Concerns about the training of Future High School Math Teachers

It is the job of University research mathematics departments, not only to promote research but also to train undergraduate and graduate mathematics students. In the United States they also have a role to help train future high school mathematics teachers. The author outlines some topics which would benefit from a better emphasis and/or links to school math, while being taught/studied at University. Areas covered include: complex analysis; lines and planes in 3-space; linear algebra; abstract algebra; trigonometry; functions; graphs; theory...The question is how should academics participate in future maths teachers...