Floating versus pulling and pushing
My first-year textbook on geology contained a picture on convection currents and plate tectonics, something like this:

Convection in the deep earth
The teacher, otherwise quite enthusiastic about the book, sighed deeply before he started talking about the picture. “This and similar images,” he said, “are well-meant but flawed. There is a fundamental misunderstanding about plate tectonics contained within them.”
He explained. Lithospheric plates move because of convection currents, so much is correct. However, a common mistake apparently made in these pictures is that they make it look like the fluid movement of the asthenosphere drives the movements of the plates floating on it. This is not true, because the plates themselves are part of the convection current. They move because of two mechanisms: ridge-push and slab-pull, the first being the pushing force created by new material created at the mid-oceanic ridges and the second being the pulling force created by a cool slab sinking back into the asthenosphere. In terms of the picture, the arrows should go right through the plates, rather than under them. More than froth on the fluid asthenosphere, the oceanic lithosphere plates are like the upper part of a conveyor belt.
A hot pan
To illustrate the principle of a convection current, a cross-sectional picture of a saucepan with boiling water was given in the textbook. It looked similar to this:

Forced convection in a saucepan
This seemed to irritate my teacher less. It looks like a simple illustration of how a convection current works. No problem, until I noticed something odd when I was making some vegetable stock. The herbs and froth were flowing towards the middle of the boiling water, rather than from the center to the edge of the pan, as the diagram would predict. In fact, they always did in my kitchen, regardless of the size of the pan or the flame beneath it. So were the authors of the textbook guilty of putting two differently flawed pictures right next to each other? In one of the first chapters of a basic introduction?
What is disregarded in the picture, I think, is that the sides of a pan become hotter than the water, which stays 100o C. So the water is heated from the sides and the bottom, and can only cool down at the top. This would cause water at the sides to go up, leaving the water in the center with nowhere to go but down. The resulting convection is opposite to the picture, which is therefore wrong. It has nothing to do with plate motion, giving the impression that the textbook got two things wrong in short succession.
A textbook exemplar
The pan of boiling water is a typical ‘exemplar’, a textbook case illustrating a scientific theory. It’s copied and re-used again and again – apparently without testing it. The examples of convection experiments I found on youtube were either ambiguous or showed a current going up along the sides of the container used:
This seemed like a solved case to me, until I cooked water in a thin-walled pan at a windy campsite. The boiling water promptly behaved as the classic diagrams, partially saving at least one of the pictures in my geology textbook. So the direction of convection currents is perhaps not easy to predict. The exemplar is partially wrong in that it does not really describe the everyday situation. I’ve been thinking about the factors influencing it, but regardless of the correct model, it seems odd that only one current direction is ever illustrated. Perhaps creation of convection models and cooking are done by different people?