Respond of Lockhart’s Lament

 Agree:

“That’s what math is— wondering, playing, amusing yourself with your imagination.” which I really agree with. Mathematics is something that requires a lot of thinking, because as Lockhart says, proofs require logic and are reached at after thinking. Similarly it also requires the use of imagination, which I think is a very necessary ability when learning math initially, for example a very simple arithmetic problem, what’s the answer for one plus one, for a child who is just learning it, they can imagine it as one candy plus one candy, when learning shapes they can imagine it as a donut and so on, and even more for the more advanced and abstract things. We have to have an initial guess and ask ourselves why before we have a desire to want to study math further.

“Just talk to them! And more importantly, listen to them” which is a very little part of the whole article, but it said the truth of being a teacher, just know more about your students and listen carefully about their feedback!

disagree:

“Teaching is not about information. It’s about having an honest intellectual relationship with your students. It requires no method, no tools, and no training. Just the ability to be real. And if you can’t be real, then you have no right to inflict yourself upon innocent children.” Just as students need to learn in order to gain, so does teaching, and it's not just limited to teaching math, as far as teaching as a whole is a difficult thing, we can show a very complete and authentic expression of what we know about knowledge of a particular subject, but for the rest of our ability, I think it's a matter of learning to hide it, and every teacher I think will have their teaching persona.

A point of contact or contrast with Skemp:

Lockhart thinks math is a pure art, so students should know the beauty of math, and as a teacher, we’d better teach them more about appreciation of math instead of the information. But Skemp thinks teaching students about instrumental learning is also important, and math could be a tool for some students, he didn’t mention a lot about math is a art. But both of them think we should make math interesting.