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Interleaving Helps Students Distinguish among Similar Concepts


Abstract and Figures

When students encounter a set of concepts (or terms or principles) that are similar in some way, they often confuse one with another. For instance, they might mistake one word for another word with a similar spelling (e.g., allusion instead of illusion) or choose the wrong strategy for a mathematics problem because it resembles a different kind of problem. By one proposition explored in this review, these kinds of errors occur more frequently when all exposures to one of the concepts are grouped together. For instance, in most middle school science texts, the questions in each assignment are devoted to the same concept, and this blocking of exposures ensures that students need not learn to distinguish between two similar concepts. In an alternative approach described in this review, exposures to each concept are interleaved with exposures to other concepts, so that a question on one concept is followed by a question on a different concept. In a number of experiments that have compared interleaving and blocking, interleaving produced better scores on final tests of learning. The evidence is limited, though, and ecologically valid studies are needed. Still, a prudent reading of the data suggests that at least a portion of the exposures should be interleaved.
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The benefit of interleaved mathematics practice is not limited
to superficially similar kinds of problems
Doug Rohrer &Robert F. Dedrick &Kaleena Burgess
Published online: 28 February 2014
#Psychonomic Society, Inc. 2014
Abstract Most mathematics assignments consist of a group
of problems requiring the same strategy. For example, a lesson
on the quadratic formula is typically followed by a block of
problems requiring students to use that formula, which means
that students know the appropriate strategy before they read
each problem. In an alternative approach, different kinds of
problems appear in an interleaved order, which requires stu-
dents to choose the strategy on the basis of the problem itself.
In the classroom-based experiment reported here, grade 7
students (n= 140) received blocked or interleaved practice
over a nine-week period, followed two weeks later by an
unannounced test. The mean test scores were greater for
material learned by interleaved practicerather than by blocked
practice (72 % vs. 38 %, d= 1.05). This interleaving effect
was observed even though the different kinds of problems
were superficially dissimilar from each other, whereas previ-
ous interleaved mathematics studies had required students to
learn nearly identical kinds of problems. We conclude that
interleaving improves mathematics learning not only by im-
proving discrimination between different kinds of problems,
but also by strengthening the association between each kind of
problem and its corresponding strategy.
Keywords Learning .Mathematics .Interleaved .Spacing .
Learning techniques inspired by research in the laboratory can
improve learning in the classroom (for recent reviews, see
Dunlosky, Rawson, Marsh, Nathan, & Willingham, 2013;
Roediger & Pyc, 2012). In the study reported here, a simple
intervention designed to improve mathematics learning was
assessed in a classroom-based experiment. We first describe
the intervention and the relevant research.
Interleaved practice
The solution of a mathematics problem requires two steps, as
is illustrated by the following example:
A bug flies 48 m east and then flies 14 m north. How far
is the bug from where it started?
This problem is solved by using the Pythagorean theorem
to find the length of a hypotenuse (
48 þ14
p¼50 ). In other
words, students first choose a strategy (Pythagorean theorem)
and then execute the strategy. The term strategy is used
loosely here to refer to a theorem, formula, concept, or proce-
dure. Learning to choose an appropriate strategy is difficult,
partly because the superficial features of a problem do not
always point to an obvious strategy (e.g., Chi, Feltovich, &
Glaser, 1981; Siegler, 2003). For example, the word problem
about the bug does not explicitly refer to the Pythagorean
theorem, or even to a triangle or hypotenuse. Additional
examples are given in Fig. 1.
Although students must learn to choose an appropriate
strategy, they are denied the opportunity to do so if every
problem in an assignment requires the same strategy. For
example, if a lesson on the Pythagorean theorem is followed
by a group of problems requiring the Pythagorean theorem,
students know the appropriate strategy before they read each
problem. The grouping of problems by strategies is termed
blocked practice, and the large majority of practice problems
in most mathematics textbooks are blocked. Blocked practice
served as the control in the study reported here.
D. Rohrer :R. F. Dedrick :K. Burgess
University of South Florida, Tampa, FL, USA
D. Rohrer (*)
Psychology PCD4118G, University of South Florida, Tampa,
FL 33620, USA
Psychon Bull Rev (2014) 21:13231330
DOI 10.3758/s13423-014-0588-3
In an alternative approach that is evaluated in the present
study, a majority of the problems within each assignment are
drawn from previous lessons, so that no two consecutive prob-
lems require the same strategya technique known as inter-
leaved practice. With this approach, students must choose an
appropriate strategy and not only execute it, just as they must
choose an appropriate strategy when they encounter a problem
during a cumulative exam or high-stakes test. Put another way,
blocked practice provides a crutch that might be optimal when
students first encounter a new skill, but only interleaved practice
allows students to practice what they are expected to know. To
create assignments with interleaved practice, the problems
within a set of blocked assignments can be rearranged (Fig. 2).
In addition to providing opportunities to practice choosing
a strategy, interleaved mathematics assignments guarantee
that problems of the same kind are distributed, or spaced,
across different assignments (Fig. 2). Spacing typically
improves performance on delayed tests of learning (e.g., for
recent reviews, see Dunlosky et al., 2013; Roediger & Pyc,
2012), and several studies have shown that spacing can
improve the learning of mathematics, in particular (Rohrer &
Tay lor, 2006,2007; Yazdani & Zebrowski, 2006). To sum-
marize thus far, interleaved practice has two critical features:
Problems of different kinds are interleaved (which requires
students to choose a strategy), and problems of the same kind
are spaced (which usually improves retention).
Previous studies of interleaved practice
Four previously published studies compared the effects of
interleaved and blocked mathematics practice (Le Blanc &
Simon, 2008; Mayfield & Chase, 2002; Rohrer & Taylor,
2007; Taylor & Rohrer, 2010). In each of the studies, partici-
pants received interleaved or blocked practice of different kinds
of problems, and interleaving produced better scores on a
delayed test. However, in each of these studies, the different
kinds of problems (and the corresponding strategies) were
nearly identical in appearance (Fig. 3). In one study, for exam-
ple, every problem included a variable raised to an exponent,
and, in another, every problem referred to a prism. We refer to
problems with shared features as superficially similar problems,
and this similarity might hinder studentsability to distinguish or
discriminate between different kinds of problems. Indeed, the
benefit of interleaved practice is often attributed to improved
discrimination, as we will detail in the Discussion section.
