheer love of it, are they?
However, many lecturers take this truth just […]