Breaking a lecture up into distinct chunks or sections is a bit of a no-brainer. It is all to do with understanding the implications of cognitive load theory, specifically that the brain can only process a small amount of new information at once. Presenting more information than the brain’s architecture can handle leads to overloading the working memory, and usually a significant decrease in learning.
Breaking your lecture into chunks provides students a chance to process each chunk before new material is presented. Designing opportunities for students to be active (black boxes) in the processing of the content also assists in facilitating the content’s understanding, and eventual transfer into long term memory.
So, here’s a possible live -streamed lecture design that considers cognitive load implications, the need for the student to be active in their learning, and is very manageable for the lecturer. The model can be applied to both live and recorded lectures, but the recorded lecture will need some more specific context discussed, which I will do in another post.
I’ve talked before about the possible mixed-mode future of live lecturing, with it being able to facilitate a breakout room. The below model considers this as a possibility.
lesson segment
rationale
tech to assist
intro
The lesson begins with a retrieval quiz. The benefit of retrieval is enormous. It strengthens the memory of key ideas and content. The purpose of this is so the knowledge can be automatically brought to cognition when new learning is presented, without taxing the working memory. The more knowledge the student can draw from, the greater the opportunity to delve into more higher order independent learning, so building students’ schema through retrieval is is a bit of a no-brainer. The lecturer will place answers on the screen, and spend 2-3 minutes explaining answers if common errors were made.
Polls Echo 360 Mentimeter Quizziz Canvas quiz
teaching
Delivering content. 10-12 min. Incremental building to application is is a bit of a no-brainer. The lecturer is conscious of the need to present content clearly and simply, very much aware of multimedia principles that promote the efficient encoding of new information. They are also aware of the importance of modelling problem solving and incorporate worked examples into the presentation. Where appropriate, the lecturer connects the new learning to real world applications, not just to make the content relevant, but more so to build the mental patterns and analogies in the students’ schemata. The lecturer also frequently mentions the reasons why decisions in the teaching are being made so as to strengthen the students’ metacognition.
PPT slides. Document camera. Students can take notes in Echo, can raise confusion flag, and ask a question at precise point in either the live stream.
student activity
Strengthening understanding This provides students a chance to take in what has just been presented, and think about the concepts before tehy are presented with more content. Essentially the student is trying to convert the abstract to the concrete. Providing students with the opportunity to complete worked examples, practise solving similarly structured problems, or discussing with a peer possible analogies to the content is valuable at this point in the lecture, and is a bit of a no-brainer.
Breakout rooms. Mentimeter open question. Echo discussions. Canvas discussions. GoFormative.
teaching
Discussion of last task if necessary – may not be if practising or completing examples. Delivering content. 10-12 min. Incremental building to application is a bit of a no-brainer. The lecturer is conscious of the need to present content clearly and simply, very much aware of multimedia principles that promote the efficient encoding of new information. They are also aware of the importance of modelling problem solving and incorporate worked examples into the presentation. Where appropriate, the lecturer connects the new learning to real world applications, not just to make the content relevant, but more so to build the mental patterns and analogies in the students’ schemata. The lecturer also frequently mentions the reasons why decisions in the teaching are being made so as to strengthen the students’ metacognition.
PPT slides. Document camera. Students can take notes in Echo, can raise confusion flag, and ask a question at precise point in either the live stream.
Formative assessment
Checking for learning A quiz of short answer opportunity to see if what you have presented so far has been understood is is a bit of a no-brainer. The questions also provide another opportunity for a student to process the content and develop a better understanding.
Questions up on screen. Zoom polling. Using Canvas discussions as student answer repository. Mentimeter. Quizziz.
teaching
Check answers – you may need to pivot the lecture if misconceptions are still prevalent. Delivering content. 10-12 min. Incremental building to application is a bit of a no-brainer. The lecturer is conscious of the need to present content clearly and simply, very much aware of multimedia principles that promote the efficient encoding of new information. They are also aware of the importance of modelling problem solving and incorporate worked examples into the presentation. Where appropriate, the lecturer connects the new learning to real world applications, not just to make the content relevant, but more so to build the mental patterns and analogies in the students’ schemata. The lecturer also frequently mentions the reasons why decisions in the teaching are being made so as to strengthen the students’ metacognition.
PPT slides. Document camera. Students can take notes in Echo, can raise confusion flag, and ask a question at precise point in either the live stream.
student activity
Strengthening understanding This provides students a chance to take in what has just been presented, and think about the concepts. Essentially the student is trying to convert the abstract to the concrete. Providing students with the opportunity to complete worked examples, practise solving similarly structured problems, or discussing with a peer possible analogies to the content is valuable at this point in the lecture.
Breakout rooms. Mentimeter open question. Echo discussions. Canvas discussions. GoFormative.
summary
Recapping key ideas. Tying the lecture all together: linking it to previous learning and real word contexts. Discussion and questions asking students to link their learning is a great way to draw attention to the key concepts again, and is a bit of a no-brainer.
Mentimeter open ended question.
I’m Paul Moss. I’m a learning designer at the University of Adelaide. Follow me on Twitter @edmerger
THE 3 A’S OF KNOWLEDGE TRANSFER: ACQUIRE, ANALOGISE, APPLY PT 2
This is the third instalment of a 4 part series aimed at assisting an educator in designing a sequence of learning that drives towards the ultimate goal of knowledge transfer. The intro post is here and the post on the first stage of developing a context of transfer, acquiring knowledge, is here
PT 2:Analogous examples
The importance of presenting analogous examples to students to facilitate transfer is made apparent by Gentner and Ratterman (1991), who purport that people learning from a single example of content tend to encode it in a context-specific manner, with the result that later remindings are often based on more obvious surface aspects. Applying knowledge to a new context from only seeing one example of the learning is significantly harder compared to providing an analogy for students, but as Reeves and Weisberg suggest, it is not enough to simply provide a single analogous examples to your students.
The beginnings of analogical reasoning
Karl Duncker was a quite remarkable German psychologist.
He dedicated considerable energy into exploring how learners approach problem solving, and his thesis on how it happens is here. His candle problem highlighted the notion of Functional Fixedness, which highlighted that once a learner has established a schema for a certain function, it is difficult for the ‘function’ to be applied in another context. Before his tragic death, suicide at 37 years of age, Duncker created the ‘radiation problem’, where he established that learners asked to solve the problem could only do so 10% of the time. It is this very low number that paved the way for considerable research into how to assist the problem solving dilemma of functional fixedness.
Gick and Holyoak are perhaps the most notable of researchers to shed light on how to mitigate functional fixedness. They found that when students were given an analogy to the Duncker tumour problem that had the same underlying structural properties, the number of students who were able to solve the problem rose from 10% to 30%. Incredibly, when they experimented by providing a 2nd analogy prior to exposing students to the radiation problem they found that 80% of students could then solve the problem. When they provided a underlying principle to students, when only a single analogy was used it did not assist students, but when 2 analogies were given, the underlying principle increased student success to 82% with a verbal principle, and 92% with a diagrammatical principle.