Therefore, the superficial similarity of the problems used in
previous studies leaves open the possibility that the test benefit
of interleaving is limited to scenarios in which students learn to
solve kinds of problems that look alike, and such a boundary
condition would curtail the utility of interleaved practice in the
classroom, where students encounter problems that are often
easily distinguished from other kinds of problems.
Present study
We compared interleaved and blocked mathematics practice
in a classroom-based experiment with a counterbalanced,
crossover design. Students learned to solve different kinds of
problems drawn from their mathematics course, and they
received the lessons and assignments from their regular
teacher over a period of nine weeks. Two weeks after the last
assignment, students sat for an unannounced test. Unlike
previous studies of interleaved mathematics practice, the dif-
ferent kinds of problems were superficially dissimilar.
A A bug flies 48 m east and then 14 m north.
How far is the bug from where it started?
B A bug flies 48 m east and then 14 m west.
How far is the bug from where it started?
Number line
C Find the length of the line segment with
endpoints (1, 1) and (5, 4).
D Find the slope of the line that passes
h the points (1, 1) and (5, 4). slope
Fig. 1 The two steps in the solution of a problem. To solve a problem,
students must choose a strategy and then execute it. Superficially similar
problems may require different strategies (A and B, or C and D), and
superficially dissimilar problems may require the same strategy (A and
C). Regardless of similarity, students know the strategy in advance when
working a block of problems requiring the same strategy
1324 Psychon Bull Rev (2014) 21:13231330
The study took place at a public middle school in Tampa,
Florida. Three teachers and eight of their seventh-grade math-
ematics classes participated. Each teacher taught two or three
of the classes. Of the 175 students in the classes, 157 students
participated in the study. Of these, 140 students attended class
on the day of the unannounced test, and only these students
data were analyzed. Nearly all of the students were 12 years of
age at the beginning of the school year.
Students learned to solve four kinds of problems drawn from
their course (Fig. 4). To confirm that students could not solve
these kinds of problems before the experiment, we administered
a pretest with one of each kind of problem. Averaged across
problems, just 0.7 % of the students supplied both the correct
answer (e.g., x= 7) and the correct solution (the steps leading to
the answer). When scored solely on the basis of answers (which
presumably included guesses), the mean score was 3.2 %.
The four kinds of problems were not only superficially
different from each other, but also quite unlike other kinds
of problems that the students had seen prior to the completion
of the experiment. For example, although students ultimately
learn how to solve many kinds of equations, a linear equation
was the only kind of equation that these students had encoun-
tered previously in school (Fig. 4A). Likewise, a linear
equation was the only kind of equation that the students had
previously graphed (Fig. 4C). The slope problem (Fig. 4D)
was also moderately unique, because the term slopeis used
only in limited contexts. However, the proportion word prob-
lem (Fig. 4B)doesresembleotherkindsofwordproblems.
For the study, we used a counterbalanced crossover design.
We randomly divided the eight classes into two groupsof four,
with the constraint that each group included at least one of the
classes taught by each teacher. One group interleaved their
practice of problems kinds A and B and blocked their practice
of kinds C and D, and the other group did the reverse.
During the nine-week practice phase, students received ten
assignments with 12 problems each. Across all assignments,
the students saw 12 problems of each of the four kinds (Fig. 4).
The remaining problems were based on entirely different topics.
Students received the ten assignments on Days 1, 15, 24, 30/31,
36, 37, 57, 58, 60, and 64. Every student received the same
problems, but we rearranged the problems to create two versions
of each assignmentone for each group. The first four prob-
lems of kinds A, B, C, and D were the first four problems of
Assignments 1, 2, 4, and 5, respectively. If a problem kind was
learned by blocked practice, the remaining eight problems
appeared in the same assignment as the first four, meaning that
the assignment included one block of 12 problems. If a problem
50 51 52 53 54 55 60 70 90
4 problems
on the
1 50 51 52 53 54 55 60 70 90
2 50 51 52 53 54 55 60 70 90
3 50 51 52 53 54 55 60 70 90
4 50 51 52 53 54 55 60 70 90
1 problem
on each of
8 previous
5 49 50 51 52 53 54 59 69 89
6 48 49 50 51 52 53 58 68 88
7 47 48 49 50 51 52 57 67 87
8 46 47 48 49 50 51 56 66 86
9 45 46 47 48 49 50 55 65 85
10 40 41 46 47 48 49 50 60 84
11 30 31 32 33 34 35 40 50 70
12 10 11 12 13 14 15 20 30 50
Fig. 2 A hypothetical set of assignments providing interleaved practice.
Each column represents an assignment, and each table entry indicates the
lesson number on which the problem is based. For example, if Lesson 50
is on ratios, the corresponding assignment includes four ratio problems
and one problem on each of eight lessons seen earlier in the school year
(or during the previous school year). Another eight ratio problems
(Lesson 50) are distributed across future assignments, with decreasing
frequency. In other words, problems of different kinds are interleaved
(which requires students to choose a strategy), and problems of the same
kind are spaced (which improves retention). Note that the arrangement
shown here is not the one that was used in the present study
Psychon Bull Rev (2014) 21:13231330 1325
kind was learned by interleaved practice, the remaining eight
problems of the same kind were distributed across the remaining
assignments. This meant that students saw the last problem of
each kind on a later date in the interleaved condition than in the
blocked condition, which is an intrinsic feature of assignments
with interleaved practice (Fig. 2). The effect of this difference in
true test delayis detailed in the Results.
