I tutor a young girl aged 11 (grade 4).

She is doing OK for her age, but I have observed that she has a tendency for rigid ways of thinking. She is usually more inclined to follow rules and stick to known ways of doing things which I think limits her learning.

Examples:

Calculating 2×7×3×5: she understands that she can multiply 2 and 5 first to get 10, and easily get the answer. However, when faced with similar tasks, she still prefers going from left to right and "does not like" to consider if there might be an easier way.

Or, consider the following exercise:

> 
> Let's add 3400 and 5700. Adam adds 34 hundred and 57 hundred and gets 9100. Ben adds 3400 and 5000 to get 8400, and adding the remaining 700 he gets 9100 as well. John adds 3400 and 700 to get 4100, then adds 5000 and also gets 9100. Explain how each of them did it. How would you do it?
> 
> 
> 

When faced with such tasks, she always "likes" the way to split the numbers because she thinks working with hundreds is "strange".

I think it is normal to understand one way easier than others. But I observed that she has a tendency to put up resistance when I try to give her exercises that are more easily solved in the ways that challenges the "order" that she thinks things should be done. I think this limits her learning, because eg. to understand why certain procedures work, or to be able to check results etc. all depend on understanding things from different angles.

How can I encourage her to think in ways that she might at first find "strange" or seemingly defying "order"?