> The example of "mental model of assignment" is ridiculous. a=b can mean whatever. It means something totally different to a mathematician than a programmer.
> "The piece of paper on the left says dog and the piece of paper on the right says cat.
We are talking about university students. I think they all have had a bit of calculus. That they had to "find the x" or "give the value of y = 1/(3/x) to the third decimal when 1) x = 3, 2) x = 5".
If your 18-year old students need to be told of "dog" and "cat" on pieces of paper in order to understand the most basic abstraction that math has, well, you, as a teacher, will find big difficulties ahead.
This is exactly the problem here. If you show a=1+1; b=3; a=b; to someone with math background, their brain will most likely explode, because they'll think that every equality has to hold at the same time.
Also I think it's impossible to hold a consistent mental model (whatever it is) if people can't form a logic behind the operation.
> "The piece of paper on the left says dog and the piece of paper on the right says cat.
We are talking about university students. I think they all have had a bit of calculus. That they had to "find the x" or "give the value of y = 1/(3/x) to the third decimal when 1) x = 3, 2) x = 5".
If your 18-year old students need to be told of "dog" and "cat" on pieces of paper in order to understand the most basic abstraction that math has, well, you, as a teacher, will find big difficulties ahead.