Math fear among high school students who are on an accelerated math track

[Data10]

@ucbalumnus

Stanford’s AP credit listings suggest that they consider calculus AB = 19+20 and calculus BC = 19+20+21 in terms of material content, although Stanford’s math placement tests are required regardless of AP scores. So 19, 20, and 21 are not really “remedial”, but Stanford is selective enough that most students are more advanced than those courses already. The faster versions 40 and 41 may not have much enrollment because the stronger in math students are already ahead of that material, while those few for whom calculus is new to them may do better at standard pacing (19, 20, 21) instead of faster pacing (40, 41).

Maybe “remedial” was a poor choice of words. I expect the overwhelming majority of Stanford students take calculus in HS (~95% of students report taking calc in Harvard freshman survey, and Stanford is likely to be higher with larger portion tech majors). Most Stanford students sufficiently learn calculus in this HS class or elsewhere, but a minority do not, as suggested by the relatively lower score on the math placement diagnostic. Stanford offers this slow-pace (compared to other Stanford classes) single-variable calc class for the minority of students who did not sufficiently learn calculus in their HS class. It may be “remedial” compared to typical Stanford classes even though students taking the class are no doubt well above average compared to overall HS population. At less selective colleges, a course like this might be the standard first math course that most students take, rather than a slower and lower level one like at Stanford.

One math professor at Stanford said they removed the faster pace 41/42 because a good portion of students in 41 were choosing to drop down to the slower pace 19/20/21 within the first few weeks of the quarter. The first course in both single-variable calc sequences had relatively little enrollment. In the final year of 41, the totals were 156 students enrolled in 19 (slower pace), and 129 students enrolled in 41 (faster pace), compared to ~2000 in math 51 variants.

@ucbalumnus

Unlike many other colleges, Stanford does not appear to have math courses lower than calculus like Princeton’s MAT 100, or “calculus with review of precalculus” like Harvard Math Ma and Mb.

Stanford has a summer online bridge program for students who fear that they are not prepared for single-variable calc in Math 19. Some quotes from the website at https://mathematics.stanford.edu/soar-mathematics-program are below.

The SOAR Mathematics Program is a free 1-unit online summer course for incoming Stanford first year students. It is aimed at helping students feel prepared to take math courses at Stanford – in particular, Math 19 and 20 (the first two quarters of the single-variable calculus).
…
Students will enhance their proficiency with precalculus mathematics, with an emphasis on higher level conceptual understanding and problem-solving. One of the primary goals of this course is to help students develop and hone the mathematical skills necessary to successfully transition to university level mathematics at Stanford University.
…
Topics will include the following:

1. Algebraic expressions and manipulations
2. Functions and graphs
3. Trigonometric functions
4. Limits: A Preview of Calculus
5. Additional topics to be determined based on student demand and interest

Stanford also offers other summer bridge program that target groups that may benefit from additional support for a smoother transition to being a freshman at Stanford, as described at Log in .Math seems to be emphasized more than other fields at many colleges, including Stanford. I expect this relates to math being a foundation subject for which it is difficult to catch up without external support. Many students who start out behind due to a weaker HS background choose to drop out of math-heavy majors like engineering, rather than try to build their math fundamentals and catch up.