Generating Mathematical Exercises for E-learning Systems Using R

INTERNATIONAL ELECTRONIC JOURNAL OF MATHEMATICS EDUCATION
e-ISSN: 1306-3030. 2019, Vol. 14, No. 3, 667-676
https://doi.org/10.29333/iejme/5784


Article History: Received 17 January 2019 Revised 9 May 2019 Accepted 9 May 2019

© 2019 by the authors; licensee Modestum Ltd., UK. Open Access terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/) apply. The license permits unrestricted use, distribution,
and reproduction in any medium, on the condition that users give exact credit to the original author(s) and the source,
provide
a link to the Creative Commons license, and indicate if they made any changes.


OPEN ACCESS
Generating
Mathematical Exercises for E-learning Systems Using
R and QTI Import Format
Eckhard Liebscher
1*
,
Ben Michael
2

1 University of Applied Sciences Merseburg, GERMANY
2
Optimax Energy Leipzig, GERMANY

* CORRESPONDENCE: eckhard.liebscher@hs-merseburg.de

ABSTRACT
In the paper a software solution is presented for the generation of instances of exercises. The
focus is on education in mathematics but the approach can be adopted in other fields such as
computer science and natural science. The present solution uses the R environment for the
generation process and LaTeX for the content presentation. In the established system, we realized
the separation of computations and design which has the advantage that it is easier to find errors
and shortcomings.

Keywords: mathematics exercises, item generation, R
INTRODUCTION
Generating
a large number of exercises automatically for the training of topics within mathematics
education is a challenging task. In this paper, we provide a software solution to generate xml-files according
to the QTI standard. These files contain exercises to be imported into a learning management system (LMS).
In our implementation we used the Ilias LMS. Many LMSs such as Ilias have an xml/QTI input filter and an
xml/QTI output interface available. In the established system, the files with exercise items are prepared for
the input via this interface. The generation process is done within the R environment. Similar solutions are
only rarely to be found in the literature. In this paper, we explain how to write R scripts which can be deployed
to generate as many instances of a specific type of exercises as desired. Here the focus is on exercises in
mathematics
but the ideas can be used for exercise generation in similar areas such as natural sciences and
computer science. The specific aims of mathematics education are studied in detail in Maron (2016). The
importance of using modern information technologies in mathematics education is worked out in Mendoza and
Mendoza (2018). In modelling the structure of exercises, we follow the ideas of the approach by Gierl and colleagues. We
refer to Gierl et al. (2015) and some other papers of these authors. There they describe thoroughly the
development of an item model and its usage in the generation of a large number of items. In Section 2 we
refine the item model and adapt it to mathematical exercises.
In our established system, we separate computations and the content of exercise items including the design
of the exercises. The computations are done using the R system and a special R script. This approach has the
advantage that we can do experiments in R until reaching the final version without changing the text content
of the exercises. Since the R script is strongly adapted to the specific aim, there is no need for a special R
package. The text content and the design of the exercises are defined in a document using elements of LaTeX
(LaTeX-like file). Since a LaTeX file containing all instances is one of the output files of the R script, a pdf-file