Shortly before the scheduled date of each assignment,
teachers received paper copies for their students and a slide
presentation with solved examples and solutions to each prob-
lem. We asked teachers to present the examples before dis-
tributing the assignment. On the following school day,
teachers presented the solution to each problem while encour-
aging students to make any necessary corrections to their own
solutions. Teachers then collected the assignments. Within
two days, one or more of the authors visited the school, scored
each assignment (without marking it), and returned the as-
signments to the teachers. Although these scores do not mea-
sure studentsmastery, because students could correct their
errors while the teacher presented the correct solutions, this
scoring of the assignments provided us with evidence of
teacher compliance with the experimental procedures.
Students were tested two weeks after the last assignment. We
asked teachers not to inform students of the test in advance,
because we did not want the final test to be affected by
cramming just prior to the test. Teachers did not see the test
before it was administered. The students were tested during their
regular class, and the teacher and one author proctored each test.
A Simplify. 8x ·4x Add exponents 32x
Simplify. Subtract exponents 2x
Simplify. 2x Multiply exponents 2 x
B Find the volume of a wedge
with radius 2 and height 3.
2πr h
Find the volume of a spheroid
with radius 2 and height 3.
3πr h
Find the volume of a spherical cone
with radius 2 and height 3.
3πr h
C The base of a prism has 5 sides.
How many faces does the prism have? base sides + 2 5 + 2 = 7
The base of a prism has 5 sides.
How many corners does the prism have? base sides x 2 5 x 2 = 10
The base of a prism has 5 sides.
How many ed
es does the prism have? base sides x 3 5 x 3 = 15
Fig. 3 Problems learned in previous studies of interleaved mathematics:
Students learned to solve several kinds of problems relating to (A)
exponent rules (Mayfield & Chase, 2002), (B) the volume of obscure
solids (Le Blanc & Simon, 2008; Rohrer & Taylor, 2007) or (C) prisms
(Taylor & Rohrer, 2010) [EE2] In each study, the different kinds of
problems (as well as the corresponding strategies) were nearly identical.
Note that each of the studies included four or five kinds of problems, but
only three are shown here
1326 Psychon Bull Rev (2014) 21:13231330
All of the test problems were novel. The test included three
problems of each of the four kinds, and each of the four pages
included a block of three problems of the same kind. We created
three versions by reordering problems within each block, and
students in adjacent chairs received different versions. Students
were allotted 36 min and allowed to use their school-supplied
basic calculator. Each test was scored on site that day by two
raters who were blind to each students group assignment. The
two raters scored each answer as correct or not correct and later
resolved the few discrepancies (17 of 1,680). Test score
reliability was moderately good (Cronbachs alpha = .78).
A repeated measures comparison of the two halves of the test
showed that interleaved practice was nearly twice as effective as
blocked practice, t(139) = 10.49, p< .001 (Table 1). The effect
size was large, d= 1.05, 95 % CI = [0.80, 1.30]. This benefit of
interleaving was observed for each of the four kinds of prob-
lems, ps < .01. The effect sizes for the four kinds (A, B, C, and
D) exhibited a positive trend (0.72, 0.45, 1.00, and 1.27, respec-
tively). This means that the interleaving benefit was larger for
problem kinds introduced later in the practice phase. In other
Problem 1. Choose Strategy 2. Execute Strategy
Solve the equation.
3(x + 1) = x + 17
Isolate x terms on one
side of the equation
3x + 3 = x + 17
2x + 3 = 17
2x = 14
x = 7
Penelope’s new tractor
requires 14 gallons of gas to
plow 6 acres. How many
gallons of gas will she need
to plow 21 acres?
Create a proportion
Graph the equation.
y = 2x + 1
Choose at least two
values of x and find
the corresponding
values of y.
x y
0 1
1 3
Find the slope of the line that
passes through the points
(3, 5) and (6, 7).
Fig. 4 Examples of the four kinds of problems used in the present studies.
(A) Solve a linear equation requiring four steps. (B) Solve a word problem
using a proportion. (C) Graph an equation of the form, y=mx +b,wherem
and bare integers. (D) Determine the slope of the line defined by two given
points with integer coordinates
Psychon Bull Rev (2014) 21:13231330 1327
words, although the true test delay (the interval between the last
practice problem and the test) was larger in the blocked condi-
tion than in the interleaved condition (see the Procedure section),
the problem kinds with larger test delay differences (i.e., that
were seen earlier in the practice phase) were associated with
smaller effect sizes.Although this negative association might
reflect order effectsthat is, all participants saw the four prob-
lem kinds in the same orderwe cannot think of a reason why
order would matter. In brief, the effect sizes for problem kinds
introduced later in the practice phase were larger than the effects
for the earlier ones, and this trend was in the opposite direction
from what would be expected if the difference in test delays
contributed to the observed effect. Furthermore, if this difference
did play a role, it might be seen not as a confound, but as an
intrinsic feature of interleaved assignments (Fig. 2).
Whereas previous studies of interleaved mathematics practice
had required students to learn kinds of problems that were nearly
identical in appearance (Fig. 3), the results reported here demon-
strate that this benefit also holds for problems that do not look
alike (Fig. 4). That is, the benefit of interleaved mathematics
practice is not limited to the ecologically invalid scenario in
which students encounter only superficially similar kinds of
problems. Although it might seem surprising that a mere
reordering of problems can nearly double test scores, it must be
remembered that interleaving alters the pedagogical demand of a
mathematics problem. As was detailed in the introduction, inter-
leaved practice requires that students choose an appropriate strat-
egy for each problem and not only execute the strategy, whereas
blocked practice allows students to safely assume that each
problem will require the same strategy as the previous problem.
However, the interleaved practice effect observed here might
reflect the benefit of spaced practice rather than the benefit of
interleaving per se. As we explained in the introduction, the
creation of interleaved mathematics assignments guarantees not
only that problems of different kinds will be interleaved, but also
that problems of the same kind will be spaced across assign-
ments, and spacing ordinarily has large, robust effects on delayed
tests of retention. We therefore believe that spacing contributed to
the large effect observed here (d= 1.05). Still, we have reason to
suspect that interleaving, per se, contributed as well. In one
previous interleaved mathematics study, students in both the
interleaved and blocked conditions relied on spaced practice to
the same degree, and interleaving nevertheless produced a large
positive effect (d= 1.23; Taylor & Rohrer, 2010). In the present
study, though, we chose to compare interleaved practice to the
kinds of assignment used in most textbooks, which is a massed
block of problems.
