Chapter 2 - (The Language of Doing Mathematics)

explore. justify. construct. develop.
investigate. represent. verify.
describe. conjecture. formulate. explain.
use. solve. discover. predict.

(chapter 2. pg. 14)

Mentioned in the book, to create a setting where students are doing mathematics means a shift in the tasks given to the students and how classrooms are organized for mathematics lessons. It should involve creating a safe risk-taking environment where students should not be afraid to make mistakes, and ideally share their ideas and defend mathematical ideas. This thus, leads us to the role of a teacher in creating "the spirit of inquiry, trust and expectations" and helping children attain mathematical proficiency - (1) conceptual understanding, (2) procedural fluency, (3) strategic competence, (4) adaptive reasoning & (5) productive disposition.

I guess the most basic process for a teacher is none other than: Plan. Do. Reflect.