ArticlePDF Available

The lag effect in secondary school classrooms: Enhancing students’ memory for vocabulary

Authors:

Abstract and Figures

Educators often face serious time constraints that impede multiple repetition lessons on the same material. Thus, it would be useful to know when to schedule a single repetition unit to maximize memory performance. Laboratory studies revealed that the length of the retention interval (i.e., the time between the last learning session and the final memory test) dictates the optimal lag between two learning sessions. The present study tests the generalizability of this finding to vocabulary learning in secondary school. Sixth-graders were retaught English–German vocabulary after lags of 0, 1, or 10 days and tested 7 or 35 days later. In line with our predictions, we found that the optimal lag depends on the retention interval: Given a 7-day retention interval, students performed best when relearning occurred after 1 day. When vocabulary was tested after 35 days, however, students benefited from lags of both 1 and 10 days. Model-based analyses show that enhanced encoding processes and stronger resistance to forgetting—but not better retrieval processes—underlie the benefits of optimal lag. Our findings have practical implications for classroom instruction and suggest that review units should be planned carefully by taking the time of the final test into consideration.
Content may be subject to copyright.
The Lag Effect in Secondary School Classrooms1
Running head: THE LAG EFFECT IN SECONDARY SCHOOL CLASSROOMS
The Lag Effect in Secondary School Classrooms: Enhancing Students’ Memory for
Vocabulary
Carolina E. Küpper-Tetzel, Edgar Erdfelder, and Oliver Dickhäuser
Department of Psychology
School of Social Sciences
University of Mannheim
68131 Mannheim, Germany
Email: kuepper-tetzel@psychologie.uni-mannheim.de
Email: erdfelder@psychologie.uni-mannheim.de
Email: oliver.dickhaeuser@uni-mannheim.de
Corresponding author’s address:
Carolina E. Küpper-Tetzel
Department of Psychology
School of Social Sciences
University of Mannheim
Schloss, Ehrenhof Ost
68131 Mannheim, Germany
Phone: +49-621-181 2145
Fax: +49-621-181 3997
Email: kuepper-tetzel@psychologie.uni-mannheim.de
PublishedinInstructionalScience:
http://link.springer.com/article/10.1007/s1125101392852
The Lag Effect in Secondary School Classrooms2
Abstract
Educators often face serious time constraints that impede multiple repetition lessons on the
same material. Thus, it would be useful to know when to schedule a single repetition unit to
maximize memory performance. Laboratory studies revealed that the length of the retention
interval (i.e., the time between the last learning session and the final memory test) dictates the
optimal lag between two learning sessions. The present study tests the generalizability of this
finding to vocabulary learning in secondary school. Sixth-graders were retaught English-
German vocabulary after lags of 0, 1, or 10 days and tested 7 or 35 days later. In line with our
predictions, we found that the optimal lag depends on the retention interval: Given a 7-day
retention interval, students performed best when relearning occurred after 1 day. When
vocabulary was tested after 35 days, however, students benefited from lags of both 1 and 10
days. Model-based analyses show that enhanced encoding processes and stronger resistance
to forgetting – but not better retrieval processes – underlie the benefits of optimal lag. Our
findings have practical implications for classroom instruction and suggest that review units
should be planned carefully by taking the time of the final test into consideration.
Keywords: Lag effect; Long-term memory; Secondary school students; Classroom-based
learning; Vocabulary learning
The Lag Effect in Secondary School Classrooms3
The Lag Effect in Secondary School Classrooms: Enhancing Students’ Memory for
Vocabulary
A large part of the knowledge that students acquire in school is quickly forgotten and
cannot be accessed when it is needed later on (Bahrick & Hall, 1991). How can teachers
address this problem? Researchers in cognitive psychology have revealed efficient learning
methods that improve retention of previously learned information (Pashler, Rohrer, Cepeda,
& Carpenter, 2007). For example, laboratory studies have demonstrated that long-term
retention of a wide range of to-be-learned materials can be enhanced when multiple
restudying units are not massed together, but rather distributed over time (e.g., mathematics
learning: Rohrer & Taylor, 2007; text passages: Rawson & Kintsch, 2005; vocabulary pairs:
Kornell, 2009). This phenomenon is called the spacing effect (i.e., massed1 versus spaced
practice). It has also been established that long-term memory benefits more from multiple
relearning units that are separated by long lags instead of short lags (e.g., vocabulary pairs:
Bahrick, Bahrick, Bahrick, & Bahrick, 1993; Bahrick & Hall, 2005). This is referred to as the
lag effect (i.e., differences in effectiveness of nonzero lags, e.g., 1-day lag compared to a 10-
day lag). Although the lag effect is related to the spacing effect, it has been argued that it is
important to distinguish between them (see Cepeda, Pashler, Vul, Wixted, and Rohrer, 2006;
Delaney, Verkoeijen, & Spirgel, 2010).
Optimal distribution of practice is not only easily implemented, but also produces
remarkable effects on learning outcomes. In his comprehensive synthesis of meta-analyses,
Hattie (2009) reported that spaced rather than massed learning clearly enhanced students’
learning (Cohen’s d = 0.71). Moreover, a recent experimental study by Küpper-Tetzel and
Erdfelder (2012) revealed large effect sizes for the difference between massed and optimally
distributed learning sessions in cued recall (Cohen’s d 1.13) and also for the difference

1 Massed practice means that the entire study time is crammed into one single learning session and the same
material is repeatedly studied over and over (i.e., studying the same material for 4 hours on Tuesday). Spaced
practice allocates the same study time to different learning sessions which, for example, take place on different
days (i.e., studying 2 hours on Monday and 2 hours on Tuesday).
The Lag Effect in Secondary School Classrooms4
between non-optimal and optimal distributions of learning sessions in cued recall (Cohen’s d
0.66). Thus, the systematic distribution of learning and relearning sessions bears the
potential to provide an extremely helpful and effective instruction method in the school
context. Küpper-Tetzel and Erdfelder (2012) demonstrated that participants’ long-term
memory performance on delayed cued recall tests (e.g., after one week or one month) is
increased by up to 89% when learning and relearning sessions are optimally distributed
across time instead of condensed into a single learning episode and by up to 29% when
learning sessions are separated by optimal lags compared to lags that are non-optimal.
How can we explain these effects? Why does memory performance improve after
optimal lags compared to non-optimal or zero lags between learning sessions? Three types of
explanations have been suggested that differ in regard to the underlying memory processes.
First, there are explanations that attribute the lag effect to enhanced encoding processes
during relearning (e.g., the study-phase retrieval theory, cf. Thios & D‘Agostino, 1976).
Then, there are explanations that propose improved maintenance processes to the time of
testing to be responsible for the lag effect. In other words, repeating the to-be-learned
material after an optimal lag is assumed to establish memory traces that are more resistant
against forgetting (e.g., the Multiscale Context Model, cf. Mozer, Pashler, Cepeda, Lindsey,
& Vul, 2009). And, lastly, there are explanations assuming that a repetition of the to-be-
learned material after adequate lags leads to better retrieval processes at test (e.g., the
contextual variability theory, cf. Glenberg, 1979). Recently, Küpper-Tetzel and Erdfelder
(2012) used Multinomial Processing Tree (MPT) modeling (Batchelder & Riefer, 1999;
Erdfelder et al., 2009) to disentangle encoding, maintenance, and retrieval contributions to
the lag effect. Their findings point to the conclusion that the lag effect is largely driven by
encoding and maintenance processes: Whereas encoding benefits from relative short (but
nonzero) lags, maintenance in memory benefits from long lags, the more so the longer the
The Lag Effect in Secondary School Classrooms5
retention interval (i.e., the time between the last learning session and the final test). In
contrast, retrieval processes seem to play only a minor role for understanding the lag effect.
The generalizability of the spacing effect to authentic learning settings has been tested
in a few applied studies. Bloom and Shuell (1981), for example, had high-school students
learn French vocabulary in a massed (30-minute unit on a single day) or a spaced fashion (10-
minute units on three consecutive days) during their regular French class. In line with
laboratory findings, students with spaced learning outperformed students with massed
learning on a test administered four days later. Other field studies demonstrated beneficial
spacing effects in preschoolers for enhancing reading ability (Seabrook, Brown, & Solity,
2005) and for promoting the acquisition of complex sentence construction (Ambridge,
Theakston, Lieven, & Tomasello, 2006).
Thus, laboratory and field studies alike suggest to use multiple repetition units and to
distribute them over time to boost long-term retention. However, teachers, who must
accomplish comprehensive curricula, often face serious time constraints that impedes
multiple repetition sessions of previously taught material. Thus, if school curricula allow only
for a small number of repetition units, for example, for one repetition session only, the
optimal timing of this unit is of major interest. Thus, the main interest is not in comparing
massed versus spaced learning, but rather to compare lags of different lengths (i.e., the lag
effect). The question is: How much time should elapse between initial teaching of the to-be-
learned material and the repetition of this material in order to enhance memory performance
in the long run?
