We teach math using an approach known as Cognitively Guided Instruction (CGI) which helps students develop their own strategies to solve a variety of problems.
Number sense is developed through Number Talks, number sense routines, problem solving, Project Based Learning, whole class conversations, and sharing out.
CGI is based on research that shows that children come to school with rich informal systems of mathematical knowledge and problem-solving strategies that can serve as a basis for learning mathematics with understanding. Students who learn the standard algorithms often learn little more than a procedure to find the correct answer with little concept development.
I place an emphasis on reasoning, justification, explicit communication of ideas, rather than a right answer.