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I'm trying to put together some thoughts on the importance of a strong college precalculus sequence (mainly I'm thinking College Algebra, where much of my experience is) for addressing socioeconomic inequality in the United States. While I'm curious to hear the thoughts of matheducators.stackexchange, I'm mainly interested in finding published writing on the subject.

The college precalculus sequence is the gateway for many students who were under-served by their high school mathematics courses to get into a wide variety of STEM and STEM-adjacent fields. A strong college precalculus program can help lessen the negative impact of a weak high school program, and a weak college precalculus program can cut some students off from STEM almost entirely.

However, in my experience, there are a wide variety of factors that negatively impact the effectiveness of the college precalculus sequence:

  • Students are often encouraged to take courses at too high a level for maximum benefit

  • Early precalculus courses often don't come with credit

  • Courses try to cover a year's worth of material (in high school) in only a semester (in college)

  • Mathematics professors are often very far removed from the experience of someone struggling with algebra

Where can I read more about:

  • The role the college precalculus sequence plays in socioeconomic feedback loops, and
  • The ways college precalculus sequences fail to meet the needs of their students?
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    $\begingroup$ "Courses try to cover a year's worth of material (in high school) in only a semester (in college)" What constitutes a "year's worth of material"? In general, I think that the assumption is that college students have more skills as students, and material is supposed to go faster. This is true in mathematics, and foreign languages, and basically any other area where there are comparable classes. $\endgroup$
    – Xander Henderson
    Jul 14, 2023 at 20:44
  • $\begingroup$ This thesis (and references therein) may be of interest: Epistemic Classism in Elite College Mathematics Education by Silas Olsen digitalcommons.colby.edu/cgi/… It focuses on calculus, but I think the principle is the same for precalculus. $\endgroup$ Aug 1, 2023 at 15:36

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Here's a hair-raising article I sometimes use as a touchstone:

Kenschaft, Patricia Clark. "Racial equity requires teaching elementary school teachers more mathematics." Notices of the AMS 52.2 (2005): 208-212.

Flitting back and forth from the richest to the poorest districts in the state [New Jersey] convinced me that the mathematical knowledge of the teachers was pathetic in both. It appears that the higher scores in the affluent districts are not due to superior teaching in school but to the supplementary informal “home schooling” of children.

It should be noted that a rather aggressive trend by U.S. colleges in the last decade has been to eliminate courses that remediate/repeat those in "weak high school program[s]" that don't come with credit (alleviating OP's bullet #2), at the expense of pushing those students into higher-level courses instead (possibly worsening bullets #1 and #3).

https://www1.cuny.edu/mu/forum/2023/01/12/cuny-ends-traditional-remedial-courses/

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    $\begingroup$ Math teachers studying more math. Game changing. But, sadly, at least in Virginia, the state just changed standards to dumb down the math background of education majors. We've lost 1/3 to 1/2 the audience in various higher level math courses which used to be populated by education majors with various forms of math specialization. $\endgroup$ Jul 15, 2023 at 3:30
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    $\begingroup$ Well, that's the human nature (and it applies well beyond teaching math.): instead of colonizing Mars, taming the climate havoc, or doing some other projects requiring the cooperation of the whole humankind, we still fight senseless wars, pull various blankets from one side to another in the name of "social justice', and just waste time on various pointless activities, consuming the dwindling resources like crazy. Unfortunately, all we can do is to try to set and promote the education and other standards locally and by personal example but even that often meets a fierce resistance. $\endgroup$
    – fedja
    Jul 26, 2023 at 13:01

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