Theoretical accounts of the interleaved mathematics effect
How does interleaving improve mathematics learning? The
standard account holds that the interleaving of different kinds
of mathematics problems improves studentsability to distin-
guish or discriminate between different kinds of problems (e.g.,
Rohrer, 2012). Put another way, each kind of problem is a
category, and students are better able to identify the category
to which a problem belongs if consecutive problems belong to
different categories. This ability to discriminate is a critical skill,
because students cannot learn to pair a particular kind of prob-
lem with an appropriate strategy unless they can first distinguish
that kind of problem from other kinds, just as Spanish-language
learners cannot learn the pairs PERRODOG and PEROBUT
unless they can discriminate between PERRO and PERO.
This discriminability account parsimoniously explains the
interleaving effects observed in previous mathematics inter-
leaving studies, because participants in these studies were
required to discriminate between nearly identical kinds of
problems (Fig. 3). For instance, one of these previous studies
included an error analysis, and it showed that the majority of
test errors in the blocked condition, but not in the interleaved
condition, occurred because students chose a strategy
corresponding to one of the other kinds of problems that they
had learnedfor example, using the formula for prism edges
rather than the formula for prism faces (Taylor & Rohrer,
2010). Furthermore, the students in this study were given a
second final test in which they were given the appropriate
strategy for each test problem and asked only to execute the
strategy, and the scores on this test were near ceiling in both
conditions. In sum, the data from this earlier experiment are
consistent with the possibility that interleaving improves stu-
dentsability to discriminate one kind of problem from another
(or discriminate one kind of strategy from another).
However, in the present study, discrimination errors
appeared to be rare. In a post-hoc error analysis, three raters
(two of the authors and a research assistant, all blind to
conditions) examined the written solution accompanying each
incorrect answer and could not find any solutions in which
students used the wrong strategy but one that solves another
kind of problem.The raters then expanded the definition of
discrimination error to include solutions with at least one step
of a strategy that might be used to solve any kind of problem
other than the kind of problem that the student should have
solved. With this lowered threshold, discrimination errors still
accounted for only 33 of the 756 incorrect answers (4.4 %),
with no reliable difference between conditions (5.1 % for
Tabl e 1 Proportions correct on test
Mean SD
Interleaved practice .72 .30
Blocked practice .38 .35
1328 Psychon Bull Rev (2014) 21:13231330
interleaved, 4.0 % for blocked). For the other incorrect
answers, students chose the correct strategy but incorrectly
executed it (45.9 %), or they relied on a strategy we could not
decipher, often because they did not show their work (49.7 %).
The virtual absence of discrimination errors is arguably not
surprising, partly because the different kinds of problems did
not look alike, and partly because some strategies were obvi-
ously an inappropriate choice for some kinds of problems
(e.g., trying to graph a line by creating a proportion). The
rarity of discrimination errors in the present study raises the
possibility that improved discrimination cannot by itself
explain the benefits of interleaved mathematics practice.
We suggest that, aside from improved discrimination, inter-
leaving might strengthen the association between a particular
kind of problem and its corresponding strategy. In other words,
solving a mathematics problem requires students not only to
discriminate between different kinds of problems, but also to
associate each kind of problem with an appropriate strategy, and
interleaving might improve both skills (Fig. 5). In the present
study, for example, students were asked to learn to distinguish a
slope problem from a graph problem (a seemingly trivial dis-
crimination) and to associate each kind of problem with an
appropriate strategy (e.g., for a slope problem, use the strategy
slope = rise/run), and the latter skill might have benefited from
interleaved practice. Yet why would interleaving, more so than
blocking, strengthen the association between a problem and an
appropriate strategy? One possibility is that blocked assignments
often allow students to ignore the features of a problem that
indicate which strategy is appropriate, which precludes the
learning of the association between the problem and the strategy.
In the present study, for example, students who worked 12 slope
problems in immediate succession (i.e., used blocked practice)
could solve the problems without noticing the feature of the
problem (the word slope) that indicated the appropriate
strategy (slope = rise/run). In other words, these students could
repeatedly execute the strategy (y
) without any
awareness that they were solving problems related to slope. In
brief, blocked practice allowed students to focus only on the
execution of the strategy, without having to associate the prob-
lem with its strategy, much like a Spanish-language learner who
misguidedly attempts to learn the association between PERRO
and DOG by repeatedly writing DOG.
It might be possible to experimentally tease apart the effects of
interleaving on discrimination and association. In one such ex-
periment, participants would receive either blocked or interleaved
mathematics practice during the learning phase, as they typically
do, and then take two tests. The first test would assess only
discrimination. For example, students might be shown a random
mixture of five problemsfour problems of one kind (e.g., word
problems requiring a proportion) and one problem of a different
kind (e.g., a word problem requiring the Pythagorean theorem)
and then be asked to identify the problem that does not fit with
the others (the Pythagorean theorem problem). Students would
repeat this task many times with different kinds of problems. On
a second test measuring both discrimination and association,
students would see problems one a time and, for each problem,
choose the correct strategy, but not execute it. Scores on the first
test (discrimination only) should be greater than scores on the
more challenging second test (discrimination and association),
with larger differences between the two test scores reflecting a
poorer ability to associate a kind of problem and its strategy.
Therefore, if interleaving improves association, the difference
between the two test scores should be smaller for students who
interleaved rather than blocked.
Category learning
Finally, although we focused here on mathematics learning,
several studies have examined the effect of interleaved prac-
tice on category learning. For example, participants might see
Problem Strategy
A bug flies 48 m east and then 14 m west.
How far is the bug from where it started?
Number line
Find the length of the line segment with
endpoints (1, 1) and (5, 4).
Find the slope of the line that passes
through the points (1, 1) and (5, 4).