Of particular note however, was Gick and Holyoak’s attention to the quality of a student’s schema when applying the analogies to the problem. What they found, consistently, was that when a student presented a good quality schema, found by having students articulate the similarities between analogies, 100% of students were able to solve the problem. This has enormous implications for the need to ensure that a well-developed schema is present when asking students to apply or transfer knowledge into a new context.
It highlights the fact that it is the bank of mental models and patterns that a student has that allows them to search and seek connections from the schema to the new learning context. If they have a good understanding of the general principles of a problem, characterised by identifying the deeper relational structure of a problem, then it is more likely they will be able to see the same structure in a new problem. As Duncker states, ‘one can transpose a solution only when one has grasped its functional value, its general principle, i.e., the invariants from which, by introduction of changed conditions, the corresponding variations of the solution follow each time.’
Gick and Holyoak’s work has been validated by other researchers. Alfieri, Nokes-Malach and Schunn conducted a meta-analytic review of research using comparison examples to assist problem solving, and found conclusive evidence that analogical reasoning using several comparisons benefits the transfer of knowledge. Jacobson et al report that providing students’ opportunity to search for the similarities of analogy structures improves problem solving and transfer capability, and adding to the weight of evidence, Markman and Gentner suggest that directing students to the structural similarities is what eventually builds the schema that the student will use to connect to new learning contexts.
So, analogy greatly assists students in being able to transfer knowledge into a new context. Providing at least 2 analogies and explicitly pointing students to the similarities appears to be the optimal context for developing the relevant schema for transferring and applying knowledge.
How to exploit this ability to transfer and apply knowledge will be the basis of the next post.
References
Language and the career of similarity. Gentner, D., & Rattermann, M. J. (1991). In S. A. Gelman & J. P. B yrnes (Eds.), Perspective on thought and language: Interrelations in development (pp. 225-277).New York: Cambridge University Press.
THE 3 A’S OF KNOWLEDGE TRANSFER: ACQUIRE, ANALOGISE, APPLY PT 1
Pt 1: ACQUIRING KNOWLEDGE EFFICIENTLY
This is the second instalment of a 4 part series aimed at assisting an educator in designing a sequence of learning that drives towards the ultimate goal of knowledge transfer. The intro post is here.
Concrete to abstract to concrete
Delivering new learning in concrete terms using concrete examples makes it easier for a student to encode the content. We assimilate or accommodate new information in the context of the patterns, mental models, examples, analogies and experiences that either already were or have been converted to the concrete in our brain, representations that have formed the basis of our schemata. Kolodner describes this reliance on prior learning as case-based scenarios1. The use of models help students to capture the mental patterns required for the knowledge to become understood. It could be suggested that this predisposition to preferring the concrete could lead one to theorise that the concrete represents understanding. However, a necessary process in the incremental development of a schema is the gradual introduction of abstractions, as they instigate the machinations of knowledge transfer.
A lot of what we teach in higher education is abstract in nature, and necessarily so: ‘The goal of learning an abstract concept is not simply knowledge of one instantiation; it is the ability to transfer, or apply conceptual knowledge to a novel isomorphic situation.’2 However, this creates two issues for learners: abstract content is inherently harder to learn than concrete content, and the links between abstract content and real word applications can often seem distant at best.
Why is it harder to learn through abstraction?
It seems our brains are wired to think in concrete terms3. So, if it is harder to learn through abstraction, why not simply avoid it altogether and convert material to the concrete for our students? Well, it all has to do with the facilitation of knowledge transfer. Resnick and Omanson4 assert that ‘learning with concrete objects supports initial understanding of the instructed concept but does not support the transfer of that knowledge to novel but relevant contexts.’ Pashler et al5 concur and extend this: ‘Many experimental laboratory studies and a growing number of classroom based quasi-experiments have found that teaching students about key principles or concepts using only abstract or only concrete representations of those concepts leads to less flexible knowledge acquisition and use than teaching students to recognize and use those key principles across a range of different situations’.
So how do we get the balance right? It appears that once we have set a foundation using concrete examples, turning to metaphor is the next step. Reece (2003)6 suggests that human analogical reasoning engaged through metaphor-based environments helps learners to incorporate new concepts into their existing mental schema. She advocates the use of metaphors believing them to be ‘especially appropriate when learners are introduced to new, abstract concepts’, and she cites Jonassen, (1981)7 who asserts that metaphor acts as a scaffolding ; that is, ‘a learner structures the to be-learned domain, the target, according to the relational structure of the concrete and more familiar domain, the source domain (see structure mapping theory in Gentner, 1983, 1989; Gentner & Markman, 1997).’
In designing effective metaphors, Carroll & Mack8 instruct that ‘Within pedagogical applications, an instructional metaphor source domain can be carefully structured so that it replicates the relational structure of the target domain’. It seems that this deliberate scaffolding of metaphor is consistent with the need to attend to the incremental building of a schema; the metaphor is designed to incrementally build abstraction by initially making connections to relational structures quite close, and then gradually making them more abstract. The student’s schema thereby develops by adding to the bank of patterns contained within.
But a well-developed schema does not necessarily mean that transfer of learning to new contexts is automatic. Gentner, Rattermann & Forbus (1993)9 report that ‘people often fail to access prior cases that would be useful, even when they can be shown to have retained the material in memory’. Transfer then, requires a lot more attention to design than just acquiring knowledge. One of the ways to achieve it is through analogous examples.
2. Do Children Need Concrete Instantiations to Learn an Abstract Concept? Jennifer A. Kaminski (kaminski.16@osu.edu), Vladimir M. Sloutsky (sloutsky.1@osu.edu), Andrew F. Heckler (heckler.6@osu.edu) – http://csjarchive.cogsci.rpi.edu/proceedings/2006/docs/p411.pdf
3. Lawson, A. E., Alkhoury, S., Benford, R., Clark, B. R., & Falconer, K. A. (2000). What kinds of scientific concepts exist? Concept construction and intellectual development in college biology. Journal of Research in Science Teaching, 37(9), 996-1018.
4. Resnick, L.B., and Omanson, S.F. (1987). Learning to understand arithmetic. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 3, pp. 41-95). Hillsdale, NJ: Erlbaum.
5. Pashler, H., Bain, P., Bottge, B., Graesser, A., Koedinger, K., McDaniel, M., and Metcalfe, J. (2007) Organizing Instruction and Study to Improve Stu. dent Learning (NCER 2007-2004). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ncer.ed.gov
6. Reece, D. 2003. Metaphor and content: An embodied paradigm for learning. Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy In Curriculum and Instruction (Instructional Technology).
7. Jonassen, D. H. (1981, April 7). Content treatment interactions: a better design model. Paper presented at the Association for Educational Communication and Technology, Philadelphia, PA.
8. Carroll, J. M., & Mack, R. L. (1999). Metaphor, computing systems, and active learning. International Journal of Human-Computer Studies, 51, 385-403.
9. Gentner, D., Rattermann, M. J., & Forbus, K. D. (1993). The roles of similarity in transfer: Separating retrievability and inferential soundness. Cognitive Psychology, 25, 524-575.
I’m Paul Moss. I’m a learning designer at the University of Adelaide. Follow me on Twitter @edmerger
Picture the setting: instead of the regular face to face lecture of 120 students, there are 40 in front of you and the other 80 are remote. How can a lecturer operate under such conditions, satisfying both contexts at the same time?
Well, each student is connected to Zoom, face to face students either through a laptop or a phone, and remote students similarly so. The face to face students have a choice – they can watch and hear the lecturer as normal, or watch and listen through the screen, as the remote student would have to do. If slides are presented, then the face to face student likely has an advantage as they can see the lecturer full size and the content on a larger screen, whereas the remote student sees only a thumbnail of the lecturer in the corner of the presentation.
So, what are some of the advantages of having face to face students being connected via Zoom too – why not just watch and listen as normal?
100% participation in formative assessment – if everyone has a device then you can assess their understanding at stages of the lecture using polls and quizzes. Beginning each lecture with a retrieval quiz is highly beneficial as it brings back into the minds of your students key ideas from past lectures that you know they need to know – helping them retrieve such content actually helps you too as new concepts will be better understood if students can automatically bring past ‘connected’ ideas into their thinking without taxing the working memory. Half way through a lecture is another good time to formatively check for understanding.
Generally asking lots of questions in a lecture is still good practice, but getting everyone involved is near impossible in a regular lecture context – now technology affords this. Getting more data helps you know if what you’re teaching is being understood.
Interactions with peers – when appropriate, students can seek clarification from a peer without disturbing the rest of the lecture room. Of course, this should only be encouraged when there is space in the lecture so students aren’t missing key ideas if talking to a peer. You can manage the chat functions to be open to all or so that students can only message you during content delivery. See here for more Zoom engagement advice.
Interactions with the lecturer – potentially, shy students in the lecture theatre can now ask a question to the lecturer, anonymously if they like, via the chat in Zoom. For some, the pressure of not wanting to appear silly by asking a question is huge, and often such students won’t ask, and then move onto the next section of the lesson without clarity on what was just taught. Now everyone can be heard.
Group work in a lecture – breakout rooms facilitate the option of having students work together to solve problems. At stages in the lecture when chunking is necessary to secure students’ attention, an option may be for students to spend some time to practise what has just been delivered, consider relevant analogies to help strengthen understanding, or collaborate on creative solutions to new problems. Addressing misconceptions or consolidation through practice is probably best done in pairs, whereas groups of 3-5 may be more suited to discussing ideas and analogies rather than practice.
Black screens can be good – the wonderful Dr David Wilson from Adelaide University provided some valuable insight in this area. There may be several legitimate reasons why a student decides to turn their video off. Of course, the best communicators make their expectations explicit and clear from the beginning, and help students with legitimate screen issues arrive at alternative ways to engage in the lecture, but sometimes a student will turn their screen off because it’s easier to engage passively. We all know that active learning is better than passive learning, but in a large lecture theatre, it can be hard to determine who is and who isn’t active, and time consuming trying to address an individual who pretends not to hear you. Now, the black screen at least gives you a chance at instantly seeing who the passive student is and a chance at addressing their decision. If you’ve made it clear that you prefer the screen on, and that those who can’t should communicate why privately to you, then if the student simply still refuses to engage when addressed, it’s easy to write down the Zoom name or student number and address it later with a friendly check-in to see if there is anything you can do to help. If the student has used a fake name, well that’s a fair bit harder, but you’d hope that having established high expectations, continually developed the metacognitive abilities of your students, and done so in a really friendly demeanour, then such a student would be in the minority.
Logistical considerationsthat may be deemed as disadvantages – it may seem daunting to get all the technology working to facilitate such a learning environment, but it is easier than you might think
ISSUE
SOLUTION
Audio feedback from multiple zooms in the lecture theatre
Students would need to be on mute unless asked a question
Teacher’s zoom camera – how can it be placed to emulate a real life view?
Placed so it captures the teacher’s whole body and gesturing as they move around (movement like in a normal lecture). This means that the camera will be at distance and not so you can only see the person’s head. It may require some configuring with the existing setup so that your camera connects to the console displaying your slides or doc camera, but quite often the lecturer will be distant from the console and using a clicker to move through slides.
Teacher’s microphone – how would the distanced camera pick up the lecturer’s voice?
Lots of lecture rooms have a microphone that is pinned to the lecturer and operates via bluetooth. A room microphone would pose problems of feedback, but if that is the only option, then face to face zoom participants must always have their mic muted and questions and answers asked in house would need to be repeated by the lecturer for the sake of the remote students – or questions are asked via zoom chat. This is actually not a bad outcome anyway as repeating the question ensures a) everyone heard it, and b) a longer processing time to engage with it.
Being able to produce worked examples and use a whiteboard to demonstrate problem solving
use a tablet as the screen share in Zoom where you can draw/write and show your workings. Alternatively, you can use your phone as the screen share and position/suspend it above your working area.
Monitoring the chat effectively
I would dedicate a section of the lecture where you stop to check for questions. This is surely just good practice anyway.
Previously perhaps the promotion of such a learning environment may have been frowned upon as a threat to lectures going ahead at all – why would we need to have a live lecture when it can be watched online, at one’s own convenience. Well, it would seem that the average cohort of lecture audience has always contained a mix of those who like and benefit from the in-person ‘live’ experience and those who prefer the remote alternative. Mixed-mode lectures offer the best of both worlds.
I’m Paul Moss. I’m a learning designer at the University of Adelaide. Follow me on Twitter @edmerger
The mind is set up to process content in a myriad of ways, but 3 processes seem particularly relevant to education: the recognition of content, when what is presented requires little processing as it matches what is already understood by the student, the assimilation of content when there is sufficient difference between what is presented and already known and the brain ‘adds’ it on to the pile, and the accommodation of content when the brain has to change and adapt what it thought was sufficient understanding, thereby producing a new way of thinking.
Carroll and Mack’s paper on ‘Metaphor, computing systems, and active learning’ presents a really interesting view on the role of metaphor in education, and in arriving at their thesis they quite elegantly explicate the 3 processes outlined above:
Carroll & Thomas (1982), for example, suggested an account that appealed to consolidation and integration of new information. On their account material to be learned is apprehended and, by hypothesis, entered into working memory. Next, and as an automatic consequence, a framework of related general knowledge (Minsky, 1973) is retrieved from long-term memory and also entered into the working memory. Finally, with the apprehension of further new material, there is a need to consolidate and compress the contents of working memory into a more integrated format. One way that this can happen is for the new material to be assimilated to the retrieved frameworks.
The appropriateness of the retrieved knowledge framework for the new material being assimilated is crucial to this account. The retrieved framework cannot be completely appropriate, for, if it were, the “new” material would be recognized not assimilated. Hence, the framework must be partially appropriate and partially inappropriate. When it is not, additional mechanisms of inference come into play to modify the old structure to accommodate novel features of the new object of knowledge (see Bott, 1978, for further discussion of such mechanisms).
IRESEARCHNET also have a really nice definition of the terms.
I’m Paul Moss. I’m a learning designer at the University of Adelaide. Follow me on Twitter @edmerger
Life can be hard. Really hard. There are practically unlimited ways that one can become stressed, and I think I must have absorbed most of them over the last 25 years.
To cut a long story short, over these years I have incorrectly dealt with these stresses, and absorbed them into my shoulders and neck. Gradually, both became like rocks, stiff, tight and inflexible. But instead of doing anything about it, I let it build and build and build to the point of being in constant physical pain, often resulting in headaches, poor sleep and sadness. I know everything is relative, and that others are experiencing real pain and loss, but it was chronically affecting my entire being.
People: friends and family, always kept telling me that I needed to stretch to relieve the muscle pain and that I should go to a physio or massage therapist. I did that a few times, but it only touched the surface, so I would go onto YouTube and search for some free yoga as they suggested. Now I’ve done yoga before, but every time I did, I would always injure myself after a couple of sessions. The reason for that is because I would, unknowingly, choose a session that wasn’t suited to where my body was at. Or, if i got passed a few sessions unscathed, I would still be in pain and always think that it wasn’t working, and so stop.
Now, despite these bad experiences, I knew I couldn’t just leave it. I also knew that it made sense that the tension would ironically have to be reduced by exercising the muscles. Yoga must be the answer.
So I got to thinking, and then finally it occurred to me 3 months ago that doing yoga should be no different from doing anything as a novice, and that I absolutely needed modelled and scaffolded support to be able to get anything out of this ancient philosophy. I’m not sure why it took me so long to register this, especially since I have written about the imperative of modelling numerous times: here, here, here, and the importance of incremental knowledge building here and here, but anyways, eventually it clicked.
So what did I do?
1. The first thing was for me to accept a different motivation: learning, and not performance. I realised that I had to accept that the years of wrenching myself would not be unwound in a couple of yoga sessions. This meant that I would have to tell myself that the process was an extended one, and that if I was to measure any improvement, I would realistically need to give myself a month of continuous practice to evaluate any effectiveness, but even then, that it would be only small if at all.
2. The second thing was to realise that I needed to be taught by someone who knew what they were doing, who knew that building strength takes time, and who offered a continuum of learning where I could start at the very beginning. I found this in the reasonably priced platform www.glo.com.
3. The third thing was to realise that I needed to choose only two 20 minute classes that offered a chance to work on specific sections of the body (upper and lower), and that I would have to repeat those two classes, and alternate between them each day.
4. The fourth thing was to accept that even though some of the beginner class stretches were ostensibly too easy, that I was in fact strengthening muscles that I would need to support more difficult and inflexible muscles in other poses. This reminded me of Engelmenn, here and here.
5. The fifth thing was to discipline myself to doing the practice each day before work. And there were a lot of times where it would have been so easy not to do it – but I knew it was only 20 minutes, and I knew that I would be glad I had done it – I was able to self-regulate.
So after 90 sessions, where am I?
I don’t wake up anymore in more pain than when I went to bed.
I still experience pain, but nowhere near as much
I am still prone to headaches, but the frequency of them is significantly reduced.
I am a lot more flexible and have noticed that I feel better in my hips as well as my lower back.
I feel stronger.
I have begun to do some running as a result of this increased liberation.
Without any shadow of doubt, I am feeling better. My mental health has improved a lot. I am not constantly plagued by a physical pain that shouldn’t even be there. I know that I still have a way to go, but the cool thing is that because things have improved quite a lot, I’m obviously on the right path – and that gives me even more motivation. I know that I can also start to increase the level of difficulty now too to strengthen even more…and that’s exciting.
Develop a plan – like a sequence of learning
For me, the greatest realisation was that to strengthen my mental health, I needed to have a plan that allowed me to gradually develop and build my knowledge of a domain that could address it. For me, it was yoga. For you, it might be swimming, running, or cooking. Patience and discipline reign supreme, but planning an incremental curriculum that will help you achieve tangible benefits is more important.
I might check back in with you in another 90 days.
I’m Paul Moss. I’m a learning designer at the University of Adelaide. Follow this blog for more stuff about education and follow me on Twitter @edmerger
This is part 2 of an essay based on self-regulated learning, and whether it needs to be taught for students to become skilled in it. Part 1 is here.
In part 1 I discussed how explicitly teaching and modelling to students how to think with knowledge potentially facilitates students being able to self-regulate such thinking. The proposition has implications for the explicit modelling of thinking critically and creatively. In this post I will expound on Zimmerman and Moylan’s 2009 paper that theorises that motivation is inextricably linked to these metacognitive processes, and just like everything else connected to learning, needs to be explicitly taught to students in equal measure for them to eventually be able to use the knowledge independently.
Zimmerman and Moylan suggest that there are 3 differentiated stages in achieving self-regulation. These can be equated with the EEFs appropriated terms: planning, monitoring and evaluation. The diagram below represents the cyclical processes of self-regulation.
FORETHOUGHT = PLANNING
IT’S A CASE OF WHICH COMES FIRST, the chicken or the egg, but in order for a student to get their learning off the ground, they need to be motivated to do so. Oftentimes in the school sector, this may not be an intrinsic motivation, with extrinsic rewards and punishments tending to dominate the setting. Upon presentation of a new learning activity, a student will process a range of thoughts evaluating whether they should in fact participate in the endeavour. Students immediately process the expectations against any prior experiences or knowledge, drawing on their schemata to ascertain the extent of having to set new goals and strategies to achieve the new learning, whilst probably concomitantly deciding if they have any intrinsic interest in the task. If they arrive at the conclusion that they don’t possess either of these motivators, your work is immediately cut out for you.
Compounding this will be the fact that students also naturally draw from that schemata the affective responses they had or indeed have built over time in dealing with similar types of activities or learning experiences. If this audit brings up negative memories, perhaps emanating from a lack of success, or serious disinterest, then this will heavily impact on their motivation to continue. It certainly won’t be the case that ‘If you build it they will come’. A student’s self-efficacy or belief that they will be able to positively engage in the task will most certainly affect their planning, strategy and goal setting capacity. So, besides forcing students to participate, what can be done to break this thought pattern?
METACOGNITION – Make explicit the possible reactions students may have to a new task: ‘You may have had a negative experience with this type of problem before, but this time is different because…’, ‘You may immediately think there’s no relevance to this task, but…’, ‘You may have not achieved the grade you wanted in the last task, but this time we are going to plan the response better…’. By making such reactions explicit, explaining how demotivating factors can arise, and providing explicit strategies that ‘show’ how a different outcome may eventuate, the teacher is training the student to think about the new context in a new way, and mitigating against poor self-efficacy inhibiting impetus.
Also crucial to setting up learning is making explicit the goal orientation of the task. Plenty of research suggests that ‘performance’ orientated goal setting, where students’ motivations to learn are primarily centered on comparison and competing against others, is tellingly inferior to having a ‘learning’ goal orientation: here. The positioning of a task’s import as being an opportunity to strengthen personal understanding against personal standards has been shown to facilitate a deepening of learning: ‘In this activity, let’s think about how we can incrementally improve our knowledge of the topic…’, ‘I want you to think about what your level of knowledge is on the topic and set yourself a goal of looking to strengthen it by the time we have finished….’, ‘In this task, we are going to concentrate on mastery…’ However, such ambition is made infinitely more difficult in a system predicated on accountability. Nonetheless, a good teacher will explicitly and inexorably focus their students’ attention on setting goals for self-improvement, and that learning is indeed a continuum that takes time and practice to master. When such purpose is part of the learning culture, once the task is successfully completed the student’s evaluation process then positively feeds into and strengthens the self-efficacy required to engage in a new learning context, regardless of how they fared compared to others in the cohort.
This personal growth rather than competitive epistemology is particularly relevant if you are trying to encourage students who are working hard but not quite succeeding – and observing others around them achieving – in the beginning of a course. These students not only need the explicit discussion of what success means (improvement against your last effort), but precise feedback that articulates what the gaps in knowledge are, and crucially, scaffolded activities that facilitate the opportunity for observed improvement against the last effort. Mastery pathways not only provide opportunity for incremental success, but also the chance to eventually catch up to the expected standard. Because success is the greatest motivator of all, when those achievements are explicitly labelled to the student, s/he will accommodate their self-efficacy to become more positive.
PERFORMANCE = MONITORING
During the task, drawing students’ attention to how they are solving problems and the progress they are making and the motivation required to do so will facilitate the eventual automaticity of such thinking. Modelling self-questioning and verbalisation of thinking processes whilst scaffolding learning through worked and completion examples builds the schema of such processes in students’ minds, and teaching students how to manage time and set up an appropriate learning space should never be assumed to be assumed knowledge. Providing as many opportunities as necessary to facilitate a culture where the student can control these learning strategies and can readily select the most appropriate tools to negotiate the context they find themselves in should be an engrained aspect of a teacher’s curriculum design. When students feel such control over the strategies they employ to negotiate the present task, their motivation and self-efficacy will be strong.
The explicit drawing of attention to higher order thinking processes during the task goes towards developing the schema for doing so in future, independent contexts. As argued in part 1, assuming students will engage in higher order thinking once knowledge is sufficiently acquired is not a good idea, as students may not do this unless they are highly motivated in the discipline or topic in question. Prompting with questions like ‘So if we know this about …., what would happen if …..?’, ‘What is the connection of this idea to the topic we looked at last week?’, ‘What would happen if we combined these 2 ideas?, ‘So imagine this scenario…., how would you solve the problem at hand?‘ If you model this thinking, students will use the model as a strategy when asked to think about knowledge in new contexts, and being able to do so will boost their confidence in engaging with knowledge in interesting ways. This confidence develops self-efficacy, and thus motivation.
SELF-REFLECTION = EVALUATING
From my experience, one of the most difficult things to do is to get students to reflect on their performance and planning after the event. This is especially difficult if the student entered the transaction with a performance goal orientation and wasn’t overly successful. The immediate deflation is palpable. Explicitly discussing this with the students is important at this very moment. But perhaps most importantly, understanding the causal attributions some students may have applied to their success or failure is necessary to ensure that they are able to benefit from the evaluation.
Many students attribute their experience to fixed ability, which is particularly detrimental if they engaged in the activity with a performance goal and didn’t succeed. The comparison against others that essentially results in a defeat if unsuccessful solidifies a negative self-efficacy, which in turn has a negative influence on the planning stage of the next learning moment. If however, the student can be persuaded by the learning continuum theory and that their ability in the task is not fixed and can in fact be improved by application of effort, practice and good revision and study techniques, then the probability of their motivation being secure for the next task is high.
Unfortunately, over time and repeated negative experiences in learning environments, some students develop entrenched negative evaluations that seriously inhibit motivation to continue or engage in future learning contexts. Procrastination may be a milder symptom of such a state, but more serious and damaging is learned helplessness, a notable defence mechanism employed that prevents a student from trying because they believe that there’s nothing that they can do to change an inevitable failure. Often, such a state becomes an unconscious default, and can only be changed by carefully designed scaffolded learning opportunities that promote success, as well as making the psychological context explicit. Of course it is time consuming, but a well-constructed audit of a student’s performance, including how they approached and revised etc for the task, will likely find a host of issues that could be rectified. A checklist may work in helping students evaluate their performance in a task, and the explicit discussion about how neglect in each element on the list is quite impactful could act as a motivator for a student to alter their preconceived beliefs that they aren’t in control of changing their learning potential.
TAKE AWAY
Teaching students about motivation and how past experiences affect the present, and helping students identify patterns of behaviour, their ‘real’ causes and how they can be adjusted is as imperative as teaching them content. Making thinking explicit can go a long way to positively affect how a student perceives a task and their ability to process, engage with, and succeed in it. The result is that students will willingly drink from the water you have led them to.
The next post will discuss how beneficial it can be for students to understand how learning actually happens.
I’m Paul Moss. I’m a learning designer at the University of Adelaide. Follow me on Twitter @edmerger
Achieving independence and self-regulation in learning is the holy grail of education, but how to go about it is as equally mystical. Essential to the quest is developing a rich schema through the building and interaction of knowledge, and whilst belief in the explicit teaching of students in how to think about their thinking processes (metacognition) and how to evaluate them as being an integral part of self-regulation is gaining momentum (EEF), this 2 part post will seek to extend the current understanding by discussing whether it is necessary to promote critical and creative thinking inside subject domains. The essay also expounds on Zimmerman and Moylan’s 2009 paper that theorises that motivation is inextricably linked to both of these metacognitive processes, can’t be omitted from the discussion, and in fact needs to be explicitly taught to students in equal measure. As Kuhn exhorts, ’People must see the point of thinking if they are to engage in it.’
WE ALL WANT 21ST CENTURY SKILLS
Whilst many argue that labelling skills such as critical thinking and creativity as ‘21st century’ does an injustice to those who for thousands of years exhibited such proficiency in them, few could argue that there is a growing demand for graduates to be strong in these areas in the age of increasingly automated and mechanised jobs. How to equip students with such skills then has become the mission of educators, but many well-intentioned educators have erroneously conflated the desired outcome with a direct pedagogy, succinctly stated by Kirschner: the epistemology of a discipline should not be confused with a pedagogy for teaching or learning it. The practice of a profession is not the same as learning to practise the profession. There are plenty of excellent voices who assent to this notion, none better then Daisy Christodoulou, specifically pointing to the fact that thinking critically or creatively relies entirely on a strong bedrock of knowledge and can’t be taught in the abstract. If we think about this it seems rather logical – you can’t think about things you have no knowledge of, and most creativity is the accommodation of knowledge already in existence. Such constraints make the application of such skills heavily context and domain dependent. But what tends to be lacking from such unequivocal pedagogy is the answer to this question: once the foundations of knowledge are secure, do students need explicit modelling of how to think critically and creatively with that knowledge? I contend that the answer is yes.
If we consider how learning is characterised by the acquisition of schema, and how crucial modelling is in that continuum, I would argue that modelling how to play with knowledge is no less important than modelling the knowledge itself. However, it is something that is often overlooked in modern curricula for three reasons:
Because we sometimes assume that students will naturally think in these ways
Because of the need to fit in so much content in so little time
Because it is hard to assess, relying on subjective and therefore unstable evaluation
The first relies on Geary’s theory of primary vs secondary knowledge. The exposition of the theory is that once sufficient knowledge is obtained, the mixing/matching and challenging/critiquing of what is understood should become axiomatic. From my experience though, without the continuous prompting by the teacher to engage with the knowledge in this way, such an outcome tends to rely heavily on a student being highly motivated in a specific domain of knowledge, with the less interested, but equally as capable student, content with achieving in assessment but not necessarily interested in exploring the content further. But what is notable however about the self-motivated student, is that they still will undertake a process of learning in how to mix and match and challenge what they know, albeit, independently: it is through the experimentation of their thinking and its evaluation that they may eventually arrive at something unique and interesting, but this ostensibly natural skill is actually being practised and refined to be maximised – and quite possibly, inefficiently, compared to what some guidance in the process could afford. When motivation to pursue a discipline is not as high, students need to be prompted to engage in ‘higher order’ thinking. Interestingly, sometimes it is only after these higher order prompts that real interest and motivation is sparked, and so the explicit provocation of them in a learning environment is important.
Sweller’s addition to Geary’s thesis, that : ‘Organizing general skills to assist in the acquisition of subject matter knowledge may be more productive than attempting to teach skills that we have evolved to acquire automatically…’ supports the earlier statement that teaching critical and creative thinking in the abstract is pointless, but it is the focus on the word ‘organising’ that is crucial here: the conclusion then is that it’s not enough to assume students will naturally engage with this type of thinking – it is only through the explicit organisation and modelling of it that will facilitate students being able to self-regulate this thinking.
Practising the application of critical and creative thinking needs time and space for it to be strengthened, and this is why the existence of the 2nd obstacle in educational contexts is so concerning. The impetus of non-invigilated exams has certainly made apparent the need for assessment to involve the application of knowledge. But to do so requires a carefully designed curriculum that facilitates such opportunity in the sequence of learning. I tend to promote a sequence patterned by the rhythm: learn, practise, apply. New knowledge is introduced by the expert, students interact with and practise using the knowledge to confirm understanding, students then apply their knowledge to do something with it. The application doesn’t have to be a large project type task. It may simply be the asking of higher order questions that include hypothesising, creating analogies, exploring various points of view, wondering if the content can be applied in other contexts, what the connections are to other aspects of the course, or brainstorming with a view to generate new ideas for a real-world context. The latter is especially relevant for the later stages of higher education.
It is such a pattern of learning that models for students how to interact with the understood knowledge they now have in their possession, a modelling process that observes what Volet (1991) imports as the necessity of identifying and making explicit how an expert thinks. This is relevant to not just when the expert is presented with new problems, but also how they think with the knowledge they already have. Palincsar &Brown (1989) concur, ‘By demonstrating the different activities by which subject matter may be processed, problems solved, and learning processes regulated, the teacher makes knowledge construction and utilization activities overt and explicit that usually stay covert and implicit.’ Like all learning, the goal is to take the metacognition to automaticity so the propensity for self-regulation in the next sequence of learning isn’t compromised by cognitive overload.
WHAT ABOUT TRANSFER?
Whether or not this explicit process of thinking within specific domains can be transferred to new contexts remains to be seen, but Simon, Anderson, & Reder (1999) arouse our curiosity when they suggest that transfer happens far more frequently than we might think. They cite reading as a prime example, but more specifically challenge a famous study by Gick and Holyoak who demonstrated that students were unable to see the abstract similarities between two problems even when they were presented side by side:
‘One of the striking characteristics of such failures of transfer is how relatively transient they are. Gick and Holyoak were able to increase transfer greatly just by suggesting to subjects that they try to use the problem about the ‘general’. Exposing subjects to two such analogues also greatly increased transfer. The amount of transfer appeared to depend in large part on where the attention of subjects was directed during the experiment, which suggests that instruction and training on the cues that signal the relevance of an available skill might well deserve more emphasis than they now typically receive–a promising topic for cognitive research with very important educational implications.’
They then continue to suggest that: ‘Representation and degree of practice are critical for determining the transfer from one task to another, and transfer varies from one domain to another as a function of the number of symbolic components that are shared.’ It follows then that for Dignath and Buttner’s claim to be valid, in their meta-analysis on Components of Fostering Self-regulated Learning, that ‘Providing students with opportunities to practice strategy use will foster the transfer of metastrategic knowledge to real learning contexts’, relies on students being able to recognise patterns or connections between contexts where they can apply their metacognition.
As stated earlier, you can’t think critically and creatively without a strong foundation of knowledge, and further, some of that thinking will be only relevant in specific domains. But it does seem likely that some of the higher order strategies stated above (hypothesising etc) would be able to be applied in a range of disciplines, and that a student observing the modelled thinking processes of a teacher in a second context will recognise some (if not many) elements learnt from their first. Once reinforced through this observation, students will begin the regular learning continuum of taking the skills to automaticity through practice. Once achieved, being able to apply the thinking in new contexts is made more possible – it will be up to further research to ascertain whether, having met these conditions, such transfer is actually possible.
WHAT DO WE WANT FROM EDUCATION?
Another consideration when teaching critical thinking draws from Kuhn, who exhorts that the development of epistemological understanding may be the most fundamental underpinning of critical thinking. In no uncertain terms, she beseeches that teachers provide the opportunity for students to reach an evaluative level of epistemological understanding, realising that simply possessing an absolute epistemology constrains and in fact eliminates a need for critical thinking, as does a ‘multiplist’ stance, allowing students a degree of apathy characterised by statements such as “I feel it’s not worth it to argue because everyone has their opinion.” The explicit modelling of an evaluative epistemology, where students are encouraged to the fact that people have a right to their views with the understanding that some views can nonetheless be more right than others, sets up a learning culture where students see the ‘weighing of alternative claims in a process of reasoned debate as the path to informed opinion, and they understand that arguments can be evaluated and compared based on their merit (Kuhn, 1991).’ Such a pedagogy may satiate an interesting question posed by Martin Robinson: ‘Should the result of a good education include all students thinking the same or thinking differently?’
The 3rd obstacle also looms large. Assessing creativity especially is a difficult thing due to its subjectivity. Rubrics are notoriously imprecise as a reliable reference in determining success or failure of creativity: what I may think satisfies one element of a rubric may be argued against by a colleague; maintaining consistency even with myself in marking is difficult. And if we don’t assess, will students not particularly interested in the topic lose motivation, and make the process a challenging one to manage? I think the answer lies within the answer to Martin Robinson’s question: surely we don’t want everyone robotically programmed. We want students to engage critically and creatively with concepts, and participate in the building of a dynamic and interesting world, so we have to have faith that the knowledge taught to our students, when learnt well, will provide avenues for curiosity that will engage them to participate. Such an epistemology then satisfies stakeholder desires to employ graduates who can think critically and creatively in a modern workplace.
So how is motivation linked to it all?
In the next post, I will extrapolate on Zimmerman’s imperative that metacognition is inextricably linked to motivation, and how educators can ensure they incorporate both in learning design.
References
Anderson, J. R., Reder, L.M., & Simon, H.A. (2000, Summer).Applications and Misapplications of Cognitive Psychology to Mathematics Education.Texas Educational Review.
Dignath, C., Buttner, G. (2008). Components of fostering self-regulated learning among students. A metaanalysis on intervention studies at primary and secondary school level. Article in Metacognition and Learning · December 2008 retrieved from here
Geary, D. (2001). Principles of evolutionary educational psychology. Department of Psychological Sciences, University of Missouri at Columbia, 210 McAlester Hall, Columbia, MO 65211-2500, USA here
Palincsar, A. S., & Brown, A. L. (1989). Classroom dialogues to promote self-regulated comprehension. In J. Brophy (Ed.), Advances in research on teaching, Vol. 1 (pp. 35–67). Greenwich, CO: JAI Press.
Sweller, J. (2008) Instructional Implications of David C. Geary’s Evolutionary Educational Psychology, Educational Psychologist, 43:4, 214-216, DOI: 10.1080/00461520802392208
Volet, S. E. (1991). Modelling and coaching of relevant metacognitive strategies for enhancing university students’ learning. Learning and Instruction, 1, 319–336.
Zimmerman, B., Moylan, A. R. (2009). Self-Regulation from: Handbook of Metacognition in Education. Routledge.
I’m Paul Moss. I’m a learning designer at the University of Adelaide. Follow me on Twitter @edmerger
Teaching to the test doesn’t work. But teaching students about the test is imperative. Not only that, exam performance IS a thing, and you can assist students to get better at that performance. It’s all about mitigating cognitive load.
GAME TIME – Any sports person will tell you that match fitness is everything. Regardless of how much you prepare, you never achieve the same level of fitness and game knowledge compared to actually playing. Why? Because when the real thing happens, not only do nerves and adrenaline consume vast amounts of energy, interfering with the ability you have coming to the surface, but lots of other unexpected occurrences happen, all leading to increased cognitive load, and leading to exhaustion quicker. The cognitive load can be so debilitating that the player has to rely on muscle memory to get them through. When a student sits an exam, adrenaline and anxiety will naturally surge through their veins. Helping them revise the content is a must, but importantly, helping them become more familiar with the game/exam context is climactical, and this can be achieved by training students to automaticity with exam technique.
ABOUT THE TEST
1. Exam layouts
Show students, and get them used to, the layout of the online exam. The more they see the module and layout of the exam and understand what the expectations are of each section, the less pressure they’ll feel when they see the real thing.
Of particular importance with students having to complete exams online is detailing the processes involved if they experience technical issues. Take them through the procedures so if it happens during the exam they don’t lose all confidence and panic. ALSO: Ensure students have read the academic integrity policy and that you discuss it repeatedly – the more you talk about academic integrity the more of it you’ll get.
MANAGEABLE Student cognitive load
Student A – no training
Student B – training
Before beginning exam
20%
20%
Exam layout
5%
0%
2. Question requirements
Ensure students know what each question is demanding of them.
How long is a piece of string?
What does a short answer look like? What gets you full marks? What does a long answer look like? What gets you full marks? How much working out is necessary? How much detail is required?
Don’t expect students to guess the answers to these questions. Students who have to worry about what constitutes a good answer expend lots of valuable cognitive load. Model the expectations by showing previous examples, past exams, etc.
Manageable student cognitive load
Student A – no training
Student B – training
Before beginning exam
20%
20%
Exam layout
5%
0%
Exam content
30%
0%
IN THE EXAM
1. Time training
Training students with timings of questions in exams will significantly propitiate cognitive load. It’s one thing to know what the question demands of you, but another to actually do it in a stressed environment. If a student isn’t used to the pressure of time, the longer the exam goes on, the greater the likelihood of their cognitive load increasing and their performance reducing as they panic with the evaporation of time. So, get them to practice doing a mock of a section in the exam – let them experience what it’s like to type in the allocated time – do their fingers get tired? What’s it like to upload if necessary etc. The more practice they get the better, but if you are running out of lesson time to train students, at least give students the chance to practice once – just one section that requires an upload process for example.
The other aspect of time training is in helping students to set personal timers. Obviously, the online exam doesn’t have all the usual cues that an invigilated exam offers: a large clock, a warning by the invigilator of 5 minutes to go, and even the cues of students completing and organising their work on the next desk. But an advantage of online exams is that students can set their own alarms to negotiate each individual section of the exam, and not accidentally spend too much time on a certain section:
Manageable student cognitive load
Student A – no training
Student B – training
Before beginning exam
20%
20%
Exam layout
5%
0%
Exam content
30%
0%
Exam timing training
20%
0%
2. Editing their work
Rereading responses is difficult for exhausted students to do at the end of a lengthy exam. It is usually at this point that they have a sense of relief, and the last thing they want to do is reread what they’ve done. Of course, it’s madness not to, to ensure there are no silly mistakes, particularly in multiple choice questions, or content mistakes. Even checking for structural, punctuation and/or spelling issues could benefit the overall grade.
So, I have to build that practice into their normal way of working, so it becomes a part of the process, and not an add on. This can really only be achieved by repeatedly physically getting students to do it: at the end of each ‘mock’ assessment, stop the test and get students to spend 4 – 5 minutes in dedication to proof reading…and explain the rationale, repeatedly: I always tell my students they WILL lose more marks with errors (they can fix) than they are able to gain by writing more response in the last 5 minutes. But without it being a normal way of working, exhausted students won’t do it automatically.
Manageable student cognitive load
Student A – no training
Student B – training
Before beginning exam
20%
20%
Exam layout
5%
0%
Exam content
30%
0%
Exam timing training
20%
0%
Editing responses
5%
0%
3. Being professional
Not panicking in certain situations is crucial in reducing cognitive load. Taking students through possible scenarios will help to calm them if the situation presents in the exam, scenarios such as: If you’re running out of time what should you focus on to get you the most marks? What to do if you can’t answer a question – do you panic and lose total focus for the rest? Should you move on and come back to questions? Are you aware that the brain will warm up and so coming back later may be easier than it is now? This last point is absolutely crucial to convey to students. As the exam progresses, lots of the exam content itself may trigger or cue retrieval of content that couldn’t previously be answered, so teaching students this metacognitive notion could make a significant difference to their overall performance.
Manageable student cognitive load
Student A – no training
Student B – training
Before beginning exam
20%
20%
Exam layout
5%
0%
Exam content
30%
0%
Exam timing training
20%
0%
Editing responses
5%
0%
Being professional
10%
5%
As you can see by the very much made up numbers, the cognitive load experienced by Student A is significantly greater than Student B, and would indubitably affect performance in the exam. The student’s knowledge would have to fight a great deal to break through the pressure.
BEGIN NOW!
The more you do something the better at it you get, provided of course you’re doing it the right way. Students don’t really get that many opportunities to learn to negotiate the exam environment on their own, especially in the current context of moving to online non-invigilated exams, and so providing them with such training is critical.
I’m Paul Moss. I’m a learning designer at the University of Adelaide. Follow me on Twitter @edmerger, and follow this blog for more thoughts on education in general.
Few would argue that a goal of education is for knowledge to be able to be transferred from one context to another. However, making it happen is not as easy as it seems, and this has implications for epistemological decisions needing to be made in designing curricula, exams, and indeed, deciding on an institutional ethos.
From research discussed below, knowledge transfer relies on two conditions:
transfer is usually only possible when a student possesses a relatively well-developed schema: the closer to expert the better
the transfer needs to happen within or close to the known and acquired domain of knowledge.
WHAT THE RESEARCH SAYS
What characterises an expert is their acquisition of schema. Experts tend to have lots of knowledge about a subject, but knowledge that is organised and elaborate in how it connects it all together. Particularly important, in terms of knowledge transfer, is the expert’s ability to see the underlying deep structure of problems, regardless of surface differences. It is this ability to make analogies with what they have previously encountered that not only improves the encoding of new content, but also its retrieval:
Experts are better than novices at encoding structure in examples and recalling examples on the basis of structural commonalities (Dunbar, 2001). For example, Novick (1988) found that students completing a second set of mathematics problems all recalled some earlier problems with similar surface features to the present problems, but students with high Mathematics SAT scores recalled more structurally similar problems and were also better at rejecting the surface features than were students with low scores.
The reason for this is that when experts think about problems, they draw on/retrieve their large reserves of schema that have evolved, through practice and deliberate exposure to worked examples, to contain the deeper structural features of question types. On the other hand, novices tend to do the reverse, only being able to identify the surface structural characteristics and thus using an inefficient means-end solving strategy (Sweller 1998). The issue with this is that it heavily taxes the working memory, and often results in cognition being overloaded. What’s worse, is that such a taxing ultimately denies the problem from becoming a part of the schema for future use – so there’s a double loss.
The implications of this for education are enormous. The need for schema is irrefutable, from Bartlett to Ausubel and even to Bruner: but for novice students to develop it efficiently, they need to engage in learning that builds knowledge over time and experience, through examples they can store and eventually make analogies with, and interestingly, as Sweller states above, not through problem solving.
So, here’s how transfer can be developed:
a student learns by an example, which with the right conditions (retrieval), is then stored in their long-term memory. At this point, only the surface structure of the problem is recognised.
The student then encounters another example that has a similar surface structure. Now the student has 2 models to draw from. At this point, only surface characteristics are likely to be seen.
The student then is provided another example but this time the surface structure is different but the deeper structure is analogous. The teacher at this point must direct student attention to the analogous deeper connections, as they usually won’t see them for themselves, as proven by Duncker’s tumour problem – see the study below.
Repeating this process eventually builds the student’s repertoire of problems they can draw from to make analogies with. The more they have, the greater the chance of them behaving like an expert, identifying the deeper structural components and working forward with the problem, thereby using less cognitive load, and inevitably adding another example to the schema.
How to deliver the analogous examples
Gentner, Lowenstein and Thompson (2003) conducted a study to ascertain what the most efficient delivery combination was. The study used 2 negotiation scenarios, one from shipping and one from travelling as a means of training students to be better negotiators. 4 contexts of delivery were investigated:
separate examples, where student were presented both examples on separate pages. Students were asked questions about each text
comparison examples, where students saw both examples on the same page and were directed to think about the similarities between the 2 stories
active comparison group, where students were presented with the first example on one page and the solutions to that example were carried to a second page that presented the second example with questions asked about the similarities between the two
a group that had no training
Clark and Mayer (2008) adapted the findings and presented them graphically:
The results showed that an active comparison was a far superior technique to train the students
Implications for exam design
There are 2 considerations in this regard:
When designing open book exams that rely on the application of knowledge (in the current climate primarily to mitigate cheating), it is important to consider the cognitive conditions for transfer to take place. If you have taught your students a range of examples that have facilitated analysis of deeper structural connections, then your question in your exam can test understanding of the deeper structural connection. If you haven’t taught your students in such a way, then your question choice will be limited to more surface level questions. If you ‘jump’ to deeper structural questions, in an attempt to make the questions harder to compensate for the openness and accessibility of the content, then the results of the exam may well be invalid, as you have tested for something that students weren’t capable of doing.
On the other hand, knowing that you can safely change the superficial structural elements of a question and test ‘real’ understanding because transfer is difficult if the concept isn’t truly understood, also mitigates against cheating as students can’t simply rely on their notes. If they can’t make the connections, an indicator of a novice learner, then they can’t benefit from the notes as an expert would – who ironically, probably wouldn’t need them anyway.
Duncker’s tumour problem
A problem that has been studied by several researchers is Duncker’s (1945) radiation problem. In this problem, a doctor has a patient with a malignant tumour. The patient cannot be operated upon, but the doctor can use a particular type of ray to destroy the tumour. However, the ray will also destroy healthy tissue. At a lower intensity the rays would not damage the healthy tissue but would also not destroy the tumour. What can be done to destroy the tumour?
Gick and Holyoak used this story to test the transference success of knowledge. Prior to the tumour problem, students are then given the story below, and another group a second story to accompany the current 2. Both additional stories have superficial differences to the tumour case, but similar structural or convergent features. They found that most students who tried to solve the tumour problem on their own had difficulty, those with the aid of one story still struggled, but those with the aid of 2 stories could see the convergent abstract similarities. In other words, they were able to see the deeper structural analogies.
A small country was ruled from a strong fortress by a dictator. The fortress was situated in the middle of the country, surrounded by farms and villages. Many roads led to the fortress through the countryside. A rebel general vowed to capture the fortress. The general knew that an attack by his entire army would capture the fortress. He gathered his army at the head of one of the roads, ready to launch a full-scale direct attack. However, the general then learned that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely, since the dictator needed to move his troops and workers to and from the fortress. However, any large force would detonate the mines. Not only would this blow up the road, but it would also destroy many neighbouring villages. It therefore seemed impossible to capture the fortress. However, the general devised a simple plan. He divided his army into small groups and dispatched each group to the head of a different road. When all was ready he gave the signal and each group marched down a different road. Each group continued down its road to the fortress so that the entire army arrived together at the fortress at the same time. In this way, the general captured the fortress and overthrew the dictator.
References
Clark, R., Mayer, R. (2008). e-learning and the Science of Instruction. Pfeiffer, San Francisco, CA.
