Guided discovery

 

Learning math instead of computations

 

WCYDWT and Anyqys

 

Problem solving

 

Khan Academy

 

Math without words

 

Learning math through games

 

Real world mathematics

 

To suggest implicitly that there are two opposing views of how math should be taught is to create a false dilemma. There are many different perspectives on how mathematics should be taught, and some of them have not even been tried on any significant scale yet.