In a simple circuit, if you replace one resistor with a resistor of a higher value will the reading the ammeter increase, decrease or not change?

The ammeter reading (current) will decrease.
V=IR
I = V/R
so I is inversely proportional to R, i.e. increasing R will cause I to decrease

V = IR

The current I is inversely proportional to the Resistance R.

That means if the Resistance R is increased the Current I will be decreased. That is because the relationship is inverse.

So if the current I is decreased, that means the reading of the ammeter is decreased as well. 

decreased

Hope this helps.