STATISTICAL COMPETENCIES IN THE TRAINING OF MATHEMATICS TEACHERS IN
2017 ENADE: AN IRT APPLICATION
Sandra Cristina Martini Rostirola, Elisa Henning, and Ivanete Zuchi Siple
Santa Catarina State University, Brazil
sandra.rostirola@ifc.edu.br
The National Students' Performance Examination [Exame Nacional de Desempenho dos Estudantes–
Enade] is a large-scale assessment instrument for Brazilian higher education programs whose results,
along with other quality indicators, allow for an evaluation of the country's higher education. This work
analyzed 2017 Enade questions for the mathematics degree program regarding the statistical
competencies of future educators. The quantitative approach methodology allowed analyzing 10,869
participants' responses through Item Response Theory (IRT) using the Three-Parameter Logistic Model.
The results indicate evidence of weakness in questions related to probability and statistics regarding t
levels of difficulty and discrimination in addition to reflecting discrepancies between the statistical
content in the official test descriptors and those found in the questions.
INTRODUCTION
The National Students' Performance Examination [Exame Nacional de Desempenho dos
Estudantes–Enade] is one of the assessment instruments that allows measuring the quality of Brazilian
higher education, both for traditional classrooms and for distance education. Enade evaluates the
performance of students in the last period of the undergraduate programs regarding the syllabus defined
in each program's curriculum and the development of competencies and skills required for a deeper
general and professional training. (Instituto Nacional de Estudos e Pesquisas Educacionais Anísio
Teixeira [INEP], 2022). This evaluation has been carried out annually since 2004, and the included
educational areas change each year in a rotation system. In 2017, it included the areas of Engineering,
Information Technology, and Teaching Degrees, including the degree in mathematics. The mathematics
degree program aims to help the development of mathematics educators' competencies, including
curriculum, evaluation, methodological aspects, and the selection and production of teaching materials.
Pedagogical knowledge, ability to solve problems, and ability to establish mathematical models
and conjectures for content areas such as statistics are included among the teaching competencies. The
latter is the main interest in this study because understanding of statistics structure and concepts allows
one to understand and be part of the social environment in which he or she is inserted, with information
interpretation, data analysis, and decision making providing an opportunity to experience citizenship.
To measure the future mathematics teacher's competencies, Enade is based on a competency matrix that
guides the skills to be assessed through the examination.
This study analyzed the 2017 Enade's questions for the mathematics degree program and future
educators' statistical competencies, measuring the quality of the test and of each item (question). The
2017 Enade examination consisted of 40 questions, five of which were essays and 35 of which were
multiple-choice questions with five alternatives—one correct answer and four incorrect distractors.
From that set of questions, two—items 20 and 21—comprise this study's analysis base because they are
related to statistics. This work aims to assess the statistical competencies of the mathematics degree
program's students who took the 2017 Enade. It should be noted that the mathematical model employed
in Enade is Classical Test Theory (CTT). However, for the purpose of a wider scope, the items were
analyzed using Item Response Theory (IRT).
METHODS
The adopted methodology is the quantitative approach from a documental perspective using
Enade’s 2017 test for the mathematics teaching degree program to analyze two questions (items) related
to the contents of probability and statistics, as described by the Reference Curriculum in the Summary
Report (INEP, 2018). The test consisted of 40 questions, five essays and 35 multiple-choice questions.
The data regarding the answer pattern from 10,869 participants were collected through microdata from
INEP. All participants who answered at least one item from the multiple-choice questions were included.
Classical Test Theory (CTT), probability models of Item Response Theory (IRT), and the
Nominal Response Model (NRM) were applied to the response pattern set of the 35 objective items.
ICOTS11 (2022) Contributed Paper - Refereed (DOI: 10.52041/iase.icots11.T14D4) Rostirola, Henning, & Siple
In S. A. Peters, L. Zapata-Cardona, F. Bonafini, & A. Fan (Eds.), Bridging the Gap: Empowering & Educating
Today’s Learners in Statistics. Proceedings of the 11th International Conference on Teaching Statistics (ICOTS11
2022), Rosario, Argentina. International Association for Statistical Education. iase-web.org ©2022 ISI/IASE