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Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning

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Making Things Hard on Yourself, But in a Good Way:
Creating Desirable Difficulties to Enhance Learning
Elizabeth L. Bjork and Robert Bjork
University of California, Los Angeles
Please describe your current position and research interests.
Elizabeth Ligon Bjork: I am Professor and Senior Vice Chair of Psychology at the University of
California, Los Angeles, Academic Senate. My research interests have included visual attention
and developmental processes but now focus on practical and theoretical issues in human memory
and learning, particularly the role that inhibitory processes play in an efficient memory system.
Robert A. Bjork: I am Distinguished Research Professor of Psychology at the University of
California, Los Angeles. My research focuses on human learning and memory and on the
implications of the science of learning for instruction and training.
How did you get interested in studying the facilitating effect of apparent impediments to
learning?
Elizabeth Bjork: My interests in optimizing learning were triggered by interactions with students
lamenting during office hours how hard they had studied, only then to perform poorly on a just-
given exam. This motivated me to examine why students’ study activities were sometimes so
ineffective.
Robert Bjork: My interests go back to my efforts—as a graduate student—to understand the
relationship of forgetting and learning, especially why inducing forgetting often enhances
subsequent learning. My interests in the application of “desirable difficulties” were fanned by my
experiences teaching and coaching and from what I learned as Chair of the National Research
Council Committee on Techniques for the Enhancement of Human Performance (1988–1994).
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What has been the real-world impact of this work?
Overall, the impact has been modest, but there are multiple indications that the impact of basic
research findings on educational practices is increasing. It is a slow process, in part, because
optimizing instruction requires some unintuitive innovations in how the conditions of instruction
are structured.
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Making Things Hard on Yourself, But in a Good Way:
Creating Desirable Difficulties to Enhance Learning
As teachers—and learners—the two of us have had both a professional and personal interest in
identifying the activities that make learning most effective and efficient. What we have
discovered, broadly, across our careers in research, is that optimizing learning and instruction
often requires going against one’s intuitions, deviating from standard instructional practices, and
managing one’s own learning activities in new ways. Somewhat surprisingly, the trials and errors
of everyday living and learning do not seem to result in the development of an accurate mental
model of the self as learner or an appreciation of the activities that do and do not foster learning.
The basic problem learners confront is that we can easily be misled as to whether we are
learning effectively and have or have not achieved a level of learning and comprehension that
will support our subsequent access to information or skills we are trying to learn. We can be
misled by our subjective impressions. Rereading a chapter a second time, for example, can
provide a sense of familiarity or perceptual fluency that we interpret as understanding or
comprehension, but may actually be a product of low-level perceptual priming. Similarly,
information coming readily to mind can be interpreted as evidence of learning, but could instead
be a product of cues that are present in the study situation, but that are unlikely to be present at a
later time. We can also be misled by our current performance. Conditions of learning that make
performance improve rapidly often fail to support long-term retention and transfer, whereas
conditions that create challenges and slow the rate of apparent learning often optimize long-term
retention and transfer.
Learning versus Performance
This apparent paradox is a new twist on an old and time-honored distinction in psychology—
namely, the distinction between learning and performance. Performance is what we can observe
and measure during instruction or training. Learning—that is, the more or less permanent change
in knowledge or understanding that is the target of instruction—is something we must try to infer,
and current performance can be a highly unreliable index of whether learning has occurred. For a
review of the history and current status of the learning versus performance distinction, see
Soderstrom and Bjork (in press).
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Learning Without Performance and Performance Without Learning
Decades ago, learning theorists were forced to distinguish between learning and performance
because experiments revealed that considerable learning could happen across a period when no
change was apparent in performance. In latent-learning experiments with animals, for example,
periods of free exploration of a maze, during which the animal’s behavior seemed aimless, were
shown—once reward was introduced—to have produced considerable learning. Similarly, in
research on motor skills, investigators found that learning continued across trials during which
the build-up of fatigue suppressed performance.
More recently, a variety of experiments—some of which we summarize below—have
demonstrated that the converse is true as well: Namely, substantial improvements in performance
across practice or training sessions can occur without significant learning (as revealed after a
delay or in another context). To the extent, therefore, that people interpret current performance as
a valid measure of learning, they become susceptible to misassessing whether learning has or has
not occurred.
Storage Strength Versus Retrieval Strength
At a theoretical level, we (Bjork & Bjork, 1992) distinguish between the storage strength and the
retrieval strength of information or skills stored in memory. Storage strength reflects how
entrenched or interassociated a memory representation is with related knowledge and skills,
whereas retrieval strength reflects the current activation or accessibility of that representation and
is heavily influenced by factors such as situational cues and recency of study or exposure.
Importantly, we assume that current performance is entirely a function of current retrieval
strength, but that storage strength acts to retard the loss (forgetting) and enhance the gain
(relearning) of retrieval strength. The key idea for present purposes is that conditions that most
rapidly increase retrieval strength differ from the conditions that maximize the gain of storage
strength. In other words, if learners interpret current retrieval strength as storage strength, they
become susceptible to preferring poorer conditions of learning to better conditions of learning.
Introducing Desirable Difficulties to Enhance Learning
and Instruction
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So what are these better conditions of learning that, while apparently creating difficulty, actually
lead to more durable and flexible learning? Such desirable difficulties (Bjork, 1994; 2013)
include varying the conditions of learning, rather than keeping them constant and predictable;
interleaving instruction on separate topics, rather than grouping instruction by topic (called
blocking); spacing, rather than massing, study sessions on a given topic; and using tests, rather
than presentations, as study events.
Before proceeding further, we need to emphasize the importance of the word desirable.
Many difficulties are undesirable during instruction and forever after. Desirable difficulties,
versus the array of undesirable difficulties, are desirable because they trigger encoding and
retrieval processes that support learning, comprehension, and remembering. If, however, the
learner does not have the background knowledge or skills to respond to them successfully, they
become undesirable difficulties.
Varying the Conditions of Practice
When instruction occurs under conditions that are constrained and predictable, learning tends to
become contextualized. Material is easily retrieved in that context, but the learning does not
support later performance if tested at a delay, in a different context, or both. In contrast, varying
conditions of practice—even varying the environmental setting in which study sessions take place
—can enhance recall on a later test. For example, studying the same material in two different
rooms rather than twice in the same room leads to increased recall of that material (Smith,
Glenberg, & Bjork, 1978)—an empirical result that flies in the face of the common how-
to-study suggestion to find a quiet, convenient place and do all your studying there.
A study of children’s learning provides a striking illustration of the benefits of varying
conditions of practice. Eight-year-olds and 12-year-olds practiced throwing beanbags at a target
on the floor with their vision occluded at the time of each throw. For each age group, half of the
children did all their practicing throwing to a target at a fixed distance (for example, 3 feet for the
8-year-olds), while the other half threw to targets that were closer or farther away. After the
learning sessions and a delay, all children were tested at the distance used in the fixed-practice
condition for their age group (Kerr & Booth, 1978).
Common sense would suggest that the children who practiced at the tested distance
would perform better than those who had never practiced at that distance, but the opposite was
true for both age groups. The benefits of variation—perhaps learning something about adjusting
the parameters of the motor program that corresponded to the throwing motion—outweighed any
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benefits of being tested at the practiced distance. Many other studies have shown that when
testing after training takes place under novel conditions, the benefits of variation during learning
are even larger.
Spacing Study or Practice Sessions
The effects of distributed practice on learning are complex. Although massing practice (for
example, cramming for exams) supports short-term performance, spacing practice (for example,
distributing presentations, study attempts, or training trials) supports long-term retention. The
benefits of spacing on long-term retention, called the spacing effect, have been demonstrated for
all manner of materials and tasks, types of learners (human and animal), and time scales; it is one
of the most general and robust effects from across the entire history of experimental research on
learning and memory.
Rather than describing any of the myriad studies that have demonstrated the benefits of
spacing, we will simply stress the importance of incorporating spacing and avoiding massing in
managing learning. Massing repeated-study activities is often not only convenient, but it can also
seem logical from the standpoint of organizing one’s learning of different topics, and it frequently
results in rapid gains in apparent learning. Good test performance following an all-night
cramming session is certainly rewarding, but little of what was recallable on the test will remain
recallable over time. In contrast, a study schedule that spaces study sessions on a particular topic
can produce both good exam performance and good long-term retention. Furthermore, because
new learning depends on prior learning, spacing study sessions optimally can also enhance
transfer of knowledge and provide a foundation for subsequent new learning.
Whether students so frequently mass their study activities because they believe that
massing is good, or simply because they get behind and are forced into massed study sessions
before exams, is not clear. There is recent evidence, though, that students believe that
information that is more important or valuable should be studied again sooner, rather than later,
perhaps owing to the intuition that restudying should happen before too much forgetting has
occurred (Cohen, Yan, Halamish, & Bjork, in press). Such an intuition, however, leads students
to avoid spacing repeated study sessions—and, of course, also to avoid the benefits of spacing.
Interleaving versus Blocking Instruction on Separate
To-Be-Learned Tasks
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Interleaving the practice of separate topics or tasks is an excellent way to introduce spacing and
other learning dynamics. In a classic comparison of interleaving and blocking (Shea & Morgan,
1979), participants practiced three different movement patterns, each requiring the participants to
knock down three of six hinged barriers rapidly on a pinball-like apparatus in a prescribed order.
All participants received 18 trials on each pattern, but in the interleaved condition, practice on a
given trial was randomly determined, whereas in the blocked condition, one pattern at a time was
practiced.
As you probably suspect, participants given blocked practice improved more rapidly than
those given interleaved/random practice. Thus, if the researchers had stopped their study at the
end of training, blocking of practice would have seemed the superior learning procedure. But,
instead, participants returned 10 days later and were retested under either blocked or
interleaved/random conditions. Under interleaved/random testing conditions, participants who
had practiced under interleaved conditions performed far better than did the blocked-practice
participants, who appeared, when tested under a random schedule, to have learned virtually
nothing. Under blocked testing conditions, performance was essentially the same for both groups,
but the small difference still favored the interleaved group.
The skills literature includes many replications of the pattern that blocked practice
appears optimal for learning, but interleaved practice actually results in superior long-term
retention and transfer of skills (for a review, see Lee, 2012), and research illustrates that learners
—as well as instructors—are at risk of being fooled by that pattern. For example, when
participants who had learned three different keystroke patterns were asked to predict their
performance on a test the next day, those given interleaved practice predicted their performance
quite closely, whereas those given blocked practice were markedly overconfident (Simon &
Bjork, 2001). In effect, the blocked-practice group misinterpreted their good performance during
practice as evidence of long-term learning, rather than a product of the local (that is, blocked)
conditions. Said differently, they misinterpreted the retrieval strength of a given keystroke pattern
as an index of its storage strength.
Other results illustrate that the benefits of interleaved practice extend beyond the learning
of motor skills. For example, when participants were asked to learn formulas for calculating the
volumes of different solids, such as a truncated cone, in either a blocked or interleaved manner,
interleaved instruction enhanced performance on a delayed test. The size of the long-term
advantage of interleaved practice was striking: 63 percent versus 20 percent of new problems
worked correctly a week later (Rohrer & Taylor, 2007).
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More recently and surprisingly, we have found that interleaving even enhances inductive
learning (Kornell & Bjork, 2008). When participants were asked to learn the styles of each of 12
artists based on a sample of 6 paintings by each artist, interleaving a given artist’s paintings
among the paintings by other artists—versus presenting that artist’s paintings one after another
(blocking)—enhanced participants’ later ability to identify the artist responsible for each of a
series of new paintings. This result is surprising because blocking would seem to make it easier to
note the commonalities that characterize a particular artist’s style. Indeed, as illustrated in Figure
1, the majority of participants—when asked after the test whether interleaving or blocking had
helped them learn an artist’s style better—definitely had the impression that blocking had been
more effective than interleaving, the opposite of their actual learning. Blocking may indeed have
facilitated noticing commonalities, but the final test required distinguishing among the artists, and
interleaving may have fostered learning the differences as well as similarities among the styles of
different artists.
Why might interleaving enhance long-term retention and transfer? One theory suggests
that having to resolve the interference among the different things under study forces learners to
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notice similarities and differences among them, resulting in the encoding of higher-order
representations, which then foster both retention and transfer. Another explanation suggests that
interleaving forces learners to reload memories: If required to do A, then B, then C, and then A
again, for example, the memory for how to do A must be reloaded a second time, whereas doing
A and then A again does not involve the same kind of reloading. Such repeated reloadings are
presumed to foster learning and transfer to the reloading that will be required when that
knowledge or skill is needed at a later time.
From the standpoint of our theoretical framework (Bjork & Bjork, 1992), learning from
reloading is an instance of a broader dynamic in human memory: Namely, that forgetting (losing
retrieval strength) creates the opportunity for increasing the storage strength of to-be-learned
information or skills. Said differently, when some skill or knowledge is maximally accessible
from memory, little or no learning results from additional instruction or practice.
