I am developing an assessment piece where the content is the same but the particular numbers are different for each student. It involves finding Triangle Centers given points using coordinate geometry. The particular skills it is assessing (for/as/of) are
- calculating distances, gradients and midpoints
- forming equations of lines
- perpendicular gradients
- simultaneous equations
- graphing points and lines
I am giving each student different randomly generated vertices and asking them to work out 4 triangles centres graph the results. As I've written it is quite guided with the main tasks being calculations between suitably chosen points and graphing. I'll be generating individualised answers as well. See below for a draft.
(I am using Mathematica to generate the initial points and answers including graphs. I export these to Excel and mailmerge them in Word. )
What are the pedagogical issues at play? References welcomed! My own ideas are shown below. I am not so interested in the technical issues involved (Google "latex random test").
- To encourage students to share skills not answers
- To give students a sense of ownership
- To combat cheating (not a concern in my case, it is more assessment for learning)
- Difficult to create individualised questions, needs a thorough understanding of the problem and it's algebraic solution
- Unintentional differenation (eg one set of numbers may require a much easier solution than another)
I have particular objective in mind for this project at this stage (paper based, an activity not a test, papers should be of the same difficulty, I like this triangle centres task), but there are some obvious extensions (other maths content, differentiation, automated marking).
Update Having run this in highschool class the main feedback I got was that it was too challenging for most. The most important pedagogical thing which emerged was the need to differentiate. To modify the task to make it easier one could:
present a partial solution
algorithmically, select points which have more simple intermediate steps.
Both of which require more work for me! Hence, it is "difficult to create individualised questions, needs a thorough understanding of the problem and its algebraic solution."