Recent laboratory and web-based studies suggest that the answer to this question is
complex (Cepeda et al., 2009; Cepeda, Vul, Rohrer, Wixted, & Pashler, 2008). In the study of
Cepeda et al. (2009) undergraduate university students studied Swahili-English vocabulary
during an initial learning session and restudied the vocabulary after lags of 0, 1, 2, 4, 7, or 14
days. All participants were tested 10 days after the restudy session. They found that memory
The Lag Effect in Secondary School Classrooms6
performance on the final test was best when the lag between initial study and restudy session
was 1 day. For lags shorter or longer than 1 day, correct vocabulary retention was decreased
10 days after practice. Thus, the appropriate timing of a repetition unit matters.
Moreover, Cepeda et al. (2008) and Cepeda et al. (2009) examined whether the
optimal lag between two learning episodes changes as a function of the retention interval.
Again, several lags were used and memory performance was assessed 168 days (Cepeda et
al., 2009) or up to 350 days (Cepeda et al., 2008) following the end of the practice phase. To
avoid floor effects due to massive forgetting during these long intervals, they used more
meaningful study material than vocabulary in these experiments (i.e., largely unknown but
true trivia facts). They found that the optimal time for relearning depends on the length of the
retention interval. More precisely, for any given retention interval, memory performance
follows an inverted-U-shaped function by first increasing with lag until reaching an optimal
lag and then decreasing again. The optimal lag is dictated by the length of the retention
interval and increases with longer retention intervals: For retention after 7 days the optimal
lag was 1 day, for retention after 35 days the optimal time for relearning was 11 days, and for
retention after a long retention interval of 350 days the optimal lag was 21 days. Furthermore,
Cepeda et al. (2008) showed that the ratio of optimal lag to retention interval length decreases
with longer retention intervals. The results of Küpper-Tetzel and Erdfelder (2012) provide
converging evidence for these lag effect trends.
These findings may have important implications for classroom instruction because
they emphasize the appropriate scheduling of a repetition unit and reveal that a lag which is
either too short or too long may have detrimental effects on retention of the to-be-learned
material across a pre-defined retention interval. In addition to classroom instruction, the
results might also be important for students’ self-regulated learning as during phases of self-
regulation, students can schedule the point of time for repetition units on their own.
The Lag Effect in Secondary School Classrooms7
A recent study by Bird (2010) investigated the interaction between specific lags (3-
vs. 14-day lag) and retention intervals (7- vs. 60-day retention interval) in a classroom setting
for second language syntax learning in university students. He found that memory
performance 60 days after practice benefited more from a 14-day lag than from a 3-day lag
between learning sessions. After a 7-day test interval no difference was detected between the
two lag conditions that he examined. The latter finding is not surprising. Previous studies
have repeatedly shown that people will perform best on a final memory test administered one
week later if they relearn the material one day after initial learning – not earlier or later (see
Ausubel, 1966; Glenberg & Lehmann, 1980; Cepeda et al., 2008; Küpper-Tetzel & Erdfelder,
2012). The interesting aspect of Bird’s study is, however, that he evaluated the lag effect in
an ecologically more valid learning environment by having participants study meaningful
content in a classroom setting rather than in a laboratory. But, as all studies did so far, Bird
investigated the lag effect in the standard population that is usually used in laboratory studies,
namely, university students.
For at least two reasons, it is important to examine the lag effect dynamics also in
younger student populations, especially in young secondary school students. First and most
importantly, it is unknown yet whether the results previously obtained with university
students and adults generalize to younger students in the school context. Second, if teachers
can rely on long-term maintenance of previously taught material in students, they can avoid
unplanned and costly review sessions, when instead new and advanced material is scheduled.
This promotes the effective use of classroom instruction time.
Thus, secondary school instruction and learning may benefit from research-based
optimization techniques of learning across time if and only if it can be demonstrated that
previous laboratory findings also hold for secondary school classroom learning. There is one
study that has investigated the spacing effect with two learning sessions in secondary school
classrooms. In Sobel, Cepeda, and Kapler (2011), students learned GRE vocabulary during
The Lag Effect in Secondary School Classrooms8
two learning sessions that were either massed in time or separated by a lag of 7 days. Five
weeks later, students performed better on vocabulary that had been practiced in a spaced
fashion than on vocabulary that had been practiced in a massed fashion. However, to date, no
study has examined the effect of lags of different lengths between two learning sessions in a
secondary school classroom setting when authentic school material is used. Therefore, the
goal of our study was to examine the lag effect in secondary school vocabulary learning and,
particularly, to test whether the interaction between lag and retention interval as revealed in
previous experimental studies (Cepeda et al., 2008; Cepeda et al., 2009) generalizes to real-
world educational settings2 and materials. In accordance with Ulrich Neisser’s advice we
aimed at investigating “cognition as it occurs in the ordinary environment and in the context
of natural purposeful activity” (Neisser, 1976, p. 7, own emphasis). Thus, we implemented
the lag effect intervention into the classroom during the regular lessons and, most
importantly, used material that was meaningful for the students. In most laboratory studies,
the material that participants learn has no further implications for their future academic
performance. This might foster contextual influences such as lag effects on memory
performance. Therefore, it is possible that the lag effects are attenuated when meaningful
material is learned in an authentic setting in which regular assessments of students’
performance impacts their future. Students may adopt strategies that lead to deeper and better
encoding of the material which, in turn, diminishes the effect of distributed learning. Hence,
it is not certain at all that the lag effect trends – as found in the laboratory – generalize to such
authentic educational environments when material is learned that has immediate and future
relevance for the population under investigation.

2Note that the research on the lag effect should be distinguished from a line of work that focuses on the benefits
of blocked versus nonblocked teaching. In the latter line of research, different pieces of information are
presented either within a single large session or allocated to multiple, but shorter sessions (Randler, Kranich, &
Eisele, 2008; Lawrence & McPherson, 2000). In the current paper, in contrast, we investigate after which lag
newly learned information should be repeated given that the goal is to retrieve this information after a pre-
defined retention interval without further study.
The Lag Effect in Secondary School Classrooms9
To test the benefits and limitations of the lag effect, we conducted a field experiment
in an authentic secondary school classroom setting and had German sixth graders practice
and re-practice new German-English vocabulary from advanced chapters of their textbook in
two learning sessions separated by a 0-day (massed), 1-day, or 10-day3 lag. Students were
tested either 7 or 35 days later on their memory performance for the vocabulary pairs. Based
on previous empirical findings (Cepeda et al., 2008; Küpper-Tetzel & Erdfelder, 2012), we
expected that students who were tested 7 days after the last learning session would show
better vocabulary recall when their two learning sessions were separated by a 1-day lag than
when the two learning sessions were separated by a 0- or 10-day lag. Hence, we assumed that
memory performance would follow an inverted-U-shaped trend with increasing lag in the 7-
day retention interval group. In contrast, after a 35-day retention interval, we predicted better
memory for vocabulary when the second learning session occurs after a lag longer than 1 day,
resulting in a trend that increases beyond a lag of 1 day and perhaps up to a lag of 10 days.
Students’ final memory performance for vocabulary was assessed with a cued recall test.
In addition to memory performance data, we also analyzed the memory processes
underlying these data using Küpper-Tetzel and Erdfelder’s (2012) MPT model to test for
converging evidence in regard to the importance of encoding and maintenance processes for
the lag effect. In order to run these model-based analyses we assessed students’ memory
performance with a free recall test that was administered right before the cued recall test.
Method
Participants
A total of 76 sixth-graders from a secondary school participated in the study. Data
from eight students had to be excluded from all analyses because they did not attend all

3 To revisit, Cepeda et al.’s (2008) findings suggest that the optimal lag for a test administered 35 days after
practice is 11 days. However, due to the predetermined school schedule, it was not possible to realize a
relearning session 11 days after the initial learning session. Therefore, the longest lag was 10 days instead.
The Lag Effect in Secondary School Classrooms10
learning sessions or failed to appear on the test session. Data from one student who was
diagnosed with dyslexia was dropped because the test scores were based on correctly written
words only. Due to experimenter error, cued recall data were not collected from one student
on the final test session. Finally, data from one participant were not included in the analyses
because she failed to follow the testing instructions. These exclusions led to 65 students4.
They were on average 11.45 years old (range, 11-13 years). Of all students, 50.8% were
male. Students came from three classrooms.
Materials
Since the study was conducted during the regular English lessons and the to-be-
learned material should be relevant to the students, 26 German-English vocabulary pairs were
selected from advanced units of the English exercise book. All words were concrete nouns
(see Appendix).
Design
We realized two learning sessions separated by a 0-, 1-, or 10-day lag and one test
session occurring after a retention interval of 7 or 35 days. This resulted in a 3 x 2 between-
subjects design. As it is often the case in applied studies, individual students could not be
randomly assigned to the different lag conditions (e.g., Seabrook et al., 2005; Randler et al.,
2008). We had to respect the classroom structure because the study was realized during their
regular English lessons. Thus, a whole classroom was assigned to a lag condition by taking
into consideration their school schedule. This resulted in 27 students in the 0-day lag group,
22 students in the 1-day lag group, and 16 students in the 10-day lag group. However, the

4 Three of the excluded participants were in the 10_7 condition (i.e., 10 days lag and 7 days retention interval),
three were in the 0_35 condition, three were in the 10_35 condition, and two were in the 1_35 condition. We ran
analyses on 7 out of the 11 excluded students for which we collected valid cued recall performance at the end of
the first learning session. We compared their mean in cued recall at the end of the first learning session (M =
18.14) to the mean of the students that were used in the final analyses (M = 19.05). There was no systematic
difference in regard to their initial memory performance, t(70) = -0.43, p = .672.
The Lag Effect in Secondary School Classrooms11
retention interval was experimentally manipulated within each classroom by randomly
assigning one half of the students to the 7-day condition (n = 35 across the three lag
conditions) and the other half to the 35-day condition (n = 30 across the three lag conditions).
Procedure
The study consisted of two learning sessions and one final test session. All sessions
were run as group sessions.
Learning sessions
The first learning session encompassed two study-test trials and lasted 45-60 minutes.
The second learning session took place after the respective lag and consisted of one study-test
trial which lasted 25-30 minutes. A study-test trial involved the presentation of the German-
English vocabulary, a recognition test, a cued recall test, and a picture quiz.
During vocabulary presentation, 26 German-English vocabulary were presented on
the front wall of the classroom with a portable LCD projector. Students were instructed to
pay attention to each word pair and to watch out for the orthography of the English words in
particular. They were not allowed to take notes or rehearse vocabulary aloud. The
presentation started after ensuring that the students understood the instructions. A German
word appeared for two seconds alone on the left side of the projection. The experimenter read
out the German word. Then, the English translation appeared on the right side and the
experimenter read out the English word. Both words of a vocabulary pair were displayed for
eight seconds. Word pairs were presented in a different random order for each vocabulary
presentation.
After vocabulary presentation, students worked for five minutes on a paper-pencil
three alternative forced choice recognition test. The test consisted of 26 rows and each row
contained a target word (English vocabulary) from the presentation and two distractors. The
distractors were English words that featured a high orthographical similarity to the English
The Lag Effect in Secondary School Classrooms12
target (see Appendix). Students were instructed to circle the target word. The order of the
rows and the words within each row were printed in a random order on each recognition test.
To prevent cheating, four parallel versions of the recognition test were used that differed with
regard to the random order of rows and words. Upon completion students were asked to turn
the recognition test sheet over and the paper-pencil cued recall test was handed out to them.
On the cued recall test, all German words were printed in random order one below the
other. The students were allotted five minutes to recall and write the English translation next
to each German word. Again, four parallel versions of the cued recall test were used that
differed regarding the random order of German words. After all students had turned the cued
recall sheet over, the picture quiz started.
The picture quiz was used as a feedback tool. Since it was not possible to give
individual feedback on the recognition and cued recall tests because of the group setting, the
picture quiz represented a good way to provide feedback. In addition, its interactive format
motivated the students, which enhanced their compliance to the study. For the picture quiz,
actual pictures of each target word were projected on the wall along with three English
words. One of the words was the target word that correctly identified the depicted picture.
The other two words were distractor words that were orthographically similar to the target
word. All distractor words were new and had not been shown before. On each trial, students
saw a picture and three words that were labeled with a red, a blue, and a yellow dot,
respectively. Each student had a red, a blue, and a yellow card. They were instructed to
indicate the target word that correctly described the picture by holding up the card with the
respective color. Afterwards, the correct target word was revealed to them. The assignment
from color to word and the order of the pictures were randomized for each picture quiz. The
picture quiz took 5-8 minutes.
The Lag Effect in Secondary School Classrooms13
Test session
The test session occurred either 7 or 35 days after the last learning session. Students
were instructed that the German-English vocabulary would not be presented to them and that
they had to retrieve the vocabulary from memory instead. The test session involved a free
recall test of German-English word pairs immediately followed by a cued recall test. For the
free recall test, students were instructed to recall as many vocabulary pairs as they could.
They were told that this was a hard task and were encouraged to write down all words they
could remember from the learning phase, even if they could only remember single words, that
is, only the German or English word of a vocabulary pair. They were allotted 5 minutes for
the free recall test. The subsequent final cued recall test was identical to the one students
received during their learning sessions except that the German words were printed in a
different random order. After completion of the test session, the students were thanked for
their help and informed that they would receive feedback on their test performance once all
tests were checked. All students received a study booklet that contained not only their test
scores, but also concrete suggestions on how to distribute their learning in order to improve
long-term retention.
Results
In analyzing the memory performance data, we focus on the cued recall performance
in the final vocabulary test as this is the practically relevant dependent variable in applied
contexts and in educational settings in particular. In addition, free recall performances will
become important in our additional data analyses in the framework of the MPT model that
allows us to disentangle the contributions of encoding, maintenance, and retrieval processes
to overall memory performance (Küpper-Tetzel & Erdfelder, 2012).
As mentioned before, the school setting did not allow the random assignment of
individual students to lag conditions. In fact, a whole classroom was assigned to a specific
The Lag Effect in Secondary School Classrooms14
lag. In order to rule out classroom-dependent factors, we controlled statistically for these
factors (see also Randler et al., 2008). We argue that students from the three classrooms
should not differ in their memory performance at the end of the first learning session. Any
difference in memory at this point of the study must be due to classroom-dependent factors
rather than the lag manipulation because lag was initiated only after the first learning session.
Possible factors that could have varied between classrooms and influenced memory
performance at the end of the first learning session are, for example, learning ability or
learning motivation. To control for these possible classroom-dependent effects, we used the
cued recall performance assessed at the end of the first learning session as an additional
predictor (i.e., covariate) in all analyses. An α-level of .05 was assumed for all analyses. All p
values reported below refer to two-tailed tests, even in case of directed predictions.
Final cued recall performance
Averaged across lag conditions, students recalled more vocabulary after a 7-day
retention interval (M = 71%, SD = 21%) than after a 35-day retention interval (M = 51%, SD
= 18%), t(62) = -6.12, p < .001,
2 = 0.38. Of greatest interest, however, were the different
memory functions resulting from increasing lags in the 7-day and 35-day retention interval
condition, respectively. To revisit, we expected that, in the 7-day retention interval group,
memory performance would follow an inverted-U-shaped trend with lags increasing from 0
to 10 days, that is, producing a peak at a 1-day lag. In contrast, given a long retention
interval of 35 days we predicted an increasing trend with lag instead. The percentage of
correctly recalled vocabulary on the final cued recall test is presented in Figure 1. In the 7-
day retention interval condition a significant negative quadratic trend emerged, t(58) = 2.32, p
= .024,
2 = 0.08. The linear trend was not significant, t(58) = 0.39, p = .702,
2 < 0.01. In
the 35-day retention interval condition, the reverse finding occurred. Here, a significant
positive linear trend was detected, t(58) = 2.00, p = .05,
2 = 0.06, but the negative quadratic
The Lag Effect in Secondary School Classrooms15
was not significant, t(58) = 0.04, p = .970,
2 < 0.01. Thus, as expected, we find that memory
for foreign vocabulary tested 7 days after practice is severely impaired if the lag is shorter
(massed) or longer (i.e., 10 days) than 1 day. The significant negative quadratic trend clearly
shows that a 1-day lag is optimal given a 7-day retention interval. In contrast, we find a
significant linear trend with increasing lag in the 35-day retention interval condition and no
significant negative quadratic trend. This means that given a 35-day retention interval
memory performance benefits from lags of 1 day and longer.
Multinomial Processing Tree analyses
Previous studies have used the combination of a test that depends heavily on retrieval
processes (e.g., free recall) and a test that depends less on retrieval processes (e.g., cued
recall) to separate the contributions of storage and retrieval processes to a memory
phenomenon (see, e.g., Hogan & Kintsch, 1971; Thomson & Tulving, 1970). Following this
approach, we also applied a free recall test in addition to the final cued recall test to
disentangle contributions of encoding, maintenance, and retrieval processes to memory
0
10
20
30
40
50
60
70
80
90
100
0 days 1 day 10 days
Percent correct final cued recall
Lag
7 days retention interval 35 days retention interval
Figure 1. Mean and standard errors of correctly recalled vocabulary on the final cued
recall test as a function of lag and retention interval.
