This question may be a bit overly-broad for MESE, but I am hoping to find some responses that can help to fill in my understanding of two similar forms of instruction that had their heyday in the 1960s and 1970s, but seem to have then diverged significantly.

The first instructional form I'm interested in is Personalized System of Instruction (PSI), also called the "Keller Plan". According to the Wikipedia article on the Keller Plan,

The Keller Plan, also called the Personalized System of Instruction (PSI), was developed by Fred S. Keller with J. Gilmour Sherman, Carolina Bori, and Rodolpho Azzi in the middle 1960s as an innovative method of instruction for the then-new University of Brasília. PSI was conceived of as an application of Skinner's theories of learning, grounded in operant conditioning strategies of behaviorism...

While traditional teaching is "same pace, different learning", a key distinguishing factor of PSI is that it instead advocates "different pace, same learning". A traditional course might have all students follow the same weekly lectures, exercises, etc., and then sit an end-of-course exam at the same date — but possibly with huge variation in learning outcomes (e.g., 95% achievement for a strong student, but just 55% for a weak one). In a course run according to PSI, all students must pass a high threshold of achievement on each module within the course (for instance 90%). The difference between weak and strong students would then be that the stronger ones be able to finish the course quicker, while the weaker ones would need more time.

I became aware of the Keller Plan as an undergraduate at the University of Michigan in the 1990s, when it was still being offered as an option for students taking 1st and 2nd semester Calculus-based Physics. While I did not take the Keller Plan Physics course myself, I did work as a peer tutor in the "Keller room" as an upperclassman, and gained a real appreciation for how well the program can work for highly motivated, disciplined, self-directed learners.

As far as I know, the Keller Plan had its widest adoption in Physics and Astronomy; I don't know if there ever was a Keller Plan / PSI Calculus or Statistics, for example. (That's one of the reasons why I'm not 100% sure this is on-topic for MESE.)

Michigan stopped offering Keller Plan Physics around 2007 or so, but a bit of Googling suggests that it was still being offered at some other Universities more recently.

The second instructional form I'm interested in is Individually Prescribed Instruction (IPI), which saw a brief period of wide adoption in the late 1960s/early 1970s. According to one summary of the program,

IPI was designed for students to "proceed through sequences of objectives that are arranged in a hierarchical order so that what a student studies in any given lesson is based on prerequisite abilities that he has mastered in preceding lessons" (Lindvall and Cox, as cited in Erlwanger, 1973, p. 51). To measure that mastery, IPI relied heavily on assessments that were checked by the teacher or an aide, who would then have the opportunity to conference with the student and check for understanding.

So the basic structures of PSI and IPI were not that different: students would work individually in "programmed" materials, complete assessments that were meant to demonstrate mastery, and get individualized help only if and when they needed it.

Unlike PSI, which was mostly taken up at the college level, IPI was implemented at the elementary level in many progressive schools. The program eventually earned a terrible reputation, however, due in large part to a notorious case study by Stanley Erlwanger, who documented a student who -- despite having demonstrated successful learning in an IPI curriculum -- had learned a bizarre array of incorrect and self-contradictory "rules" for operating with fractions. Erlwanger's landmark "Benny" study demonstrated that the IPI curriculum was not capable of measuring the difference between mere performance and actual understanding. By the late 1970s, IPI had essentially disappeared from the landscape of American education.

With all of that as background, here are my questions.

  1. Was PSI ever used for college-level mathematics, as it was for Physics -- and if so, what kind of success or failure did it achieve?
  2. Are there any online, open-source repositories of PSI or IPI materials?
  3. Were there any structural differences between the PSI and IPI programs that might account for the different trajectories these two programs followed? (One obvious difference was that PSI was mostly used at the post-secondary level; I'm wondering whether there were other issues that had to do with the design of the materials themselves.)

2 Answers 2


I've done a lot of reading on the topic of remedial math education in college (i.e., topics up to elementary algebra), and the one and only thing that seems firmly established is this: independent work for such students has catastrophic results.

One example is the attempt to run remedial math courses via online systems like MOOCs, which has been terminated many times, wherever it was tried. One analyst concluded that "The failure rates were so high that it seemed almost unethical to offer the option" (link).

The paper I was most recently reading by Kristina P. Corey Legge, Does Mandatory Supplemental Instruction Work in Developmental Math Education? (doctoral thesis, Temple University, 2010) studied elementary algebra students in three treatments: (1) standard lecture, (2) lecture plus mandatory supplemental instruction with peers, (3) individualized pacing with computer software and professorial coach. While groups (1) and (2) were statistically indistinguishable (as is usually the case in such studies), the individualized group (3) had a 20% greater failure/dropout rate. This follows similar findings in other literature. (link; see results Table 4.23 on p. 59)

Of course, many of us involved in academics are self-driven and welcome opportunities to learn on our own. I could hold out hope that people holding baccalaureate degrees are more generally in this category. But for lower-level learners (perhaps the majority of college students today), the one solid piece of the literature is that individualized learning is a disaster. Instead, approaches that have shown promise in recent years have been things like learning communities and so forth. (link)

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    $\begingroup$ I think all of this is true. It's notable perhaps that Keller Plan courses are (as far as I can tell) usually recommended as good options for high-achieving college students who want to get through the course work faster, not remedial students who need extra help. $\endgroup$
    – mweiss
    Commented Nov 20, 2017 at 18:43

In 1982 I was a student in a Keller plan Mathematical methods course. It was the worst grade I ever got at university as it required persistence and planning, rather than ability to answer questions under pressure. Then in the early 2000s I developed a PSI course "Quantitative methods for business". With online testing, it was a lot simpler to administer, though our university still required supervised testing as well. For some students it was miraculous, and they overcame their lifelong (these were often mature students) fear or anxiety about maths. For others, their lack of discipline meant they failed to complete in time.

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    $\begingroup$ Could you provide some more information about the Mathematical Methods course? Do you mean "Methods" as in "a teaching methods course for preservice teachers", or "Methods" as in (e.g.) "Mathematical methods for advanced physics" or the like? And could you provide some additional info about where these courses were offered? $\endgroup$
    – mweiss
    Commented Nov 20, 2017 at 19:17
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    $\begingroup$ Mathematical Methods - second year University course, included things like splines, non-linear search methods. Can't remember much else. University of Canterbury in the Mathematics department. Oh - now it is coming back to me - it was Numerical methods not mathematical methods.Stuff that computers do now, but this was before computers were cheap. $\endgroup$
    – Nic Petty
    Commented Nov 20, 2017 at 19:40

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