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Cognitive Load Theory

Dylan Wiliam described Cognitive Load Theory as "the single most important thing for teachers to know", and I have to agree. I find it provides rationale and practical strategies for the principles of Explicit Instruction discussed in the previous section, and it has transformed the way I teach. Indeed, I have felt compelled (much to my wife's dismay) to write a talk entitled"How Cognitive Load Theory changed my life" as part of my "How I wished I'd taught maths" workshop -click here for more details. Cognitive Load Theory is focussed upon the conditions that make learning easier for students, and it is fascinating to look at this alongside Bjork's work in theMemory section which extols the advantages of making learning harder. For me, the matter is resolved by using the principles of Cognitive Load Theory to aid the early knowledge acquisition phase, removing all unnecessary load on working memory, and then utilising concepts such as spacing, interleaving, testing, variation and other desirable difficulties later in the learning process. In this section we look at key "effects" of the Cognitive Load Theory relating to worked examples, presentation of information, goal-free problems and the development of problem solving skills, and the practical implications they have for the classroom.

Before we dive into the research papers, Oliver Caviglioli has produced some amazing sketchnote summaries of the 2011 Cognitive Load Theory book, which really help illustrate the key ideas:
Chapters 1 and 2
Chapters 3 and 4 Chapters 5 and 6 Chapters 7 and 8
Chapters 9 and 10
Chapters 11 to 18
Complete Download

Also, this report from the New South Wales Centre for Education Statistics and Evaluation is just about the most clear and concise summary of Cognitive Load Theory that I have seen
Research Paper Title: Cognitive Architecture and Instructional Design (there is also a short review of the development of Cognitive Load Theory that gives a good summary of the key points: Story of a Research Programme)
Author(s): John Sweller, Jeroen J. G. van Merrienboer, and Fred G. W. C. Paas My Takeaway:
It is no exaggeration to say that Cognitive Load Theory has changed my life. Well, my teaching life, at least. It explains so many of the struggles and mistakes I have seen my students making over the years, and I am just fuming that it has taken me 12 years to discover it. But better late than never! This paper is an outstanding overview of Cognitive Load Theory, together with its related effects and implications for instructional design. Cognitive Load Theory is concerned with how cognitive resources are focussed and used during problem solving and learning. The key principle is that our working memories are severely limited, and that once a student's working memory reaches "cognitive load", no learning takes place. Indeed, it was a real eye-opener for me to discover that students could be working hard, and yet not actually be learning anything. What can be done about this? Well, as teachers we need to help reduce both the intrinsic and extraneous loads:

Intrinsic load - this is determined by the interaction between the nature of the learning tasks and the expertise of the learner. It depends on the amount of element interactivity in the tasks that must be learned. Something like learning the names of polygons has a relatively low element interactivity, as knowing the name of a pentagon is not necessary to know the name of an octagon - hence they can be learned separately. However, something like solving an equation has a relatively high element interactivity as you need to combine many dependent skills together to arrive at the answer. The degree of element interactivity also depends on the expertise of the learner, because what are numerous elements for a low-expertise learner may be only one or a few elements (i.e. chunks) for a high-expertise learner. As we have seen in previous sections, working memory capacity is severely limited (possibly being as low as 3 to 5 items), but the intrinsic load can be reduced by:

By ensuring students have sufficient knowledge, which can be organised in their long-term memory as schema. This allows students to work with a sizeable "chunk" of information (or schema) as if it was one item, which frees up capacity in working memory. As we have seen from the papers by Anderson and Willingham in the Cognitive Science section, knowledge matters!

Presenting complementary visual and auditory information together

Extraneous load - this is load that is not necessary for learning (indeed, it is unhelpful), and it typically results from badly designed instruction and the way material is presented to the learner. This extraneous load can be reduced by:

The use of goal free problems

Making use of worked examples

Carrying out completion tasks

The careful integration of related information

Reducing redundant information

In short, as teacher we need to take steps to focus students' limited working memory capacity on the things that matter, removing everything else, whilst at the same time ensuring students have sufficient background knowledge to better deal with the limitations of their fragile working memories. For an in-depth discussion with a maths teacher who regularly practices the lessons from Cognitive Load Theory, you can listen to my interview with Greg Ashman. The papers that follow in this section look in detail at the concepts introduced above and their implications for explicit instruction. My favourite quote:
The design of practice and the organization and presentation of information is the domain of instructional designers. Although there are many factors that a designer may consider, the major thesis of this paper is that the cognitive load imposed by instructional designs should be the pre-eminent consideration when determining design structures. Limited working memory is one of the defining aspects of human cognitive architecture and, accordingly, all instructional designs should be analyzed from a cognitive load perspective. We argue that many commonly used instructional designs and procedures, because they were designed without reference to working memory limitations, are inadequate.

