Rigour is over-emphasized in the teaching of Mathematics to the detriment of its Understanding. Teaching should always be conceptual first before representing them formally and using rigour.
The best example is Faraday vs. Maxwell. In one communication Faraday actually says it "frightened" him to see Maxwell's mathematics but that his "Conclusions" were so clear that he could think and work from them. Faraday thought and worked with concepts and mental models while Maxwell gave them a formal and rigorous representation.
The best example is Faraday vs. Maxwell. In one communication Faraday actually says it "frightened" him to see Maxwell's mathematics but that his "Conclusions" were so clear that he could think and work from them. Faraday thought and worked with concepts and mental models while Maxwell gave them a formal and rigorous representation.