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 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.


Clark, R., Mayer, R. (2008). e-learning and the Science of Instruction. Pfeiffer, San Francisco, CA.

Image sourced from here

I’m Paul Moss. I’m a learning designer. Follow me on Twitter @edmerger

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