Statistical Methods – What Is the Problem Here?

Abstract

The concepts taught during a Statistical Methods course make use of different mathematical skills and competencies. The idea of presenting a real problem to students and expect them to solve it from beginning to end is, for them, a harder task then just obtain the value of a probability given a known distribution. Much has been said about teaching mathematics related to daily life problems. In fact, we all seem to agree that this is the way for students to get acquainted of the importance of the contents that are taught and how they may be applied in the real world. The definition of mathematical competence as was given by Niss (Niss 2003) means the ability to understand, judge, do, and use mathematics in a variety of intra– and extra – mathematical contexts and situations in which mathematics plays or could play a role. Necessary, but certainly not sufficient, prerequisites for mathematical competence are lots of factual knowledge and technical skills, in the same way as vocabulary, orthography, and grammar are necessary but not sufficient prerequisites for literacy. In the OEDC PISA document (OECD, 2009), it can be found other possibility of understanding competency which is: reproduction, i.e, the ability to reproduce activities that were trained before; connections, i.e, to combine known knowledge from different contexts and apply them to different situations; and reflection, i.e, to be able to look at a problem in all sorts of fields and relate it to known theories that will help to solve it. The competencies that were identified in the KOM project (Niss 2003; Niss and Hojgaard 2011) together with the three “clusters” described in the OECD document referred above were considered and adopted with slightly modifications by the SEFI MWG (European Society for Engineering Education), in the Report of the Mathematics Working Group (Alpers 2013). At Statistical Methods courses often students say that assessment questions or exercises performed during classes have a major difficulty that is to understand what is asked, i.e, the ability to read and understand the problem and to translate it into mathematical language and to model it. The study presented in this paper reflects an experience performed with second year students of Mechanical Engineering graduation of Coimbra Institute of Engineering, where the authors assessed Statistical Methods contents taught during the first semester of 2017/2018 and 2018/2019 academic years. The questions in the assessment tests were separated into two types: ones that referred only to problem comprehension and its translation into what needed to be modelled and calculated and others where students needed only to apply mathematical techniques or deductions in order to obtain the required results. The research questions that authors want to answer are: