What Do We Mean by Doing Mathematics: Reflection on Jean Piaget's Quote

This week we will explore what do we mean by doing mathematics. To many of us, math is/was a problem that was meant to be solved by following a set of procedures that were taught to us ( lectured) S you read the assigned readings, I want you to consider whether what is being discussed in the texts is consistent with how you were taught.
For your discussion, I would like you to reflect on this quote by Jean Piaget - "Each time one prematurely teaches a child something he could have discovered himself, that child is kept from inventing it and consequently from understanding it completely." - Piaget 1970. What does the above quote mean to you? How do you think that statement might affect the way math is taught to a child? Do you feel that statement is consistent with how you learned math? How does this quote correlate with what you have read this week.
1. Van de Walle Chapter 1: Setting a Vision for Learning High-Quality Mathematics
2. Geist, E. (2006). Children are Born Mathematicians: Encouraging and Promoting Early Mathematical Concepts in Children under Five. Retrieved from: http://www(dot)waece(dot)org/cdlogicomatematicas/ponencias/eugenegist_pon_ing.htm