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Procedia - Social and Behavioral Sciences 154 ( 2014 ) 99 – 103

ScienceDirect

1877-0428 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Peer-review under responsibility of National Research Tomsk State University. doi: 10.1016/j.sbspro.2014.10.119

THE XXV ANNUAL INTERNATIONAL ACADEMIC CONFERENCE, LANGUAGE AND

CULTURE, 20-22 October 2014

Teaching of Statistics: Formation of Statistical Reasoning

Jean-Claude Régnier

a

, Ekaterina Kuznetsova

b

*

abNational Research Tomsk State University, 36, Lenin Ave., Tomsk, 634050, Russia aLumière University Lyon 2, 86 rue Pasteur 69635 LYON Cedex 07, France

Abstract

The article presents the results of theoretical analysis of formation of statistical reasoning as a major goal of teaching statistics. The authors interpreted the theory of fundamental situations by G. Brousseau to describe the nature of statistical reasoning and essential concepts of statistics mastered in the course of its acquisition. The authors defined a number of crucial factors that should be taken into account in teaching of statistics, such as sociocultural position of students towards statistics, category of student and status of statistics as school/university discipline.

© 2014 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of National Research Tomsk State University. Keywords: Education; statistics; statistical reasoning; fundamental situations

1. Introduction

The formation of statistical reasoning may be interpreted from various perspectives. The framework of our study is based on the following assumptions: firstly, we consider the formation of statistical reasoning to be one of the essential purposes of studying statistics; secondly, it is possible to create favourable conditions to encourage the formation of statistical reasoning. Our study is based on recent studies in teaching of statistics and on treatment of our experience of teaching statistics and using it for research and other purposes.

We consider the teaching of statistics to be a theoretical domain that studies the process of transmission, dissemination and acquisition of statistical knowledge, especially in school or university studies. All these processes cannot be reduced to statistics.

* Corresponding author. Tel.: +7-913-848-60-59 . E-mail address: evoinel@gmail.com

© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

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Our study is also based on the concepts of fundamental situations and inherent processes of statistics, defined and developed by G. Brousseau (2004). This approach is based on the research of fundamental situations of statistics that are also known as typical situations, representative situations or generic situations. Taking into account these fundamental situations allows us to get the necessary information to design efficient situations for teaching statistics. 2. Theoretical assumptions and research methodology

2.1. Characteristics of fundamental situations of statistics

The formation of statistical reasoning is connected with the increase in the level of conceptualization of risks in decision making. This increase is parallel to the increase in one’s competence to construct a model of risk control. Statistical reasoning promotes rejection of the frequent use of the idea of the truth in favor of mastering the idea of probability and plausibility.

In a problem situation proper to a case-study the means of conceptualization and techniques of statistics are given to a student in order for him/her to conceptualize and to acquire them, transforming them into psychological instruments (Vygotsky, 1985; Rabardel, 1995). These psychological instruments can be used to control decision making in uncertain situations.

Statistical reasoning stimulates three types of cognitive operations: deduction, induction and eduction. Statistical interpretation, an integral part of statistical reasoning, is formed around these three operations (Fig. 1).

The distinction between regular reasons and fortuitous reasons is the point where statistical reasoning is to be applied. Thus, statistical reasoning represents a certain way to interpret the world, the way of thinking that we call statistical reasoning.

Y. Chevallard (1978) in his pioneer works analyses the teaching of statistics and proposes an original interpretation of the range of problems of statistics. He assumes that statistics deals with research and construction of scientific dialectics of regularities and perturbations in the analysis of phenomena characterised by variability. Variability is the concept that we consider to be fundamental for statistics.

The aforementioned assumption led us to a definition of statistics that can serve to facilitate the transmission of statistical knowledge in classroom situations: statistics is a sort of a common language, a general method connected to various scientific domains that deals with groups of individuals, variables and relations between them to draw the most probable and plausible conclusions and to claim these conclusions about the properties of group to be valid for a bigger entity, sometimes obscure. These conclusions are to be considered probable, not obligatorily true.

Fig. 1. Structure of statistical reasoning

Induction Deduction

Eduction

Interpretation Statistical reasoning

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The major actions in statistics can be described by the following verbs (Table 1): Table 1. Verbs typical of statistical approach

Gather, produce, construct Record, test, sample, measure.

Treat Organise, describe, compare, link, adjust,

predict, foresee. Interpret

Decide

2.2. Students’ role in teaching statistics

We consider the student’s status in the educational system to be an important factor that should be taken into account in the process of organization and realization of educational process. A categorization is required to define the universal situations of teaching that proceed from the characteristics of fundamental situations of statistics suitable for teaching in various student groups. We have defined eight categories (Table 2):

Table 2. Basic categories of students [ST1] Primary school pupil [ST2] Secondary school student [ST3] High school student

[ST4] University student specialising in statistics

[ST5] University student specialising in a discipline that makes ample use of statistics [ST6] University sutdents specialising in a discipline that makes rare or no use of statistics [ST7] Professional in statistics

[ST8] Professional in non-statistical discipline occasionally using statistics

The works of G. Brousseau are more focused on the first category [ST1]. In our previous works we mainly observed university students specialising in educational sciences that rarely use statistics [ST6]. J.-C. Oriol (Oriol, Régnier, 2003a, 2003b, 2004) presented his observations of university students specialising in statistics [ST4] and university students that use statistics regularly [ST5]. It is evident that the common characteristics of all these categories are a strong difference between the categories and a fluctuant homogeneity within the categories.