Generation Effects and Using Tests (Rather Than Presentations) as Learning Events
An effect that rivals the spacing effect for its generality and its significance for instruction and
learning is the generation effect, which refers to the long-term benefit of generating an answer,
solution, or procedure versus being presented that answer, solution, or procedure. Basically, any
time that you, as a learner, look up an answer or have somebody tell or show you something that
you could, drawing on current cues and your past knowledge, generate instead, you rob yourself
of a powerful learning opportunity. Retrieval, in effect, is a powerful “memory modifier” (Bjork,
1975).
Closely related to the generation effect are the benefits that accompany retrieving
information studied earlier. Much laboratory research (for example, Landauer & Bjork, 1978;
Carrier & Pashler, 1992) has demonstrated the power of tests as learning events, and, in fact, a
test or retrieval attempt, even when no corrective feedback is given, can be considerably more
effective in the long term than reading material over and over. The reason why rereading is such a
typical mode of studying derives, we believe, from a faulty model of how we learn and
remember: We tend to think of our memories as working much like an audio/video recorder, so if
we read and reread or take verbatim notes, the information will eventually write itself on our
memories. Nothing, however, could be further from the way we actually learn and remember.
Unfortunately, the effectiveness of tests as learning events remains largely
underappreciated, in part because testing is typically viewed as a vehicle of assessment, not a
vehicle of learning. As Henry L. Roediger, Kathleen B. McDermott, and Mark A. McDaniel
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describe in their essay in this chapter, however, recent research using more educationally realistic
materials and retention intervals has clearly demonstrated the pedagogical benefits of tests (for
example, Roediger & Karpicke, 2006). Similar to the pattern with variation, spacing, and
interleaving, repeated study opportunities appear, in the short term, to be more effective than
repeated testing, but testing produces better recall in the long term.
Two other pedagogical benefits of tests must be mentioned: First, tests have
metacognitive benefits in terms of indentifying whether information has or has not been
understood and/or learned. A student’s ability, for example, when going back over a chapter in a
textbook, to judge whether information will be recallable on an upcoming examination is severely
limited, whereas attempting to answer a fellow student’s questions on the chapter can identify
what has and has not been learned.
The second, related benefit is that tests can potentiate the effectiveness of subsequent
study opportunities even under conditions that insure learners will be incorrect on the test
(Kornell, Hays, & Bjork, 2009). Even taking a test before a first reading of to-be-learned material
can potentiate one’s learning of it, and not only for the specifically pretested information but also
for related information (e.g., Little & Bjork, 2011). Thus, when needing to read a new chapter in
your textbook that is followed by test questions, you may want to try answering those questions
first and then read the chapter. Again, the basic message is that we need to spend less time
restudying and more time testing ourselves.
Concluding Comments
For those of you who are students, we hope we have convinced you to take a more active role in
your learning by introducing desirable difficulties into your own study activities. Above all, try to
rid yourself of the idea that memory works like a tape or video recorder and that re-exposing
yourself to the same material over and over again will somehow write it onto your memory.
Rather, assume that learning requires an active process of interpretation—that is, mapping new
things we are trying to learn onto what we already know. (There’s a lesson here for those of you
who are teachers—or parents—as well: Consider how you might introduce desirable difficulties
into the teaching of your students or children.)
Be aware, too, when rereading a chapter or your notes, that prior exposures create a sense
of familiarity that can easily be confused with understanding. And perhaps most importantly, keep
in mind that retrieval—much more than restudying—acts to modify your memory by making the
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information you practice retrieving more likely to be recallable again in the future and in different
contexts. In short, try to spend less time on the input side and more time on the output side, such
as summarizing what you have read from memory or getting together with friends and asking
each other questions. Any activities that involve testing yourself—that is, activities that require
you to retrieve or generate information, rather than just representing information to yourself—
will make your learning both more durable and flexible.
Finally, we cannot overstate the importance of learning how to manage your own learning
activities. In a world that is ever more complex and rapidly changing, and in which learning on
one’s own is becoming ever more important, learning how to learn is the ultimate survival tool.
Suggested Further Reading
Bjork, R. A. (2011). On the symbiosis of learning, remembering, and forgetting. In A. S.
Benjamin (Ed.), Successful remembering and successful forgetting: a Festschrift in honor of
Robert A. Bjork (pp. 1-22). London, UK: Psychology Press.
