I have long felt that the convention that writes the numerator above the denominator in fractions is the wrong way round. The consequences don't bothe mathematicians but sometimes cause beginners to stumble.

When children first encounter a fraction like $3/5$ they think "divide something in $5$ parts and take $3$ of them". In that description you see the $5$ before the $3$. Writing "$3/5$" counterintuitively names the number you take before telling the reader how many parts there are.

When adding fractions, you must deal first with the denominators to find a common one. Only then do you think about the numerators. When you teach that to schoolchildren you require them to read from bottom to top.

In calculus, $dy$ is (roughly speaking) the change in $y$ caused by the change $dx$ in $x$. That sentence talks about the cause before the effect. Not how causality works.

I have long felt that the convention that writes the numerator above the denominator in fractions is the wrong way round. The consequences don't bother mathematicians but sometimes cause beginners to stumble.

When children first encounter a fraction like $3/5$ they think "divide something in $5$ parts and take $3$ of them". In that description you see the $5$ before the $3$. Writing "$3/5$" counterintuitively names the number you take before telling the reader how many parts there are.

When adding fractions, you must deal first with the denominators to find a common one. Only then do you think about the numerators. When you teach that to schoolchildren you require them to read from bottom to top.

In calculus, $dy$ is (roughly speaking) the change in $y$ caused by the change $dx$ in $x$. That sentence talks about the cause before the effect. Not how causality works.