«A Model for Teaching Basic Engineering Statistics in Slovenia Andreja Drobnič Vidic1 Abstract Statistics contents are commonly included in ...»
Metodološki zvezki, Vol. 3, No. 1, 2006, 163-183
A Model for Teaching Basic Engineering
Statistics in Slovenia
Andreja Drobnič Vidic1
Statistics contents are commonly included in university curricula.
Slovenian students in general have a lack of problem solving and
application knowledge in mathematics and basic statistics. Moreover,
engineering students have a lack of teamwork skills, needed in their
professional careers. In order to reduce these shortcomings we designed a model for teaching basic statistics to engineering students. The problembased learning (PBL) approach served as the basis for this model. We adapted it to the requirements of a basic engineering statistics course and to the environment of a Slovenian university. Four main factors of the model are described in detail: problems, which enable the development of problem solving skills and application of knowledge; PBL teachers, who need to change their roles and activities in the instruction; aims of the students, and the alternative assessment. The article also makes reference to a pedagogical experiment, in which we verified this model.
1 Introduction In Slovenia, the teachers of statistics at high schools and at universities are often non-statistics experts. Teachers of this professional profile teach statistics to around 80% of students taking one of the higher education programmes. Many of them have a low level of application of statistical knowledge and a weak problem solving competence. This situation is a result of the traditional curriculum design in secondary schools and universities, which is also reflected in poor interdisciplinary cooperation and in failure to integrate knowledge from different science domains.
The problem-based learning approach integrated in the traditional curriculum seemed particularly well adapted to teaching basic statistics to students in higher education programmes. Therefore, we designed a PBL model for the purposes of teaching statistics to engineering students. After the description of PBL Andreja Drobnič Vidic, Faculty of Mathematics and Physics, Jadranska 19, SI-1000 Ljubljana, Slovenia, email@example.com, firstname.lastname@example.org.
164 Andreja Drobnič Vidic characteristics and advantages for using PBL in basic statistics for engineers the four most important factors for the model are described in more detail. The article also makes reference to a pedagogical experiment, in which we verified this model.
2 Basic statistics course in Slovenia Statistics is a relatively young, but rapidly growing science, as it is used for different purposes, in connection with different disciplines. Therefore teaching statistics is an extremely complex and demanding task. This is especially true for those teachers of mathematics who are not experts in statistics. In Slovenia, many teachers of the basic statistics course in secondary schools and universities are not statisticians. Before study year 2002/03 Slovenia did not have any study programmes of statistics. Therefore, teachers of basic statistics courses have to gain knowledge by self-learning or by helping each other to promote good statistics teaching strategies. While data management, basic processing and data display seem to be less problematic, students at university level often find it difficult to understand statistics through the theory of probability calculation.
Practical real data are difficult to relate to a theory based on mathematical derivation and theoretical distributions.
Teaching statistics is a delicate job in other countries, too (Cobb, 1993). We can find an extensive literature about this particular field. Many authors in Proceedings of teaching statistics ICOTS5 (Mendoza, 1998) or Journal of statistics education, for instance, have pointed to useful statistics teaching methods, focused
around one of the following features:
• teaching statistics through concrete real-life cases (Moore and McCabe, 2003; Wood and Wasimi, 1998),
• teaching statistics with computer programs (Rossman et al., 2002),
• cooperative learning with group work (Garfield, 1993; Magel, 1998), or
• active learning with experiments (Scheaffer et al., 1996).
Typically, a “basic statistics course” at university contains a general overview of basic statistics: from collection of data and information, sampling and calculation of basic statistical parameters to devising statistical hypotheses. At University of Ljubljana (UL) there are around three quarters of students with a basic statistics course in their university curriculum. According to our survey (Drobnič Vidic, 2003), 70 % of students, registered as first-year students at UL in 2001/02, had a course in basic statistics in their university curriculum. From among all regular and part-time students in higher professional education study programmes at UL, 81 % of students, registered as first year students in 2001/02, had a basic statistics course in their university curriculum. From among all partA Model for Teaching Basic Engineering Statistics in Slovenia 165 time students in higher professional education study programmes at UL, 97 % of students, registered as first year students in 2001/02, had a basic statistics course in their university curriculum. Therefore, it may be concluded that the study programmes which are closer to professional fields more frequently require basic statistical knowledge. In this article, we are focusing on a teaching strategy for a basic engineering statistics course in Slovenia. A so – called “basic engineering statistics course” is offered to students in higher professional education study programmes aimed at future engineers in different fields, such as geodesy, mining, computer and information science, safety, practical mathematics, civil engineering, etc.
Slovenia participated in TIMSS international research 1995 and 1999. This participation yielded a comparative analysis of mathematic and statistic competences (the latter constituting an integral part of mathematics in secondary school curricula) in the Slovene secondary school population as compared to the secondary school population worldwide. The analyses pointed to two main weaknesses of the Slovene secondary school population, namely a low level of application of (statistical) knowledge and weak problem solving competence (Japelj et al., 2002; Drobnič Vidic, 2003). This situation is a result of a traditional curriculum design in secondary schools and universities, which is also reflected in poor interdisciplinary cooperation and in failure to integrate knowledge from different science domains.
On the other hand, corporations and employers have frequently and publicly complained about the lack of professional awareness and low level of communication and teamwork skills in engineering graduates. Numerous surveys and industry assessments place communication and teamwork at the top of their list of desirable skills for new engineering graduates, because most of engineering is done cooperatively (Garfield, 1993). Students who have experienced cooperative learning tend to have more highly developed critical thinking and problem solving skills, a lower level of anxiety, and better and longer information retention. Moreover, engineers are called on to absorb vast amounts of information that is increasing more rapidly than the ability of the engineering curricula to cover it.