Bjork, R. A., & Bjork, E. L. (2006). Optimizing treatment and instruction: Implications of a new
theory of disuse. In L-G. Nilsson and N. Ohta (Eds.), Memory and society: Psychological
perspectives (pp. 109–133). Hove, East Sussex, England, and New York: Psychology Press.
Bjork, R. A., Dunlosky, J., & Kornell, N. (2013). Self-regulated learning: Beliefs, techniques, and
illusions. Annual Review of Psychology. 64, 417-444.
References
Bjork, R. A. (1975). Retrieval as a memory modifier. In R. Solso (Ed.), Information processing
and cognition: The Loyola Symposium, pp. 123–144. Hillsdale, NJ: Erlbaum.
Bjork, R. A. (1994). Memory and metamemory considerations in the training of human beings. In
J. Metcalfe and A. Shimamura (Eds.), Metacognition: Knowing about knowing (pp. 185–205).
Cambridge, MA: MIT Press.
Bjork, R. A. (2013). Desirable difficulties perspective on learning. In H. Pashler (Ed.),
Encyclopedia of the mind. Thousand Oaks: Sage Reference.
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Bjork, R. A., & Bjork, E. L. (1992). A new theory of disuse and an old theory of stimulus
fluctuation. In A. Healy, S. Kosslyn, & R. Shiffrin (Eds.), From learning processes to cognitive
processes: Essays in honor of William K. Estes (Vol. 2, pp. 35–67). Hillsdale, NJ: Erlbaum.
Carrier, M., & Pashler, H. (1992). The influence of retrieval on retention. Memory & Cognition,
20, 633–642.
Kerr, R., & Booth, B. (1978). Specific and varied practice of a motor skill. Perceptual and Motor
Skills, 46, 395–401.
Kornell, N., & Bjork, R. A. (2008). Learning concepts and categories: Is spacing the “enemy of
induction”? Psychological Science, 19, 585–592.
Kornell, N., Hays, M. J., & Bjork, R. A. (2009). Unsuccessful retrieval attempts enhance
subsequent learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 35,
989–998.
Landauer, T. K., & Bjork, R. A. (1978). Optimum rehearsal patterns and name learning. In M. M.
Gruneberg, P. E. Morris, & R. N. Sykes (Eds.), Practical aspects of memory (pp. 625–632).
London: Academic Press.
Lee, T.D. (2012). Contextual interference: Generalizability and limitations. In N.J. Hodges &
A.M. Williams (Eds.), Skill acquisition in sport: Research, theory, and practice (2nd ed) (pp. 79-
93). London, UK: Routledge.
Little, J. L., & Bjork, E. L. (2011). Pretesting with multiple-choice questions facilitates learning.
In L. Carlson, C. Hölscher, & T. Shipley, (Eds.), Proceedings of the 33rd Annual Conference of the
Cognitive Science Society (pp. 294-299).
Roediger, H.L., & Karpicke, J.D. (2006). Test-enhanced learning: Taking memory tests improves
long-term retention. Psychological Science, 17, 249–255.
Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics practice problems improves
learning. Instructional Science, 35, 481–498.
Shea, J.B., & Morgan, R.L. (1979). Contextual interference effects on the acquisition, retention,
and transfer of a motor skill. Journal of Experimental Psychology: Human Learning and
Memory, 5, 179–187.
Simon, D., & Bjork, R. A. (2001). Metacognition in motor learning. Journal of Experimental
Psychology: Learning, Memory, and Cognition, 27, 907–912.
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Smith, S. M., Glenberg, A. M., & Bjork, R. A. (1978). Environmental context and human
memory. Memory & Cognition, 6, 342–353.
Soderstrom, N. C., & Bjork, R. A. (in press). Learning versus performance. In D. S. Dunn
(Ed.), Oxford bibliographies online: Psychology. New York: Oxford University Press.
Tauber, S. K., Dunlosky, J., Rawson, K. A., Wahlheim, C. N., & Jacoby, L. L. (2013). Self-
regulated learning of a natural category: Do people interleave or block exemplars during
study? Psychonomic Bulletin & Review, 20, 356-363.