Fig. 5 Discrimination and association. The solution of a mathematics problem requires that students discriminate one kind of problem from another and
associate each kind of problem with an appropriate strategy. Interleaving might improve both skills
Psychon Bull Rev (2014) 21:13231330 1329
photographs of different kinds of birds (jays, finches, swallow,
etc.) one at a time, in an order that was either blocked (each of
the jays, then each of the finches, etc.) or interleaved (jay,
finch, swallow, etc.), and interleaving would produce greater
scores on a subsequent test requiring participants to identify
previously unseen birds (e.g., Birnbaum, Kornell, Bjork, &
Bjork, 2013; Kang & Pashler, 2012; Kornell & Bjork, 2008;
Wahlheim, Dunlosky, & Jacoby, 2011; but see Carpenter &
Mueller, 2013). As with the results of previous interleaved
mathematics tasks, the positive effect of interleaving on cate-
gory learning could also be attributed to an improved ability to
discriminate between, say, a jay and a finch. To our knowl-
edge, though, it remains an untested possibility that this effect
might also reflect a strengthened association between each
category (e.g., finches) and the category name (finch). The
relative contributions of enhanced discrimination and stronger
associations to interleaving effects could be disentangled by
an experiment analogous to the mathematics experiment pro-
posed in the previous section: Participants would receive two
tests: a discrimination-only test requiring them to sort birds (or
identify the one bird that is different from others), and the
usual test requiring them to name novel birds, which would
require both discrimination and association. In summary, al-
though strong evidence exists showing that interleaved prac-
tice can improve both mathematics learning and category
learning, it seems unclear why either of these effects occur.
Author Note This work was supported by the Institute of Education
Sciences, U.S. Department of Education, through Grant No.
R305A110517 to theUniversity of South Florida (PI: D.R.). The opinions
expressed are those of the authors and do not necessarily represent the
views of the U.S. Department of Education. We thank Sandra Stershic for
her help with the data analysis, and we thank Jennifer DeMik, Brendan
Paul, Nancy Self, Liberty Middle School, and Hillsborough County
Public Schools for their participation.
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... In this study, we aimed to determine whether the completion of fully online courses in foundational medical sciences created using strongly evidence-based learning practices led to robust gains in knowledge on those subjects by comparing learners' performances on a pre-course quiz to their performance on a post-course quiz. Examples of these evidencedbased learning practices include use of short videos [13], real-world examples [14], spaced repetition [15], interleaving [16], frequent low-stakes formative assessments [17,18], and others. Additionally, we compared learners' self-confidence on the pre-and post-course quizzes in order to measure changes in confidence that accompany any observed change in knowledge. ...
... Additionally, many of the course lessons include real-world examples, including interviews with clinicians and patients, which can also enhance student learning [14]. Finally, all lessons include spaced repetition and interleaving of the subjects to enhance retention of the subject matter [15][16][17][18]. The lessons were released sequentially over the course period, with a final exam at the end of the course. ...
... Different methods of construction of online and blended courses can greatly affect the outcomes of those courses [21][22][23]. The courses included in this study were purpose-built for online learning using the best practices according to our current knowledge, such as using short videos and relevant clinical examples, with authentic, applied, real-world examples, spaced repetition of concepts, and interleaving [13][14][15][16][17][18]. Therefore, it is important to consider curricular design as a potential confounding factor when comparing disparate online courses. ...
The early stages of medical school involve education in a number of foundational biomedical sciences including genetics, immunology, and physiology. However, students entering medical school may have widely varying levels of background in these areas due to differences in the availability and quality of prior education on these topics. Even students who have recently taken formal courses in these subjects may not feel confident in their level of preparation, leading to anxiety for early-stage medical students. These differences can make it difficult for instructors to create meaningful learning experiences that are appropriate for all students. Additionally, actual or perceived differences in preparation may lead fewer students from diverse backgrounds to apply to medical school. Therefore, creating an efficient and scalable way to increase students' knowledge and confidence in these topics addresses an important need for many medical schools. We recorded pre- and post-course quiz scores for 9790 individuals who completed HMX online courses, developed in accordance with evidence-based learning practices and covering the fundamentals of biochemistry, genetics, immunology, pharmacology, and physiology. Each question was accompanied by a Likert scale question to assess the learner's confidence in their answer. Learners' median post-course quiz performance and self-assessed confidence significantly increased relative to pre-course quiz performance for each course. Improvements were consistent across US-based medical schools, non-US medical schools, and course runs open to the public. This indicates that online courses created using evidence-based learning practices can lead to significant increases in knowledge and confidence for many learners, helping prepare them for further medical education. Supplementary information: The online version contains supplementary material available at 10.1007/s40670-022-01660-4.
... This confirms previous research that the quality of students' individual writing is more related to the regularity of their reflections rather than the amount of reflective writing they produce in crammed sessions [44]. The value of spaced practice [41,32] and interleaving [31] for students have also been shown in multiple other studies from the learning sciences literature [5]. We further investigated the extent to which the writing engagement behaviours changed in the feedback intervention cohort. ...
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Reflective writing is part of many higher education courses across the globe. It is often considered a challenging task for students as it requires self-regulated learning skills to appropriately plan, timely engage and deeply reflect on learning experiences. Despite an advance in writing analytics and the pervasiveness of human feedback aimed to support student reflections, little is known about how to integrate feedback from humans and analytics to improve students' learning engagement and performance in reflective writing tasks. This study proposes a personalised behavioural feedback intervention based on students' writing engagement analytics utilising time-series analysis of digital traces from a ubiquitous online word processing platform. In a semester-long experimental study involving 81 postgraduate students, its impact on learning engagement and performance was studied. The results showed that the intervention cohort engaged statistically significantly more in their reflective writing task after receiving the combined feedback compared to the control cohort which only received human feedback on their reflective writing content. Further analyses revealed that the intervention cohort reflected more regularly at the weekly level, the regularity of weekly reflection led to better performance grades, and the impact on students with low self-regulated learning skills was higher. This study emphasizes the powerful benefits of implementing combined feedback approaches in which the strengths of analytics and human feedback are synthesized to improve student engagement and performance. Further research should explore the long-term sustainability of the observed effects and their validity in other contexts.
