I just discovered that transfer learning can be divided into two types. The first is near transfer which involves skills and knowledge which are applied the same way every time while the second, far transfer, is the ability to transfer those skills and knowledge to other situations. An example of these would be for near, the students are taught to calculate percentages and can apply them to any problem in the book. This is an example of near transfer because students can apply what they've learned to the same type of problems. To be considered far transfer, students would have to be able to go to the store and calculate the percentage taken off a jacket based on the original price and the new price.
This is where so many math teachers get frustrated. They see students can do the problems and can pass a test but when they are asked to use the same knowledge in a more real world situation or to a situation that is not identical to the context of what they learned, students can't and we wonder what happened. Now we know. They've mastered the material as a near transfer but not a far transfer.
One thing that's been noticed is that real world application is often times more complex than the problems students have solved in the classroom. I've heard it said that real life is so much messier because the answers are not as neat and tidy as most problems students experience in class. Consequently, it is possible that the problems taught in class are too simplistic and this can make it much more difficult for students to perform far transfer.
Fortunately, there are some things teachers can do to help students learn to apply knowledge via far transfer rather than remaining in near transfer. The first is to engage students in working with real world applications of what they've learned. Unfortunately, this can be much harder in Math because many teachers, including myself, do not always know how certain topics and concepts are used in real life. Next, it is important to help connect what students are currently learning with what they have learned in the past. For instance, we teach students to solve equations and inequalities the same way so as we teach inequalities, we can talk about solving regular equations.
If students are given extensive practice for routine skills such as addition, subtraction, multiplication, and division so students can perform them quickly and accurately. Being fluent and comfortable, also contributes to a better near transfer because students can focus on the concept rather than struggling with the arithmetic. As far as assigning problems for a specific skill or topic, it is important to assign a variety of problems because the more varied contexts students see, the easier it is for them to transfer the knowledge from near to far learning. This means that instead of having all problems with the equal sign on the right, make sure it is appears on the right side.
Furthermore, it is important to for the instructor to point out the underlying principles are used in different situations so students see how to use them in a variety of situations. This makes it easier for students to utilize far transfer because they've been learning to recognize the underlying principals and then apply them. Finally, students need to be taught to reflect on their own thinking so they can improve their learning.
It has been suggested that all learning goals be written in two parts. The first part covers the procedural objective which is the part where students learn the steps such as in learning to solve two step equations. The second is the declarative part which involve the conceptional knowledge or how to apply it to a variety of situations or contexts. The second part is so much harder because I've never thought of doing it. Let me know what you think, I'd love to hear.
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