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... Successfully retrieved information should contribute to conceptual learning (Endres et al., 2017;Karpicke et al., 2016;Ortega-Tudela et al., 2019;Roediger & Karpicke, 2006b;Roelle & Berthold, 2017;van Gog & Kester, 2012;Waldeyer et al., 2020), as students are forced to "reactivate and operate on memory traces either by elaborating mnemonic representations or by creating multiple retrieval routes to them" (Roediger & Karpicke, 2006a, p. 197). From the perspective of desirable difficulties (Bjork & Bjork, 2011) adding retrieval could make the induced generative processes of non-interactive teaching more difficult which may stimulate additional consolidation processes that promote deep comprehension. Second, the generative processing view argues that non-interactive teaching is additionally effective because teaching triggers generative processing (i.e., inference-making, elaborations) ...
Article
Teaching previously learned contents to (fictitious) peers is regarded as a beneficial activity that aids learning. However, it is still an open question which cognitive mechanism (generating versus retrieving information) account for this learning‐by‐teaching effect. To examine the role of retrieval during generative processing while learning‐by‐teaching, we conducted an experiment. After a learning phase about the human respiratory system, university students (N = 108) either taught the learned contents with (open‐book teaching) or without (closed‐book teaching) access to the learning material. Students in the control group restudied the contents. Results indicated that teaching was not more beneficial than restudying regarding students’ learning outcome (i.e., retention, drawing knowledge, transfer knowledge). However, open‐book teaching was more effective than closed‐book teaching regarding students’ retention. This effect was mediated by the richness (i.e., number of concepts) and completeness of students’ explanations. The findings suggest that retrieval failure may constrain potential effects of closed‐book explaining. This article is protected by copyright. All rights reserved.
... It is important that the difficulty be desirable and not so difficult the learner cannot process the material or lose motivation or self-efficacy towards the target material. Importantly, just because something is made to be difficult or more cognitively taxing, does not necessarily make it desirable or mean it will improve long-term learning (Bjork & Bjork, 2011;Metcalfe, 2011;Persellin & Daniels, 2018). Common examples of DDs are: ...
Thesis
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Improving retention of learned content by means of a practice test is a learning strategy that has been researched since a century and has been consistently found to be more effective than comparable learning strategies such as restudy (i.e., the testing effect). Most importantly, practicing test questions has been found to outperform restudy even when no additional information about the correct answers was provided to practice test takers, rendering practice tests effective and efficient in fostering retention of learning content. Since 15 years, additional scientific attention is devoted to this memory phenomenon and additional research investigated to what extend practicing test questions is relevant in real-world educational settings. This dissertation first presents the evidence for testing effects in applied educational settings by presenting key publications and presenting findings from a methodological review conducted for this purpose. Within this dissertation, theories are presented why practicing test questions should benefit learning in real-world educational settings even without the provision of additional information and key variables for the effectiveness of practicing test questions are presented. Four studies presented in this dissertation aimed at exploring these assumptions in actual university classrooms while also trying to implement new methods of practicing learning content and thus augment course procedures. Findings from these studies—although not often consistent—will be incorporated and interpreted in the light of the theoretical accounts on the testing effect. The main conclusion that can be drawn from this dissertation is that, given the right circumstances, practicing test questions can elicit beneficial effects on the retention of learning content that are independent of additional information and thus taking a practice test per se, can foster retention of real-world learning content.
Article
Background Many learning methods of mathematical reasoning encourage imitative procedures (algorithmic reasoning, AR) instead of more constructive reasoning processes (creative mathematical reasoning, CMR). Recent research suggest that learning with CMR compared to AR leads to better performance and differential brain activity during a subsequent test. Here, we considered the role of individual differences in cognitive ability in relation to effects of CMR. Methods We employed a within-subject intervention (N=72, MAge=18.0) followed by a brain-imaging session (fMRI) one week later. A battery of cognitive tests preceded the intervention. Participants were divided into three cognitive abilitity groups based on their cognitive score (low, intermediate and high). Results On mathematical tasks previously practiced with CMR compared to AR we observed better performance, and higher brain activity in key regions for mathematical cognition such as left angular gyrus and left inferior/middle frontal gyrus. The CMR-effects did not interact with cognitive ability, albeit the effects on performance were driven by the intermediate and high cognitive ability groups. Conclusions Encouraging pupils to engage in constructive processes when learning mathematical reasoning confers lasting learning effects on brain activation, independent of cognitive ability. However, the lack of a CMR-effect on performance for the low cognitive ability group suggest future studies should focus on individualized learning interventions, allowing more opportunities for effortful struggle with CMR.
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