*arrow_back*Back to Research

#### Memory: Forgetting, Spacing and Interleaving

*Once students have successfully Encoded information, we need to ensure that those memories are stored and can be retrieved. The papers in this section dig into this absolutely fascinating area, specifically with regard to forgetting, spacing and interleaving. The power of Testing was such a revelation to me that it is a separate section. There are also profound implications for students' revision, which will also be dealt with explicitly in the Revision section. The underlying message running throughout these papers blows my mind - in order to improve learning, we need to make it more difficult. This may appear in direct opposition to the work outlined in the Cognitive Load Theory section, which described conditions needed to make learning as easy as possible. For me, the matter is resolved by using the principles of Cognitive Load Theory in early skill inquisition and during the encoding process, removing all unnecessary load on working memory, and then adopting the recommendations of Bjork and others for increasing the challenge. Bjork's paper on Desirable Difficulties brings this all together beautifully.*

**Research Paper Title:**Learning Versus Performance: An Integrative Review

**Author(s):**Nicholas C. Soderstrom and Robert A. Bjork

**My Takeaway:**

It is no exaggeration to say that this paper has changed my whole approach to teaching. The main premise is one of those things that sounds so obvious when you say it out loud, but I had been missing it for the first 12 years of my career: learning and performance are two different things. The ultimate goal of instruction should be to facilitate long-term learning—that is, to create relatively permanent changes in comprehension, understanding, and skills of the types that will support long-term retention and transfer. During the instruction or training process, however, all we can observe and measure is performance. That would all be fine, apart from the rather inconvenient fact that current performance can be a highly unreliable guide to whether learning has happened. During lessons, teachers, consciously or otherwise, provide cues and prompts to elicit correct answers. Students are also pretty good at mimicking, which allows them to say what they think the teacher wants to hear. All of this boosts performance, but may have no impact on learning. Hence, we are at risk of being fooled by current performance, which can lead us as teachers to choose less effective conditions of learning over more effective conditions - i.e. use strategies that lead to short-terms gains in performance, such as teaching to a particular test. Moreover, it can lead students to prefer certain revision techniques, such as cramming, over others as they can see short-term improvements in performance. Here is the ultimate kicker - high performance may lead to lower learning! This next point is so important that i I am going to put it in bold:

**when we design lessons to boost pupils performance, we may actually hinder their long term learning. Likewise, conditions that induce the most errors during acquisition are often the conditions that lead to the most learning**. The reasons behind this incredible finding are discussed in the paper

*On the Symbiosis of Learning and Forgetting*below. The crucial distinction between learning and performance has huge implications for teaching, revision and lesson observation are huge, and is directly to related to concepts such as spacing, interleaving, and overlearning which will be discussed further in this section.

**My favourite quote:**

*Given that the goal of instruction and practice— whether in the classroom or on the field—should be to facilitate learning, instructors and students need to appreciate the distinction between learning and performance and understand that expediting acquisition performance today does not necessarily translate into the type of learning that will be evident tomorrow. On the contrary, conditions that slow or induce more errors during instruction often lead to better long-term learning outcomes, and thus instructors and students, however disinclined to do so, should consider abandoning the path of least resistance with respect to their own teaching and study strategies. After all, educational interventions should be based on evidence, not on historical use or intuition.***On the Symbiosis of Learning and Forgetting**

Research Paper Title:

Research Paper Title:

**Author(s):**Robert A. Bjork

**My Takeaway:**

The work of Robert Bjork and Elizabeth Bjork has blown my mind. Their "

**Theory of Dissuse**" outlines the importance and - wait for it - the

*benefits*of forgetting. They explain that each item in memory has a storage strength and a retrieval strength. Storage indicates how well an item is embedded in long-term memory and retrieval indicates how easily an item can be brought to mind when needed. Ideally, we want our students to have both. But here is the key point - attempts to increase retrieval strength improve performance in the short term but very quickly fade. Worse still, trying to retrieve something from memory too quickly can interfere with our ability to store it more strongly. Cramming, cues, and teaching to a test, all serve to make it easier to retrieve that information, but do not give it chance to develop a high storage strength and hence become embedded in long-term memory. This all sounds pretty bad for teaching - but there is good news: if we wait until we’ve started to forget something, retrieval practice increases our ability to recall it in the long term. Therefore, the best way to increase storage strength is to allow memories to fade before trying to retrieve them. The conclusion is both simple and profound:

**the best way to remember is to forget**. This has huge implications for both teaching and revision. Firstly, it sets up nicely the work on interleaving and spacing that we will cover later in this section. But it also calls into question the idea of giving students loads of the same type of question to do following the teaching of a new concept. Sure, they can all do the questions by the end of the lesson (high retrieval strength), but then when asked to do a similar question next lesson, or next week, students often cannot (low storage strength). How do we rectify this? Well, maybe we give students less questions to answer on a given topic (to borrow a phrase from my past as an Economics student, there is a diminishing marginal utility to each one), allow them to forget it, and then cover the material again at a later date. This cycle of practising, forgetting, and then practicing again, as opposed to keep practising the same thing, allows the storage strength of these skills to increase, which is needed for long-term learning. Of course, this will be a frustrating experience for students, as well as us teachers, and crucially performance in the short-term may decrease. So, both students and teachers may need informing of the power of forgetting, and the crucial distinction between learning and performance.

**My favourite quote:**

*Perhaps the prime example of forgetting enhancing learning is the spacing effect, one of the most robust and general effects from the entire history of experimental psychology When a second study opportunity is provided after a delay following a first study opportunity, rather than being presented with little or no delay, long-term recall is enhanced, often very significantly. Again, though, were the studied material to be tested following a short delay or a long delay, we would observe that the longer delay results in poorer recall of the studied material—that is, more forgetting. Similarly, interleaving, rather than blocking, the learning trials on separate to-be-learned tasks produces more forgetting between trials on a given task during the learning phase, but tends to enhance long-term retention and transfer.*

**Research Paper Title:**Making Things Hard on Yourself, But in a Good Way: Creating Desirable Difficulties to Enhance Learning

**Author(s):**Elizabeth L. Bjork and Robert Bjork

**My Takeaway:**

This is paper is one of the best things I have ever read. It is directly related to the issue of distinguishing between learning and performance, and argues the seemingly counter-intuitive point that you improve learning by making it more (desirably!) difficult. Bjork defines a difficulty as desirable if it makes retrieval practice harder in the short term but acts to increase retention and transfer. Therefore, these deliberate difficulties will likely lead to a reduction in short-term performance, but an improvement in long-term learning. The implications for lessons (and of course lesson observations!) are huge. The authors suggest the following strategies to induce desirable difficulties:

1) allowing students to forget some of the material covered before it’s reintroduced (spacing);

2) mixing up different content in order to prevent students developing the illusion of knowledge (interleaving);

3) asking questions about material which has already been covered rather than restudying it in order to prevent students developing a false sense of familiarity and fluency (retrieval practice);

4) varying the conditions in which instruction takes place in order to prevent contextual cues from building up and making it harder for students to transfer what they’ve learned to new contexts (variation);

5) progressively reducing the frequency and quantity of feedback given in order to prevent students from becoming dependent on external sources of expertise (see the Marking and Feedback section for a discussion on this amazing final strategy).

I fully agree with all of this, and we will look at some of Bjork's describable difficulties in the papers that follow, but I will add one thought - if things are always too difficult for students, then motivation quickly disappears, and no teaching strategy can be effective if your students have switched off and have zero desire to engage in the learning process. Indeed, the principle of describable difficulty does seem in contrast to Dan Willingham's view of thinking discussed on the Cognitive Science section - if thinking is too hard, students stop thinking - as well as Cognitive Load Theory, which seems to me to be a model based on making thinking as easy and focused as possible. Much like David Didau (in this wonderful blog post on the same paper), I feel students need to taste success first in order to be motivated (see the Zimmerman article on the importance of self-efficacy in the Motivation and Praise section for more on this), then try to ensure that key knowledge and processes are successfully encoded via a process of explaining, modeling, scaffolding and practising as suggested by Cognitive Load Theory, before finally things can become deliberately difficult. Didau proposes what seems a very sensible three stage plan to achieve this: Encode success, Promote internalisation, Increase challenge.

