What Education iIs

I saw a sentence "Education is not the learning of facts, but the training of mind to think" at the front desk of the educational institution at which my daughter is studying English, while I was waiting to pick my daughther up.

Because you already have "my daughter" in the sentence, the reader will easily understand who you are referring to. This substitution also avoids having "my daughter" three times in two sentences.

After I picked up my daughter, I asked her if she knowsew the meaning of the sentence.

This verb is part of what happened in the past (picked up, asked, knew).

She read the sentence for a while and t. Then shen told me that it means what is important wais not the knowledge itself but how to think.

Here the present tense is used to report what she said because she is making a generalization (a statement about something that is generally true). She is not talking about a specific event in the past.

I separated her actions into two sentences to make it easier for the reader to understand quickly.

I deleted "the" before "knowledge" because the sentence is not referring to a specific body of knowledge; it is referring to all knowledge.

After arriving at home, she began to check and think about the mistakes she made ion her exams.

"Arriving home" is correct, but the wording is what we usually use for busses, trains, planes that follow a schedule. The word "arrive" is somewhat formal in English, and a native speaker would probably say, "After we got home." This phrase is widely used in all time frames: when we get home, if she gets home, when did you get home? will they get home? etc.

We think about something, or we think of something. A preposition is needed before "think"

What Education iIs

I changed to all capital letters as it is a title.

I saw aThe other day, I saw an interesting sentence. "Education is not the learning of facts, but the training of mind to think." It was at the front desk of the educational institution at which my daughter is studying English, whilere I was waiting to pick my daughter up.

This sentence is a bit too long so I broke it up a bit as well. But you can tweak it to your liking, as long as it's not too long.

But just "I saw a sentence" at the start is a bit awkward, so I added the time it happened and an adjective, to make it sound more natural. You can change the time and adjective to your liking.

After arriving at home, she began to check and think about the mistakes she made in her exams.