Knowledge transfer from one context to another depends on student learning at least two things: 1) the relevant concepts or skills, and 2) the situations to which they apply. Students are more likely to transfer knowledge from one context to another when instructional examples are abstract and relatively free of surface details. Instead of "tell-and-practice" where instructors often tell the students about the formula they need to use, and then practice using the formulas, it is much better to allow students to develop their "solutions" to a number of contrasting cases before they are told the formula through a mini lecture. Contrasting cases force the students to see beyond the surface differences and explore the underlying deep structure. These contrasting cases constitute what is called an invention activity where students undertake productive activities to note these differences and produce a general solution for all these cases. Such productive activities help students to let go of old interpretations and develop new ones.
Schwartz particularly advocates the use of mathematical tools or procedures in solving invention activities to encourage preciseness and yet general in the solution presentation. They also allow reflection on how the structure of the mathematical tools accomplish their work in the solution of the problems. However, this does not have to be the case. Invention activities can prime students in areas that do not involve quantitative analysis (Yu and Gilley, 2009).
In Schwartz's case, the combination of using visual (problem presentation), numeric (expressing solutions in quantitative mathematical terms), and verbal (student presentation of their solutions) helps to reinforce learning.
In computer science, when we ask our students to create "invent" a solution to a programming assignment, this is an invention activity. The difference with other cases is that invention activities are used as scaffolding for further learning, whereas, in this case, the programming assignment is used to learn the material. In other cases, the students usually don't "invent" the final solution. In the case of computing, the students must get to the final solution themselves. Is that why so many students get frustrated with computer programming? After all, Schwartz did note that students can get tired of repeatedly adapting their inventions.
Schwartz, D., and Martin, T. 2004. Inventing to Prepare for Future Learning: The Hidden Efficiency of Encouraging Original Student Production in Statistics Instruction. Cognition and Instruction. 22(2) 129 - 184.
Yu, B., Gilley, B. 2009. Benefits of Invention Activities Especially for Cross-Cultural Education. Retrieved on October 16, 2009 from http://www.iated.org/concrete2/view_abstract.php?paper_id=8166.