**My favourite quote:**

*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.***Spacing and Interleaving of Study and Practice**

Research Paper Title:

Research Paper Title:

**Author(s):**Shana K. Carpenter

**My Takeaway:**

This is a really nice introduction to the concepts of spacing and interleaving, which are two of Bjork's "desirable difficulties" described above. Best of all, both of these concepts are relatively easy to implement. The

**Spacing Effect**refers to the findings that learning is better when two or more exposures to information are separated in time (i.e. spaced apart) than when the same number of exposures occurs back-to-back in immediate succession. The

**Interleaving Effect**contrasts a "blocking" approach, whereby students study the same type of material over and over again before moving on to a different type of material, against an "interleaving" approach, where students practice all of the problems in an order that is more random and less predictable. It is quite easy to get the two concepts mixed up (for me, anyway!), and the two are inextricably linked as interleaving produces spacing, but a good way to think about it might be that spacing describes the scheduling of exposures to a single concept (A), and interleaving describes the scheduling of exposures to multiple concepts (A, B, and C). The general findings are that both spacing and interleaving can produce significant benefits with regard to memory and learning, and these will be discussed further in the papers in this section. Spacing is relatively easy to implement. You just need to ensure you routinely revisit material at fixed intervals throughout the year - and a paper in this section provides guidance for what those fixed intervals should be. Similarly, tapping into the benefits of interleaving could be as simple as adapting how you present questions in class and modifying your existing homeworks and assignments slightly, as will be discussed in the papers in this section. Before we move on, a key point that also needs raising is that blocked practice might be more appropriate when a skill is first being learned. After all, spacing and interleaving work by inducing students to retrieve concepts from long-term memory. If concepts are not there in the first place, then there is nothing to retrieve!

**My favourite quote:**

*Students and instructors are faced with these decisions on a daily basis. Research on human cognition has shown that learning can be significantly affected by the way in which repetitions are scheduled. This research can help inform the decisions that students must make concerning when to study information in order to maximize learning.*

**Using Spacing to Enhance Diverse Forms of Learning**

Research Paper Title:

Research Paper Title:

**Author(s):**Shana K. Carpenter, Nicholas J Cepeda, Doug Rohrer, Sean H. K. Kang & Harold Pashler

**My Takeaway:**

The concept behind spacing is relatively simple, and its effects can be profound. This paper finds that performance on final tests of learning is improved if multiple study sessions are separated (spaced apart) in time rather than massed in immediate succession. The optimal length of the spacing depends on when the material is going to be tested. In general, longer spacings are more beneficial when the test is a long way away, whereas shorter spacing are more beneficial for tests in the near future. These longer periods may be weeks or even months. Three practical recommendations for teachers:

1) Teachers should dedicate part of each lesson to reviewing concepts learned several weeks earlier. I often do this during the starter, either by means of a low-stakes quiz (see the Testing section), or using something like Corbett Maths 5-a-day. The key is careful planning to ensure that as much previously taught material as possible comes up again.

2) Homework assignments should be used to re-expose students to important information they have learned previously. We have a Revision section at the start of every homework, but as will be discussed in the Interleaving papers that follow, there may be a way to make this even more effective.

3) Teachers should give exams and quizzes that are cumulative. This again suggests the benefits of low stakes quizzes, which not only tap into the benefits of The Spacing Effect, but which also utilise the Retrieval Effect that will be discussed in the Testing section

This last point even has an added benefit - as well as re-exposing students to information that they have previously learned, cumulative exams and quizzes also provide students with a good reason to review information on their own, hence hopefully improving their revision strategies. Revision is covered in a later section.

