Framing

Solving problems usually involve a variety of concepts and skills. Some problems can be approached from a number of angles but usually, when one goes down a "wrong track", it may take sometime to recover unless one is aware of the backtracking points and be able to try alternate paths. The perception / judgment that is used in problem solving is called epistemological framing. It refers to the class of tools and skills that one would bring to a particular situation or context for problem solving. As a simple example, some students may rely on memorized facts to solve a problem, while others may rely on logical reasoning, etc.

Bing and Redish (2009) identify four common framing clusters that students commonly use of mathematics to solve physics problems: calculation, physical mapping, invoking authority, and math consistency. Calculation refers to the algorithmic use of established computational steps to derive a solution, e.g. calculus rules, geometry rules, algebraic rules, etc. Physical mapping refers to the mapping between mathematics with the student's intuition of the physical or geometrical situation at hand to support their arguments and reasoning. Invoking authority points to the resource / book / journal / quote / person / etc. to support a claim. Math consistency appeals to the other math ideas and concepts that are demonstrably consistent to offer validation of an argument.

As I reflect on these four framing clusters, I wonder how these clusters can be detrimental for beginning computer science students. Take for example, calculation, the meaning of "=" in math as equating two entities, like x = y, is so different from computer science use of assigning one value to a variable. Similarly, there is hardly any connection between how computer science models physical objects, like tree, or student, and how we intuitively understand and interact with them. Students are also often surprised at what they can do and cannot do with a programming language. They lack the source(s) of "authority" to guide them in their learning. One comment that I often hear from students when they are learning a new programming language is "I didn't know you can do that!". Finally, although computer science students know that computers are consistent and logical, the subtleties of programming language syntax and the precision of logic that is also highly dependent on the sequence of execution in a program can be frustrating and overwhelming to them. Identifying some of these framing clusters that students bring into the classroom may help in their learning process.

Reference:

Bing, T. J. and E. F. Redish (2009, Jul). Analyzing problem solving using math in physics: Epistemological framing via warrants. Available at http://arxiv.org/pdf/0908.0028.