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I imagine there must exist a fair amount of literature and discussion about the idea of somehow redesigning college math courses, and the entire college math curriculum, to be self-paced.

Question: What are the most notable works that have been done along these lines? What should I read before attempting to implement my own self-paced courses and curriculum?

I am also interested in hearing your own thoughts and ideas about whether or not self-paced math courses are a good idea in a college setting, and how they might be implemented.

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    $\begingroup$ [guest's comment didn't fit; here is part 2] ...Other than that, on the specifics, make sure you look at the literature and practice (e.g. old texts) in "programmed instruction" or "programmed learning". In particular, check out all the books by K. A. Stroud. $\endgroup$ – Chris Cunningham Dec 19 '19 at 3:06
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    $\begingroup$ The UK's Open University is probably worth looking at. $\endgroup$ – Dave L Renfro Dec 19 '19 at 12:39
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    $\begingroup$ Also, tuition is charged per semester, so a student needing to spend a year to cover Calculus I, would likely be charged tuition for a course, times two. Your idea, while I like it, would require enormous restructuring of virtually all college/university and governmental (in terms of eligibility for federal financial aid) policies. If there do exist programs for "self-paced learning", many of the students enrolled would likely need 5 to 6 years of studY (and have to pay a corresponding increase in tuition required to earn an undergrad degree. That may be no issue for the rich... but.... $\endgroup$ – amWhy Dec 20 '19 at 1:26
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    $\begingroup$ I'm not sure there is a substantial literature. An early study reached largely negative conclusions: Schoen, Harold L. "Self-Paced Mathematics Instruction: How Effective Has it Been in Secondary and Postsecondary Schools?." The Mathematics Teacher 69, no. 5 (1976): 352-357. JSTOR link. $\endgroup$ – Joseph O'Rourke Dec 20 '19 at 13:07
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    $\begingroup$ @MatthewDaly AFAIK, colleges want (or are required?) to teach (or "teach") 120 credit hours no matter how many courses a student gets credit for. So, in the end the student will be "learning" something like hip-hop dancing or crocheting instead of calculus, is this better? $\endgroup$ – Rusty Core Dec 20 '19 at 17:30
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Usually, "self-paced" or "personalized learning" courses are managed via technology. An interesting review of the current state of the industry was published yesterday (as I write this) at Technology Review by Natalie Wexler:

A 2019 report from the National Education Policy Center at the University of Colorado on personalized learning—a loosely defined term that is largely synonymous with education technology—issued a sweeping condemnation. It found “questionable educational assumptions embedded in influential programs, self-interested advocacy by the technology industry, serious threats to student privacy, and a lack of research support.”

Judging from the evidence, the most vulnerable students can be harmed the most by a heavy dose of technology—or, at best, not helped. The OECD study found that “technology is of little help in bridging the skills divide between advantaged and disadvantaged students.” In the United States, the test score gap between students who use technology frequently and those who don’t is largest among students from low-income families. A similar effect has been found for “flipped” courses, which have students watch lectures at home via technology and use class time for discussion and problem-solving. A flipped college math class resulted in short-term gains for white students, male students, and those who were already strong in math. Others saw no benefit, with the result that performance gaps became wider.

Observing a case where a young student gave up on trying to add 8 and 3 and instead starting doodling on the iPad that was quizzing them, the author further writes:

If Kevin had been asked to combine 8 and 3 by a teacher rather than an iPad, there’s a greater chance he would have been interested in trying to do it. “It’s different when you’re learning from a person and you have a relationship with that person,” cognitive psychologist Daniel Willingham has said. “That makes you care a little bit more about what they think, and it makes you a little bit more willing to put forth effort.”...

In addition to sapping motivation, technology can drain a classroom of the communal aspect of learning. The vision of some ed tech advocates is that each child should sit in front of a screen that delivers lessons tailored to individual ability levels and interests, often on subjects chosen by the students themselves. But a vital part of education is different kids bouncing their ideas off each other...

Full story here.

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    $\begingroup$ Too much of a "link only" answer, since the only substance of your answer are two copy-paste quotes from a linked story. Better to have left a comment with you "Full story here" link. $\endgroup$ – amWhy Dec 21 '19 at 0:26
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    $\begingroup$ I found this to be a helpful answer, thank you! $\endgroup$ – eternalGoldenBraid Dec 21 '19 at 10:50
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Here are some problems I see with asynchronous self-paced instruction. Let me begin by first setting forth some assumptions I have about what self-paced likely entails.

  • Instruction is automated: the content is largely produced asynchronously to your use. You are not directly interacting with a teacher. Instead, you are likely watching little tutorial videos and/or reading.
  • Grading of the course is automated: you probably are using some system to either give short answer or multiple choice responses which can be scored by a computer. It is very unlikely you are submitting complete arguments or writing proper work for a human to properly evaluate

Both of the above features are almost essential since they keep the cost of such instruction at a minimum. Unfortunately, you get what you pay for in this case because:

  • Lack of human interaction robs you of the chance to have unique experiences in the classroom with your peers. Jokes, shared suffering, asking questions and/or seeing your peers ask questions... these are not going to happen with automated instruction.
  • Temptation to game the system: when you know the homework is just a computer game then it is awful tempting to treat it as such. On the other hand, if the homework is given in real time by a professor who expresses actual interest in your maturation as critically thinking students then it is much less likely you ignore the homework.
  • Inability to identify outliers: part of the job of a professor is to identify excellence or diamonds in the rough. This is one of the more subtle parts of teaching, to see past bad preparation to see the student for what they could be rather than what they appear to be in the present. I cannot fathom an automated system which does such a service justice.

Now, perhaps none of these things matter since the math we are thinking about is just a general education requirement. Even so, I know some of our best Math majors came from majors where math was just a general education requirement. If that gen-ed course had been automated, they might never had the chance to forge a relationship with a professor passionate about math. I think that is a great loss since such non-traditional lateral entries to the math major are some of our most creative students.

I should make an important caveat from what I say above. Most of my criticism is based on the automation and lack of professional guidance in the education. In fact, I am all for self-paced instruction provided it is guided by actual professors in a individually crafted fashion. Furthermore, I think it works best when there is a single test at the end of the study, like a "CLEP". This path is not for all students. Students must be self-motivated and above average for this to work. Ideally in the summer when there are not a lot of other distractions etc.

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  • $\begingroup$ +1 I think you may mean "CLEP", not "CIEP", maybe? Which is a nice point, but seems to be opposite current trends. E.g., In the last decade, my university has removed college exit exams, made uniform final exams across course sections impossible, and asserted that "high stakes testing" (e.g., any must-pass exam) is now frowned upon throughout academia. $\endgroup$ – Daniel R. Collins Dec 22 '19 at 6:51
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    $\begingroup$ @DanielR.Collins I would not be surprised that universities sacrifice rigor under the auspices of being nice. But, it is weird to eliminate CLEP-type tests since the students who use them do so of their own volition. I think we ought to turn that frown upside down. $\endgroup$ – James S. Cook Dec 22 '19 at 16:11

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