DESCRIPTIVE STATISTICS ON PSYCOLOGY MATHEMATIC LEARNING

The academic courses were intended to give a epistemological and methodological basis: In particular, the economy of education or psychology would mobilise the use of statistics tools, but the systematic study of the mastery of statistics concentrated on "qualitative and quantitative methods". To support the learning of statistical concepts and techniques, a problem situation was proposed whose solution was provided by the production of a "methodological dossier" describing a specific study: The dossier was supervised by a tutor.
Descriptive Statistics are used to describe the basic features of the data gathered from an experimental study in various ways. A descriptive Statistics is distinguished from inductive statistics. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. It is necessary to be familiar with primary methods of describing data in order to understand phenomena and make intelligent decisions.[1] Various techniques that are commonly used are classified as:
•Graphical displays of the data in which graphs summarize the data or facilitate comparisons.
•Tabular description in which tables of numbers summarize the data.
•Summary statistics (single numbers) which summarize the data.
In general, statistical data can be briefly described as a list of subjects or units and the data associated with each of them. Although most research uses many data types for each unit, this introduction treats only the simplest case.
There may be two objectives for formulating a summary statistic:
1. To choose a statistic that shows how different units seem similar. Statistical textbooks call one solution to this objective, a measure of central tendency.
2. To choose another statistic that shows how they differ. This kind of statistic is often called a measure of statistical variability.
Figure 2.1-2 : As mediações do aluno face ao saber estatistico
The problem situation, which is purposed for the students, is similar to the situation that they are going to find at the final exams. Those situations are evaluated and scored by one corrector-teacher who gives the results and correction guide for the students. Currently, in the context of the program, the reactions of the students for the
evaluation of this activity are collected by the tutor-teacher, however those reactions
are not expressed by exchange of emails. Problem situation types are similar to the
questions that confront the students in mathematics didactical situations.
Nevertheless, it seems that statistics learning requires a supplementary situation
through the effective use of concepts and techniques, of problem situations of applied
statistics. It seems the statistical didactic needs to consider the above condition as an
important characteristic, but this supplementary aspect should not be necessary for
mathematics didactic. If the mathematics learning is related to resolution of
mathematical problems which can remain into the mathematics field, it does not seem
possible to conceptualise the statistics learning unless the students have been
confronted with problem-situation “outside” of the statistical mastery. In particular,
the students should be conducted to do a statistical modelisation of those outside
problem situations. What we called (for commodity linguistic) a problem situation of
applied statistics.
We make reference to these invariants through other fundamental questions arisen from the reflection of author-teacher.
• (Q2) What types of supports (digital or paper) and which conditions make
distance statistical teaching efficient?
• (Q3) What are the minimal mathematical and statistical pre-requisites for a
novice and non-specialist student?
• (Q4) What didactic situations can be organized considering the specificities of the
sciences of education students in the situation of distance education learning, and
the finalities of the tutorial developed by tutors with a basic level of expertise in
statistics. It seems that the theoretical framework of the didactic of statistics can help us to answer the four central questions: (Q1), (Q2), (Q3) et (Q4). The use of resources
associated with Internet and pertinent and not too sophisticated hypermédiatisations
are elements, which constitute and support efficient statistics teaching. Another hypothesis related to the conditions of efficiency can be related to the tutor-teacher education in statistics
mastery.
3. The return to the issue of statisitcs education
The important issue of statistics teaching-learning has in the main, arisen from
quantitative methods teaching, as well as from qualitative methods (e.g. when the
analysis of content is approached as analysis of textual data based on lexicometrics).
We can realise that the majority of the students have low ability in mathematics.
Some developed a negative relationship with statistics, supporting a negative attitude
of distrustful and also unconditional repulsion for this area of knowledge. In distance
studies situations, the student is isolated. This situation is particularly investigated for
the significance of absence and presence of the teacher (Jacquinot, 1993). The risk of
increased isolation is the possibility of abandoning the process. The exchanges by
mail become a resource in which students can discharge aggressive feelings and
reduce the stress. The analysis of the messages reveals the role of the representations,
which are mobilised in adult education process. The exercise seems to be dependent
on a behaviourist conception of human learning (Skinner, 1968, 1979) rather than a
constructivist or socio-constructivist perspective (C.R.E.S.A.S., 1987; Vygotski,
1985). Without the negation of the efficacy of the behaviourist approach for shortterm
