In our own practice, we’ve observed that findings by Richland, Zur, and Holyoak (2007) hold true: students can transfer their knowledge and skills to new situations if they’re able to figure out what the new situation has in common with tasks they’ve already navigated successfully. For example, some kids would have a tough time determining what the following word problems have in common:
- Ryan sells 14 candy bars that cost $1.25 each. How much money does he collect?
- If each of the 5 players on a basketball team scores 8 points in the game, how many points does the team score altogether?
- A baker can decorate 40 cookies each hour. How many will he frost during a four-hour shift?
Identify the Steps in a Multi-Step Procedure
Catrambone (1996 and 1998) suggests that students label the steps in multi-step procedures, such as conducing experiments, solving complex math problems, or writing. Such labels make it easier to compare the approach needed to work through similar tasks that appear different on the surface.
Producing a piece of academic writing is one of the most complex multi-step tasks asked of students. Generally the student must establish an argument, provide and explain evidence, rebut conflicting arguments, and all the while relate each point to the main point. Comparing one essay with another, though, might confuse some students. If one piece is about the use of allusion in a poem and another about the merits of recycling, what could the essays possibly have in common? Challenging students to label the steps each author conducted (stating thesis, referring back to thesis with each topic sentence, providing evidence, explaining evidence, etc.) makes it apparent that good essays, no matter the topic, have a lot more in common than might appear. Identifying the steps used to complete a task make the similarities between different tasks stand out, helping students to recognize how they can use the steps they already know to accomplish novel outcomes.
Provide Both Concrete Examples and Abstract Representations
Students often understand concrete examples best, but concrete examples can be hard to generalize so that the principles in them can be applied to other scenarios. Goldstone and Son (2005) found that learning is maximized when students are given a combination of concrete examples and abstract representations. The best learning outcomes occurred when students were exposed to concrete examples first, then gradually introduced to the abstract principle. Deans for Impact states that a combination of concrete examples and abstract representations “help students recognize the underlying structure of problems.”
To use this principle in a physics class, an instructor might begin teaching the concept of momentum by assigning the following word problems (i.e. concrete examples) and asking students to find the answers:
- Find the momentum of a 7-kilogram bowling ball traveling 17 MPH.
- Find the momentum of an 85-gram marble traveling 17 MPH.
- Find the momentum of a 450-kilogram car traveling 20 MPH.
- Find the momentum of a 283-ounce matchbox car traveling 20 MPH.
“Momentum is determined by the mass of an object and its speed. The formula for calculating momentum at a given moment is p=(m)(v), where m=mass and v=velocity.”
Most textbooks provide concrete examples and formulas, but few ask students to do the work of defining the relationship between the two. This is where lasting, transferable understanding is formed.
In our example of the physics class, the instructor must help the students to see the relationship between their answers to the concrete scenarios and the abstract principle that defines momentum. Ideally, students will come up with a statement defining the relationship between the two, such as, “More mass and/or higher velocity results in more momentum. When mass, velocity, or both are decreased, momentum decreases.” That is transfer at work.