What contracting, equal, and expanding schedules actually look like
Imagine you have four study sessions to learn a set of facts. In an equal schedule, you space them evenly—say, one session every three days. In a contracting schedule, the gaps shrink: you might study on day 1, day 4, day 6, and day 7, so the sessions bunch up toward the end. In an expanding schedule, the gaps grow: day 1, day 2, day 4, day 7, with each break longer than the last. These three patterns are the main ways researchers have tested how to distribute a fixed number of learning sessions over time [1].
The question is whether one of these patterns is universally best, or whether the answer depends on how long you need to remember the material afterward—what researchers call the retention interval. That is the interval between the last study session and the test.
Why the retention interval changes which schedule wins
The evidence points to a trade-off. A contracting schedule helped retention when the test came relatively soon after learning [1]. One way to think about it: bunching sessions near the end gives the material a fresh, recent boost, which pays off when you need it shortly afterward. An expanding schedule, by contrast, was better when the test was far away—35 days later in this comparison [1]. Spreading sessions further apart early on may build a more durable memory that holds up over a longer delay.
Computational models of memory make this same point from a different angle. When researchers compared models of how memory strength changes over time, the models made robust but opposing predictions about the optimal spacing of study sessions [4]. In other words, the mathematics of forgetting itself implies that the best schedule is not fixed—it depends on the retention interval you are optimizing for.
When the schedule pattern may matter less than the number of sessions
Not every study finds that the pattern of spacing is the decisive factor. In one experiment on declarative knowledge, participants practiced items across multiple sessions with the number of repetitions increasing, decreasing, or staying constant. Retention depended strongly on the total number of sessions in which an item appeared, but not on how the repetitions were distributed among those sessions [2]. That result is consistent with a computational model of skill acquisition and retention, and it suggests that for some kinds of learning, getting more separate sessions matters more than whether those sessions contract, expand, or stay equal [2].
This does not contradict the finding that schedule type matters for retention interval. It sharpens the question: the contracting-versus-expanding difference showed up when researchers deliberately varied the retention interval [1], whereas the session-count study did not examine how retention interval changes the optimal distribution [2]. So the two results can both be true—schedule pattern may matter most when you are tuning for a particular delay, while total session count may dominate otherwise.
What this means for learning something practical, like vocabulary
In second-language vocabulary learning, a meta-analysis of 48 experiments found that longer spacing was no better than shorter spacing on an immediate test but was more effective on a delayed test [3]. That fits the broader pattern: the benefit of more spread-out practice shows up when retention is tested later. The same meta-analysis found that equal and expanding spacing were statistically equivalent for vocabulary learning [3], which is a useful caution—the contracting-versus-expanding distinction that appeared in the retention-interval study [1] may not always translate into a measurable difference for every kind of material.
The meta-analysis also found that the size of the spacing effect varied with the retention interval, among other factors [3]. So the practical takeaway is not a single universal schedule. If you need the material soon, a schedule that concentrates sessions closer to the test—contracting—has support [1]. If you need it weeks later, spreading sessions out—expanding—has support [1]. And for some materials, simply arranging more separate sessions may matter more than the exact shape of the gaps [2].
Sources used in this answer
Contracting, equal, and expanding learning schedules: The optimal distribution of learning sessions depends on retention interval
A contracting learning schedule was beneficial for shorter retention intervals, while expanding schedules were better for a long retention interval of 35 days, showing the optimal schedule depends on retention interval.
Enhancing learning and retention through the distribution of practice repetitions across multiple sessions
Retention of declarative knowledge depended strongly on the total number of sessions in which an item appeared, but not on whether practice repetitions increased, decreased, or remained constant across sessions; the study did not examine how retention interval affects the optimal distribution.
Spaced Practice and Second Language Vocabulary Learning
In second-language vocabulary learning, longer spacing was as effective as shorter spacing on immediate posttests but more effective on delayed posttests, equal and expanding spacing were statistically equivalent, and variability in effect size was explained partly by retention interval.
Optimizing memory retention with cognitive models
Computational models of memory made robust and opposing predictions about the optimal spacing of study sessions depending on the retention interval.