1. learning to struggle successfully is far more important than mastering the chain rule.
2. If you start with excellent students, then you can set those students up to struggle on much harder and deeper questions.
My point, really, is that a curriculum that manages to not "lose" anyone will also fail to strike a good balance between "struggle" and "hand-hold" if 90% of your students start off as "Excellent".
The hardest part about designing a course is figuring out when students should struggle, and when to hold their hands. The answer will vary depending upon the quality of the students. Excellent teaching aimed at excellent students looks very different from excellent teaching aimed at mediocre students. Differentiating instruction is Teaching 101, and differentiation in universities often happens at the institutional or program level.
E.g., are Khan Academy's descriptions of the product rule better than Chicago's Math 160? For certain students, yes. For others, emphatically not! Neither option is "better" in an absolute sense, but each is definitely "better" for any given student.
There is nothing wrong with a course of study that's designed for the top 1% of high school graduates. And admissions mistakes do not equal bad teaching. On the contrary, torpedo'ing the entire curriculum to make sure that every student makes it through would be grossly irresponsible.
Well... obviously not! But:
1. learning to struggle successfully is far more important than mastering the chain rule.
2. If you start with excellent students, then you can set those students up to struggle on much harder and deeper questions.
My point, really, is that a curriculum that manages to not "lose" anyone will also fail to strike a good balance between "struggle" and "hand-hold" if 90% of your students start off as "Excellent".
The hardest part about designing a course is figuring out when students should struggle, and when to hold their hands. The answer will vary depending upon the quality of the students. Excellent teaching aimed at excellent students looks very different from excellent teaching aimed at mediocre students. Differentiating instruction is Teaching 101, and differentiation in universities often happens at the institutional or program level.
E.g., are Khan Academy's descriptions of the product rule better than Chicago's Math 160? For certain students, yes. For others, emphatically not! Neither option is "better" in an absolute sense, but each is definitely "better" for any given student.
There is nothing wrong with a course of study that's designed for the top 1% of high school graduates. And admissions mistakes do not equal bad teaching. On the contrary, torpedo'ing the entire curriculum to make sure that every student makes it through would be grossly irresponsible.