To Know Why It Is So 知其所以然
“知其然知其所以然(When you learn you need to understand why it is so.)” is a common phrase teachers tried to carve into our minds back in China.
Recently, I found myself passing the phrase down to my high schooler. It started when my help was needed for her math questions. Rather than giving a quick answer and then disappearing, I put myself into wars: insisting on reading the corresponding textbook section together, asking comprehension questions regarding every single word in the theorem/formula, suggesting prove the theorem. “If you TRULY understand a theorem/formula, once figuring out why it is so and applying it to a couple of meaningful problems, you will be able to solve any problems related to it.”
“Mathematical Induction” is a great example, remembering that majority of the college students at the class I was a TA for couldn't apply it on their HW.
The “why it is so” part of the story came after many years when I saw the topic on my daughter’s textbook. Spending time together to understand why the method itself makes sense, how the method works like climbing a ladder etc., will hopefully carve this philosophy of learning into her mind.