aspects, we our questions remain regarding the long-term aspects involved in the
learning process. Therefore, the course on quantitative methods was organised with an
alternation model that made explicit concepts and techniques, and the problem
situations in which they operate. The possible solutions for these problems were
introduced in self-evaluative and self-corrective procedures (Régnier 2000). The
introduction written for the course of methodology was intended to explain the
significance of our pedagogical and didactic approach (Régnier & Trancart, 2001;
Bezille & Régnier, 2001) The analysis of the contents of the messages reveals problems on the meta-cognitive activities (Noël 1991), which are important in making decisions and obtaining a balance between emotional and rational aspects. The major obstacle for statistics learning is not the memorization of formulas, but the absence of the understanding of meaning of models constructed for the realization of a instrumental study of an object. The priority criterions are: the pertinence of the choice of the formula, the validation and the pertinence of the choice of the formula, the validation and efficacy of the interpretation of the results which produce this formula. The statistics teaching is not a final point but a way to instrumental statistics. This instrumental technical process
might be psychological (Vygostki, 1985; Rabardel, 1995) and is useful for the
sciences of education mastery, because it is an important tool to understand the ways
in which the validation of scientific knowledge is produced. The students noted that there is a repetition of the teaching of mathematics, in which experience of learning was sometimes difficult in a near or distant schooling past. In addition, it was observed that the effects of a social representation could make opposition between qualitative and quantitative methods. A detailed analysis of the discourse and the practices revealed that most of the researchers and lecturers have as a main form of data analysis, the qualitative methods. In general, this is not just a pertinent choice, but mainly because they do not know about the concepts of statistical techniques.
3.1. Pedagogical and didactical of the instrument to help the learning:
methodological instrument
The elaboration of the methodological dossier is placed at formative logic, and
intends to facilitate the individual significant construction of concepts, of instruments,
and of the techniques required for the qualitative and quantitative methods. The
realisation of this dossier, with the supervision of the tutor is compulsory. At the
beginning of the program the deadlines were fixed for the submission of the dossiers.
This document should be based on a questionnaire and an interview. The student
should choose a theme that was validated by the tutor, who checked the relevance of
same.
3.2. Obstacles and difficulties found by students: attempts of remediation
The questions raised by the introduction of this pedagogical instrument are related to
the statistical knowledge constructed by the students associated with the elaboration
of the methodological dossier. The analysis of the data from a random sample of all
the methodological dossiers, provided a comparison with the answers of the
questionnaires completed by a group of students, and the results of the final exams
reveal positive effects about the learning of concepts and statistical techniques
(Régnier 2002a, Régnier, Mazzoleni, De Smet, 2003). In this present article, due to space constraints, only the results related to the first examination of message exchanges by students are presented. We intended to reach the understanding of phenomena that happens at the learning-teaching situation during the quantitative methods course with students with non-scientific bases (e.g.Humanities) and non-specialists in Statistics. The identification of difficulties, of obstacles and mistakes is an important stage of the project of investigation. In the current stage, the analysis of message contents indicates elements related to obstacles of learning:
• Didactical contract
• Autonomy of the student (Régnier 2000)
• Subjacent conceptualisations in the application of data construction and data
analysis methods
3.3. The understanding of the didactical contract for the students:
One of demands for the elaboration of the dossier is: “ this questionnaire must have 5
questions which cover 4 types of variables which will be approached by this course”.
A range of opinions exchanged expressed some difficulties of learning. For example,
the sentence: “at least 5 questions” appeared to generate problems.
3.4. Inferences about the process of autonomy of the student
At the end of academic year 2001/2002, a student expressed the idea that “as I learn
the basic concepts of statistics, shortcomings in my understanding of more complex
issues become evident”, in other words: increasing the level of understanding in
statistics, generates more complex statistical questions.
3.5. About the questionnaire
The messages related to questionnaires revealed the difficulties in the degree of
modelisation and conceptualisation required. Therefore, we thought that the
construction and the conduction of the research by questionnaire constituted pertinent
problems situations through which students could learn basic statistical concepts. In
our didactical perspective, this perspective is inverted. The analysis of the messages
reveals the way in which students learn from the problem situation of the
methodological dossier. Therefore, the doubts related to the questions which have the
possibility of several answers, related to the concept of vector-variable, the notion of
open question, the notion of quantitative variable, the notion of continue quantitative
variable etc.