**My favourite quote:**

*The key criterion is that information should be reviewed after a period of time has passed since the initial learning. Particularly if the goal is long-term retention, the findings from Cepeda et al. (2008) suggest that the ideal time to review information may be several weeks or months after it was initially learned.*

**Research Paper Title:**Spacing effects in learning: A temporal ridgeline of optimal retention

**Author(s):**Nicholas J Cepeda, Edward Vul, Doug Rohrer, John T Wixted & Harold Pashler

**My Takeaway:**

After the last paper you may be thinking: "wouldn't it be great if someone could tell me the optimal time to revisit content with my students depending on when their test is?". Well, your wish is my command. This study offers a rough guide. The research looked to trial a number of different gaps with a number of different retention intervals. The gap + the RI = the total time between initial study and test. They did not find any magic ratio between the gap and the retention interval. As predicted, as the retention interval increased, so too did the optimal gap for retesting, but not in a constant fashion Indeed, the ratio of retention interval to gap falls. Mr Benney has written a wonderful blog post that contains a graph plotting optimal spacing intervals based on the data. For example, if you finish a topic today and the test is in 60 days then (perhaps) your optimum gap before restudy would be 10 days which leaves an RI of roughly 50 days (a 1:5 ratio or gap being 20% of RI), whereas If your class finishes a topic today and the test is in 114 days then (perhaps) your optimum gap before restudy would be 14 days which leaves an RI of 100 days (a 7:50 ratio or gap being 14% of RI). This is not surprising if we assume that the optimal time to retest someone is when they are on the verge of forgetting. As Mr Benney explains:

*It seems that it is preferable to have the restudy session within a shortish time of the original study despite the fact it gives a very long RI. This is surely because if the gap was any bigger too much of the original study material would have been forgotten and retrieval strength would be practically zero. It is better to keep a relatively short gap and trade off with a very long RI. I imagine a spacing session much later than the optimum gap would be more like a reteaching lesson rather than a restudy/recall lesson.*

However, as the authors of the research point out, there is a danger in going too far the other way. The compression of learning into a too-short period is likely to produce misleadingly high levels of immediate mastery that will not survive the passage of substantial periods of time. Moreover, while there are costs to using a gap that is longer than the optimal value, these costs are much smaller than the costs of using too small a gap value, as evidenced by the fact that, as gap increases, accuracy increases steeply and then declines much more gradually. Hence, if in doubt, leave the intervals between tests of recall longer than shorter. Students need time to be on the verge of forgetting in order for the Testing Effect to display its full power.

**My favourite quote:**

*To put it simply, if you want to know the optimal distribution of study time, you need to decide how long you wish to remember something. Although this poses challenges for practical application, certain conclusions can nonetheless be drawn. If a person wishes to retain information for several years, a delayed review of at least several months seems likely to produce a highly favorable return on a time investment— potentially doubling the amount ultimately remembered, holding study time constant—as compared to less temporally distributed study.*

**Research Paper Title:**Interleaving Helps Students Distinguish among Similar Concepts

**Author(s):**Doug Rohrer

**My Takeaway:**

Students confusing related concepts is the single biggest cause of errors on my Diagnostic Questions website. Classics include confusing area and perimeter, the rules for adding and multiplying fractions, mean and median, the laws of algebra - the list goes on! This wonderful paper which summarises the key findings from a wide range of interleaving research which suggests that interleaved mathematics practice helps students learn to distinguish between different kinds of problems. This is obviously a critical skill because solving a mathematics problem requires that students first identify what kind of problem it is, which means that they must identify those features of a problem that indicate which concept or procedure is appropriate. Identifying the kind of problem is not always easy. Take solving equations. The familiar instruction, “

*Solve for x*” does not indicate which one of several solving strategies is appropriate. For instance, students must use the quadratic formula to solve some equations (e.g., x

^{2}− x − 100 = 0), and they must factorise to solve others (e.g., x

^{3}− x = 0). Then there is completing the square, not to mention linear equations, cubic equations, equations involving fractions, and so on! Solving a mathematics problem requires students to know which strategy is appropriate and not only how to execute the strategy. The key point here is that with blocked practice, students need not identify an appropriate strategy because every problem in the assignment can be solved by the same strategy. In essence, blocking provides scaffolding. This might be useful when students meet a new concept, but students who receive only blocked assignments do not have the opportunity to practice without this crutch, and studies quoted here suggest this has negative consequences for long-term learning. So, what are we to take from this? Firstly, it seems clear that interleaving practice problems on homeworks and tests is likely to have a significant advantage on long-term learning, and this will be discussed in the papers that follows. But what are the implications for the actual teaching of related concepts? For me, there are two extremes:

1) Teach related concepts together and block practice each. For example, teach the mean, then practice the mean. Then teach the median, and practice the median, and so on, until all four averages have been covered. What happens with that approach - students confuse those related concepts as they have not had sufficient opportunity to distinguish between them.

