Yeah I'm not buying it. (Clarification: I am not one of his students. I was sitting in on his lecture.)

A couple of teenage girls attempt to hang up a very sparkly "Happy Birthday!" banner between two trees in the riverbank park. They take a couple of tries to get it the right way around and the right way up before realising they have no way to actually attach it to the trees.

Regular reminder that “you can only learn this through experience” is a cop out. You must have to notice *something* from the experience and hence it should be possible to *help* someone notice it.

A couple of teenage girls attempt to hang up a very sparkly "Happy Birthday!" banner between two trees in the riverbank park. They take a couple of tries to get it the right way around and the right way up before realising they have no way to actually attach it to the trees.

Two men walk out of the food court carrying paper bags of takeaway. They walk down the nearest hallway in the shopping centre. “I don’t know where this leads,” says one of them. “But I’m just going with it.”

For ∫sin(x)*e^cos(x)dx,
I would set u=cos(x).

I have a feeling it probably would work to set u=e^cos(x), but I’m absolutely certain u=cos(x) will work and its not worth trying something else if I’m time poor, and definitely not worth remembering a whole separate trick for one specific situation.

Oh I love integration by parts and substitution and the choices are my favourite part too.

The point is that if by “what’s u and what’s v?” someone means “which one gets differentiated and which one gets integrated”, then it’s meaningless to me.

Yes, but even with that there is no way of knowing when I do it if I will end up with u’v or uv’ on the left hand side!

Lecturer said “the only way to get good at this is to do lots and lots of them”.
NO!!
Just doing them isn’t enough! You have to THINK about them. Take note of what made each problem different or similar to the others. Take note of when a choice made it hard or easy. Take note when you’re improving.

I remember integration by parts as
“∫u’v dx=uv-∫uv’ dx
or
∫uv’ dx=uv-∫u’v dx”
(Actually it’s “∫uv dx=uv-∫uv dx but one has a dash at the start and the other has a dash at the end”).
Therefore it’s VERY confusing to me when someone asks “if you integrate this by parts, what’s u and what’s v?”.

Two men walk out of the food court carrying paper bags of takeaway. They walk down the nearest hallway in the shopping centre. “I don’t know where this leads,” says one of them. “But I’m just going with it.”

An orange backhoe scoops up rubble and deposits it into the back of a big orange truck. A man in orange high-viz gear wipes grey dust off the window of the truck with a cloth, only for a cloud of dust from the latest load of rubble to cover the window again.

*Gah* It doesn’t MATTER whether ChatGPT’s solution is right, it matters whether you UNDERSTAND!

An orange backhoe scoops up rubble and deposits it into the back of a big orange truck. A man in orange high-viz gear wipes grey dust off the window of the truck with a cloth, only for a cloud of dust from the latest load of rubble to cover the window again.

Force the student to take breaks every so often.

Eg, if you want P(X > 10), then there are two things happening here: the event "X>10" and its probability. The event "X>10" is a part of the x-axis, so colour in that part of the x-axis first. THEN colour in the bit above it to show the probability that goes with it.

When colouring in probabilities of events in normal (or other) distributions, can I recommend colouring just the axis first, and THEN the area above it?

Must have been satisfying.

Parallel lines are like “spooky action at a distance”. Like this angle over here is 30°, but because this line WAY over here is parallel to that one, this angle WAY over here is also 30°.

So angles problems are the ultimate in numberless word problems.

Wordle 1,573 3/6.

1: Y b b b G …
2: b G b b G …
3: G G G G G …

That was a lucky guess at Guess 3.

A person stands very awkwardly on the outdoor escalator: sideways with one hand in front and one behind, gripping the handrails. As I get closer it’s revealed that they are standing this way to fit both feet in rollerblades on the one step. When they reach the bottom, they glide gracefully away.

A person stands very awkwardly on the outdoor escalator: sideways with one hand in front and one behind, gripping the handrails. As I get closer it’s revealed that they are standing this way to fit both feet in rollerblades on the one step. When they reach the bottom, they glide gracefully away.