# How does the Forgetting curve change after repeated exposure to the same item we would like to memorise?

There has been a long debate going on on the actual form of the Forgetting curve, but my question will be about its change when we review a previously memorised fact - Unfortunately, I couldn't seem to find too much information (or perhaps I used wrong terms) on this topic.

Maybe the most up-to-date and least divisive research paper on the topic of the actual form of the Forgetting curve would be Averell, L., & Heathcote, A. (2011). The form of the forgetting curve and the fate of memories. Journal of Mathematical Psychology, which I have seen referenced here multiple times. According to it the shape of the curve is best described as $$R(t) = a + (1-a)*b*(1+t)^{-β}$$ which would yield $1$ at $t=0$ if the encoding happened without a problem (which we assume did). My concrete question would be that how the three parameter change after repeated exposure to the fact (where we assume that at this specific $t_r$ the retention increases to $1$ again). I think it is fair to assume that it is going to be yet another curve describable with a Power function starting at $t_r$ which should have a higher asymptote as the original function.

A picture (although not scientific nor correct in terms of the actual form) illustrating my question has been already posted here at How are these review-forgetting curve calculated?, although for different purposes than mine.

## 1 Answer

Currently, I am working on various demonstration graphs of various spacing effect algorithms. From the research it seems like two of the parameters exist to constrain the outputted values...

The parameters a and b are also assumed bounded between zero and one, and hence R(t) is similarly bounded, which must necessarily be the case as R(t) is a probability. Enforcing this bound is important as otherwise data fits can be inflated (see Navarro, Pitt, & Myung, 2004, for further discussion).

I think Ebbinghaus' original function R(t) = e ^ -(t/s) (see this thread) can more easily explain things. t is time and s is the strength of the memory. After every review, s increases. If you plot this out, you see that if you increase s, the forgetting curve function flattens out.

• Welcome to Psychology.SE. You suggested to "see Navarro, Pitt, & Myung, 2004, for further discussion" yet there is no reference information in order to find the article. – Chris Rogers Dec 16 '18 at 15:14
• @ChrisRogers I quoted a part from the paper that OP referenced. – George Boole Dec 17 '18 at 20:23