2) Teach related concepts completely separately. So, teach the mean, then teach adding fractions, then area of a triangle, before returning to teaching the median. I have not been able to find specific research on this approach, but I would be fascinated by it. Whilst it undoubtedly taps into the benefits of interleaving, my concern is that it does not allow students to compare and contrast the related concepts, and to pick up on the connections between them. Take averages. In the scenario described here, how do we teach students about the appropriateness of using each average, or solve complex problems involving more than one of them, when they are taught so far apart?

I think the solution is to teach related concepts in isolation in early skill acquisition phrase, using the principles of Explicit Instruction and Cognitive Load Theory, and then carefully bring them together later on. So, introduce the mean in Year 7 term 1, perhaps as part of a unit on number operations, or using a calculator. Then introduce the median at the start of Year 8, and the mode sometime towards the end of the year. Continually revisit these concepts throughout the two years via starters, low-stakes quizzes and homeworks. Then, in Year 9 it is time to bring them all together in a unit on statistical inferences. At this stage, with students fluent in each of them, similarities and differences between the related concepts can be made explicit. Of course, this would have big implications for a school's existing schemes of work, homeworks and assessments, but the effort put into getting this right could have huge payoffs.

Finally, as highlighted in the quote, there is little doubt that interleaving makes learning more difficult and is likely to lead to a short term dip in performance. Both students and teachers need to be aware of this.

**My favourite quote:**

*Students might balk because interleaving increases the difficulty of a question or problem. A group of questions or problems are easier when all relate to the same topic or concept. By contrast, answering a set of interleaved biology questions might require students to consult material presented in previous chapters, and an interleaved mathematics assignment prevents students from simply repeating the same procedure throughout the assignment. Students will therefore make more errors, and work more slowly, when assignments are interleaved. This in itself is not problematic because the aim of classroom instruction is ultimate mastery, not error-free learning. Still, some students might be unwilling to make the extra effort. In this scenario, interleaving is like bad-tasting cough syrup—ineffective because children refuse to use it.*

**The Effects of Cumulative Practice on Mathematics Problem Solving**

Research Paper Title:

Research Paper Title:

**Author(s):**Kristin H Mayfield and Philip N Chase

**My Takeaway:**

This study is discussed in the paper above, but deserves its own place here, not least because it is mathematics specific. College students in need of mathematics intervention attended dozens of sessions over a period of several summer months in which they solved problems using five algebraic rules about the laws of indices. One group of students learned the rules

through a procedure akin to blocking, in which each rule was learned and then practiced extensively before moving on to the next rule. Another group learned the same rules through a procedure akin to interleaving, which involved continuous practice of previously-learned skills. For example, after learning two types of skills (e.g., order of operations and multiplying indices), students practiced a mixture of problems involving these two skills. A third skill was then introduced (e.g., finding the roots of indices) and this skill was then added to the practice set along with the two previously-learned skills, such that participants practiced a mixture of problems tapping all three skills. A fourth skill was then added, followed by a mixture of problems tapping all four skills, and so on, until all five skills had been learned and practiced. Subjects were tested 1 or 2 days after the last practice session, and they returned for a second test between 4 and 12 weeks later, depending on their availability. On both tests, the interleaved practice group outscored the blocked practice group by factor of at least 1.3, both on skill-based questions and crucially also on problem solving. The next few papers that we will look at extol the benefits of interleaving in terms of the the content of homework and assessments. However, I feel this paper is more about how topics are taught. Previously I would have taught a topic in a block (say fractions), assessed it, and then moved on. The lesson here is that once I have taught fractions, I need to ensure fractions regularly appear in the study of other topics. This could be as simple as ensuring they are parts of homework and starters, but better still they should be integrated within the new topics. So, fractions become part of negative numbers, calculating the mean, and so on. Such an approach goes by many different (often incorrectly applied) labels, such as Mastery or Shanghai. But one thing is clear, it has significant implications for the planning of curriculum and schemes of work.