2.3. Place of statistics in education

Table 3. Basic categories of students [STATUS1] Major discipline [STATUS2] Complementary discipline [STATUS3] Introductory discipline

[STATUS4] Discipline in the framework of programme for teachers of statistics [STATUS5] Discipline in the framework of statistically-based research

The fundamental situations of teaching of statistics should correspond to the discipline status as well as the definite category of students. The status of statistics as a school/university discipline determine the content of topics to be covered in the process of teaching statistics (Table 3).

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3. Results and discussion

We obtained some interesting results of statistical analysis of data that we have gathered after several years of studies conducted among our students (BA, MA, PhD) that specialise in educational sciences. We organised a series of surveys and interviews. When BA students of the 3rd year of studies were asked to cite three words they associate with statistics at the beginning of academic year the major proportion (1/3 to 1/2 in different groups) claimed that they associate statistics with mathematics and mathematical concepts (calculation, numbers, graphs, etc.). Within this group of students who associated statistics with mathematics a significant proportion (1/8 to 1/5) also claimed to have negative associations with statistics of the type presented in Table 4:

Table 4. Some frequent associations with the word «Statistics»

Word 1 Word 2 Word 3 Phrase

mathematics complicated disagreeable requires a particular way of reasoning

mathematics difficult failure

mathematics incomprehensible lie I have problems with this science that may be used to manipulate public opinion

The analysis of these data confirms our assumption on the negative effect of associations provoked by the student’s painful memories of learning mathematics at school on perception of statistics.

The analysis of the data obtained from various groups of students allows us to identify the phenomenon that we refer to as sociocultural position. We identified five positions that should be taken into account in searching of fundamental situations of statistics as facilitating or impeding the formation of statistical reasoning:

1) [SCP1] Position 1 manifests itself in the rejection of statistics based on total distrust to statistics due to assimilating statistics to statistical data and their manipulative interpretations in society.

2) [SCP2] Position 2 can be seen in the rejection of statistics by educated people. The argumentation of this position is based on the following ideas: a) There exists no statistical demonstration; b) Statistics is not mathematics; c) Statistics is not a science.

3) [SCP3] Position 3 manifests itself in the rejection of statistics by educated people based on the assumption that statistics is a branch of mathematics and one’s attitude to statistics depends on his/her attitude to mathematics.

4) [SCP4] Position 4 can be observed in the situation of unconditional acceptance of statistics based on one’s strong conviction and firm belief in the results of statistical analysis.

5) [SCP5] Position 5 manifests itself in acceptance of statistics on the conditions based on the assumption that statistics is a useful science for any person. It should be underlined that the results of statistical analysis are to be approached with a critical mind.

We assume that taking into account the aforementioned sociocultural positions in teaching statistics can help to eliminate some of the problems related to students’ negative attitude towards statistics.

4. Conclusion

In the framework of this study we analysed our 7-year experience of teaching both in class and with the use of e-learning technologies. Our observations were partially outlined in previous papers (Régnier, 2003, 2005). Our research is based on the theory of situations in teaching (Brousseau, 1998). We used a model of teaching triangle based on three positions: teacher – student – discipline (statistics). Another crucial component of this model is the environment which is not necessarily the classroom environment. Within the context of e-learning a student becomes physically isolated and the relations between teacher and students are conditioned by presence or absence of a student in virtual classroom. This situation has its own peculiarities that should be taken into account in teaching statistics along with all the other factors. We assume the formation of statistical reasoning to be one of the crucial goals of modern teaching of statistics that cannot be reached without paying attention to students, their

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personal experience and attitude to statistics as well as to the status of statistics in a particular educational programme.

References

Brousseau, G., Balacheff, N., Cooper, M., Sutherland, R. & Warfield, V. (1998). Theory of educational situations. Grenoble: La Pensée Sauvage. Brousseau, G. (2004). Fondamental situations and inherent processes of statistics. XIIth Summer school of teaching statistics. Corps, France Chevallard, Y. (1978). Remarques on teaching of statistics. Marseille: I.R.E.M. d'Aix-Marseille.

Oriol, J.-C. & Régnier, J.-C. (2004). Benford law and the practice of questionnaire-based survey: application in the fondamental situations of statistics. XXXVIth Conference on Statistics SFDS. Montpellier, France.

Oriol, J.-C. & Régnier, J.-C. (2003a). Functioning of educational stimulation in statistics. Example of introduction of the concept of the confidence interval. XXXVth Conference on Statistics SFDS. Lyon, France.

Oriol, J.-C. & Régnier, J.-C. (2003b). Functioning of educational stimulation in statistics in introduction of the concept of correlation. Mathematical French-speaking Congress.Tozeur, Tunisia.

Oriol, J.-C. (2002). Realisation of questionnaire-based survey: an educational means in inferential statistics at the University. Réaliser une enquête par questionnaires: un outil didactique pour la statistique inférentielle à l'Université. 3rd European-Latin-Americam Meeting on the Technological and Professional Education. Havana, Cuba.

Rabardel, P. (1995). People and technologies: cognitive approach to modern instruments. Paris: Armand Colin. Régnier, J.-C. (2003). Statistical education and e-learning. Satellite Statistics and the Internet. Berlin, Germany.

Régnier, J.-C. (2005). Study of difficulties in learning statistics in the framework of e-learning. Educate: Psychology and Educational Sciences. Paris: L’Harmattan.

References

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