My PhD is, in part, looking at methods for dynamically generating mathematics assessment. I have been compelled to submit a poster abstract for the School of Science and Technology internal research conference in May. I wrote this today and it is highly informed by my experience of and reflection on teaching Scientific Mathematics, so I reproduce it here.
"Dynamic generation of problems in formative assessment of mathematical subjects"
Mathematics is a subject you cannot learn without having a go at some problems. Indeed, it may be necessary for students to repeat a technique many times before understanding and confidence is achieved. However, this can be time consuming and tedious for the tutor, who must set many similar problems, and variety in the activity may be necessary to engage the interest of all students.
A problem is made up of a question and a context. Part of the beauty of mathematics is its application to many different fields: a question on one technique in mathematics might be written into a problem in one of several diverse topics in science or engineering, or even finance or other subject areas. To a student, these may appear to be different (varied) problems even though the same technique is being learned. The core mathematics of a question can be written and rules be applied to form this into different problems for different fields.
Once the format has been set many similar problems can be written which teach the same lesson simply by altering the numbers in the question. There is no need for the tutor to manually make this repetition; this process can be automated. Then a great many problems can be generated based on a single manually written question. In some cases it might be necessary to include a diagram or simulation which varies dynamically also.