**My favourite quote:**

*In summary, the results from the current study suggest that incorporating cumulative practice into training procedures will lead to high levels of performance on novel, untrained skills. More specifically, what are typically thought of as advanced mathematics skills, such as applying individually trained rules in a novel situation and synthesizing rules into novel combinations, can be facilitated through a cumulative practice training procedure. Neither providing extra practice on each component rule nor incorporating individual reviews of previously trained rules proved to be adequate to produce similar results, particularly on problem-solving skills.*

**Research Paper Title:**Interleaved Practice Improves Mathematics Learning

**Author(s):**Doug Rohrer, Robert F. Dedrick, and Sandra Stershic

**My Takeaway:**

This study is fascinating. Previously I had thought interleaving had to involve completely changing the order lessons are taught. However, that is not the case. Seventh-grade students saw their teachers’ usual maths lessons and received regular homework assignments. Every student received the exact same problems, but the scheduling of the problems was altered so that students received blocked or interleaved practice. Later, students received a review of all the content, followed 1 or 30 days later by an unannounced test. Students following the interleaving program performed significantly better on both tests, with a greater difference in performance found on the test taken 30 days later, suggesting a significant impact on retention. Now, the "blocked practice" approach is one I have used regularly. Teach students fractions, give them an assignment on fractions. Then teach them equations, given them an assignment on equations. Then it is time for angles and averages, then let's have a review of all four topics, and then a half term test. Our assignments do consist of short revision questions at the start which are taken from a variety of questions throughout the year, but the main focus of each assignment is undoubtedly on the topic that has just been covered. This paper suggest that approach is not quite good enough. The assignments should consist of a mixture of questions from previous topics, and not just the quick-fire revision ones. Moreover, each assignment should contain a

*majority*of questions from other topics, not a minority. For example, the kind of fractions problems that would have appeared as questions 4, 6 and 9 on our first assignment should be included in the second assignment instead, alongside questions on equations and any other topics previously taught, and so on. I particularly like the fact that there are no implications for changing the way or order topics are taught, or the content of assignments - it is simply a case of varying the composition of the assignments themselves. This seems like a very quick win.

**My favourite quote:**

*Benefits of interleaved practice have been consistently observed with a variety of mathematics skills and with students in elementary school, middle school, and college. As argued here, these benefits arise because interleaved practice provides students with an opportunity to learn how to choose an appropriate strategy (or learn that they cannot do it). In short, interleaved practice simply provides students with an opportunity to practice the very skill they are expected to learn.*

**Research Paper Title:**The Benefit of Interleaved Mathematics Practice is not limited to Superficially Similar kinds of Problems

**Author(s):**Doug Rohrer, Robert F. Dedrick & Kaleena Burgess

**My Takeaway:**

This paper discusses the point raised in the previous paper, but then takes it further. The correct solution to most mathematical problems involves two steps: identify the strategy needed to solve the problem, and then successfully carry out that strategy. The authors argue that most mathematical assignments deny students the opportunity to practice that first step - identifying the 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. Similarly, blocked practice fundamentally changes the pedagogy of worded problems, where often the majorly difficulty is not carrying out the strategy required to solve the problem, but actually identifying what that strategy should be. An alternative approach is interleaving, where a majority of the problems within each assignment are drawn from previous lessons, so that no two consecutive problems require the same strategy. 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. Such interleaved practice also ensures that problems are spaced, which can tap into the benefits related to The Spacing Effect. Interestingly, unlike the previous paper, the authors do not attribute the benefit of interleaving to merely enabling students to better discriminate between problems. They argue 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. 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. Interleaved practice can help the development of both of these crucial skills. However, I must point out that many of Bjork's "desirable difficulties" seem inappropriate in early skill acquisition phrase. A degree of blocked practice may be necessary in lessons when a topic is being introduced, followed by interleaved practice for homework.

**My favourite quote:**

*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, interleaved practice requires that students choose an appropriate strategy 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.

blocked practice allows students to safely assume that each problem will require the same strategy as the previous problem.

