Reminder: Question-asking is the engine that drives mathematical investigations. (I like that phrase! It's so true!)
(1) You can only use what you remember!
According to a study carried out by Socony-Vacuum Oil Company (no, I don't have the reference) students retain:
10% of what they read
20% of what they hear
30% of what they see
50% of what they see and hear
70% of what they discuss with others
90% of what they teach someone else
(2) Preparation for the "real world" of work
Here's what principal aerodynamics engineers from Boeing and the Washington State Software Association had to say:
What do we look for in employees?
We hire those who have demonstrated that they...
Enjoy the process of learning and know how to learn independently
Thrive on intellectual challenges
Are creative and flexible in how they solve problems
Have a good understanding of fundamentals
(mathematics, science, economics, manufacturing)
Can manage knowledge and information, as well as tasks and things
Can operate effectively in a team environment
Have good communication skills
adapted from a handout of Tamara Veenstra's