We forget that so much of our knowledge of mathematics is learned, but it was done so early that it feels natural. Ideas can be presented assuming this education is present. People, (who are afraid of ridicule generally), can suffer from the fact that there can be confusion between a lack of education, and ignorance. Math can seem like a trial, if it's practical application is unclear. The "When am I going to need calculus ?" argument of a schoolboy. In the same way children and people are introduced to mathematics, with practical associations, so this should be continued as deeper associations, and concepts are introduced. There is the need to show a direct practical use.The more it is use...

We forget that so much of our knowledge of mathematics is learned, but it was done so early that it feels natural. Ideas can be presented assuming this education is present. People, (who are afraid of ridicule generally), can suffer from the fact that there can be confusion between a lack of education, and ignorance. Math can seem like a trial, if it's practical application is unclear. The "When am I going to need calculus ?" argument of a schoolboy. In the same way children and people are introduced to mathematics, with practical associations, so this should be continued as deeper associations, and concepts are introduced. There is the need to show a direct practical use.The more it is used the more natural it will seem. In schools there is the presumption, that they might be the last chance a person has to learn. It needs to be interesting or it will be forgotten anyway, (Unless you count aversion Therapy.) We should not be educated in mathematics just for it's own sake, but for the way mathematics can show us about other things, and help put them into perspective. Some of the expressions of mathematics in Nature can be breathtaking. and their existence sustains the knowledge that there is always logic in the chaos.