**Research Paper Title:**Effect of Overlearning on Retention

**Author(s):**Jaems E Driskell, Ruth P Willis and Carolyn Cooper

**My Takeaway:**

The important distinction between learning and performance naturally raises the question: when do I know if my students have practiced enough? A score of 10/10 is certainly a good performance, but how much of that is down to mimicry, and how much has been retained in long-term memory? That leads to the concept of

**overlearning**- or, as I like to think of it, practising beyond mastery. This meta-analysis finds a moderately positive effect on long-term retention of overlearning. In short, learning can still occur after performance has seemingly peaked. I took two things away from this paper. Firstly, I will no longer settle for a single good performance on, say, a fractions test. Students need to continue practising, even if they do not see a visible improvement in performance. Concepts such as spacing in lessons and interleaving in homeworks will help with this. Secondly, students need to be informed of this concept, otherwise there is the danger they will moan at the fact you are making them do something they can already do.

**My favourite quote:**

*One question that organizations and training practitioners face is the question Of how much training is enough. One approach is to provide the level Of training that is estimated to meet the requirement of the average trainee. That is, if the average trainee can achieve proficiency in 5 sessions, then this becomes the level Of training provided to all. A second approach is to provide training to meet some set criterion, such as one errorless performance of the task. In this case, each individual is trained until he or she reaches the criterion level. A third approach, overlearning. requires that training continue for a period past this initial mastery level. The results of this meta-analysis document the effectiveness of overlearning and show that retention is enhanced when learning proceeds beyond initial mastery*

**Research Paper Title:**The Effects of Overlearning and Distributed Practise on the Retention of Mathematics Knowledge

**Author(s):**Doug Rohrer and Kelli Taylor

**My Takeaway:**

The final paper on interleaving from my Doug Rohrer collection, and this has equally big implications. In two experiments, 216 college students learned to solve one kind of mathematics problem before completing one of various practice schedules. In Experiment 1, students either massed 10 problems in a single session or distributed these 10 problems across two sessions separated by 1 week. The benefit of distributed practice was nil among students who were tested 1 week later but extremely large among students tested 4 weeks later. In Experiment 2, students completed three or nine practice problems in one session. The additional six problems constituted a strategy known as overlearning, but this extra effort had no effect on test scores 1 or 4 weeks later. A few things struck me. Firstly, the improvement in performance from distributed practice was not seen immediately - this is important for both students and teachers to know. Secondly, as has been pointed out in the previous studies, most mathematics textbooks rely on a format that emphasises overlearning and minimises distributed practice, as do most of the worksheets and sets of questions I give my students to do in class. Finally, with regard to overlearning, the authors do not dismiss it (and indeed, with the problem of distinguishing between learning and performance discussed earlier in this section, it is dangerous to assume a student has learned something based purely on a good test score), but instead suggest a better use of students' finite time. The authors sum this up very nicely: "

*we suggest that assignments should err slightly in the direction of too much practise, perhaps by including three or four problems relating to each new concept in the most recent lesson (in addition to any examples given in the written lesson or class lecture). However, beyond these first three or four problems, the present data suggest that the completion of additional problems of the same type is a terribly inefficient use of study time. Instead, our findings suggest that the student should devote the remainder of the practise session to problems drawn from earlier lessons in order to reap the benefits of distributed practise*"

**My favourite quote:**

*With this distributed practise format, each lesson is followed by the usual number of practise problems, but only a few of these problems relate to the immediately preceding lesson. Additional problems of the same type might also appear once or twice in each of the next dozen assignments and once again after every fifth or tenth assignment thereafter. In brief, the number of practise problems relating to a given topic is no greater than that of typical mathematics textbooks, but the temporal distribution of these problems is increased dramatically.*

**Research Paper Title:**

**Why interleaving enhances inductive learning**

Author(s):Monica S. Birnbaum, Nate Kornell, Elizabeth Ligon Bjork & Robert A. Bjork

Author(s):

**My Takeaway:**

A fascinating paper to end our discussion on interleaving (for now!). An inductive approach to teaching involves showing examples of how a concept is used in the hope that students will ‘notice’ how the concept works, as opposed to a deductive approach, whereby the teacher provides the material pupils need to think about and reduces the quantity of information they are required to hold in working memory. It would seem sensible to think that a deductive approach works best, and indeed when learning basic content that does seem to be the case. However, this research suggests that students tend to understand and remember more when learning occurs inductively, but only if this is combined with an interleaved approach to studying content. In short - students best learn a rule by seeing examples containing the rule mixed up with examples that don’t. Why does this work? Well, frequent alternation of categories (interleaving) has the advantage of highlighting features that serve to distinguish categories. Conversely, infrequent alternation of categories (blocking) has the advantage of highlighting information that remains constant across the members within a category. For me, it depends what you want to achieve. If you wish students to become fluent in a particular skill or concept, then a blocking approach is likely to be best. However, if you want students to be able to distinguish between problems, recognising key features and selecting the most appropriate method to use (as is often needed for more wordy questions, questions where the required method is not obvious, or on high-stakes tests), then interleaving is necessary. The research we looked at in the Explicit Instruction section suggests that students need key knowledge and processes to be stored in long term memory before they can become effective problem solvers, so my takeaway is that blocked practice may be optimal when students first encounter a skill, but interleaving is needed for students to develop their learning further. On a related note - learners (and teachers!) are likely to find the process of interleaving more difficult than blocking. This is largely because they have to think more, and may see a short term dip in performance. Crucially, they may feel they are not learning as much and begin to lose motivation. This relates directly to Bjork's "desirable difficulties" discussed earlier in this section.

**My favourite quote:**

*The great majority of the participants in the present study, as well as those in prior studies, judged that they had learned more effectively with blocked than with interleaved study. Thus, a bit of practical advice to learners and educators seems warranted: If your intuition tells you to block, you should probably interleave.*

**Environmental context and human memory**

Research Paper Title:

Research Paper Title:

**Author(s):**Steven M Smith, Arthur Glenberg and Robert A Bjork

**My Takeaway:**

Another of Bjork's "desirable difficulties" concerns varying the location of where learning and retrieval take place. In this fascinating study, the authors gave participants a lost of words to learn and had them study either in the same room twice or in two separate rooms (one a cluttered basement, the other a windowed office). Three hours later, the students were moved into a third ‘neutral room’ and asked to recall as many of the words as they could. Those who studied in the same room managed an average of 16 out of 40 whereas those who studied in two different rooms recalled 24 words. The experiment showed strong recall improvements with variation of environmental contexts.This has become known as the

**Variation Effect**and since then there are been many other studies which have replicated this findings. Why does varying conditions work? Well, it may enhance long-term learning because the material becomes associated with a greater range of memory cues that serve to facilitate access to that material later. Whilst it is clear that this experiment is concerned with the recall of words - and so we must be very careful in making any wild claims about solving mathematical problems - the fact that recall in mathematics plays an important part suggests that we should take note of these results. For me, there are two clear implications. Firstly, wherever possible vary where students in school learn and practice retrieval. My students sit in the same seats, in the same classrooms, most of the time. And yet, when it comes to taking their exams they are suddenly thrust into a brand new environment. As a result of this paper, I now routinely change my seating plans, and where possible try to take advantages of room changing opportunities. There is the potential cost of disruption and daft behaviour that this "new environment" brings, but the potential benefit far outweighs these. Secondly, a simple piece of advice to pass onto students when revising is to vary where they do their revision. Try a different room, a different time of day, etc. Anything that varies the environmental conditions is likely to lead to better retrieval.

**My favourite quote:**

*Another type of explanation of the results can be found in Tulving and Watkins' (1973) continuity hypothesis, which states that recall and recognition require essentially the same retrieval process(es), but that free recall involves such processes to a greater extent than does recognition. In free recall, where the experimenter provides few explicit retrieval cues, the subject must make use of varied sources of cues to provide access to the stimuli. Environmental context could be one such source of cues. In cued recall there is more specific retrieval information, and in recognition memory the subject is supplied with highly effective, explicit cues, thereby reducing his dependence on other cue sources.*