... Interleaving represents a form of spaced practice in which the emphasis is on the sequence of items rather than on the amount of spacing between each presentation and the next. Blocked items are presented in a massed fashion, with one complete set of items being followed by a complete set of another group of items (such as AAABBBCCC), whereas an interleaved presentation alternates between the items (such as ABCABCABC; Rohrer, 2012). ...
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This article provides a conceptual review of the principles of input spacing as they might relate specifically to oral task repetition research and presents some of the common methodological considerations from the broader input spacing literature. The specific considerations discussed include the interaction between intersession intervals and retention intervals, the manipulation of posttests as a between‐participants variable, the number of task repetitions, absolute versus relative spacing, the criterion of learning, task type versus exact task repetition, and blocked versus interleaved practice. Each of these considerations is discussed with links, as appropriate, to the relevant empirical input spacing and task repetition literature. The purpose of this review is to highlight how, in many cases, these methodological considerations have been overlooked by task repetition researchers, including in studies where input spacing has and has not been a direct focus, and to suggest ways of addressing these methodological shortcomings in future research. A one‐page Accessible Summary of this article in non‐technical language is freely available in the Supporting Information online and at https://oasis‐
... For example, interleaved practice distributes learning, which may lead to more durable learning overall (Cepeda et al., 2006;Foster et al., 2019). Interleaved practice may also encourage learners to notice di erences between similar problem sets and therefore improve learners' use of appropriate knowledge in each situation (Kang & Pashler, 2012;Rohrer, 2012;Wahlheim et al., 2011). Thus, when implementing interleaved practice, it is important to be mindful of the cost of switching between tasks (Hausman & Kornell, 2014). ...
This chapter provides an overview of the development of three foundational cognitive processes that are relevant for learning in general and for math learning in particular: executive functions, long-term memory, and visuospatial thinking. The chapter begins by reviewing both traditional and state-of-the-art research methods that psychologists use to address questions relating to both cognitive development and learning. Next, the chapter includes a review of behavioral and neural evidence for each of the constructs of interest; an overview of how these processes develop with age; and a discussion of how these processes can inform learning, with a particular focus on K–12 math instruction. Additionally, each section describes how the development of these processes is influenced by environmental factors, such as socioeconomic status, sleep, and parenting, as well as individual variation and atypical development. Finally, the chapter offers evidence-based suggestions for improving both general learning, such as study habits and planning; and math learning, such as reasoning about fractions and algebra.
... In this case, this would be accountable as the learning method that would create the creative ability for the students and apply the creative idea skills to be adapted with the solutions (Jaeger & Adair, 2014). This was based on multiple techniques to stimulate gaining new and challenging feelings during the study (Rohrer, 2012;Wamalwa & Masibo, 2020), and this method could be an aspiring development after using the new learning pattern with the students congruently with the concept of the development of the learning procedure in the twenty-first century integrated with the psychology method to be a more suitable way (Kehinde, 2021;Roediger & Pyc, 2012;. In addition, the teaching technique of STEM was applied with science, technology, engineering and mathematics by using with the creative idea skills of the students. ...
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This research had the objective to compare the learning results with the creative ideas in product design work for product design student groups by using new and old teaching models. The group sampling comprised senior student groups of the Department of Design Education, King Mongkut’s Institute of Technology Ladkrabang totaling 60 people that were classified into two learning groups: 1. The group that used the teacher-centered method totaling 30 people,and 2.the integration learning group of STEM and flipped classroom totaling 30 people. The learning assessment of the creative ideas used the thinking skills test for the product design with the reliability value for Kr-20 that had a difficulty value of (p)=0.436, discrimination value of (r)=0.359, reliability value for KR-20=0.7657 or 76%, and the Cronbach's alpha coefficient that was equal to 0.7286 or 72%. In comparing the result, it was found that the effectiveness for the new teaching model emphasized the integration with multiple teaching techniques by measuring the score level values of the creative ideas that had a higher level than the original teaching model, which used the teacher-centered method. This had a statistical significance level of .05. Moreover, this showed the result of the satisfaction assessment of the students, who learned by using the integration teaching technique of STEM and a flipped classroom to be an excellent level (mean=4.47; SD=0.579), including the happiness relationship during the study (mean=4.65; S.D.=0.483), which had a statistical significance level of .05. Received: 12 January 2022 / Accepted: 6 April 2022 / Published: 5 May 2022
... Doing so can be a way to introduce not just inter-item spacing but also interleaving of itemsthat is, the intermixing of different concepts, categories, or other types of materials during learning (Kang, 2016). The interleaving of closely related concepts when studying, or interleaved practice, has shown promise at enhancing learning and memory in such educationally-relevant domains as mathematics (e.g., Rohrer, 2012) and physics (e.g., Samani & Pan, 2021). However, the optimal approach with which materials are interleaved has yet to be fully established (particularly for such domains as language learning; e.g., Pan, Lovelett, et al., 2019), and the evidence base in favour of interleaved practice is less established than that for the other aforementioned effective learning strategies. ...
Over the past two decades, digital flashcards—that is, computer programmes, smartphone apps, and online services that mimic, and potentially improve upon, the capabilities of traditional paper flashcards—have grown in variety and popularity. Many digital flashcard platforms allow learners to make or use flashcards from a variety of sources and customise the way in which flashcards are used. Yet relatively little is known about why and how students actually use digital flashcards during self-regulated learning, and whether such uses are supported by research from the science of learning. To address these questions, we conducted a large survey of undergraduate students (n = 901) at a major U.S. university. The survey revealed insights into the popularity, acquisition, and usage of digital flashcards, beliefs about how digital flashcards are to be used during self-regulated learning, and differences in uses of paper versus digital flashcards, all of which have implications for the optimisation of student learning. Overall, our results suggest that college students commonly use digital flashcards in a manner that only partially reflects evidence-based learning principles, and as such, the pedagogical potential of digital flashcards remains to be fully realised.
