What's the Name of That Book??? discussion

This topic is about
The Last of the Really Great Whangdoodles
SOLVED: Children's/YA
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SOLVED. Children's book series, two children are mentored by an old professor (?) who teaches them a new way of thinking [s]
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Some weird additional details that I remember:
I'm pretty sure the girl's name was Lucy because I kept on thinking of the Chronicles of Narnia while I was reading it (not totally sure though)
I know that the mentor/professor guy had this unusual umbrella that was clear plastic with bright yellow flowers on it
I know Lucy (or her brother) always looked on the ground when they walked home from school and they would describe the pavement but the mentor told them to look up and enjoy life or something along those lines
There was this weird but cool sequence where Lucy (?) looks into this hedge and she finds this little maze in it but then she looked away (i think?) and the illusion was gone. I remembered that part because it made me really look for the little details in things like that.
Thanks to all who answer!