This was a great lesson. i'm going to make flashcards of the things tort here & then put them into a memory-boosting software called Supermemo which will show me the flashcards regularly in such a way that it'll be impossible to forget the ideas. I once studied a really great maths book called Engineering Maths by KA Stroud - it was very smooth & gentle - it didn't assume the reader already knew a lot. But then i forgot most of the ideas because we forget nearly everything we learn. That's why i want to use Supermemo for this stuff. (btw i think tort is a better way of spelling taught as it's mor lojikal)
Mathematics should be taught graphically. Show students how a bridge, or a building is designed using algebric geometry. Cognitive association makes math a reality, and enables pragmatic understanding.
I actually can't picture anything in math, this would just help some students (graphical students) and would disadvantage other students (number students). I have a hard time imagining anything until I completely turn it into numbers. Same with every graphical counting method ever, I found them slow and boring even if they have less likelyhood of human error.
Dear Eddie, I totally disagree with you on the difference between indefinite and definite integrals. The difference is not in the limitation or in the existence of C. These are "external" factors. The essence in much deeper. What is the difference between multiplying and calculating the area of a rectangle? The first is one of many mathematical operations, the second is the method of finding a physical quantity. The first is the MEANS, the second is the METHOD. So, indefinite integral is another mathematical operation for converting a derivative to its primitive. But definite integral - one of the most powerful TOOLs in mathematics and, practically, in all sciences and knowledge areas.
