Skill mastery v.s. Conceptual approach
We all learn arithmetic in Primary school using the standard multiplication and division algorithms. NTCM has reformed their curriculum using 8 Focal points (see previous post) to develop mastery of these skills by the 5th grade. However, there are many books which focus on problem solving rather than skill mastery. The video below shows out two reference books for elementary school show alternate approaches to arithmetic, namely multiplication and division.
Math Education: An Inconvenient Truth
A very informative video of different approaches and techniques to solve the same problem. Ultimately, this is a question of efficiency vs understanding. Stay tuned till the end of the video for a surprise.