Research Paper Title: Cognitive Load Theory, Learning Difficulty and Instructional Design
Author(s): John Sweller
My Takeaway:
As well as providing an excellent overview of Cognitive Load Theory, this paper highlights the contrasting problem solving strategies of novices and experts, and thus introduces one of my favourite concepts: the Goal Free Effect. This has a big implication for teaching, especially when introducing new concepts to students. Goal-specific problems are those in which the top-level goals (i.e. final answer) can only be achieved by successfully completing the sub-goals (i.e. the steps leading up to it). When faced with goal-specific problems, novice learners tend to embark upon a means-end analysis. In essence, this means the student tries to juggle all the possible sub-steps that minimize the difference between the current state (the problem) and the end state (the goal). This is a backwards-thinking approach, and it is no surprise that it quickly overloads working memory. I know I have said this before, but it is worth repeating - even though students are working hard in such a scenario, their cognitive overload means they are not actually learning anything. Just as important is the fact that this means-end approach is incompatible with the development of schema, meaning that whilst the students may solve the specific problem at hand, they are unlikely to actually be learning. Learning is a change in long term memory, not just solving one specific problem. A relatively simple solution is to instead present students with 'goal-free' problems, which focuses attention upon working forward from the information present one step at a time, rather than trying to hold multiple possible steps in mind at once. A classic example in maths is instead of giving students a complex, multi-step question whose goal is to find the size of "angle x", instead ask them to find the size of as many angles as they can. Similar things can be done to trigonometry questions, or even when working with cumulative frequency diagrams. This breaks the process down and reduces the burden on novices' working memories. As will be discussed in the remaining papers in this section, once students become expert enough in a given topic, they are likely to have sufficient working memory capacity to dedicate to solving goal-specific problems. The key (and difficulty!) is judging when to introduce them, but in early skill acquisition, goal-free problems seem to be the way to go.
My favourite quote:
This means-ends procedure is a highly efficient technique for attaining the problem-goal. It is designed solely for this purpose. It is not intended as a learning technique and bears little relation to schemas or schema acquisition. In order to acquire an appropriate problem solving schema, students must learn to recognize each problem state according to its relevant moves. Using a means-ends strategy, much more must be done. Relations between a problem state and the goal state must be established; differences between them must be extracted; problem operators that impact favourably on those differences must be found. All this must be done essentially simultaneously and repeated for each move keeping in mind any subgoals. Furthermore, for novices, none of the problem states or operators are likely to be automated and so must be carefully considered. According to cognitive load theory, engaging in complex activities such as these that impose a heavy cognitive load and are irrelevant to schema acquisition will interfere with learning.
Research Paper Title: Cognitive Architecture and Instructional Design
Author(s): John Sweller, Jeroen J. G. van Merrienboer, and Fred G. W. C. Paas
My Takeaway:
I include this wonderful paper again as I find it the best for discussing the Worked Example Effect and the Completion Problem Effect.
Worked Example Effect
The Worked Example Effect, perhaps more than any other identified by Cognitive Load Theory, has had the most significant impact on my teaching. In short, the Worked Example effect attempts to explain the finding whereby learners who study worked examples perform better on test problems than learners who solve the same problems themselves. When I first came across this, I didn't believe it - surely you learn more from trying to solve problems than by reading the solution. But the key is in the "trying to solve problems". The rather counter-intuitive result is due to the fact that studying worked examples focuses all attention on the correct solution and procedure, reducing the extraneous load compared to a means-end analysis that the learner may embark upon if left to their own devices. This is likely to lead to the development and acquisition of all-important schema which will help the students transfer their knowledge to related contexts. I look at worked examples in greater detail in the sections on Making the most of Worked Examples and The Importance of the Choice of Examples.

Completion Problem Effect
There is an obvious danger when just presenting students with worked examples, as opposed to problems to solve, that they do not fully engage with the examples. As all the work has been done for them, where is there incentive to think? And, as we have seen, if students are not thinking then they cannot be learning. I have seen this many times myself - some students will pay little attention during the worked examples, and then (surprisingly!) get stuck when they are set to work on their own. This is where the simple idea of requiring students to complete various pieces of information and steps within a worked example comes into play. This could be as simple as creating a full worked solution and then Tipexing or deleting key sections for the students to complete, or even pausing whilst going through a worked example on the board, and asking students to predict (maybe using mini-whiteboards) what comes next. Completion problems provide a bridge between worked examples and conventional problems. The authors put it like thus: worked examples are completion problems with a full solution, and conventional problems are completion problems with no solution. A good progression might be to start with completion problems that provide almost complete solutions, and gradually work to completion problems for which all or most of the solution must be generated by the learners. This is something that will be addressed further in the Making the most of Worked Examples section.

My favourite quote:
There is considerable evidence that, compared to conventional problems, they decrease extraneous cognitive load, facilitate the construction of schemas, and lead to better transfer performance. In short duration studies, results indicated that completion problems are equally effective as worked examples intermixed with conventional problems. In studies of a longer duration, completion problems may better help learners to maintain motivation and focus their attention on useful solution steps that are available in the partial examples.
Research Paper Title: Reducing Cognitive Load by Mixing Auditory and Visual Presentation Modes
Author(s): Seyed Yaghoub Mousavi, Renae Low, and John Sweller
My Takeaway:
This paper introduces both the Split-Attention Effect and the Modality Effect, both of which have significantly changed my teaching.

Split Attention Effect
We have seen that the worked-example effect occurs because worked examples reduce extraneous cognitive load, but there can be no guarantee that all worked examples appreciably reduce cognitive load. This is especially true if the worked example consists of a diagram, and a separate worked solution, neither of which are intelligible without the other. The learner must split their attention between the two forms of presentation, which increases the cognitive load. Hence, when presenting students with worked examples where a diagram is involved (for example, most geometry topics), the text solution should be carefully integrated within the diagram, and not separate from it. This will prevent students from having to deal with these two forms separately and reduce the extraneous cognitive load. Similarly, keeping all aspects of a question visible at the same time (i.e. without having to constantly turn the page over) will also help reduce this unnecessary load.

Modality Effect
To understand the importance of the modality effect we need to understand the components of working memory. The Central Executive acts a bit like a supervisor, The Phonological Loop deals with speech and sometimes other kinds of auditory information, the Visuo-Spatial Sketchpad holds visual information and the spatial relationships between objects, and the Episodic Buffer integrates new information with information already stored in long-term memory. They key point here is that working memory gets overloaded if too much information flows into one of these components, but we can use different components to aid processing. Hence, the capacity of working memory may be determined by the modality (auditory or visual) of presentation, and the effective size of working memory may be increased by presenting information in a mixed (auditory and visual mode) rather than in a single mode. There are two key implications of this for me.
1) Make use of complementary representations of concepts. This will be discussed more in the next paper.
2) When students are presented with written information, talking over the top of it can cause overload as both are processed by the auditory component (after text is read, it is processed as if it is being heard). The problem is made even worse if the text on the slide and the words I am saying out loud are the same, as here we have redundant information, and hence an example of the Redundancy Effect, which will be discussed further later in this section. So, the simple practice of putting up a slide of text and allowing the students the opportunity to read it in silence BEFORE reading it aloud or discussing it can reduce the modality effect by decreasing the extraneous load. For me, the biggest change this has made is encouraging me to shut up a little more. Previously I would start my students off on some problems, and then feel an incessant need to provide a running commentary over the top - "read the question carefully", "remember to show your working", etc. I thought I was being helpful, but in fact I was overloading my students' finite working memories as they were having to process my oral ramblings together with reading the text of the problems they were solving. In short, I was inhibiting their learning.

My favourite quote:
We began by indicating that basic research into the characteristics of working memory has suggested that this processing system is divided into at least two partially independent subprocessors: an auditory system devoted heavily to language and a visual system for handling images, including writing. Because both systems can be used simultaneously, limited working memory capacity might be effectively increased if information that must be stored or simultaneously processed is presented in a manner that permits it to be divided between the two systems, rather than processed in one system alone. As a consequence, informationally equivalent material that may be difficult to process in a purely visual manner may be more easily handled if it can be presented partially in both modalities.

Research Paper Title: The Instructive Animation: Helping Students Build Connections Between Words and Pictures in Multimedia Learning
Author(s): Richard E. Mayer and Richard B. Anderson
My Takeaway:
This paper further discusses the Modality Effect, but this time in the context of a dual-coding model, which will be discussed in greater detail in the next paper. The authors conducted an experiment in which students studied an animation depicting the operation of a bicycle tire pump or an automobile braking system, along with concurrent oral narration of the steps in the process, and tested their performance on both a retention test and a problem solving test against groups who had the animation alone, narration alone, or no instruction. On both tests, the group who had the animation alongside the oral narration performed the best. The authors conclude that these results are consistent with a dual-coding model in which retention requires the construction of "representational connections" and problem solving requires the construction of "representational and referential connections". The obvious implication for teaching from this paper is that pictures and words together can be more effective than pictures or words alone. If the oral description is there to support the comprehension of the animation, then it should benefit students by easing the strain placed on their working memories. Hence, I now make more use of carefully selected diagrams, as well as GIFs, Geogebra demonstrations and interactive Desmos graphs. For example, introducing circle theorems using something like this, combined with my oral narration over the top, has really helped my students grasp the key concepts. But it can be a fine balance, and we should be careful not to simply use a different form a multi-media for the sake of it. For example, in the Real Life Maths section, I discuss a paper where the use of video to support maths comprehension had a negative effect on performance as students assumed the medium was easier to understand and hence put less effort into their thinking.
My favourite quote:
What makes an instructive animation? The results presented in this article demonstrate that animation per se does not necessarily improve students' understanding of how a pump or a brake works, as measured by creative problem solving performance. For example, in both experiments, students who received animation before or after narration were able to solve transfer problems no better than students who had received no instruction. In contrast, when animation was presented concurrently with narration, students demonstrated large improvements in problem-solving transfer over the no-instruction group. We conclude that one important characteristic of an instructive animation is temporal contiguity between animation and narration. We hypothesize that contiguity of words and pictures during instruction encourages learners to build connections between their verbal and visual representations of incoming information, which in turn supports problem-solving transfer.
Research Paper Title: Research‐Based Principles for Designing Multimedia Instruction
Author(s): Richard E. Mayer
My Takeaway:
The paper above offered just a small taste of the Cognitive Theory of Multimedia Learning, which has been developed over many years by Richard Mayer, and others. There are clear parallels to be drawn with Cognitive Load Theory in its representation of working memory and emphasis on the importance of reducing extraneous load, but is primarily focussed upon the design of instruction materials. The theory is based upon three key assumptions:
1) dual channel assumption-people have separate channels for processing visual and verbal material
2) limited capacity assumption-people can process only a limited amount of material in a channel at any one time
3) active processing assumption-meaningful learning occurs when learners select relevant material, organize it into a coherent structure, and integrate it with relevant prior knowledge
The key principle in the Cognitive Theory of Multimedia Learning is The Multimedia Principle - people learn more deeply from words and graphics than from words alone, which was examined in the paper above. However, this is just the beginning, and this paper provides an excellent introduction into the other principles of this theory, all of which have direct practical relevance to the design and presentation of worked examples, demonstrations, worksheets, etc. Many are related to the effects of Cognitive Load Theory, but two that particularly stood out to me were:
The Signalling principle - People learn more deeply from a multimedia message when cues are added that highlight the organization of the essential material. Hence, finding ways to focus students' attention on the parts of examples that really matter is crucial.
The Coherence Principle - People learn more deeply from a multimedia message when extraneous material is excluded rather than included. The non-essential "fluff" I tend to put around examples (usually pathetic jokes) is only doing my students harm. Likewise, this also calls into question fun murder mystery style investigations. After all, we know from Willingham in the Cognitive Science section that students remember what they think about.
This whole paper is a fascinating read, and the theory itself provides a nice complement to the findings and recommendations from Cognitive Load Theory.
My favourite quote:
What makes an instructive animation? The results presented in this article demonstrate that animation per se does not necessarily improve students' understanding of how a pump or a brake works, as measured by creative problem solving performance. For example, in both experiments, students who received animation before or after narration were able to solve transfer problems no better than students who had received no instruction. In contrast, when animation was presented concurrently with narration, students demonstrated large improvements in problem-solving transfer over the no-instruction group. We conclude that one important characteristic of an instructive animation is temporal contiguity between animation and narration. We hypothesize that contiguity of words and pictures during instruction encourages learners to build connections between their verbal and visual representations of incoming information, which in turn supports problem-solving transfer.

Research Paper Title: Cognitive Architecture and Instructional Design
Author(s): John Sweller, Jeroen J. G. van Merrienboer, and Fred G. W. C. Paas
My Takeaway:
I include this wonderful paper again as I find it the best for discussing the Redundancy Effect. In the past I had assumed that simply repeating the same information twice, but in a different form, would at worst have a neutral effect on learning. After all, what harm can it do? Moreover, surely it is good to be told something twice - giving students two opportunities to get it? But if that extra information is redundant - i.e. if students can infer all they need for the initial presentation - then I am likely to be imposing an unnecessary load upon students working memories. We must be careful to distinguish this from the split attention effect. Split-attention occurs when learners are faced with multiple sources of information that must be integrated before they can be understood. The individual sources of information cannot be used by learners if considered in isolation, hence the need for integration. The redundancy effect occurs when multiple sources of information are self-contained and can be used without reference to each other. This is because that redundant information is very difficult to ignore, and hence must be processed in students' limited working memories. The message for me is clear: if a concept cannot be understood without a second piece of information, then carefully integrate the two pieces of information together. If the second piece of information is not needed, then leave it out! This is especially true when information is presented in written form on a slide, and yet I feel the incessant need to also read it out to students. Redundant, inhibiting and incredibly annoying!
My favourite quote:
Redundancy is a major effect that should be considered seriously by instructional designers. A large range of experimental results indicate the negative consequences of including redundant material when designing instruction. We know of no experimental work demonstrating advantages of redundancy, and we suspect that such a result only could be obtained under conditions where one set of instructional materials was so poor that any redundant alternative would inevitably confer benefits.

Research Paper Title: Teaching Complex Rather Than Simple Tasks: Balancing Intrinsic and Germane Load to Enhance Transfer of Learning
Author(s): Jeron J G Van Merrienboer, Liesbeth Kster and Fred Paas
My Takeaway:
So far the focus of Cognitive Load Theory has been on making thinking as easy for students in the sense that all their limited working memory capacity should be focused entirely on the thing we want them to think about to prevent cognitive overload occurring. In other words, as teachers we should try to:
1) eliminate unhelpful extraneous load via worked examples, the careful presentation of information and the use of goal free problems
2) reduce intrinsic load by helping students acquire the background knowledge necessary so that sub-components of a complex task are automated.
However, what if we reduce these two types of loads so much that thinking actually becomes too easy? This fascinating (and controversial!) paper addresses this issue by introducing the concept of Germane Load. This can be viewed as "good cognitive load", in that it directly contributes to learning. It does this by aiding the construction of cognitive structures and processes that improve performance. The authors of this paper found that whilst load reducing extraneous load is effective in producing high retention of the material, these techniques hinder the transfer of learning. They argue that there is a need to vary the conditions of practice and only give limited guidance and feedback in order to induce germane cognitive load and improve transfer. In other words, in order to improve learning (in particular the transfer of skills to new contexts), we need to make learning more difficult... but difficult in the right way! This is a concept similar to Bjork's fascinating idea of "desirable difficulties" that will be discussed at length in the Memory section.
The reason this paper is controversial is that one of the originators of Cognitive Load Theory, John Sweller, has distanced himself from the concept of germane load as he believes it makes his theory impossible to falsify. For example, assuming that the overall load is kept constant, a decrease in performance will be attributed to a rise in extraneous load that impairs germane cognitive processes. Conversely, if the performance increases it will be attributed to a germane load enhancement made possible by a drop in extraneous load.
What is my takeaway from all this? Well, I'll be honest - I am not 100% sure! Building in the concept of germane load might be making Cognitive Load Theory unnecessarily complicated. My take is this: during initial skill acquisition we need to ensure thinking is as focused and easy for the student as possible using all the principles we have discussed in the papers above. But, we need to ensure that thinking is not too easy. If students are cruising through lessons on autopilot, then their learning is unlikely to be deep, and learning without the ability to transfer it to new situations is not really learning at all. Of course, this is a fine balance, and will be covered in far more detail in the Memory sections.
My favourite quote:
In general, well-designed instruction should decrease extraneous load and optimise germane load, within the limits of total available capacity in order to prevent cognitive overload. However, this article is mainly about the situation that even after the removal of all sources of extraneous cognitive load, the element interactivity of the complex tasks is still too high to allow for efficient learning. Thus, it is about balancing intrinsic load, which is caused by dealing with the element interactivity in the tasks, and germane load, which is caused by genuine learning processes. The structure of our argument is as follows. First, we discuss research findings indicating that germane-load inducing instructional methods used for practicing simple tasks are not used for practicing complex tasks, at the cost of transfer of learning. Second, we argue that the element interactivity of learning tasks should be limited early in training to decrease their intrinsic load, so that germane-load inducing methods might be used right from the start of the training program. Cognitive Load during Problem Solving: Effects on Learning
Author(s): John Sweller
My Takeaway:
One huge question from all we have seen so far on Explicit Instruction and Cognitive Load Theory is: " how do we get our students to become good problem solvers?". This paper offers the first clue. Two of the main strategies involved in problem solving are:
1) Schema acquisition. This involves recognising similarities between novel and previously solved problems, and calling upon knowledge stored in long term memory to apply to the new situation.
2) Means-end analysis. This is a generic problem-solving strategy that we all possess, and it involves measuring your current state, evaluating how far you are from the solution state and then deciding which moves may get you closer.
For students to become good problem solvers they need to form mental schema from domain-specific knowledge which they can then apply to different situations. Unlike experts, novices lack the appropriate schema to recognise and memorise problem configurations. They set about solving problems by focusing on the detail and ignoring structure, embarking upon a means-end analysis. This would all be fine, apart from the claim in this paper that solving problems via such a strategy is itself is not an effective way for novices to develop these crucial mental schema. Why? Well, because trying to solve problems in this manner ( problem-solving search via means-end analysis) is cognitively demanding. the learner has to maintain the following aspects of the problem in his or her mind: current problem state, goal state, differences between these two states, operators that reduce the differences between the goal state and the present state, and subgoals. This overloads working memory, and hence the mental schema are not developed. Indeed, even if you manage to solve the problem, you might not recall the solution method, and hence you might not actually learn anything from the process. In other words, during a means-end approach to solving a problem, local goals and relationships may swamp the more global relationships. My key takeaway from this is a rather big one - students may not learn key knowledge and procedures from problem solving. Sure, they mauy solve the problem, but they are unlikely to be able to solve a related one (and almost certainly not an unrelated one, because the idea of a generic "Problem Solving skill" is flawed, as we shall see in the Problem Solving section), and it is an ineffective way of teaching the fundamental skills and procedures required to solve the problem. Problem solving is not a learning device. Problem solving must come at the end of the process, after the necessary domain specific knowledge has been learned. So, what are the implications for the classroom? Well, firstly, students should not be exposed to complex problem too early in the learning process. Secondly, I believe there is little point going through lots of difficult exam questions in the hope students understand them and make connections between related questions. I have been there myself - going through a series of unrelated problems with a class of 30 Year 11s, successfully answering my prompt-filled questions, and happily nodding along when I ask them if they get it. But any apparent success from teaching problem solving to novices is likely to be just mimicry. The skills will not be transferred. This will be covered further in the Problem Solving section, but the key point is that if basic skills are not in place, then problem-solving search via means-end analysis suggests that there will simply not be enough capacity in working memory for students to develop the mental schema necessary to learn and transfer.
My favourite quote:
Most mathematics and mathematics-based curricula place a heavy emphasis on conventional problem solving as a learning device. Once basic principles have been explained and a limited number of worked examples demonstrated, students are normally required to solve substantial numbers of problems. Much time tends to be devoted to problem solving and as a consequence, considerable learning probably occurs during this period. The emphasis on problem solving is nevertheless, based more on tradition than on research findings. There seems to be no clear evidence that conventional problem solving is an efficient learning device and considerable evidence that it is not. If, as suggested here, conventional problems impose a heavy cognitive load which does not assist in learning, they may be better replaced by nonspecific goal problems or worked examples. The use of conventional problems should be reserved for tests and perhaps as a motivational device.

Research Paper Title: The Expertise Reversal Effect
Author(s): Sweller, J., Ayres, P. L., Kalyuga, S. & Chandler, P. A.
My Takeaway:
So far all the talk has been of using Explicit Instruction and the key features of Cognitive Load Theory as the best method of teaching students to become fluent in the facts and procedures they will need to learn more complex skills. Specifically, in early skill acquisition, learning from worked examples is very advantageous, and learning by solving problems is not. However, as this paper describes, instructional techniques that are highly effective with inexperienced learners (novices) can lose their effectiveness and even have negative consequences when used with more experienced learners (experts), hence the Expertise Reversal Effect. The argument is that worked examples contain information that is easily determined by the more experienced learners themselves and, therefore, can be considered redundant. As we have seen via the Redundancy Effect, devoting working memory to redundant information effectively takes away a portion of the learners' limited cognitive capacity that could be devoted to the more useful germane load. Moreover, this redundant information may even interfere with the schemas constructed by experienced learners, preventing them from seeing the deeper connections in problems that are essential for transfer. For example, what if students have solved a problem differently to how I have presented it in thew worked example? At this stage of development, working through complex problems independently is likely to be more beneficial for long-term learning than studying worked examples. Of course, one major difficulty of this is recognising when students have made the transition from novice to expert and hence can start to be exposed to more complex problems. It is a delicate balancing act! What I have started doing is making worked examples "optional" for students once we have covered the basics of a topic. That way they can judge themselves whether they are at the stage where using worked examples will help or hinder them.
My favourite quote:
When a problem can be solved relatively effortlessly, analyzing a redundant worked example and integrating it with previously acquired schemas in working memory may impose a greater cognitive load than problem solving. Under these circumstances, practice in problem solving may result in more effective learning than studying worked examples because solving problems may adequately facilitate further schema construction and automation

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Cognitive Load Theory on Mr Barton Maths

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arrow_back Back to Research Cognitive Load Theory Dylan Wiliam described Cognitive Load Theory as "the single most important thing for teachers to know", and I have to agree. I find it provides rationale and practical strategies for the principles of Explicit Instruction discussed in the previous section, and it has transformed the way I teach.

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(Skip to the resources by clicking here)

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Look under 'resources'. In particular the scaffolded questions and the numberless questions 

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Look under 'resources'. In particular the scaffolded questions and the numberless questions 

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Edexcel Functional Skills in Mathematics | Pearson qualifications

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Edexcel Functional Skills in Mathematics - Entry Level 1-3 and Levels 1 and 2.

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Cognitive Load Theory (Cognitive Load Theory - the idea that working memory is limi... Abbreviated to CLT, the idea that working memory is limited ... More ) has recently become 'The Next Big Thing' in teaching. Dylan Wiliam tweeted on 26 January 2017 that he had 'come to the conclusion Sweller's Cognitive Load Theory More is the single most important thing for teachers to know.' This is an emphatic statement and it is important to consider the implications. As teachers, there are huge demands on our time, so when considering a new strategy it is essential to evaluate the evidence.

CLT, first researched by Sweller (Sweller, 1998) towards in the late 1980s, is based around the idea that our working memory - the part of our mind that processes what we are currently doing - can only deal with a limited amount of information at one time. Reif's (Reif, 2010) description of cognitive load is extremely useful: 'The cognitive load involved in a task is the cognitive effort (or amount of information processing) required by a person to perform this task.' There are a number of excellent resources freely available online that explain CLT (see Paas et al. (Paas et al., 2003) for a useful overview), so we will only touch on the foundations of the theory here that will be useful for the rest of the article.

The theory identifies three different forms of cognitive load:

Intrinsic cognitive load: the inherent difficulty of the material itself, which can be influenced by prior knowledge of the topic

Extraneous cognitive load: the load generated by the way the material is presented and which does not aid learning

Germane cognitive load: the elements that aid information processing and contribute to the development of 'schemas'.

CLT suggests that if the cognitive load exceeds our processing capacity, we will struggle to complete the activity successfully. In summarising CLT, De Jong (De Jong, 2010) states that 'cognitive load theory asserts that learning is hampered when working memory capacity is exceeded in a learning task'.

Working memory should be seen as short term and finite, whereas long-term memory can be seen as infinite. The aim should be to move knowledge to long-term memory because when a student is exposed to new material, they can draw on this previous knowledge and the cognitive load is reduced. However, if subject knowledge is incomplete, the student is unable to fall back on the long-term memory and the working memory becomes overloaded, leading to working memory failures. According to Gathercole and Alloway (Gathercole and Alloway, 2007), indications of working memory failures include:

incomplete recall

failing to follow instructions

place-keeping errors

task abandonment.

Of course, there are many other reasons for these that are not related to CLT; however, if teachers understand how this theory applies to their classroom, they can plan their lessons in a way that takes into account cognitive load.

Reducing cognitive load

Intrinsic cognitive load can be reduced by breaking down the subject content, sequencing the delivery so that sub-tasks are taught individually before being explained together as a whole. The idea is to not overwhelm a student too early on in the introduction of new work.

Extraneous cognitive load can be reduced by the way in which instructions are presented. We make sense of new material by referencing schema or mental models of pre-existing knowledge. Lack of clarity in instruction puts too high a load on the working memory, and so too much time is spent problem-solving the instructions as opposed to new schema formation. For example, lessons that use PowerPoint with excessive writing and the teacher talking at the same time, can inadvertently generate excessive cognitive load and lead to working memory failures. Chandler and Sweller (Chandler and Sweller, 1991) write that 'Cognitive Load Theory suggests that effective instructional material facilitates learning by directing cognitive resources towards activities that are relevant to learning.'

Van Merriënboer et al. (Van Merriënboer et al., 2003) recommend using simple-to-complex sequencing to try to reduce cognitive load. They advise starting with worked-out examples (where a full solution is shown, which students then have to apply to a new question), then moving into completion assignments (where a partial solution is given and they have to complete it themselves), and then moving to conventional tasks, where they are simply given the question. This acts as a form of Progressively introducing students to new concepts to suppor... scaffolding More , which helps students to learn independently, without necessarily needing the help of their teacher for each stage.

Renkl and Atkinson (Renkl and Atkinson, 2003)further investigated this fading form of scaffolding. They suggestedthat moving through activities sequentially could reduce intrinsic load, as learners will have already mastered some of the knowledge they need to work out a solution in an earlier skill stage. Therefore, their research recommends beginning with a model (a complete example), gradually removing completed steps, which the learner will have to complete independently, and finally leaving just the to-be-solved problem.

These principles can be readily applied in the classroom by beginning with a model answer, then providing a writing frame/structure with a lot of information, followed by a writing frame/structure with less information, then finally a question that learners must complete independently without a writing frame. It is worth, though, being aware of the 'expertise reversal effect' suggested by Kalyuga et al. (Kalyuga et al., 2003), whereby if you continue to provide worked-out examples for experts, their usefulness is significantly reduced. Cognitive load theorists suggest this is because worked-out examples contain information that an expert could work out for themselves, making it redundant and therefore extraneous cognitive load rather than useful germane cognitive load.

Presenting information to minimise cognitive load

Chandler and Sweller (Chandler and Sweller, 1992) found evidence of the split-attention effect. This occurs when different sources of information discussing the same topic are separated by time or space, such as a diagram with a key that corresponds to separate text next to it. When information is presented in this way, it is left to the learner to attempt to amalgamate it, which generates extraneous cognitive load. Therefore, it is recommended that if one of the sources adds nothing new, it should be eliminated. However, if it is essential to include both sources, they should ideally be physically integrated (e.g. texts and diagrams combined). This way, extraneous cognitive load is reduced and working memory capacity can be used for intrinsic and germane cognitive load instead.

A word of caution

There are, of course, issues with CLT. Reif (Reif, 2010) writes that if cognitive load is reduced too much, 'the entire learning process would consist of too many small steps - and would thus become unduly fragmented and long'. There are also issues to do with the hypothesis being unfalsifiable. Doug Holton (Holton, 2009) points out that it is difficult to measure cognitive load, and therefore difficult to generate evidence to prove the theory.

An important question, though, is whether it is useful in the classroom. Ashman (Ashman, 2017) has explained that an understanding of CLT changed his maths teaching, and offers the following four examples:

1. I don't read out my slides - avoid simultaneous oral and text presentation

2. Break it down, further - pause for practice between individual problem types (this leads directly into number 3)

3. Example-problem pairs - give a worked example alongside an almost identical question

4. Stop after five minutes - advise students never to spend more than five minutes trying to solve a homework problem

So is CLT the single most important thing for a teacher to know? Perhaps not - it is a bold claim. But, if used correctly, it can improve teacher instruction, which is an important variable in the complex classroom environment.

KEY TAKEAWAYS

Break down subject content when introducing new topics and pause regularly to check understanding.

Present instructions clearly without using too many sources of information at the same time.

Be wary of reducing cognitive load too much - the learning process should be manageable, but not overly fragmented.

Dominic Shibli is Senior Lecturer in the School of Education at the University of Hertfordshire. Prior to that he was Head of Science and SLE for the North Herts Teaching Alliance.

Rachel West has a BSc in psychology and has been teaching psychology for three years. She is interested in raising awareness of the ways in which psychological theory can be applied to teaching practice.

References

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Cognitive Load Theory and its application in the classroom

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Cognitive Load Theory (CLT) has recently become 'The Next Big Thing' in teaching. Dylan Wiliam tweeted on 26 January 2017 that he had 'come to the conclusion Sweller's Cognitive Load Theory is the single most important thing for teachers to know.' This is an emphatic statement and it is important to consider the implications.

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The importance of cognitive load theory | Society for Education and Training

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Lecturer and SET Fellow Dan Williams explains why there is one learning theory he feels all teachers should be aware of.

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arrow_back Back to Research

Worked Examples: Making the most of them

It was my reading of Cognitive Load Theory that first prompted my appreciation of the power of worked examples. Understanding that studying worked examples could be more effective for learning than solving problems blew my mind and prompted me to read all I could about how to make the worked examples I used in class as effective as possible. This section provides a summary of what I found.

Research Paper Title: The Contributions of Studying Examples and Solving Problems to Skill Acquisition
Author(s): J. Gregory Trafton and Brian J. Reiser
My Takeaway:
The first paper in this section has two major findings which, whilst they may seem obvious, are both of crucial importance. The researchers conducted experiments designed to answer two key questions they had about the most effective way to study from worked examples.
Does separating source examples from target problems hamper learning?
The researchers conducted an experiment comparing participants who solved a target problem immediately after the source example (Alternating Example) versus those who studied a block of source examples followed by a block of solving target problems (Blocked Example). Subjects who solved problems interleaved with examples took less time on the target problems than subjects who studied a block of source examples and a block of target problems. Crucially, participants in the Alternating Example condition also submitted more accurate solutions than subjects receiving blocked examples.
Is solving sources better than studying examples if the examples are not accessible during subsequent problem solving?
This is a key question. There is a danger that we can get too caught up in the power of examples, and think that students do not need to solve any problems at all. However, the researchers found that participants who attempted to solve problems performed better than those who merely studied worked examples. As we shall see in the sections on Testing, it is this retrieval process induced when answering a question that is so important to learning, and if students are never compelled to access their memories of those examples, then they will never benefit from, what we will come to call the Testing Effect. Hence, we can conclude that subsequent problem solving appears to be required to derive the full benet of studying examples
My favourite quote:
In summary, studying examples is clearly a very effective method to improve learning. In order for an
example to be most effective, however, the knowledge gained from the example must be applied to solving a new problem. The most efficient way to present material to acquire a skill is to present an example, and then a similar problem immediately following. We hypothesize that this presentation method allows subjects to construct rules that are general enough to work for both the example and the rule. Although the extra practice solving sources may speed target problem solving, apparently more effective problem solving rules are formed when target problem solving can be guided by an accessible source example.

Research Paper Title: Learning from Examples: Instructional Principles from the Worked Examples Research
Author(s): Robert K. Atkinson , Sharon J. Derry , Alexander Renkl , Donald Wortham
My Takeaway:
There are so many fascinating concepts discussed throughout this paper extolling the virtues of worked examples, and when they are most effective. Concepts such as the split-attention effect, and variability of problem types are also discussed, which we have covered in the Cognitive Load Theory section. The quote I have chosen for this paper summarises the main findings nicely, and serves as an excellent set of guidelines for the use of worked examples during lessons. I am going to focus on one that has directly changed the way I teach, and which is directly related to the finding from the paper above: Example-Problem Pairs. I used to do a load of worked examples at the start of the lesson, and then give the students a set of problems to work on for the remainder of the lesson. The problem (and it seems so obvious now) was that by the time I had done the 3rd worked example, students had forgotten the first as they had not had the opportunity to practice it for themselves. Hence, they would start working on the questions, get stuck, and I would need to go through it all again. This paper recommends interleaving worked examples with related questions for students to solve alone. When doing a worked example in class, I now split my board in two, having the worked example on the left, and a mathematically similar example for my students to try themselves immediately afterwards on the right. It sounds so simple, but the positive effects have been quite startling. Greg Ashman discussed this strategy when describing how he plans his lessons when I interviewed him for my podcast, and he has written a blog post all about his use of Example-Problem Pairs here.
My favourite quote:
First, transfer is enhanced when there are at least two examples presented for each type of problem taught. Second, varying problem sub-types within an instructional sequence is beneficial, but only if that lesson is designed using worked examples or another format that minimizes cognitive load. Third, lessons involving multiple problem types should be written so that each problem type is represented by examples with a finite set of different cover stories and that this same set of cover stories should be used across the various problem types. Finally, lessons that pair each worked example with a practice problem and intersperse examples throughout practice will produce better outcomes than lessons in which a blocked series of examples is followed by a blocked series of practice problems.

Research Paper Title: Design-Based Research Within the Constraints of Practice: AlgebraByExample
Author(s): Julie L. Booth, Laura A. Cooper, M. Suzanne Donovan, Alexandra Huyghe, Kenneth R. Koedinger & E. Juliana Paré-Blagoev
My Takeaway:
We have seen the benefits of learning by worked example in our study of Cognitive Load Theory, in particular with the example-problem pairs approach. We have also seen the benefits of students explaining their thinking in our look at Student Self-Explanations. So, what happens when you combine these two powerful findings together? This paper seeks to demonstrate. The study in question came about from a challenge to identify an approach to narrowing the minority student achievement gap in Algebra 1 without isolating minority students for intervention. They attempted to do this by designing and testing 42 Algebra 1 assignments with interleaved worked examples that targeted common misconceptions and errors. The worked examples contained three parts:
1) the worked example
2) a section to reflect on what certain aspects of the worked meant, and how and why they were carried out that way
3) a related problem to complete
Hence, it is the middle section - the opportunity for self-explanation - that differentiates this approach from the example-problem pair approach. Notice also how the students are compelled to self-explain, which seems important given the findings from the Renkl paper in the Self-Explanations section that the majortiy of studetns do not spontaneously use self-explanation strategies. The results were impressive. The approach provides a boost in performance, with the greatest impact on students at the lower end of the performance distribution. On the researcher-designed assessment of conceptual understanding, treatment students in the lower half of the performance distribution outscored comparable control students by approximately 10 percentage points. Treatment students overall scored 7 percentage points higher on a test composed entirely of released items from the state standardized tests, and 5 percentage points higher on the conceptual posttest. Procedural posttest scores were also 4 percentage points higher in the treatment group, even though control students had twice the practice solving problems on the assignments. As a result of this, together with the related research into the power of self-explanations, I have added that third element to my example-problem pair approach.
My favourite quote:
Of equal significance, AlgebraByExample achieved these gains with an intervention that meets all the constraints imposed by the districts: it targets all students, it can be used with any existing Algebra 1 curriculum, and it is an asset that teachers can use with minimum disruption to their practice. Moreover, study teachers reported that students using AlgebraByExample required less teacher support to complete assignments than those using control assignments, and reported rethinking their own practice in response to students' positive experiences with worked examples.

Research Paper Title: Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples
Author(s): Julie L. Booth, Karin E. Lange, Kenneth R. Koedinger, Kristie J. Newton
My Takeaway:
This study takes worked examples with student self-explanations to the next level by considering the inclusion of incorrect examples. This is something I have always been wary of. I can see the benefits of non-examples when it comes to understanding factual definitions in maths (such as "what is a polygon?"), but is there a danger that exposing students to non-procedures (i.e. incorrect worked examples) will lead to them developing misconceptions? The authors cite findings from previous research that outline two reasons why the inclusion of incorrect examples might be of benefit to learning. First, they can help students to recognise and accept when they have chosen incorrect procedures, leading to improved procedural knowledge over practice alone or correct examples plus practice. Second, and perhaps more important, it can draw students' attention to the particular features in a problem that make the procedure inappropriate. Therefore a combination of correct and incorrect examples is beneficial because the incorrect examples help to weaken faulty knowledge and force students to attend to critical problem features (which helps them not only to detect and correct errors, but also to consider correct concepts), while the correct examples provide support for constructing correct concepts and procedures, beyond that embedded in traditional instruction. In their study, the authors conducted two experiments, both focussed on the Algebra 1 course take in high-schools in the US. They sought to answer two questions:
1) Do worked examples with self-explanation improve student learning in Algebra when combined with scaffolded practice solving problems? The results were a resounding "yes".
2) Are there differential effects on learning when students explain correct examples, incorrect examples, or a combination thereof? Results indicated that students performed best after explaining incorrect examples; in particular, students in the Combined condition gained more knowledge than those in the Correct only condition about the conceptual features in the equation, while students who studied only incorrect examples displayed improved encoding of conceptual features in the equations compared with those who only received correct examples.
The authors have a really nice way of summarising this key finding: "This finding is especially important to
note because when examples are used in classrooms and in textbooks, they are most frequently correctly solved examples. In fact, in our experience, teachers generally seem uncomfortable with the idea of presenting incorrect examples, as they are concerned their students would be confused by them and/or would adopt the demonstrated incorrect strategies for solving problems. Our results strongly suggest that this is not the case, and that students should work with incorrect examples as part of their classroom activities."
My favourite quote:
Our results do not suggest, however, that students can learn solely from explaining incorrect examples. It is important to note that all students saw correct examples, regardless of condition, not only because they are regularly included in textbooks and classroom instruction, but because the correctly completed problems the students produced with the help of the Cognitive Tutor could also be considered correct examples of sorts. We maintain that students clearly need support for building correct knowledge, however, if that support is coming from another source (e.g., guided practice with feedback), spending additional time on correct examples may not be as important as exposing students to incorrect examples.

Research Paper Title: Learning from Worked Examples: What happens if mistakes are included?
Author(s): Cornelia S Grosse and Alexander Renkl
My Takeaway:
I include this paper as a word of caution before getting too carried away with exposing students to incorrect worked examples. The authors found that learning from worked examples where errors are included can enhance learning and transfer, but only if students have good prior knowledge of the topic. This makes perfect sense. Firstly, if students do not understand the topic, then how are they to spot the mistakes? Secondly, in the context of Cognitive Load Theory, if their understanding is not secure, then their working memories are likely to become overloaded whilst searching for the right and wrong answers simultaneously. This finding is supported by a paper from Große, C. S., & Renkl, A (behind a pay-wall) which found that relatively novice learners cannot benefit from incorrect examples when they are expected to locate and identify the error in the example themselves. Again, It makes sense that novice students would have difficulty with this component, given that they likely make many of the mistakes themselves and may not recognize them as incorrect. So what are we to make of this? It seems clear that students need a certain amount of knowledge of a topic in order to benefit from exposure to mistakes in worked examples. If they do not know what is right, how can they know and explain what is wrong? Hence, I would be leaning towards correct worked examples combined with student explanation in initial skill acquisition, moving onto clearly labelled incorrect worked examples combined with student explanation once students begin to get familiar with the concepts.
My favourite quote:
Learning with incorrect examples poses challenging demands on the learners. They have to represent not only the correct solution in their working memory, but also the incorrect step with an explanation why it is wrong. Learners with low prior knowledge who cannot form larger chunks for information coding can easily be overtaxed.

Research Paper Title: Structuring the Transition From Example Study to Problem Solving in Cognitive Skill Acquisition: A Cognitive Load Perspective
Author(s): Alexander Renkl and Robert K. Atkinson
My Takeaway:
This paper provides a challenge to the Example-Problem Pair approach heralded by the papers above. The authors propose that instead of providing students with a complete worked example, followed by a problem for them to solve, followed by a complete worked example, followed by problem to solve, etc (i.e. the Example-Problem Pair approach), instead a fading procedure is more effective. This involves providing a complete worked example, and then following this up with an almost complete worked example but with one step removed that students need to complete. There are obvious parallels to be drawn here with the Completion Effect noted in the Cognitive Load Theory section. The researchers two things that are of particular relevance to this section:
1) The fading procedure produced reliable effects on near-transfer items but not on far-transfer items. Near-transfer problems have the same deep structure but different surface structures. In other words, the strategy to solve them is exactly the same, but the context is different. Far-transfer problems have both a different context and a different deep structure. In other words near transfer is the acquisition of relatively simple rules, whereas far transfer is more a measure of understanding.
2) It was more advantageous to fade out worked- out solution steps using a backward approach by omitting the last solution steps first instead of omitting the initial solution steps first (i.e., a forward approach).
So, we have an alternative to the example-problem pair approach, which has been shown to outperform its rival, both in this study and the one that follows. This begs the obvious question: when do we use each one? For me, it depends on the complexity of the problems and the prior knowledge of the class. Relatively simple problems probably lend themselves better to an example-problem approach. Likewise, with students with higher prior knowledge, or students who have seen the topic before (i.e. in a revision lesson), I would favour the example-problem approach. However, for more complex problems or with students who are struggling, the fading approach seems very appropriate.
My favourite quote:
First, a complete example is presented (model). Second, an example is given in which one single solution step is omitted (coached problem solving). Then, the number of blanks is increased step by step until just the problem formulation is left, that is, a to-be-solved problem (independent problem solving). In this way, a smooth transition from modeling (complete example) over coached problem solving (incomplete example) to independent problem solving is implemented.

Research Paper Title: Transitioning From Studying Examples to Solving Problems: Effects of Self-Explanation Prompts and Fading Worked-Out Steps
Author(s): Robert K. Atkinson, Alexander Renkl and Mary Margaret Merrill
My Takeaway:
This paper aims to plug the one remaining gap in the fading procedure for worked examples proposed in the paper above - how to improve performance on far-transfer problems? Well, just like we saw in the Booth papers above, we can improve the effectiveness of worked examples by prompting student explanations. Here the researchers designed experiments which combined fading with the introduction of prompts designed to encourage learners to identify the underlying principle illustrated in each worked-out solution step. They set up four conditions: Example-Problem Pair (EP), Example-Problem Pair Plus (EP+) which contained the self-explanation prompts, Backwards Fading (BF) and Backwards Fading Plus (BF+). Crucially, the experiment was designed in a way so that participants had to complete the exact same number of solution steps in each condition - it was just in the EP approach they all came together, whereas in the BF model they were introduced more gradually. The key findings were as follows:
1) the BF condition was associated with a higher solution rate of near-transfer problems than EP
2) a simple prompting procedure can substantially foster both near and far transfer. Hence, the acquisition not only of relatively simple rules (i.e., near transfer) but also of understanding (i.e., far transfer) can be fostered by this instructional procedure. It is also notable that the advantage of prompting could be achieved without significantly increasing learning time
3) there was no evidence of an interaction between the use of fading and the use of self-explanation prompts on any of the measures. This may be regarded as a positive finding from an educational point of view because both instructional means produced at least medium effects on learning outcomes and were combined without causing any decrement in performance.
For me, there are two key takeaways here. Firstly, the fading procedure must be taken seriously. Secondly, prompting students to self-explain is effective no matter how the worked examples are presented, and hence is something of a no-brainer when it comes to teaching and modelling.
My favourite quote:
One may ask whether it is practical to use the instructional procedures analyzed in this article for teaching skills in well- structured domains. Overall, the use of prompts that encourage the learners to figure out the principle that underlies a certain solution step can be recommended for several reasons, including the fol- lowing: (a) it produces medium to high effects on transfer performance, (b) these effects are consistent across different age levels (university and high school), (c) it does not interfere with fading, (d) it is very easy to implement (even without the help of computer technology), and (e) it requires no additional instructional time.

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Worked Examples: Making the most of them on Mr Barton Maths

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arrow_back Back to Research Worked Examples: Making the most of them It was my reading of Cognitive Load Theory that first prompted my appreciation of the power of worked examples. Understanding that studying worked examples could be more effective for learning than solving problems blew my mind and prompted me to read all I could about how to make the worked examples I used in class as effective as possible.