The Lag Effect in Secondary School Classrooms16
performance. To measure these three types of processes, we used the Encoding-Maintenance-
Retrieval multinomial model for free-then-cued-recall recently proposed by Küpper-Tetzel
and Erdfelder (2012). This model uses performance data at different points in time (i.e.,
during practice and during the final test session) and from different tests (i.e., free and cued
recall) to estimate seven parameters representing underlying memory processes: one
probability of associative encoding (e), two probabilities of associative maintenance in
memory until the final test (ms and mu for maintenance following successful vs. unsuccessful
cued recall during practice, respectively), two probabilities of successful retrieval in free and
cued recall (rf and rc, respectively), and two probabilities of single word retrieval in free
recall in case of successful vs. unsuccessful associative encoding or maintenance (s and u,
respectively). For a detailed model description we would like to refer to Küpper-Tetzel and
Erdfelder (2012) since a full exposition goes beyond the scope of this work.
The multiTree software (Moshagen, 2010) was used for all MPT model analyses. The
Type I error level was set to α = .05 for all model-based analyses. A sensitivity analysis was
performed using G*Power 3.1 (Faul, Erdfelder, Buchner, & Lang, 2009). This analysis
showed that with N = 1,419 data points, a significance level of α = .05, and a desired power
of 1-β = .95, the detectable effect size for G2 goodness-of-fit tests based on df 35 is ω
0.16 (i.e., a small effect; cf. Cohen, 1988). Thus, all G2 model tests reported below allowed
detecting already small deviations from the model.
Following Küpper-Tetzel and Erdfelder (2012), we restricted the free-then-cued-recall
MPT model to obtain a parsimonious specification with only one maintenance parameter m.
This was achieved by setting the maintenance probabilities ms (maintenance after successful
cued recall at the end of practice) and mu (maintenance after unsuccessful cued recall at the
end of practice) equal in each condition. This model version fit the data (G2(30) = 41.16, p =
.084). Furthermore, we tested the additional restriction that the probability of associative
retrieval in cued recall, rc, is equal across experimental conditions. Indeed, the G2 difference
The Lag Effect in Secondary School Classrooms17
test was not significant, G2(5) = 4.11, p = .534, with rc being estimated to .96. Thus, our
model-based findings are based on this restricted model version. The overall goodness-of-fit
test indicates a good fit to the data (G2(35) = 45.27, p = .115).
Of greatest interest for the evaluation of the theories are the probability estimates for
associative encoding e, associative maintenance m, and associative retrieval rf. Maximum
likelihood estimates and standard errors for these three parameters are summarized in Figure
2. As shown in Figure 2A, the associative encoding parameter e followed an inverted-U-
shaped trend with increasing lag in the 7-day retention interval condition. More precisely,
associative encoding increased significantly between the 0-day and the 1-day lag condition,
ΔG2(1) = 21.94, p < .001, and decreased between the 1-day lag and the 10-day lag condition,
ΔG2(1) = 24.18, p < .001. In the 35-day retention interval condition, we found descriptively
the same inverted-U-shaped trend with increasing lag. However, the only significant effect
was the decrease in associative encoding between the 1-day and the 10-day lag condition,
ΔG2(1) = 4.67, p = .031. The increase between the 0-day and the 1-day lag condition did not
reach significance, ΔG2(1) = 1.27, p = .260.
As illustrated in Figure 2B, the parameter for associative maintenance m was affected
differently by the length of the retention interval. In the 7-day retention interval condition,
associative maintenance increased between the 0-day lag and the 1-day lag, ΔG2(1) = 26.66,
p < .001, and decreased again between the 1-day and 10-day lag condition, ΔG2(1) = 12.50, p
< .001. There was no difference in associative maintenance between the 0-day and the 10-day
lag, ΔG2(1) = 0.73, p = .392. In the 35-day retention interval condition, associative
maintenance increased significantly between both the 0-day lag and the 1-day lag, ΔG2(1) =
13.21, p < .001, and between the 0-day and the 10-day lag, ΔG2(1) = 13.75, p < .001. We
detected no difference between the two spaced conditions for associative maintenance,
ΔG2(1) = 0.15, p = .700.
The Lag Effect in Secondary School Classrooms18
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0days 1day 10days
Probability estimate for
associative encoding e
InterstudyInterval
7 days retention interval 35 days retention interval
a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0days 1day 10days
Probability estimate for
associative maintenance m
InterstudyInterval
b
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 days 1 day 10 days
Probability estimate for
associative retrieval rf
Lag
c
Figure 2. Parameter estimates and standard errors for the probability of associative encoding e
(2a), for the probability of associative maintenance m (2b), and for the probability of associative
retrieval rf (2c) as a function of lag and retention interval.
The Lag Effect in Secondary School Classrooms19
Results for associative retrieval rf during free recall are displayed in Figure 2C. Retrieval was
equal across all lag conditions in the 7-day retention interval condition, ΔG2(2) = 0.11, p =
.949. In the 35-day retention interval condition, we detected a significant decrease in
associative retrieval between the 0-day and 10-day lag condition, ΔG2(1) = 9.23, p = .002, as
well as the 1-day and 10-day lag condition, ΔG2(1) = 7.57, p = .006.
Discussion
The current field experiment examined the effect of different lags between two
learning sessions on memory performance for foreign language vocabulary in sixth graders
after 7 and 35 days. The findings are in line with our predictions.
In essence, students’ memory for German-English vocabulary that was assessed one
week after practice benefited most from a 1-day lag between initial study session and restudy
session. In line with the predictions, lags of shorter (massed practice) or longer (10-day lag)
length led to lower students’ performance. However, when vocabulary memory was
measured about one month after practice, students were best off in the two distributed
practice conditions (i.e., 1-day and 10-day lag). Thus, we conclude that the optimal lag for
reviewing vocabulary that is tested after 35 days is located beyond a 1-day lag, with a 10-day
lag leading to comparable benefits for memory performance. At first this seems to be at odds
with the findings of Cepeda et al. (2008) who revealed a significant increase between a 0-day
up to an 11-day lag in the 35-day retention interval group. However, it is important to keep
the sample in mind. Whereas Cepeda et al.’s (2008) sample consisted of adults only; we
investigated young students explicitly in our field experiment. It makes sense to assume that
the optimal time for relearning depends not only on the length of the retention interval, but in
part also on learner characteristics (e.g., working memory skills (Gathercole, Pickering,
Ambridge, & Wearing, 2004; Gatherhole, Lamont, & Alloway, 2006) or forgetting rates
(Brainerd, Reyna, Howe, Kingma, & Guttentag, 1990)). Our findings hint at this possibility.
The Lag Effect in Secondary School Classrooms20
Additional lag effect studies (laboratory and field experiments), however, are needed to
obtain a better understanding of learning in young students. Those studies should use a
broader variation of lag and retention interval to shed light on the systematic dependency of
optimal lag and retention interval for secondary school vocabulary learning.
In order to assess the practical significance of the obtained effects, we calculated
Cohen’s d effect size measures between the massed (lag = 0 days) and the best lag condition
for each retention interval separately. In the 7-day retention interval condition, there was a
35% increase in correct vocabulary recall between the massed and the optimal 1-day lag.
Stated differently, students in the 1-day lag condition remembered on average nine words
more than students in the massed practice condition. This translates to a very large effect size
(Cohen’s d = 1.69). However, increasing the lag to 10 days led to a decline in performance of
34%. This means that students recalled on average nine vocabulary words less in the 10-day
lag condition than in the optimal 1-day lag condition. This results in a large effect size of
Cohen’s d = 2.07. In the 35-day retention interval condition, we found a 28% and 38%
increase in memory performance between the massed and the 10-day and the massed and the
1-day condition, respectively. Students in the two distributed lag conditions recalled on
average 7 to 10 vocabulary words more than students in the massed condition. Again, this
results in large effect sizes (Cohen’s d = 1.41 for the comparison with the 1-day lag group
and Cohen’s d = 0.87 for the comparison with the 10-day lag group).
These are remarkable effects that allow us to make promising suggestions to
educators and learners. Also, as proposed by Dempster (1988), we obtained these effects in a
real-world educational environment by using relevant material and by keeping the classroom
setting as naturalistic as possible by using group learning sessions and the integration of the
field experiment in ongoing lessons. Both points should encourage teachers to implement the
lag effect as instruction method in the classroom. Other applied studies (e.g., Reynolds &
Glaser, 1964; Seabrook et al., 2005; Sobel et al., 2011) have already demonstrated beneficial
The Lag Effect in Secondary School Classrooms21
spacing effects in the classroom. Our field study extends this line of research by investigating
the effect of different lags. We reveal an important boundary condition for classroom
instruction. More precisely, teachers who face time constraints should take the retention
interval into account when planning a repetition unit. Choosing a too long or a too short
interval between study sessions can lead to detrimental effects on memory performance
depending on the length of the retention interval. For example, if a surprise test of new
vocabulary is due one week after the end of the practice phase (i.e., without interim learning),
teachers can boost students’ performance by introducing the vocabulary eight days before the
test and program a repeating unit one day after initial learning. Given the restriction of only
two learning sessions, they should refrain from introducing the new vocabulary at an earlier
point in time, say two and a half weeks before the final assessment, and initiating a repeating
lesson one week before the test. The inverted-U-shaped trend with increasing lag in the 7-day
retention interval condition clearly shows that a further extension of the lag beyond one day
has substantial negative effects on students’ vocabulary memory.
