Mathematics says a lot with a little. The reader must participate. At every stage, he/she must decide whether or not the idea being presented is clear. Ask yourself these questions:
· Why is this idea true?
· Do I really believe it?
· Could I convince someone else that it is true?
· Why didn't the author use a different argument?
· Do I have a better argument or method of explaining the idea?
· Why didn't the author explain it the way that I understand it?
· Is my way wrong?
· Do I really get the idea?
· Am I missing some subtlety?
· Did this author miss a subtlety?
· If I can't understand the point, perhaps I can understand a similar but simpler idea?
· Which simpler idea?
· Is it really necessary to understand this idea?
· Can I accept this point without understanding the details of why it is true?
· Will my understanding of the whole story suffer from not understanding why the point is true?Putting too little effort into this participation is like reading a novel without concentrating. After half an hour, you wake up to realize the pages have turned, but you have been daydreaming and don’t remember a thing you read.