George Gadanidis claims number sense teaching is about developing what already comes naturally to the child. It is allowing children to develop their own procedures, not ready made algorithms, so that they strike upon procedures that are most useful dependent on the situation. "It's what they think that matters, not what we tell them to think." (p. 33)
Marilyn Burns would take the position that teaching about number sense is practicing mathematical thinking, which is best learnt through games, especially for K-6. It's not just about getting answers, it's about solving problems and finding approaches to those problems that require mathematical thinking.
Through these games (and the resulting math talk and play) children discover relationships between/across numbers. It is also about making reasonable judgements based on the knowledge of the relationships and comparisons of numbers. This means determining if a solution to a problem makes sense, based on the student's understanding of numbers. In order to arrive at these solutions, students need to use mental math, reasonable estimation, and proper judgement and selection when it comes to procedures or operations.