Design principles for final answer assessment in linear algebra: implications for digital testing

Abstract

Digital testing, such as multiple-choice questions and final answer items, offers many advantages in higher educational assessment practices. Well-designed digital grading is more reliable and faster than hand grading and is scalable to larger classes. The validity of digital grading is open to criticism, particularly in mathematics where much of mathematics is based on processes and reasoning and not on the final answer achieved. At a technical university in the Netherlands, we have been increasing our use of digital short answer testing in calculus and linear algebra for service mathematics. To assess the validity of this mode of assessment, we graded a linear algebra test in two ways: short answer grading (where answers were considered either correct or incorrect) and the so-called 'hypothetical grading', where we assigned a grade based on the fully worked solution. Certain types of items proved to be more suitable for short answer (and hence digital) testing than others. We concluded our analysis with a set of design principles for digital or short answer testing in linear algebra.