Using STACK to Assess Information Transfer in Mathematics
A presentation of work carried out with co-author Reima Halmetoja.
Rämö, Oinonen, and Vikberg (CERME 2015) define a category of mathematical assignment tasks called “Information transfer” by which they mean questions that “require transformation of information from one form to another, as well as processing this information”. This involves, e.g. drawing a picture of a given situation, interpreting, and explaining.
We discuss how these kind of tasks can be modelled using e-assessment in undergraduate university mathematics courses. For example, a problem in elementary linear algebra asks a student whether given vectors span the three dimensional space. This is divided into steps each of which requires transforming information from the previous step to a different setting as follows: 1) Form an equation from the given vectors, 2) represent that equation as a matrix, 3) manipulate the matrix to see if there is a solution, and 4) finally interpret what that means as an answer to the original question. A student receives automatic feedback from each step supporting the solution process. There are also reflective questions, not automatically assessed, that ask a student to pause and think how to justify their answer.
We also discuss how different goals can be achieved by considering the way students input mathematical content as answers. For example, in some situations, it may be better to present a grid where a student can fill in the entries of a matrix. On others, students are asked to enter the entries as a list of vectors therefore not predetermining the dimensions.