When a+b is harder than b+a

Is 1+4 a harder calculation than 4+1? It may be if you are 2+3 years old. I asked my 7-2 year old great niece Noelle the following sequence of questions. I include how long it took her to answer.

Bill: How old are you?

Noelle: (2 seconds) 5

Bill: What is 3+2

Noelle: (3 seconds) 5

Bill: What is 2+3

Noelle: (2 seconds) 5

Bill: What is 4+1

Noelle: (1 seconds) 5

Bill: What is 1+4

Noelle: (8 seconds) 5

Bill: What is 7 take away 2

Noelle: (4 seconds) 5

Bill: What is the least d such that there is general dth-degree equation.

Noelle: (11 years) 5

Bill: What is the least k such that the kth Ramsey Number is not known

Noelle: (21 years) 5

The most interesting of these to me was that 1+4 took much longer than 4+1. Why is this? To do 1+4 she starts at 1 and adds 1 to it four times so its 1 + 1+ 1+ 1+ 1. To do 4+1 she starts with 4 and adds 1 once, 4+1. More generally, if we don't use the addition is commutative and we view +1 our basic operation than the complexity of a+b is b.

It is important to realize that concepts such as commutativity of addition which are now obvious to us as adults, there was a time when it was not obvious. Or perhaps not obviously useful for calculations.

Could a model of children's addition be defined and studied? Would this be a Math Project, a Math Ed Project, or a Child-Development Project? Has it already been done? I suspect that how children learn things has been studying extensively, but that well defined questions of complexity-of-children's-addition has not. My ONE data point suggests that the complexity of a+b is b, but to really study this you would of course need more samples. SO, if any of you relatives that are 5 or under (but can talk), and try this out, let me know what you find.