All mathematics is applied mathematics. Pure mathematics is just mathematics applied to mathematics.
This is problematic, because the way mathematics is currently taught only small number of students actually grok it and make deep connections that enable them to build up on what they previously learned and learn more. Others have the constant feeling of things getting progressively harder to understand and use.
I'm sure that most people (including engineers) would benefit from the ability think and really internalize concepts taught in high school level.
Pedagogical research is almost entirely directed towards small children. Psychologists have studied children and know the common hangups children have. What are common misconceptions, how to use them to make children learn. How they learn to count numbers past ten. Competent teacher can help small children to learn faster.
I think it's possible to teach most people to think _in math_ but it's much slower process.
This is problematic, because the way mathematics is currently taught only small number of students actually grok it and make deep connections that enable them to build up on what they previously learned and learn more. Others have the constant feeling of things getting progressively harder to understand and use. I'm sure that most people (including engineers) would benefit from the ability think and really internalize concepts taught in high school level.
Pedagogical research is almost entirely directed towards small children. Psychologists have studied children and know the common hangups children have. What are common misconceptions, how to use them to make children learn. How they learn to count numbers past ten. Competent teacher can help small children to learn faster.
I think it's possible to teach most people to think _in math_ but it's much slower process.