An innovation from the last few decades, called problem-based learning (PBL), seemed to be particularly adapted to teaching basic statistics to engineering students in higher education programmes. This approach enables a higher applicability of knowledge, it enhances problem-solving competences and combines most of the previously mentioned features used in statistics teaching and learning. Consequently, we designed a PBL model for the purposes of teaching basic statistics to engineering students.
166 Andreja Drobnič Vidic 3 Problem-based learning Problem-based learning (PBL) is an instructional approach in which a problem takes the central role in the learning process and constitutes the motivation for the student’s activities. Boud and Feletti (1998) consider the PBL as one of the most influential innovations of the last decades and define it as a carefully planned curriculum, which is entirely based on practical cases and on solving practical problems. PBL offers an environment in which learning is triggered and guided by a problem. This means that students are confronted with a problem prior to the acquisition of new knowledge.
PBL first appeared in different medical faculties (McMaster University in Canada, the Medical School of Maastricht University in the Netherlands) (David et al., 1999: 2-3). Later on, it spread to different disciplines, such as law, economy, psychology, chemical engineering, architecture, etc (Woods, 1994: preface; Eitel and Gijselaers, 1997). One of the basic characteristics of PBL is that it trains students to become better able to work in a group of experts. It also enhances cooperative problem solving related to typical situations of the student’s expert field, e.g. medicine.
PBL is mainly characterised by the following features:
1. PBL is a way of organising instruction by focusing on a problem as a motivation for the student’s activities. The problem should be professionally relevant and as close as possible to real-life situations. Moreover, it should be ill structured, complex and designed in such a way that the students cannot simply solve it by using their prior knowledge. It should be perceived as interesting by the students. Problem-solving activities enhance the development of cognitive methods and critical thinking. In order to be able to solve the problem, students must gain new knowledge corresponding to the definition of educational objectives of the curriculum. As the focus is shifted to the PBL situation, the choice of adequate problems becomes very important (Schmidt and Moust, 1998;
Schmidt and Moust, 2000; Gijselaers and Schmidt, 1990; Dolmans and SnellenBalendong, 2000).
2. Students usually solve problems in small groups (4-15 students), where cooperative learning is encouraged. Students are also stimulated to search for new information, and solve a part of a given problem as independent learners. They are assisted by a tutor, who is acquainted with the field, but need not necessarily be a teacher. The tutor guides the learning process. The problem-solving usually
follows a 7 Steps Model (Table 1):
3. Learning in a group according to the 7 Steps Model enables a constructivist knowledge acquisition (Hendry, Frommer, and Walker, 1999). At the beginning of the problem-solving cycle the students should draw on their prior knowledge, whereby possible ways of problem solving and the gaps in knowledge are determined. It is often claimed that the PBL derives from the premises of A Model for Teaching Basic Engineering Statistics in Slovenia 167 constructivism (Hendry, Frommer, and Walker, 1999) and that this learning method is based on constructivist principles. It is important for the students to integrate new knowledge in their own cognitive structures so as to establish a connection with the prior information. Thus the gained knowledge can be used in new situations. All these processes are stimulated by group discussion and immediate feedback information on the level of knowledge acquisition.
Table 1: Problem-solving according to the 7 Steps Model (Moust et al., 2001: 30).
4. The teacher is no longer a lecturer and the only source of knowledge, since the students do not get information directly from him / her. The teacher is a facilitator, who assists the students in the skills acquisition process and develops the students’ independent-learning capacities (Wilkerson and Hundert, 1998;
Vermunt and Verloop, 1999). The classical lecturing can play only a supportive role in the process. Teachers should be acquainted with the level of the students’ prior knowledge and should help activate this knowledge. Facilitators should be dynamic, able to adapt the learning materials to the innovations in the education field as well as capable of integrating the theory with the practice.
5. PBL is a student-centred method of learning (Cannon and Newble, 2000).
Students are trained for independent learning. This feature facilitates lifelong learning. In student-centred learning the students become responsible for their own work and do not have the feeling that learning was imposed on them. The quality of the gained knowledge is much more important than the transfer of the knowledge from the teacher to the student. Students as well as teachers should move from the “teaching paradigm” to the “learning paradigm” (Barr and Tagg, 1995).
6. PBL offers the possibility to develop other competences and skills (Moust, Bouhuijs, and Schmidt, 2001: 13): problem-solving skills, skills required for effective group work and independent learning. Woods (1994: 2-3) studied also the self-assessment skills, where the students critically evaluate their individual work and progress as well as the work carried out by the whole group. All these skills are important for effective independent learning.
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7. The teacher must change assessment methods if he or she wants the students to follow the main goals set by the PBL approach. It is, in fact, the assessment system which dictates learning and work carried out by students (Driessen and Van der Vleuten, 2000). If the teacher does not assess an item the students will not learn it (Lovie-Kitchin, 2001: 149-155). Therefore assessment in PBL is at least as important as curriculum design. In PBL the acquired knowledge and the student’s ability to solve real-life problems are assessed rather than the
student’s test writing skills. Assessment is usually composed of different elements:
the tutor’s grade is complemented by self-assessment and peer-assessment grades.
A very important function of assessment is to give the student immediate feedback information on whether his /her learning process is adequate, whether the expected development is achieved and whether a certain knowledge or skill needs to be improved. At the beginning of the PBL the students should be acquainted with the kind of knowledge and skills which are going to be assessed.