**SideShow Post #64**

To which I replied in Post #67I had a teacher once who said that if you can't explain it to an eight-year-old, you don't understand it.

The above prompted SideShowBob Post #71Your teacher seems to have had some weird ideas. Perhaps he was an English teacher with no knowledge of advanced mathematics & physics.

I majored in mathematics & physics. I would not expect to be able to teach calculus or other mathematics beyond algebra & Euclidean geometry to a typical 8-year old, yet I used those disciplines when working in a DOD think tank for 3 years after graduating from college.

The above remarks by you indicate that you do not realize that calculus & mathematics beyond algebra & Euclidean Geometry require a lot of prerequisite knowledge.You miss the point: Your inability to teach reflects your inability to teach, not the student's inability to learn.

**It would be interesting to try to teach Differential Geometry to the 8-year old without first teaching Euclidean geometry & differential calculus.**

**Why do you think that subjects like Differential Geometry (aka Metric Geometry) are not usually taught prior to the 4th year in college? The reason is that mathematics is analogous to a building which requires a foundation as well as stories 1-10 below the eleventh story.**

**You seem to view mathematics courses as analogous to history. You can learn American history with no knowledge of European or ancient history. You cannot learn calculus or Differential Geometry without several prerequisite courses.**

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To teach the 8-year old such disciplines would require first teaching quite a few prerequisite courses. It would require the equivalent of several semesters of other mathematics.

To teach the 8-year old such disciplines would require first teaching quite a few prerequisite courses. It would require the equivalent of several semesters of other mathematics.