Ordinary Differential
Equations and Memorization
Presented by Alyssa Cuervo,
Laura Harmon, and Michael Kutan
The Equation
• We must assume two things:
– All outside variables can be combined into
one constant, k
– The rate of memorization is proportional to
what is left to learn (with L being what is
learned in fraction form)
dL/dt = k (1 – L)
Finding L(t) and k
dL/dt = k (1 – L)
…
…
…
L(t) = 1-e-kt
k = (-ln(|1-L|)/t
Our Hypothesis
• One’s personal k increases with longer
study time
• One’s personal k decreases with an
increased list size
The Initial Test
• Three participants were asked to perform a
series of memorization tasks
– Participants had three lists of 20 random three-digit
numbers to memorize
– Participants would have 1 minute to study the 20
numbers
– Participants were asked to write down whichever
numbers they remember (only numbers in the correct
rank were counted)
– Participants would repeat the process up until 10 tries
or until they have memorized the entire list correctly
(when L=1)
First Change: Study Time
• Participants were asked to study a fourth
list with 2 minutes at each study session
instead of 1
• Participants were also asked to study a
fifth list with 3 minutes instead
Second Change: List Size
• Participants were asked to study a sixth
list with fifty numbers with 1 minute study
sessions
• Participants were also asked to study a
seventh list with one hundred numbers
with 1 minute study sessions
Conclusion
• An individual’s personal k has been found
to vary due to many outside parameters
• An increase in study was not found to be
necessarily beneficial
• An increase in list length was always
detrimental the participant
Reference
• Blanchard, Devaney, and Hall's Differential
Equations: Third Edition
Thank You!