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The aim of the research is to study the impact of The interleaved learning strategy in a blended learning environment on cognitive achievement for students with middle school learning disabilities (LD) in Kuwait, and the research sample (50) students in the sixth grade average of government education schools specialized in teaching students with learning disabilities (LD), and applied a pre-learning test then the sample was taught with interleaved learning strategy where five concepts were given to the subject of ratio and proportionality of the virtual class without intervals and then repeated the same period of time and then repeated the same Concepts in a different order of the following classes in order to stimulate neural pathways to retain information in long-term memory after which a post- learning test was applied and the results showed the positive impact of both the interleaved learning strategy and the e-learning environment at the level of achievement and acquisition of knowledge among students
Written for pre-service and in-service educators, as well as parents of children in preschool through grade five, this book connects research in cognitive development and math education to offer an accessibly written and practical introduction to the science of elementary math learning. Structured according to children's mathematical development, How Children Learn Math systematically reviews and synthesizes the latest developmental research on mathematical cognition into accessible sections that explain both the scientific evidence available and its practical classroom application. Written by an author team with decades of collective experience in cognitive learning research, clinical learning evaluations, and classroom experience working with both teachers and children, this amply illustrated text offers a powerful resource for understanding children's mathematical development, from quantitative intuition to word problems, and helps readers understand and identify math learning difficulties that may emerge in later grades. Aimed at pre-service and in-service teachers and educators with little background in cognitive development, the book distills important findings in cognitive development into clear, accessible language and practical suggestions. The book therefore serves as an ideal text for pre-service early childhood, elementary, and special education teachers, as well as early career researchers, or as a professional development resource for in-service teachers, supervisors and administrators, school psychologists, homeschool parents, and other educators.
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Purpose: To understand how educational disparities unfolded after COVID-19 broke out, this study examined differences in effects of relevant factors on academic achievements before and after the COVID-19 outbreak. Design/methodology/data/approach: Data collected in two time points (2019 and 2020) from 2,699 middle school students as part of the Busan Education Longitudinal Study were used. Structural equation modeling (SEM) was applied to investigate the changes in relationship of the educational outcomes in Korean Language, English Language, and Math, with parental education, parental support, education expenditure, learning attitude, self-directed learning, and previous achievement. Findings/Results: The distributions of test scores demonstrated the possibilities of learning loss in subjects of Korean and English and educational disparities in the subjects of Korean and math. The SEM results revealed that student variables became more influential than parent variables after the pandemic. Especially, the effect of previous achievement on current achievement and the effect of self-directed learning on learning attitude became more prominent. Value: This study provides empirical evidence of the possible effects of COVID-19-related disruptions in education on educational achievements and disparities.
Objective: To investigate the effect of an online module in promoting study strategies based on neuroscience applied to education for first-year dental students at the University of the Andes in Santiago, Chile. Methods: Four weeks after the start of the 2018 first academic semester, all 82 first-year dental students (72% females, 28% males, average 19.0 years old) were invited to voluntarily and anonymously complete the self-reported Study Strategies Questionnaire (SSQ) in a session of an Introduction to Dentistry course, which served as a baseline. Subsequently, the session included an interactive workshop on learning how to learn so that students could analyse how the human brain learns and relate this information to mental tools to foster learning. Furthermore, during the semester, students were sent information via email to reinforce the content they were exposed to during the learning how to learn activity so that they could use the toolbox of study techniques to improve their learning in all subjects. At the end of the semester, students were invited to voluntarily and anonymously complete a second SSQ to assess the effects of the study intervention. Exam marks from the previous (2017) and studied year (2018), as well as both SSQ results, were compared and analysed using IBM Statistical Package for the Social Sciences (SPSS). Results: A total of 75 and 71 students answered the SSQ before and after the intervention, respectively. The mean exam mark from 2017 was 63.7% (SD=8.8), while in 2018, it was 69.6% (SD=5.0) (p<0.044); the effect size of the intervention was 0.75. The most significant changes observed after the intervention were reductions in the number of students who studied while checking messages on their smartphones (p=0.001), studied by highlighting and/or underlining in their notes or textbooks (p<0.0001) and studied the day before an exam (p>0.0001). On the other hand, there were significant increases in the number of students who studied without access to social networks (p=0.046), wrote notes or words in the margins of texts (p=0.001), practised self-testing (p=0.001), and studied the day before an exam (p<0.0001). Conclusions: An online module to promote evidence-based study strategies in first-year dental students can have an impact on increasing students' marks as well as on some practices that can improve their academic achievements and learning.
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Sets of mathematics problems are generally arranged in 1 of 2 ways. With blocked practice, all problems are drawn from the preceding lesson. With mixed review, students encounter a mixture of problems drawn from different lessons. Mixed review has 2 features that distinguish it from blocked practice: Practice problems on the same topic are distributed, or spaced, across many practice sets; and problems on different topics are intermixed within each practice set. A review of the relevant experimental data finds that each feature typically boosts subsequent performance, often by large amounts, although for different reasons. Spacing provides review that improves long-term retention, and mixing improves students' ability to pair a problem with the appropriate concept or procedure. Hence, although mixed review is more demanding than blocked practice, because students cannot assume that every problem is based on the immediately preceding lesson, the apparent benefits of mixed review suggest that this easily adopted strategy is underused.
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This article constitutes an optimistic argument that basic research on human cognitive processes has yielded principles and phenomena that have considerable promise in guiding the design and execution of college instruction. To illustrate that point, four somewhat interrelated principles and phenomena arc outlined and some possible implications and applications of those principles and phenomena are put forward.
