By Carolina Kuepper-Tetzel

“What is one of the most difficult things to teach your students?” When you ask teachers in different sectors, one answer that will probably get a lot of hits and lead to agreeing nods is “Transfer!” The ability to apply learned principles and knowledge to solve novel problems or tackle new, unfamiliar tasks. Indeed, it turns out that transfer is extremely hard to achieve. The issue with transfer is that it requires students to reason on an abstract level. For successful transfer, students need to have understood and be able to extract the abstract principles of previously solved tasks and apply these to new tasks which usually have little overlap regarding surface features, i.e., they look different, but require similar principles to solve them.

Thus, the question is: How can transfer be boosted in students? One strategy that has been shown to support transfer is concrete examples – but only, if done properly. The basic idea of concrete examples is to provide students with many different concrete examples for abstract ideas and principles. In general, humans are better in understanding and working with concrete information than with abstract information. Thus, a form of scaffolding can be to offer many concrete examples in the beginning when explaining principles that are more complex and abstract. However, there is an often overseen problem that can occur with this strategy: Getting stuck in this beginning stage of providing concrete examples! Sticking with concrete examples only can lead to quite the contrary result (remember, the goal is to achieve transfer): Inflexible knowledge because students simply memorize the concrete examples making transfer impossible.

For that reason, the key aspect of concrete examples is essentially to slowly move away from concrete representations towards more abstract representations of the task. This process is called concreteness fading (1). A stylized illustration of what concreteness fading looks like is provided below.

Thus, the point is that students need both concrete and abstract representations in order to reach mastery and, in turn, being able to transfer principles to novel tasks. To provide a more concrete example of the process (this is so meta :-D), let’s look at a study that has compared different instruction methods varying in concreteness on performance in transfer tasks.

Fyfe, McNeil, and Borjas (2) investigated three instruction methods to teach second- and third-grade pupils math equivalence problems (e.g., 3 + 4 + 5 = 3 + _?): Concrete condition, Abstract condition, and Concreteness Fading condition.

In the Concrete condition, real objects (toy puppets and scales) were used to teach the math equivalence problems. The instructor did not move away from these concrete examples when explaining the math problems. In the Abstract condition, no concrete examples were used and pupils were taught using math equivalence number problems only. In the Concreteness Fading condition, the instructor started with concrete objects (toy puppets and scales), then moved to a paper-based version that increased in the abstractness of the representation, but still used the objects from before (e.g., image of a scale and puppets), and lastly concluded with a numeric representation (numbers only; ‘4+3 = 4+_‘). All equivalence problems used during the Instruction Phase were relatively easy (5+2 = 6+_?) compared to the ones pupils had to solve during the Transfer Test Phase (4+8+9 = 4+_?). Examples of the transfer problems can be seen below.

What did they find? The results are clearly in favour of using concreteness fading: On average, pupils solved more transfer problems correctly when they were instructed using concreteness fading compared to the other two conditions. In line with the argument mentioned above, the poorest performance was shown in the Concrete condition. This demonstrates that heavy use of concrete objects and examples without abstracting from them can be detrimental to solving novel problems in the future.

Taken together, students need both types of representations (concrete and abstract) to achieve mastery and demonstrate transfer. Concreteness fading is a process that combines these representations systematically by avoiding cognitive overload. Teachers are left with a quite difficult task here, namely to find good concrete examples and transition examples in order to make concreteness fading work. Working together with colleagues from the same subject may be a helpful first step to find ways to make concreteness fading work for a specific subject. Concreteness fading can be done in different ways: The main idea being providing concrete examples first, then substituting concrete bits with more abstract info, and, finally, move completely to an understanding of the abstract principles.

Blake Harvard (@effortfuleduktr) has blogged about his take on concreteness fading earlier this year in his post A More Concrete Classroom. and invited other teachers to brainstorm additional ways to implement concreteness fading. Feel free to chime in here or there.

Cover image: Image by Monika from Pixabay

References

(1)  Goldstone, R. L., & Son, J. Y. (2005). The transfer of scientific principles using concrete and idealized simulations. Journal of the Learning Sciences, 14, 69-110.

(2)  Fyfe, E. R., McNeil, N. M., & Borjas, S. (2015). Benefits of “concreteness fading” for children’s mathematics understanding. Learning and Instruction, 35, 104-120.