[vingt-2]

What I don't understand is why the OP is even trying to teach stuff in which his sister is obviously not interested. He is seeking a solution to the wrong problem. "How do you get someone interested in math so he can develop the will to learn it ?" is the problem he should solve before trying to teach her anything. If he fails getting her attention on mathematics, then he's lost the game and she'll have to wait until she gets interested, or just do something else (which is fine, by the way).

What I think is most depressing on another note, is that even though she clearly isn't learning maths, she'll probably stay in the average of her class, and with this attitude eventually even get a university degree in domains where comprehension of maths is the cornerstone.

I'm a software engineering student at what you'd call a "valued" university. It is unarguably essential to understand basic university maths, and yet so many of my friends would just give their faith into "applying formulas" with little to no idea on what's going on in fairly easy topics like introductory linear algebra, and they'll even sometime get As because the teacher gave up when he asked for a little reasoning on the midterm (failing half the class) and gives a silly final.

I think the issue is more that we force people into doing what they don't want to do. Her sister doesn't have to understand maths at her age, she can wait until she feels the need to (and she will for these simple maths problems, but later).