Bulletin UASVM Horticulture, 69(2)/2012
Print ISSN 1843-5254; Electronic ISSN 1843-5394
Randomly Generated Multiple-Choice Tests Using (La)Tex
and Pseudorandom Number Generators
Cristina-Olimpia RUS1), Mircea-Dan RUS2)
1)
Faculty of Horticulture, University of Agricultural Sciences and Veterinary Medicine Cluj-Napoca,
Calea Mănăştur 3-5, 400372 Cluj-Napoca, Romania; [email protected].
2)
Faculty of Automation and Computer Science, Technical University of Cluj-Napoca,
Str. Memorandumului 28, 400114 Cluj-Napoca, Romania; [email protected].
Abstract. We are interested in developing, using TeX/LaTeX and a pseudorandom number generator
(PRNG), an automated system for student exams that would generate for each student a unique
multiple-choice test, based on a previously constructed database of multiple-choice problems. Even
with a small set of problems, we show that it is possible to obtain a large variation of tests, by
randomly selecting and randomly ordering the problems, based on predefined criteria, and by
randomly permuting the choices of each problem.
Keywords: LaTeX, linear congruential generator, multiple-choice test, PRNG, TeX
Introduction. The use of multiple-choice tests in evaluating the knowledge, skills
and abilities of students is still one of the most commonly used assessment formats
worldwide. Though often maligned, when it is well and carefully prepared, it allows
transparent and comprehensive coverage of content in a remarkably effective way. The
preparation of a multiple-choice test for a large number of students usually requires the tests
to be different from one student to another (in order to avoid “dishonest practices” that are
typical to this type of test), yet overall similar, in order to achieve an accurate and impartial
assessment. This task can be a tedious one if it is not approached in a systematic manner.
Aims and objectives. Our goal is to design and implement, using free multiplatform
computer software, an automated process of generating large numbers of individual multiplechoice tests from a small number of items (i.e., questions, problems, sets of questions or
problems, etc.) that are grouped by similarity, using randomized selection based on similarity
and by permutation of the order of items in each test and of choices in each item.
Materials and methods. In designing the “multiple-choice test generator” (MCTG),
we choose to put each item in a separate file and then organize the files in folders by
similarity of the items. Then, we define a three-step procedure that randomly selects one item
from each group, permutes the choices of each item and finally places all the items in a
random order to build a test. The randomization is achieved using a standard linear
congruential generator from (Lewis et al., 1969) as the pseudorandom number generator, and
the algorithm of (Fisher and Yates, 1948) for generating (pseudo)random permutations; we
refer also to the modifications of these algorithms in (Durstenfeld, 1964) and (Knuth, 1998).
We choose to implement the MCTG using TeX (and LaTeX), which is a system for
computer typesetting that is freely available on all major operating systems and which has the
advantages of being fast, stable, flexible, popular, standard, easy to learn, content-oriented
and having better output than “normal” word processors or text editors, while being mathfriendly (see (Knuth, 1984)). In this way, each item is created as a standalone .tex file, which
is then randomly selected by a master .tex file that finally outputs the tests into a single PDF
file.
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The basis of our implementation is the definition of a new LaTeX environment that
permutes the order in which its contents is typeset. These environments can be nested, in
order to achieve the complexity required by the MCTG. The idea started from a recent
discussion on tex.stackexchange.com (see http://tex.stackexchange.com/questions/40815/).
For the generation of pseudorandom numbers, we use the implementation of the linear
congruential generator of Lewis et al. given by Donald Arseneau in “random.tex”, that is
included in all standard LaTeX distributions. Also, the paper of (v. Bechtolsheim, 1988)
provided an excellent tutorial into the subtleties of TeX coding.
Results and Discussion. The result of our work is a LaTeX package that can be
easily used by anyone familiar with TeX and LaTeX to build (on-the-fly) a large number of
different multiple-choice tests provided that the questions/problems have been previously
created using a predefined and flexible template. As an example, using a set of 50 problems
grouped in 25 folders of 2 similar problems each, we generated (based on the principles
described in the previous sections) a number of 1000 different random tests, each containing
25 problems, a process that took about 6 minutes on a regular PC.
The system is flexible enough to allow almost any kind of customization in the way
the text is formatted or in the page layout, while it can be expanded to include other type of
tests where variation can be achieved by single or complex randomization. Further
developments will include automatic generation of random questions or problems based on
predefined templates.
Our system is a viable alternative to existing LaTeX packages, like “eqexam” or to
other more complex solutions (e.g., (Grün and Zeileis, 2008), (Sojka, 2003))
Conclusion. We addressed the problem of designing and implementing a multiplechoice test generator, using free multiplatform computer software. The result is a LaTeX
package that can be used to build very fast any number of random tests from a limited set of
questions. The formatting and typographical layout of the tests is fully customizable. Future
versions of the package will include automatic generation of random problems based on
predefined templates.
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