Project 1B
Part 3
Cepeda, N.J., Vul, E., Rohrer, D., Wixted, J.T., & Pashler, H. (2008). Spacing effects in learning: A
temporal ridgeline of optimal retention.
To achieve enduring retention, people must study information on multiple occasions. How does the
timing of study events affect retention? Study aimed at characterizing spacing effects over significant
durations.
1,354 individuals were taught a set of facts and given a review after ≤3.5 months. A final test at a
further delay of ≤1 year. At any given test delay, an increase in the interstudy gap at first increased,
and then gradually reduced, final test performance. The optimal gap increased as test delay
increased. However, when measured as a proportion of test delay, the optimal gap declined from
about 20 to 40% of a 1-week test delay to about 5 to 10% of a 1-year test delay. Interaction of gap
and test delay: many educational practices are highly inefficient.
Very large and nonmonotonic spacing effects that unfold over very long periods of time, when study
time is equated across conditions. Retention surface: final test performance plotted as a function of
study gap and RI:
Fig. 4. A functional approximation of recall on the final test (as a proportion), plotted as a function of gap and test delay (retention
interval). The red ridgeline comprises the points representing the optimal performance for each test delay. The forgetting function for each
gap is a power function. The location of the ridgeline indicates that as test delay increases, the optimal gap increases, and the ratio of
optimal gap to test delay decreases.
1. For any gap duration, recall performance must decline as a function of RI (test delay) in a
negatively accelerated fashion in order to produce the familiar forgetting curve consistent with >100
years of memory findings.
2. For any RI greater than zero, an increase in study gap should cause recall to first increase and then
decrease.
3. As RI increases, the optimal gap should increase, as shown by the direction of the red ridgeline.
4. As RI increases, the ratio of optimal gap to RI should decline.
The surface in Figure 4 is an instance of the following general form:
recall = A(bt + 1)^-R,
A: immediate recall performance (i.e., when test delay (t) is 0). R: the rate of forgetting. b: a temporal
scaling parameter. Initial recall performance (A) varies with gap (g) according to the function:
A = p + (1 – p)e^ag,
p and a: parameters. This function ensures that an increase in gap causes immediate recall
performance to decline from perfection (when g = 0) to an asymptote equal to p. The rate of
forgetting (R) also varies with gap, according to the function:
Part 3
Cepeda, N.J., Vul, E., Rohrer, D., Wixted, J.T., & Pashler, H. (2008). Spacing effects in learning: A
temporal ridgeline of optimal retention.
To achieve enduring retention, people must study information on multiple occasions. How does the
timing of study events affect retention? Study aimed at characterizing spacing effects over significant
durations.
1,354 individuals were taught a set of facts and given a review after ≤3.5 months. A final test at a
further delay of ≤1 year. At any given test delay, an increase in the interstudy gap at first increased,
and then gradually reduced, final test performance. The optimal gap increased as test delay
increased. However, when measured as a proportion of test delay, the optimal gap declined from
about 20 to 40% of a 1-week test delay to about 5 to 10% of a 1-year test delay. Interaction of gap
and test delay: many educational practices are highly inefficient.
Very large and nonmonotonic spacing effects that unfold over very long periods of time, when study
time is equated across conditions. Retention surface: final test performance plotted as a function of
study gap and RI:
Fig. 4. A functional approximation of recall on the final test (as a proportion), plotted as a function of gap and test delay (retention
interval). The red ridgeline comprises the points representing the optimal performance for each test delay. The forgetting function for each
gap is a power function. The location of the ridgeline indicates that as test delay increases, the optimal gap increases, and the ratio of
optimal gap to test delay decreases.
1. For any gap duration, recall performance must decline as a function of RI (test delay) in a
negatively accelerated fashion in order to produce the familiar forgetting curve consistent with >100
years of memory findings.
2. For any RI greater than zero, an increase in study gap should cause recall to first increase and then
decrease.
3. As RI increases, the optimal gap should increase, as shown by the direction of the red ridgeline.
4. As RI increases, the ratio of optimal gap to RI should decline.
The surface in Figure 4 is an instance of the following general form:
recall = A(bt + 1)^-R,
A: immediate recall performance (i.e., when test delay (t) is 0). R: the rate of forgetting. b: a temporal
scaling parameter. Initial recall performance (A) varies with gap (g) according to the function:
A = p + (1 – p)e^ag,
p and a: parameters. This function ensures that an increase in gap causes immediate recall
performance to decline from perfection (when g = 0) to an asymptote equal to p. The rate of
forgetting (R) also varies with gap, according to the function:
