As part of my PhD reading, I have been getting to grips with “Cognitive Load Theory” by Sweller, Ayres and Kalyuga. Unfortunately, this is one of those academic books that are expensive and only really viable for those with access through a university library. It is unfortunate because the book is full of insights. The chapter on biologically primary versus biologically secondary knowledge is particularly rich.
However, here I will focus on the discussion of the use of worked examples. The study of worked examples was critical to the development of cognitive load theory. We shouldn’t run away with the impression that worked examples represent an optimal form of teaching. Yes, the effect has been measured many times and withstood replication. However, this is partly due to the fact that worked examples are pretty amenable to research and so have been studied a great deal.
I have learnt two significant concepts.
1. It is better to present worked examples one at a time
It seems that presenting three worked examples of different types of problem and then asking students to practice is less effective that presenting each worked example on its own, followed by practice of that type of example. It is obvious why this would be the case when viewed from the perspective of cognitive load and yet not obvious enough for me to figure this out for myself.
Typically, I present several variations on a problem type before asking students to practice because, well, that’s what I’ve always done. I am now working on ways to integrate worked examples and practice more thoroughly. I have started to present worked examples and then ask students to complete a very similar problem using the same set of steps. This has the additional bonus of highlighting the students who get off the bus at the very first stop and yet it is still useful for those with a little more insight; they have to follow the given process.
I am sure that Siegfried Engelmann has known this since about 1967 but, hey, I’m late to the party.
2. The worked example effect has been demonstrated in ill-structured domains
It not all about algebra. Ill-structured problems are those messy, liberal-arts-type tasks that have no simple problem states and solution steps. “Discuss the meaning of this passage,” is given as an example.
Here are a couple of experiments that are described in the book;
“Firstly, Rourke and Sweller (2009) required university students to learn to recognise particular designers’ styles from the early Modernist period using chair designs. It was found that a worked example approach was superior to problem solving in recognising these designs. Furthermore the worked example effect extended to transfer tasks in the form of other designs, based on stained glass windows and cutlery.
Secondly, in two experiments, Oksa, Kalyuga, and Chandler (2010) presented novices (Grade 10 students) with extracts from Shakespearean plays. One group was given explanatory notes integrated into the original text, whereas a second group had no such notes. Results indicated that the explanatory notes group outperformed the unsupported group on a comprehension task and reported a lower cognitive load… half of the students were provided model answers or interpretations to key aspects of the text. Those model answers are equivalent to problem solutions. In contrast, students with no explanatory notes were required to make their own interpretations, an activity equivalent to problem solving. The fact that the model answers resulted in more learning than requiring students to make their own interpretations in this very ill-structured domain provides strong evidence that the worked example effect is applicable to ill-structured problem domains.”
The book goes on to describe the effectiveness of model answers as worked examples that help English language learners to write English literature essays.
Get on it, English teachers.
Filling the pail 
Reblogged this on The Echo Chamber.
To be fair, I don’t know an English teacher in my department that doesn’t think that model answers are the absolute key to everything we do. I think we spend more time on them than most other things!
Interesting post Greg. Thanks!
This is what we do Greg. Been waiting for you science types to catch up 🙂
That’s interesting. I’ve not seen the ‘explanatory note integrated into the original text’ thing.
I have never thought of this topic in these terms but it seems to me now that it is largely the same thing: When my son was about 8 he wanted to learn to code HTML. Although I hacked away at web pages I didn’t have a lot of knowledge myself. What to do? Get him a book to read? I said “Come here, I’ll show you.” So I showed him how to get and read the source code for web pages. I said “Find a web page you really like”. Okay we got one. Then we opened up the source code. I said, now compare these tags here to what appears on the web page. Can you see which tags do what? A number of things were obvious from the start. Then I said, “Now see if it works for you”, and we started swapping in content and playing with the tags. Before long he was editing his own tags and starting from model pages and building his own. The more he did it the more he could build stuff independently. It was all from model “solutions”.
I learned LaTeX the same way. In fact, almost every mathematician I know learned LaTeX this way: You find an existing source file that does roughly what you want. You study the way it was coded, you understand what does what. Then you strip out the content and add your own. Over time you get to prefer stuff so you swap in and out commands and start making your own macros. From time to time you go and read something when you don’t see examples you like. The reference material, however, is not your primary source: it’s a back-up. The main source is the existing example(s) from which you work.
I had always thought this was a form of discovery learning. Indeed, in a sense that is what it looks like. But what it is, really, is the worked example effect — you learn by imitating an existing example. With time, exposure, and varying contexts you learn to extend that solution so that it transfers to new situations. In fact, even more than that .. with LaTeX you start right off the bat with the problem of transfer: You’ve go a document to write, and you just use the existing model as a template. So you START with transfer. Over time you learn the solution itself through transferring it to enough contexts that you know what each element of the solution provides, and which parts are irrelevant to the new context.
Greg,
Traditionally text books do this breaking down into single worked examples repeated. They do a set of examples of one type — say using Sine to find a side. Then another type — Cosine to find a side. Then Tangent etc.
What I see resulting is many students who can do the problems, but only once they have been given which function to use.
What I think we need to do more of is worked examples of how we pick our method, not just worked examples of the method itself. So when you say Typically, I present several variations on a problem type before asking students to practice that presentation needs to include how you chose the different variations on the solution, as well as the solution itself.
I spend as much time in class showing students how to identify a quadratic as I do solving them. That can still be done by worked example.
Is there a clash between presenting and practising one worked example at a time and the research findings on interleaving (Bjork)?
Damian
Note that what I’m describing relates to the very first stage of training.
Ok. Presumably then moving on to interleaving once pupils have worked through separate examples. Or returning at a later date to practise a mix of the questions. That makes sense as if I want pupils to master addition, subtraction, multiplication and division of fractions I would spend time on each one then return and get them to practise a mix. Best of both worlds then. Laying down the right “memory” then interleaving to improve long term recall. Hopefully.
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