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I bet pretty much everyone would have a correct mental model of assignment if the problem was stated like that.

Try this experiment with five people at a public place, say exactly what you said, and give them exactly one try at the correct answer. I'll give $10 to charity for each one that getes it right. If all five of them get it wrong, you owe me an upvote.

(Fair warning, the terms of this bet are ridiculously unfair to you.)

My bet is on lutorm, the point is that the original questions are ambiguous and if you remove some of the ambiguity you increase the chances of someone getting it right.

My theory is that those who got it right (at least most of them) didn't get it because they "formed a consistent model". But simply because they made the same assumptions people before them did when creating the language. But of course, would need more data to be more sure of anything.

I explained this to some as, "values from from right to left across the equals sign. In this case 10 flows into a, 20 flows into b, then the value of b, 20, flows into a, making a 20 and b 20." I think it's a matter of saying what '=' means in words that people can understand since it doesn't mean '=' in the mathematically sense (which is '==' or '===' depending on language).

You may want to re-read the article. It never said that having a correct mental model of assignment meant anything at all. It said having a _consistent_ mental model of assignment was what was important. Correctness can be taught, but people who cannot maintain a consistent model will always fail, because even if they're taught the correct way, they won't apply it consistently.

Ok, sorry for misspeaking, but I don't think it changes the conclusion. I don't know how to measure consistency in my example, but correctness necessarily implies consistency.

> 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. Say:

That's why the first group (the predicted to be successful group) is defined as forming a consistent mental model and not necessarily the correct one:

> 44% of students formed a consistent mental model of how assignment works (even if incorrect!)

How about students who reason like this:

I don't know what the notation means and there is no way for me to know what it means. Therefore I'm going to use a different interpretation in each question to minimize the variance in my grade.

That gave me a good laugh. The funny thing is I've actually used this strategy on a few occasions. It's a completely legit critique.

> 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.

but algebra is specifically non-directional. If I saw "a=10 b=20 a=b" as a non-programming, I'd assume the answer was "not possible".