CONCLUSION
In this article, I attempted to draw a description and analysis of a program of distance
education teaching, identifying the difficulties and obstacles found by the students in
statistical learning as part of field of technical and conceptual instruments of
quantitative methods. The data collection obtained by emails during discussions
contains elements to answer our questions. Therefore, the data presents similar
invariants identified in subjects who are confronted with statistical learning processes.
In the statistical didactic field, our aim is develop knowledge about phenomena
linkage with statistics learning and teaching processes. Those phenomena are
understood through the complexity of pedagogical program distance teaching
education. The pedagogical intention was based on conditions of efficiency of the
perspective of statistics education for all. Evidently, methodological difficulties arose
within this project. Therefore, according to the inquests completed by the students,
distance is a limitation that should be included in the protocols. The hypothesis of
efficiency of the elaboration of the methodological dossier related to the individual
construction of knowledge and the development of competencies in the statistical
field remains likely, but we are trying construct a finer and adapted experimental
protocol in which the modalities of distance education, increases reliability.
We identified that in addition to the similar characteristics of traditional face-to-face
teaching education (e.g., doubts arisen from students, attitudes with statistics,
obstacles to learning and understanding of concepts and techniques of this field), the
situation of distance learning-teaching education amplifies the stress related to the
absence of direct mediation of lecturer. That is why the tutors have capital importance.

1. The distance teaching and e-learning of statistics in educational sciences:
contextualisation and construction of a study object examining student
population
1.1. Program Contents
The program curriculum is formed of 12 courses which are related to the fields of teaching education, and two courses related to methodology and statistics.
1.2. Tutorial of students on their experiences of teaching education and the
role of Internet
The principal pedagogical resource is comprised of traditional lectures presented on hard copy (paper). However, a pedagogical program to help with the studies was composed of two main elements:

1.2.1. Training Exercises for the exams (Exercices d'Entraînement à
l'Examen) [EEE]
For each course the students would produce an intermediate written work which was
produced from specific instructions. This exercise is constituted by formative evaluation developed either by the author of the course or one of his assistants. The corrected text is devolved for the student with an evaluation guide. The only function of the score is to regulate the formative evaluation.

2. Statistics distance teaching and learning: the didactic and pedagogy
problematization
In this program, the tutors also have an important pedagogical role on supervision of
the elaboration of the “methodological dossier”. The analysis of this aspect provoked
the discussion of a central and first question:
(Q1) What should be the tools and procedures, which should be purposed and
constructed for the statistics non-specialists tutors, develop their supervision work
with the participant student?
During the development of the program were elaborated documents for giving theoretical support to the tutors. With base on the pedagogical and didactical engineering it was developed a first material support called guide of elaboration of methodological dossier. This tool was constructed based on the messages daily exchanged between the participants at the list of discussion and from other sources.

2.1. An inspiration from the situations didactics theory and Conceptual fields
The analysis of pedagogical actions involved in this program Statistics teaching makes a demand for considerations of two aspects:
- The Statistics learning-teaching of “novice” and non-specialists students(Régnier 2002b)
- The distance teaching education requires that the students develop specific competences related to the self-learning supported by tutorial and certain level of autonomy that allow them manage the absence and presence of the supervisor.
The didactical situations theory (Brousseau, 1998) offers us the systematic model of didactical triangulation, in which we can distinguish the three poles: teacher, student and Statistics. However, the context in which happens the didactical action does not have the same components of a conventional classroom. At the distance teaching program the student is physically isolated. The relationships between lectures, tutors and students are dialectically organised by the absence-presence in the context of the virtual classroom. The pole of teacher himself/herself is a system constituted for the roles of evaluator, author and tutor. The relationship between the author of the statistics and quantitative methods course and the student happens initially through a material support of paper fascicules. Subsequently, that relationship occurs through the digital support of the hypermedia, which has the written statistical knowledge an the product of the operation of didactic transposition.
Figure 2.1-1 : Didactic Triangulation at the context distance teaching
Initially, the students contact with statistical knowledge is based on the material supports of the courses, which are composed of textual knowledge and problem situations that lead to the application of the concepts and techniques presented. Students are then able to resolve and correct the problems presented by the course documents on their own. The difference between this form of teaching and “face-toface teaching” is that the knowledge is not the result of oral verbalization followed by comments, which are regulated by the student’s reaction. Evidently, the format of hypermedia allowed audio-visual sequences of the intervention of the author teacher, but these interactions cannot be considered yet.
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