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Many students are being left behind by an educational system that some people believe is in crisis. Improving educational outcomes will require efforts on many fronts, but a central premise of this monograph is that one part of a solution involves helping students to better regulate their learning through the use of effective learning techniques. Fortunately, cognitive and educational psychologists have been developing and evaluating easy-to-use learning techniques that could help students achieve their learning goals. In this monograph, we discuss 10 learning techniques in detail and offer recommendations about their relative utility. We selected techniques that were expected to be relatively easy to use and hence could be adopted by many students. Also, some techniques (e.g., highlighting and rereading) were selected because students report relying heavily on them, which makes it especially important to examine how well they work. The techniques include elaborative interrogation, self-explanation, summarization, highlighting (or underlining), the keyword mnemonic, imagery use for text learning, rereading, practice testing, distributed practice, and interleaved practice. To offer recommendations about the relative utility of these techniques, we evaluated whether their benefits generalize across four categories of variables: learning conditions, student characteristics, materials, and criterion tasks. Learning conditions include aspects of the learning environment in which the technique is implemented, such as whether a student studies alone or with a group. Student characteristics include variables such as age, ability, and level of prior knowledge. Materials vary from simple concepts to mathematical problems to complicated science texts. Criterion tasks include different outcome measures that are relevant to student achievement, such as those tapping memory, problem solving, and comprehension. We attempted to provide thorough reviews for each technique, so this monograph is rather lengthy. However, we also wrote the monograph in a modular fashion, so it is easy to use. In particular, each review is divided into the following sections: General description of the technique and why it should work How general are the effects of this technique? 2a. Learning conditions 2b. Student characteristics 2c. Materials 2d. Criterion tasks Effects in representative educational contexts Issues for implementation Overall assessment The review for each technique can be read independently of the others, and particular variables of interest can be easily compared across techniques. To foreshadow our final recommendations, the techniques vary widely with respect to their generalizability and promise for improving student learning. Practice testing and distributed practice received high utility assessments because they benefit learners of different ages and abilities and have been shown to boost students’ performance across many criterion tasks and even in educational contexts. Elaborative interrogation, self-explanation, and interleaved practice received moderate utility assessments. The benefits of these techniques do generalize across some variables, yet despite their promise, they fell short of a high utility assessment because the evidence for their efficacy is limited. For instance, elaborative interrogation and self-explanation have not been adequately evaluated in educational contexts, and the benefits of interleaving have just begun to be systematically explored, so the ultimate effectiveness of these techniques is currently unknown. Nevertheless, the techniques that received moderate-utility ratings show enough promise for us to recommend their use in appropriate situations, which we describe in detail within the review of each technique. Five techniques received a low utility assessment: summarization, highlighting, the keyword mnemonic, imagery use for text learning, and rereading. These techniques were rated as low utility for numerous reasons. Summarization and imagery use for text learning have been shown to help some students on some criterion tasks, yet the conditions under which these techniques produce benefits are limited, and much research is still needed to fully explore their overall effectiveness. The keyword mnemonic is difficult to implement in some contexts, and it appears to benefit students for a limited number of materials and for short retention intervals. Most students report rereading and highlighting, yet these techniques do not consistently boost students’ performance, so other techniques should be used in their place (e.g., practice testing instead of rereading). Our hope is that this monograph will foster improvements in student learning, not only by showcasing which learning techniques are likely to have the most generalizable effects but also by encouraging researchers to continue investigating the most promising techniques. Accordingly, in our closing remarks, we discuss some issues for how these techniques could be implemented by teachers and students, and we highlight directions for future research.
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The authors examined the methodologies of articles in teaching-and-learning research journals, published in 1994 and in 2004, and classified them as either intervention (based on researcher-manipulated variables) or nonintervention. Consistent with the findings of Hsieh et al., intervention research articles declined from 45% in 1994 to 33% in 2004. For nonintervention articles, the authors recorded the incidence of “causal” statements (e.g., if teachers/schools/parents did X, then student/child outcome Y would likely result). Nonintervention research articles containing causal statements increased from 34% in 1994 to 43% in 2004. It appears that at the same time intervention studies are becoming less prevalent in the teaching-and-learning research literature, researchers are more inclined to include causal statements in nonintervention studies.
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There has been a recent upsurge of interest in exploring how choices of methods and timing of instruction affect the rate and persistence of learning. The authors review three lines of experimentation—all conducted using educationally relevant materials and time intervals— that call into question important aspects of common instructional practices. First, research reveals that testing, although typically used merely as an assessment device, directly potentiates learning and does so more effectively than other modes of study. Second, recent analysis of the temporal dynamics of learning show that learning is most durable when study time is distributed over much greater periods of time than is customary in educational settings. Third, the interleaving of different types of practice problems (which is quite rare in math and science texts) markedly improves learning. The authors conclude by discussing the frequently observed dissociation between people’s perceptions of which learning procedures are most effective and which procedures actually promote durable learning.
The learning benefits of contextual interference have been frequently demonstrated in different settings using novice learners. The purpose of the present study was to test such effects with skilled athletic performers. Scheduling differences for biweekly additional (“extra”) batting-practice sessions of a collegiate baseball team were examined. 30 players (ns = 10) were blocked on skill and then randomly assigned to one of three groups. The random and blocked groups received 2 additional batting-practice sessions each week for 6 wk. (12 sessions), while the control group received no additional practice. The extra sessions consisted of 45 pitches, 15 fastballs, 15 curve-balls, and 15 change-up pitches. The random group received these pitches in a random order, while the blocked group received all 15 of one type, then 15 of the next type, and finally 15 of the last type of pitch in a blocked fashion. All subjects received a pretest of 45 randomly presented pitches of the three varieties. After 6 wk. of extra batting practice, all subjects received two transfer tests, each of 45 trials; one was presented randomly and one blocked. The transfer tests were counterbalanced across subjects. Pretest analysis showed no significant differences among groups. On both the random and blocked transfer tests, however, the random group performed with reliably higher scores than the blocked group, who performed better than the control group. When comparing the pretest to the random transfer test, the random group improved 56.7%, the blocked group 24.8%, and the control group only 6.2%. These findings demonstrate the contextual interference effect to be robust and beneficial even to skilled learners in a complex sport setting.
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.
Both metacognitive and associative models have been proposed to account for children's strategy discovery and use. Models based on only metacognitive or only associative mechanisms cannot entirely account for the observed mix of variability and constraint revealed by recent microgenetic studies of children's strategy change. We propose a new approach where metacognitive and associative mechanisms interact in a competitive negotiation. This approach provides the flexibility to model the observed variability and constraint.