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Four alternatives to the four fours
The "Four Fours" is a very well-known little problem that encourages some creative thinking and use of the order of operations. The purpose of this post is to show you four fourfoursesque puzzles I've created which have encouraged some great learning.
Things not sides
When doing algebra and solving equations, there is this move we often make which is usually called "doing the same thing to both sides". Quite recently this phrase of "both sides" has begun to bother me.
Spotless dice
Upon Amie聽Albrecht and Cathy Wilton's request, I am writing a blog post about a problem we worked on at One Hundred Factorial recently. A聽few weeks ago we became interested in problems involving removing spots from dice.
The right order for the fundamental trig identity
If you google "fundamental trig identity" you will get many many images and handouts which all list the fundamental trig identity as:
[Read more about The right order for the fundamental trig identity]
Do you get tired of the same topics?
In the Drop-In Centre, the majority of students visit to ask for help learning in a very small number of courses, mostly the first-year ones with "mathematics" in the title. Of course, any student from anywhere in the uni can visit to ask about maths relating to any course, and we do see them from everywhere, but the courses called Maths 1X have between them a couple of thousand students per semester and that's a lot of people who might need help to learn how to learn.
Showing how to be wrong
After writing the previous blog post (Finding errors by asking how your answer is wrong) and rereading one I wrote three years ago (Who tells you if you're correct?), I got to thinking about how students are supposed to learn how to check if they are right.
Finding errors by asking how your answer is wrong
One of the most common situations we face in the MLC is when a student says, "I'm wrong, but I don't know why". They've done a fairly long calculation and put their answer into MapleTA, only to get the dreaded red cross, and they have no idea why it's wrong and how to fix it. One of the major problems is that many students can't tell if it's because they've entered the syntax wrong, or done something wrong in their algebra, or completely misinterpreted the question, or if MapleTA itself has a bug and isn't accepting the correct answer.
[Read more about Finding errors by asking how your answer is wrong]
Pretending not to know
Yesterday the Maths 1M students handed in an assignment question that asked them to prove a property of triangles using a vector-based argument. It's not my job to help students do their assignment questions per se, but it is my job to help them learn skills to solve any future problem. This kind of problem, I find, is really hard to learn generalisable skills from.
My cat's bottom
Did you know that cats have scent glands just inside their bottoms that are constantly being filled with liquid and are squeezed as their poos come out, and if their poos are too skinny the glands are not squeezed enough and get over-full making them very painful and inflamed? Neither did I, until my cat Tabitha Brown started bleeding out of her bottom.
Let's
One of my friends and a past MLC staffer graduated from her PhD yesterday (congratulations Jo!). One of my strongest memories of Jo is when she told me something about my teaching that I never knew I was doing, but that she saw as an essential part of what I was trying to achieve at the MLC. That's what I want to share with you today.
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