The second aim of the present paper was to examine the underlying memory
processes of these lag effect trends and to test different explanations of lag and spacing
effects. Therefore, we applied the Encoding-Maintenance-Retrieval (EMR) multinomial
processing tree model for lag effect data that has recently been proposed and validated by
Küpper-Tetzel and Erdfelder (2012). We found that the inverted-U-shaped trend in the 7-day
retention interval condition is produced by an increase in encoding and maintenance
processes between the 0-day and the 1-day lag condition and a decrease of these processes for
a lag of 10 days. In contrast, retrieval processes are not affected by different lags in the 7-day
retention interval condition. Furthermore, the linear increasing trend in memory performance
in the 35-day retention interval condition is produced by enhanced maintenance processes
and not by better encoding or retrieval processes. In other words, maintenance processes are
primarily responsible for the differences in memory performance trends with increasing lag
The Lag Effect in Secondary School Classrooms22
between the 7-day and the 35-day retention interval conditions. Better maintenance of the
material to the time of testing explains why performance remains stable in the 35-day
retention interval group and drops in the 7-day retention interval group for a lag beyond 1
day. Thus, the increase of the optimal lag with increasing retention interval is largely due to
stronger resistance to forgetting induced by relearning after long as compared to short lags.
In summary, theories that focus on encoding and maintenance processes in explaining
lag effect trends (i.e., study-phase retrieval theory and Multiscale Context Model) are
corroborated by our findings. Theories emphasizing the role of retrieval processes for the lag
effect (i.e. contextual variability theory), in contrast, are not in line with the EMR model
findings. If anything, there was a decrease rather than the predicted increase in retrieval
probabilities across the different lag conditions. The current findings are similar to those
obtained in the laboratory study by Küpper-Tetzel and Erdfelder (2012) with respect to the
underlying processes.
To conclude, our field study clearly shows that vocabulary learning in secondary
school can benefit from adequate distribution of review units. In line with previous
experiments (Cepeda et al., 2008; Cepeda et al., 2009), we reveal that the optimal lag
increases as a function of retention interval. Given the circumstances under which the field
study was conducted (i.e., heterogeneous student population and group learning sessions),
these robust findings are encouraging and allow us to provide teachers with valid and useful
suggestions. Based on the current findings, we recommend that when only one repeating
lesson is feasible (e.g., due to time constraints), then the timing of the first learning lesson
should be chosen appropriately by taking the desired length of the retention interval into
consideration. This means that shorter lags between first and second learning should be
chosen if the pre-defined retention interval is short and longer lags are appropriate when it is
long.
The Lag Effect in Secondary School Classrooms23
Of course, not only educators can benefit from our findings, but also young students
can be instructed to distribute their learning properly and boost their memory performance.
They have acquired the necessary cognitive resources to understand such learning strategies
and to apply them (e.g., Brehmer, Li, Müller, von Oertzen, & Lindenberger, 2007; Pressley &
Hilden, 2006). In the present study, we created teacher and student booklets to inform
teachers and students about the study findings and their implications. These booklets
contained detailed information on the study and the results, as well as hands-on suggestions
for classroom instruction and self-regulated learning. In addition, our empirical findings and
analyses of the underlying cognitive processes have important implications for the
development of computer-based learning tools. Currently, Mozer and colleagues are
developing a web-based tutor for learning facts or vocabulary. This tool is based on
assumptions of the Multiscale Context Model (Mozer et al., 2009) – which are in agreement
with our findings. The tool prompts students individually as to when to review specific
vocabulary in order to enhance memory performance on a final test at a predetermined time
in the future. Thus, this learning tool incorporates an appropriate theory of human memory
(i.e., Multiscale Context Model) which considers the complex interaction between optimal
lag and retention interval. The overall benefit of this learning tool is currently being
evaluated5.
Our study contributes to applied human learning research in educational contexts.
Similar to Seabrook et al. (2005) or Randler et al. (2008), we were not allowed to assign
students from different classrooms randomly to their lag condition. We are aware of this
limitation which, in the present case, could not be avoided due to the restricted freedom of
scheduling and due to the strict classroom structure that had to be obeyed. To cope with this
problem, we controlled for possible classroom effects statistically. Using this approach, we
revealed robust lag effects in foreign vocabulary learning similar to those found in previous

5For detailed information see
http://www.cs.colorado.edu/~mozer/index.php?dir=/Research/Projects/Optimization%20of%20learning/
The Lag Effect in Secondary School Classrooms24
completely randomized experiments. This enables us to provide teachers with better
recommendations for their classroom instruction. Future studies should follow this line of
classroom-based research and examine whether the lag effect as found for verbal learning
transfers to other educational domains as, for instance, learning in mathematics and physics.
Rohrer and Taylor (2006, 2007) revealed reliable spacing effects for geometry and
permutation problems in the laboratory and Grote (1995) demonstrated beneficial spacing
effects for physics learning in an authentic classroom setting. However, the generalizability
of lag effects and potential interactions with the retention interval has not yet been examined
for mathematics and physics learning. This should be the focus of future studies. In general,
more applied studies in authentic classroom settings are needed since they broaden the
evidence and validity of well-known memory effects for naturalistic learning environments.
Although these studies are extensive and challenging, they promise to have the greatest
impact on everyday educational routines.
Acknowledgements
The authors express their gratitude to the school principal, Mr. Michael Hohenadel, to
the teachers, and the students of the Elisabeth secondary school in Mannheim for making this
study possible. We thank the graduate students of the first author’s service learning seminar,
Dagmar Klein, Martin Knab, Sharmila Pushpakanthan, Sonja Sobott, and Sarah Zelt, for data
collection and four anonymous reviewers for helpful comments on an earlier version of the
manuscript.
The Lag Effect in Secondary School Classrooms25
References
Ambridge, B., Theakston, A. L., Lieven, E. V., & Tomasello, M. (2006). The distributed
learning effect for children‘s acquisition of an abstract syntactic construction. Cognitive
Development, 21, 174–193. doi: 10.1016/j.cogdev.2005.09.003
Ausubel, D. P. (1966). Early versus delayed review in meaningful learning. Psychology in the
Schools, 3, 195-198. doi: 10.1002/1520-6807(196607)3:3<195::AID-
PITS2310030302>3.0.CO;2-X
Bahrick, H. P., & Hall, L. K. (1991). Lifetime maintenance of high school mathematics
content. Journal of Experimental Psychology: General, 120, 20-33. doi: 10.1037/0096-
3445.120.1.20
Bahrick, H. P., & Hall, L. K. (2005). The importance of retrieval failures to long-term
retention: A metacognitive explanation of the spacing effect. Journal of Memory and
Language, 52, 566–577. doi: 10.1016/j.jml.2005.01.012
Bahrick, H. P., Bahrick, L. E., Bahrick, A. S., & Bahrick, P. E. (1993). Maintenance of
foreign language vocabulary and the spacing effect. Psychological Science, 4, 316–321.
doi: 10.1111/j.1467-9280.1993.tb00571.x
Batchelder, W. H., & Riefer, D. M. (1999). Theoretical and empirical review of multinomial
process tree modeling. Psychonomic Bulletin & Review, 6, 57–86. doi:
10.3758/BF03210812
Bird, S. (2010). Effects of distributed practice on the acquisition of second language English
syntax. Applied Psycholinguistics, 31, 635-650. doi: 10.1017/S0142716410000172
Bloom, K. C., & Shuell, T. J. (1981). Effects of massed and distributed practice on the
learning and retention of second-language vocabulary. Journal of Educational Research,
74, 245–248.
The Lag Effect in Secondary School Classrooms26
Brainerd, C. J., Reyna, V. F., Howe, M. L., Kingma, J., & Guttentag, R. E. (1990). The
Development of Forgetting and Reminiscence. Monographs of the Society for Research in
Child Development, 55, 1–109. doi: 10.2307/1166106
Brehmer, Y., Li, S.-C., Müller, V., von Oertzen, T., & Lindenberger, U. (2007). Memory
plasticity across the life span: Uncovering children's latent potential. Developmental
Psychology, 43, 465-478. doi: 10.1037/0012-1649.43.2.465
Cepeda, N. J., Coburn, N., Rohrer, D., Wixted, J. T., Mozer, M. C., & Pashler, H. (2009).
Optimizing distributed practice: Theoretical analysis and practical implications.
