There and Back Again: Near and Far Transfer

Imagine for a moment that you are landing in a city you have never visited before, and you have to find your way from the airport to your hotel. When you land and get off the plane, what do you do? What steps might you have to take to navigate your way from the airport terminal all the way to the comfort of your 4-star hotel room? If you have travelled before, what aspects from your prior experiences, if any, might you draw upon to get you to your hotel in this new, unfamiliar city?

Near vs. Far Transfer

Hopefully you will be able to take advantage of some of your previous travel experiences in the above scenario thanks to what is known as transfer. Transfer is when knowledge learned in one domain is applied to a different domain. A domain is the topic or the subject matter of the to-be-learned knowledge. An everyday example of transfer comes from navigating a mass transit system. Suppose you grew up in a place where the only mass transit option was the city bus. When learning how to ride the bus, you figured out that a key to getting on the right bus was the sign found at the top of each bus, which displayed the line number and the terminal destination for that bus. This information was critical because it indicated which route the bus was going to follow, and whether the bus was heading towards the stop you want or away from the stop you want. This information is useful because it tells you if the bus is heading in the direction you want to go.

Now suppose you then find yourself in a new city, such as Washington, DC, and you want to ride their Metro, which is their subway system. You would demonstrate transfer by applying what you know about riding the bus (i.e., the source domain) to riding the subway (i.e., the target domain). Subway trains also display the line number and the terminal destination at the front of each train.

We might say that transferring knowledge from riding a bus on one line to riding a bus on a completely different line isn't much of a stretch because they are both busses, and they both use a destination sign to communicate with the rider. That is an example of near transfer because it involves learning within the same domain (i.e., riding the bus). What would be an example of far transfer? Learning how to ride the subway would be an example of far transfer because the surface features vary slightly and so does the setting or context (e.g., bus stops vs. subway stations).

Why Might Transfer Fail?

Although transfer can be very useful, it can also be very hard to accomplish. Why is transfer hard, and what are some of the ways that it might fail?

Transfer might fail when there is a mismatch between the learning setting and the application setting. A lot of learning occurs in the classroom, and it is the hope of every teacher that students transfer their lessons to real life. A semi-famous counterexample is a study of Brazilian street children making change [1]. When working on the streets, these children were able to perform fairly complicated computations in their heads. But when they were asked problems that had the same deep structure, and only the surface features changed (i.e., isomorphic problems), then they failed to solve the problems. In other words, the Brazilian street merchants were not able to transfer what they knew from selling candy to the classroom environment.

Another way in which transfer might fail is when the surface features of the problem change. One of my favorite examples of transfer failure comes from geometry [2]. In this example, children learn how to calculate the area of a parallelogram. When learning this particular skill, the problem is accompanied by the following diagram (see Fig. 1).

Figure 1. To calculate the area, drop two perpendicular bisectors.

The student is shown that when you drop two perpendicular bisectors (lines 1 & 2), which form two triangles of equal size that essentially equate the parallelogram with a rectangle. Since students already know how to compute the area of a rectangle, they can easily solve this problem. However, when the students are asked to compute the area of the following parallelogram (see Fig. 2), the children claim that they never learned how to solve this type of problem!

Figure 2. How do you calculate the area of this parallelogram?

This is a rather tragic example because it means that the students cannot see the applicability of their knowledge in the two different situations. This is an example of the failure of near transfer.

The STEM Connection

To reiterate, transfer is hard and can fail for multiple reasons. It can fail when the learning and application settings do not match. It can also fail when the learner does not recognize the connection between the surface features of what they learned (e.g., a parallelogram resting on its base) and a slightly different case (e.g., a parallelogram that is rotated and resting on its side). 

Why does the setting and surface features matter? In a previous post, we learned about procedural knowledge, which can be modeled using what is called a production rule. Production rules have two parts: a condition and an action. When I see this (condition), then I should do that (action).

   Production Rule: [ Condition ] => [ Action ]

We can model problem solving in geometry as a series of production rules. We might, for example, say: 

  Condition: If I see a parallelogram,
    AND: My goal is to compute the area;
  Action: Then, calculate the product of the base and the height. 

One potential explanation why transfer fails is because the condition (i.e., the left side of the production rule) is not general enough for the learner to see when his or her knowledge applies. The goal of education is to help students generalize their knowledge to the point where they can see how it applies across settings and across seemingly disparate situations.


Share and Enjoy!

Dr. Bob

For More Information

[1] Carraher, T. N., Carraber, D., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3, 21-29.

[2] Wertheimer, M. (1945). Productive thinking. New York, NY: Harper.