Abstract:

Personalizing the evaluation process to the student characteristics and skill, is one of the indicators for evaluating the University Quality within the framework offered by the European Higher Education Area. This paper describes an innovative technique by which we are able to create as many different mathematical tests as students we have in class. We are able to prepare an exam of mathematics completely adapted to every student. In this way, each of them will have their own exam, which is different for everyone.
Using at the same time three software (R, Asymptote and Maxima in a Latex framework), it is possible to elaborate questions with graphics and mathematical calculus. Every time a test is generated, graphs and data are completely different from the rest of the tests.
Carrying out this evaluation methodology without using a computer and a suitable program would be almost an impossible task. It would take us a long time, taking into account that we have nearly one hundred students in the classroom.
We have designed a process where we produce a document divided into four parts:
A first one, in R code, which is responsible for generating the random data set for the test.
A second part, in Asymptote code, which makes the graphs that the student will have to analyze.
The third part in Maxima code, which is responsible for carrying out mathematical calculations of each question in the exam.
And finally, everything is included in a latex framework where the structure of the whole exam is drafted.
Summarizing, we are playing with the following programming languages:
ASYMTOTE: The Vector Graphics Language
Asymptote is a powerful descriptive vector graphics language that provides a natural coordinate-based framework for technical drawing. Labels and equations are typeset with LaTeX, for high-quality PostScript output.
A major advantage of Asymptote over other graphics packages is that it is a programming language, not only a graphic program.
MAXIMA: Maxima is a full-featured CAS (computer algebra system) that is specialized in symbolic operations but it also offers numerical capabilities such as arbitrary-precision arithmetic: integers and rational numbers which can grow to sizes limited only by machine memory, and floating point numbers whose precision can be set arbitrarily large ("bfloats").
Maxima is a general-purpose system, and special-case calculations such as factorization of large numbers, manipulation of extremely large polynomials, etc. are sometimes better done in specialized systems.
R: Like many other languages, R supports matrix arithmetic. R data structures include scalars, vectors, matrices, data frames (similar to tables in a relational database) and lists. The R object system has been extended by package authors to define objects for regression models, time-series and geo-spatial coordinates.
R supports procedural programming with functions and, for some functions, object-oriented programming with generic functions. A generic function acts differently depending on the type of arguments it is passed. In other words the generic function dispatches the function (method) specific to that type of object.

Keywords:

Mathematical tests, Asymptote, Maxima, R.