Experimental Psychology, 56, 236–246. doi: 10.1027/1618-3169.56.4.236
Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in
verbal recall tasks: A review and quantitativesynthesis. Psychological Bulletin, 132 , 354-
380.
Cepeda, N. J., Vul, E., Rohrer, D., Wixted, J. T., & Pashler, H. (2008). Spacing effects in
learning: A temporal ridgeline of optimal retention. Psychological Science, 19, 1095–
1102. doi: 10.1111/j.1467-9280.2008.02209.x
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2.th ed.). Hillsdale,
NJ: Erlbaum.
Delaney, P. F., Verkoeijen, P. P. J. L., & Spirgel, A. (2010). Spacing and testing effects: A
deeply critical, lengthy, and at times discursive review of the literature. In B. H. Ross
(Ed.), Psychology of Learning and Motivation: The psychology of learning and
motivation: Advances in research and theory (pp. 63–147). Academic Press.
Dempster, F. N. (1988). The spacing effect: A case study in the failure to apply the results of
psychological research. American Psychologist, 43, 627–634. doi: 10.1037/0003-
066X.43.8.627
The Lag Effect in Secondary School Classrooms27
Erdfelder, E., Auer, T.-S., Hilbig, B. E., Aßfalg, A., Moshagen, M., & Nadarevic, L. (2009).
Multinomial processing tree models: A review of the literature. Zeitschrift für Psychologie
/ Journal of Psychology, 217, 108–124. doi: 10.1027/0044-3409.217.3.108.
Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G. (2009). Statistical power analyses using
G*Power 3.1: Tests for correlation and regression analyses. Behavior Research Methods,
41, 1149–1160. doi: 10.3758/BRM.41.4.1149
Gathercole, S. E., Lamont, E., & Alloway, T. P. (2006). Working Memory in the Classroom.
In Susan J. Pickering (Ed.), Working Memory and Education (pp. 219–240). Burlington:
Academic Press.
Gathercole, S. E., Pickering, S. J., Ambridge, B., & Wearing, H. (2004). The Structure of
Working Memory From 4 to 15 Years of Age. Developmental Psychology, 40, 177–190.
doi: 10.1037/0012-1649.40.2.177
Glenberg, A. M. (1979). Component-levels theory of the effects of spacing of repetitions on
recall and recognition. Memory & Cognition, 7, 95–112. doi: 10.3758/BF03197590
Glenberg, A. M., & Lehmann, T. S. (1980). Spacing repetitions over 1 week. Memory &
Cognition, 8, 528-538. doi: 10.3758/BF03213772
Grote, M. G. (1995). Distributed versus massed practice in high school physics. School
Science and Mathematics, 95, 97-101. doi: 10.1111/j.1949-8594.1995.tb15736.x
Hattie, J. (2009). Visible Learning: A synthesis of over 800 meta-analyses relating to
achievement. New York, NY: Routledge.
Hogan, R. M., & Kintsch, W. (1971). Differential effects of study and test trials on long-term
recognition and recall. Journal of Verbal Learning and Verbal Behavior, 10, 562–567.
doi: 10.1016/S0022-5371(71)80029-4.
Kornell, N. (2009). Optimising learning using flashcards: Spacing is more effective than
cramming. Applied Cognitive Psychology, 23, 1297-1317. doi: 10.1002/acp.1537
The Lag Effect in Secondary School Classrooms28
Küpper-Tetzel, C. E., & Erdfelder, E. (2012). Encoding, maintenance, and retrieval processes
in the lag effect: A multinomial processing tree analysis. Memory, 20, 37-47. doi:
10.1080/09658211.2011.631550
Lawrence, W. W., & McPherson, D. D. (2000). A comparative study of block scheduling and
traditional scheduling on academic achievement. Journal of Instructional Psychology, 27,
178-182.
Moshagen, M. (2010). multiTree: A computer program for the analysis of multinomial
processing tree models. Behavior Research Methods, 42, 42–54. doi:
10.3758/BRM.42.1.42.
Mozer, M. C., Pashler, H., Cepeda, N. J., Lindsey, R., & Vul, E. (2009). Predicting the
optimal spacing of study: A multiscale context model of memory. In Y. Bengio, D.
Schuurmans, J. Lafferty, C. K. I. Williams, & A. Culotta (Eds.), Advances in Neural
Information Processing Systems (pp. 1321–1329). La Jolla, CA: NIPS Foundation.
Neisser, U. (1976). Cognition and reality: Principles and implications of cognitive
psychology. New York, NY US: Freeman.
Pashler, H., Rohrer, D., Cepeda, N. J., & Carpenter, S. K. (2007). Enhancing learning and
retarding forgetting: Choices and consequences. Psychonomic Bulletin & Review, 14, 187-
193. doi: 10.3758/BF03194050
Pressley, M., & Hilden, K. (2006). Cognitive Strategies. In D. Kuhn, R. S., Siegler, W.
Damon, & R. M. Lerner (Eds.), Handbook of child psychology: Vol 2, Cognition,
perception, and language (pp. 511-556). Hoboken, NJ, US: John Wiley & Sons Inc.
Randler, C., Kranich, K., & Eisele, M. (2008). Block scheduled versus traditional biology
teaching-an educational experiment using the water lily. Instructional Science, 36, 17-25.
doi: 10.1007/s11251-007-9020-y
Rawson, K. A., & Kintsch, W. (2005). Rereading effects depend on time of test. Journal of
Educational Psychology, 97, 70-80. doi: 10.1037/0022-0663.97.1.70
The Lag Effect in Secondary School Classrooms29
Reynolds, J. H., & Glaser, R. (1964). Effects of repetition and spaced review upon retention
of a complex learning task. Journal of Educational Psychology, 55, 297–308. doi:
10.1037/h0040734.
Rohrer, D., & Taylor, K. (2006). The Effects of overlearning and distributed practise on the
retention of mathematics knowledge. Applied Cognitive Psychology, 20, 1209–1224. doi:
10.1002/acp.1266.
Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning.
Instructional Science, 35, 481-498. doi: 10.1007/s11251-007-9015-8
Seabrook, R., Brown, G. D., & Solity, J. E. (2005). Distributed and massed practice: From
laboratory to classroom. Applied Cognitive Psychology, 19, 107–122. doi:
10.1002/acp.1066.
Sobel, H. S., Cepeda, N. J., & Kapler, I. V. (2011). Spacing effects in real-world classroom
vocabulary learning. Applied Cognitive Psychology, 25, n/a. doi: 10.1002/acp.1747.
Thios, S. J., & D‘Agostino, P. R. (1976). Effects of repetition as a function of study-phase
retrieval. Journal of Verbal Learning & Verbal Behavior, 15, 529–536. doi:
10.1016/0022-5371(76)90047-5
Thomson, D. M., & Tulving, E. (1970). Associative encoding and retrieval: Weak and strong
cues. Journal of Experimental Psychology, 86, 255–262. doi: 10.1037/h0029997.
The Lag Effect in Secondary School Classrooms30
Appendix
List of vocabulary word pairs and distractor words
Cue word Target word Distractor words in recognition test
1 Burg castle cartel cattle
2 Dieb thief belief chief
3 Eisenbahn railway doorway motorway
4 Engel angel bangle tangle
5 Feuer fire dire wire
6 Fluss river diver liver
7 Frosch frog fog food
8 Fuchs fox box lox
9 Handtuch towel tower town
10 Hof yard dart lard
11 Holz wood rood good
12 Hügel hill bill pill
13 Kehle throat road goat
14 Küste coast coach coal
15 Kuh cow low row
16 Landkarte map gap nap
17 Mauer wall call mall
18 Mond moon mood noon
19 Müll rubbish rubber rumbler
20 Schaf sheep deep sleep
21 Spiegel mirror marrow narrow
22 Stein stone alone clone
23 Stern star staff starch
24 Suppe soup group loup
25 Träne tear deer gear
26 Zucker sugar sucker suffer
... Several studies indicate that the optimal spacing interval durationproviding maximal memory performancedepends on and changes with the retention interval duration. As a consequence there is no overall best spacing interval duration, but instead the optimal spacing interval duration, but also the U-shape pattern, described above, depend on the time point the learner is finally tested (e.g., [17,[20][21][22]). In a comprehensive meta-analysis, Cepeda et al. [5] already provided evidence for the relation between spacing and retention intervals. ...
... Memory formation can roughly be subdivided into three major steps (e.g., [24]): Encoding (transformation of environmental information into working memory), consolidation (transfer of working memory content into longer term memory stores) and retrieval (reactivation of memory contents stored in the brain). Evidence from recent studies even indicate a fourth major step, namely maintenance [20][21][22]26]. Of course, test performance reflects a mixture of all three or four major steps and we cannot claim that our analysis of the Learning Period purely reflects encoding and consolidation and the analysis of the Final Test Period purely retrieval (but see [20] for a nice way of disentangling). ...
... These results fit well to findings from the literature, that the optimal spacing interval duration depends on the retention interval length (e.g., [5,6,17,[20][21][22]). Particularly interesting for our present results are recent studies by Küpper-Tetzel et al. [20,22]. ...
Article
Spaced learning produces better learning performance than extended learning periods without or with little interruptions. This “spacing effect” exists on different time scales, ranging from seconds to months. We recently found large spacing effects with a hithero rarely investigated 12-hours spacing interval. The present study tested for potentially larger learning effects in the temporal vicinity of 12 hours and analyzed spacing effects separately for learning and forgetting. 102 participants learned 40 German-Japanese vocabulary pairs in separate conditions with 7.5 minutes and 4-, 8-, 12-, and 24-hours spacing intervals. Two final tests were executed after retention intervals of 24 hours and 7 days. The 7.5-min spacing interval produced a steeper initial learning curve than all other spacing intervals. 24 h after the last learning unit, we found almost no forgetting in the 4-, 8- and 12-hours spacing conditions, but about 9.3 % and 3.6 % forgetting in the 7.5 min and 24 hours spacing conditions. After 7 days, forgetting was in the range of 13 % for all conditions between 4 and 24 hours. The 7.5 minutes condition produced 34 % forgetting. Our results indicate that spacing intervals in the range of 8 hours ± 4 hours provide high learning performance and can be easily integrated in our daily schedules.
... Spacing effects have been seen across age groups. Benefits have been seen in infants (Rovee-Collier et al., 1995), elementary and middle school children (Carpenter et al., 2009;Foot-Seymour et al., 2019;Sobel et al., 2011), high school students (Bloom & Shuell, 1981;Küpper-Tetzel et al., 2014), and healthy adults, including older adults (Cepeda et al., 2008;Simone et al., 2013). ...
... As well, Page 3 of 20 Foot-Seymour and Wiseheart Cognitive Research: Principles and Implications (2022) 7:5 there aren't yet enough classroom studies to support use of the spacing effect across the entire range of educational materials. Some of the applied classroombased studies that have been conducted with verbal and factual material show spacing benefits for word and phonics learning (Seabrook et al., 2005), word and fact learning (Carpenter et al., 2009;Sobel et al., 2011), second language learning (Bloom & Shuell, 1981;Küpper-Tetzel et al., 2014), and text comprehension (Rawson & Kintsch, 2005;Verkoeijen et al., 2008). These studies all showed benefits of spacing. ...
Article
Full-text available
Spaced learning—the spacing effect—is a cognitive phenomenon whereby memory for to-be-learned material is better when a fixed amount of study time is spread across multiple learning sessions instead of crammed into a more condensed time period. The spacing effect has been shown to be effective across a wide range of ages and learning materials, but few studies have been conducted that look at whether spacing can be effective in real-world classrooms, using real curriculum content, with real teachers leading the intervention. In the current study, lesson plans for teaching website credibility were distributed to homeroom elementary teachers with specific instructions on how to manipulate the timing of the lessons for either a one-per-day or one-per-week delivery. One month after the final lesson, students were asked to apply their knowledge on a final test, where they evaluated two new websites. Results were mixed, suggesting that classroom noise might lessen or impede researchers’ ability to find spacing effects in naturalistic settings.
... There has been considerable research on spacing effects within L2 vocabulary research. What we know about the topic is largely based on findings from deliberate decontextualised learning (e.g., Alfotais, 2019;Bahrick & Phelphs, 1987;Bloom & Shuell, 1981;Bolger & Zapata, 2011;Callan & Schweighofer, 2010;Goossens, Camp, Verkoeijen, Tabbers, & Zwaan, 2012;Kang, Lindsey, Mozer, & Pashler, 2014;Karpicke & Bauernschmidt, 2011;Kornell, 2009;Küpper-Tetzel, Erdfelder, & Dickhäuser, 2014;Lotfolahi & Salehi, 2017;Nakata, 2015;Nakata & Suzuki, 2019;Nakata & Webb, 2016;Pashler, Zarow, & Triplett, 2003;Pavlik Jr & Anderson, 2005;Schuetze, 2015). Publications that concentrate on intentional learning have most frequently adopted the paired-associate paradigm where participants are instructed to memorise the form and meaning of target words and the majority of these studies have clearly supported a positive effect of spacing on deliberate learning. ...
Thesis
The aim of this thesis is to study the role of imagery in L2 captioned video by examining modality (Study 1), contiguity (Study 2), and spacing (Study 3) effects in incidental vocabulary learning from extensive TV viewing. An experimental design was employed in which one hundred seventy-three Algerian EFL learners in their third year of the Linguistics Bachelor programme were randomly assigned to either a Control, View, or Non-View group. Treatment participants watched two full-length seasons of documentary series extending to eight viewing hours, over a six-week period of two-week intervals. The View group watched the episodes in the form of L2 captioned video while the Non-View group had the imagery hidden and were therefore exposed to L2 audio and L2 captions only. Four levels of word knowledge were measured: meaning recall and recognition (posttest only) and spoken and written form recognition (pretest-posttest). Study 1 assessed the effect of obscuring imagery on incidental learning of twenty words using a between-participants design. The results showed successful word learning regardless of the presence of imagery. Study 2 investigated the effect of verbal-visual contiguity (the co-occurrence of a word and its visual referent) on incidental learning of twenty-eight words using a within-participants design (View group only). It introduced contigfrequency, contigduration, and contigratio as three measures of contiguity on two timespans (∓7 seconds and ∓25 seconds) that were longer than those used in previous studies. The results showed that the amount of time visual referents appeared on the screen (contigduration), measured in a ∓25 second timeframe relative to the verbal occurrence, was predictive of learning. These results were more pronounced in the meaning recognition test. Study 3 explored whether words would be learned better when their occurrences were spread across viewing sessions (spaced condition), as compared to appearing within a single session (massed condition) by measuring the incidental learning of eight matched word pairs using a between-items design. It also examined whether learning in these two spacing conditions was influenced by the presence of imagery. The results revealed a positive effect of spaced occurrences in the Non-View group but not the View group, suggesting that a spacing advantage is more likely when fewer cues are available. These results were limited to knowledge of meaning only.
... Some evidence also suggests that expanding gaps might lead to better initial learning as well as similar or even better retention outcomes, as compared to fixed gaps (Kanayama & Kasahara, 2016;Kang, Lindsey, Mozer, & Pashler, 2014;Karpicke & Bauernschmidt, 2011;Pyc & Rawson, 2007;Schuetze, 2015). Finally, spaced repetition of L2 vocabulary terms has also been found to improve retention in classroom contexts (Bloom & Shuell, 1981;Kupper-Tetzel, Erdfelder, & Dickhauser, 2014;Nakata, 2015; but see Rogers & Cheung, 2018). Overall, the evidence suggests that spacing effects do indeed extend to L2 vocabulary learning, in both laboratory and classroom contexts, even benefiting retention for periods of years. ...
Article
Full-text available
We investigated whether learning and retaining vocabulary in a second language (L2) can be improved by leveraging a combination of memory enhancement techniques. Specifically, we tested whether combining retrieval practice, spacing, and related manipulations in a ‘multidomain’ pedagogical approach enhances vocabulary acquisition as compared to a typical learning approach. In a classroom-laboratory design, 48 Turkish university students studying L2 English were trained on 64 English words over 17 days. They were assigned to either a ‘typical’ study regimen of (re)studying the words on the first day (initial study) and last day (cramming) of training, or an ‘optimized’ regimen of retrieval practice (retrieving the words), moreover with feedback, spaced throughout the period, moreover with expanding gaps. The target words were tested before training (pre-test) and one and 11 days afterwards (post-tests). Mixed-effects modeling revealed a training-group by test-session interaction, due to greater improvements from optimized training (a striking 18 percentage-point accuracy increase from pre-test to both post-tests) than typical training (an 8 percentage-point increase). Further analyses showed that the optimized training advantages were mainly driven by high (rather than low) frequency words. Overall, the results suggest that a multidomain approach of combining different memory enhancement techniques can lead to substantial gains in both the learning and retention of L2 words, as compared to a typical study pattern. The findings have implications for L2 learning and pedagogy.
Article
Full-text available
[Full text link: https://rdcu.be/cSXY3] Research on the psychology of learning has highlighted some straightforward ways of enhancing learning. However, effective learning strategies are underutilized by learners. In this Review, we discuss key research findings on two specific learning strategies: spacing and retrieval practice. We focus on how these strategies enhance learning in a variety of domains across the lifespan, with an emphasis on research in applied educational settings. We also discuss key findings from research on metacognition—learners’ awareness and regulation of their own learning. Learners’ underutilization of effective learning strategies could stem from false beliefs about learning, lack of awareness of effective learning strategies, or the counter-intuitive nature of these strategies. Findings in learner metacognition highlight the need for improving learners’ subjective mental models of how to learn effectively. Overall, the research discussed in this Review has important implications for the increasingly common situations in which learners must effectively monitor and regulate their own learning. [Nature Reviews Psychology, August 2022]
Article
This meta‐analysis investigates earlier studies of spaced practice in second language learning. We retrieved 98 effect sizes from 48 experiments (N = 3,411). We compared the effects of three aspects of spacing (spaced vs. massed, longer vs. shorter spacing, and equal vs. expanding spacing) on immediate and delayed posttests to calculate mean effect sizes. We also examined the extent to which nine empirically motivated variables moderated the effects of spaced practice. Results showed that (a) spacing had a medium‐to‐large effect on second language learning; (b) shorter spacing was as effective as longer spacing in immediate posttests but was less effective in delayed posttests than longer spacing; (c) equal and expanding spacing were statistically equivalent; and (d) variability in spacing effect size across studies was explained methodologically by the learning target, number of sessions, type of practice, activity type, feedback timing, and retention interval. The methodological and pedagogical significance of the findings are discussed.
Article
Full-text available
This paper examined lag effects in the learning of second language (L2) grammar. Moreover, following the Desirable Difficulty Framework for L2 practice, the present study investigated whether lag effects could be explained by other sources of difficulty. Using digital flashcards, 117 English language learners (aged 10–18) learned two grammatical structures over two different sessions at a 1-day or 7-day intersession interval (ISI). Learners’ performance was analyzed at two retention intervals (RIs) of 7 and 28 days, respectively. Linguistic difficulty was compared by examining two different structures, while learner-related difficulty was analyzed by comparing learners who differed in terms of age, proficiency, and time required to complete the training. Results showed no main effect of ISI, a main effect of RI, and a small but significant ISI × RI interaction. Linguistic difficulty and age did not interact with ISI or RI. However, longer lags led to significantly higher scores for faster learners and learners of higher proficiency, while shorter lags promoted significantly higher scores for slower learners and learners of lower proficiency. The findings provide some support for the Desirable Difficulty Framework in its potential to explain L2 lag effects.
Article
Full-text available
The aim of this study is to analyze the effect of different schedules of repeated reading practice on intentional vocabulary learning, and constitutes a partial replication and extension of the authors’ previous study on incidental vocabulary learning. Two groups of Taiwanese EFL learners (n = 72) engaged in five repeated reading sessions; one group had the sessions on consecutive days (1-day intersession interval, ISI), whereas the other had them once a week (7-day ISI). Apart from reading for meaning, the students were also asked to focus on 36 target words. The students were tested before and immediately after the treatment. Moreover, a delayed posttest was scheduled at a retention interval (RI) of 4 and 28 days for the intensive group and spaced group respectively (considering an ISI/RI ratio of 25%). The results indicate that the short-spaced repeated reading sessions had a significantly more positive effect on vocabulary learning on both immediate and delayed posttest than the long-spaced sessions. The benefits of the short-spaced schedule were clearer in the current study on intentional vocabulary learning than in the authors’ previous study on incidental learning through repeated reading.
Article
This study investigates whether spacing with temporal gaps between sessions promotes retention or forgetting of English vocabulary in low-achieving students. Participants were 19 Chinese L1 students receiving after-school English remedial instruction in a junior high in Taiwan. As part of their class activities, they learned three English words under a massed condition (six consecutive trials for each word in one session) and three English words under a spaced condition (two trials per session over three weekly sessions). The spacing of the words was manipulated within participants, and the words for the two conditions were counterbalanced across the participants. Vocabulary learning outcomes were assessed by an immediate test administered after the final session of learning and two delayed tests administered 2 and 4 weeks later. The design was replicated with four cycles of learning with four sets of words. Results showed that the participants demonstrated better retention for the spaced words than the massed words in both the immediate and the two delayed tests. The spacing effect was robust, replicated across three sets of words, except for the last one. These results suggest that distributing learning over weeks promotes English vocabulary learning and retention (rather than forgetting) in low-achieving EFL students.
Article
Full-text available
An analysis of life span memory identifies those variables that affect losses in recall and recognition of the content of high school algebra and geometry courses. Even in the absence of further rehearsal activities, individuals who take college-level mathematics courses at or above the level of calculus have minimal losses of high school algebra for half a century. Individuals who performed equally well in the high school course but took no college mathematics courses reduce performance to near chance levels during the same period. In contrast, the best predictors of test performance (e.g., Scholastic Aptitude Test scores and grades) have trivial effects on the rate of performance decline. Pedagogical implications for life span maintenance of knowledge are derived and discussed.
Article
Full-text available
Multinomial processing tree (MPT) models have become popular in cognitive psychology in the past two decades. In contrast to general-purpose data analysis techniques, such as log-linear models or other generalized linear models, MPT models are substantively motivated stochastic models for categorical data. They are best described as tools (a) for measuring the cognitive processes that underlie human behavior in various tasks and (b) for testing the psychological assumptions on which these models are based. The present article provides a review of MPT models and their applications in psychology, focusing on recent trends and developments in the past 10 years. Our review is nontechnical in nature and primarily aims at informing readers about the scope and utility of MPT models in different branches of cognitive psychology.
Article
The spacing effect would appear to have considerable potential for improving classroom learning, yet there is no evidence of its widespread application. I consider nine possible impediments to the implementation of research findings in the classroom in an effort to determine which, if any, apply to the spacing effect. I conclude that the apparent absence of systematic application may be due, in part, to the ahistorical character of research on the spacing effect and certain gaps in our understanding of both the spacing effect and classroom practice. However, because none of these concerns seems especially discouraging, and in view of what we do know about the spacing effect, classroom application is recommended.
Article
High school students enrolled in a French course learned vocabulary words under conditions of either massed or distributed practice as part of their regular class activities. Distributed practice consisted of three 10-minute units on each of three successive days; massed practice consisted of all three units being completed during a 30-minute period on a single day. Though performance of the two groups was virtually identical on a test given immediately after completion of study, the students who had learned the words by distributed practice did substantially better (35%) than the massed- practice students on a second test given 4 days later. The implications of the findings for classroom instruction and the need to distinguish between learning and memory are discussed.
Book
This unique and ground-breaking book is the result of 15 years research and synthesises over 800 meta-analyses on the influences on achievement in school-aged students. It builds a story about the power of teachers, feedback, and a model of learning and understanding. The research involves many millions of students and represents the largest ever evidence based research into what actually works in schools to improve learning. Areas covered include the influence of the student, home, school, curricula, teacher, and teaching strategies. A model of teaching and learning is developed based on the notion of visible teaching and visible learning. A major message is that what works best for students is similar to what works best for teachers - an attention to setting challenging learning intentions, being clear about what success means, and an attention to learning strategies for developing conceptual understanding about what teachers and students know and understand. Although the current evidence based fad has turned into a debate about test scores, this book is about using evidence to build and defend a model of teaching and learning. A major contribution is a fascinating benchmark/dashboard for comparing many innovations in teaching and schools.
Article
In a 9-year longitudinal investigation, 4 subjects learned and relearned 300 English-foreign language word pairs. Either 13 or 26 relearning sessions were administered at intervals of 14, 28, or 56 days. Retention was tested for 1.2.3. or 5 years after training terminated. The longer intersession intervals slowed down acquisition slightly, but this disadvantage during training was offset by substantially higher retention. Thirteen retraining sessions spaced at 56 days yielded retention comparable to 26 sessions spaced at 14 days. The retention benefit due to additional sessions was independent of the benefit due to spacing, and both variables facilitated retention of words regardless of difficulty level and of the consistency of retrieval during training. The benefits of spaced retrieval practice to long-term maintenance of access to academic knowledge areas are discussed.
Article
There have been many claims by cognitive psychologists that working memory (WM) plays a role in learning during childhood, supported by studies demonstrating close links between WM skills and measures of learning and academic achievement. An important shortcoming of this approach is that it does not illuminate how and why WM is needed in the everyday classroom activities that form the basis for learning. A consistent finding from a large number of studies is a close relationship between children's performance on indicators of scholastic attainments and their WM skills. Young people with low scores on standardized assessments of reading and mathematics usually score poorly on complex memory span tasks that involve both the processing and temporary storage of verbal reading material. To illuminate the specific nature of the failed learning episodes that may be contributing to the failure of such children to make normal scholastic progress, classroom behavior of three children with poor WM abilities was observed. Four different kinds of learning failure were observed with high frequency in each of these children that could be attributed to the children failing to meet the WM demands of the activity: forgetting instructions, failing to meet combined processing and storage demands, losing track in complex tasks, and forgetting from episodic long-term memory at high rates. The chapter concludes that learning failures impair the children's chances of abstracting knowledge and skills that form the basis for functioning in the complex cognitive activities associated with the domains of literacy and mathematics.