1. ON TEACHING STATISTICS IN E-LEARNING ENVIRONMENTS
Grigore ALBEANU,
Manuela GHICA
Spiru Haret University, Bucharest

2. Abstract
An approach on teaching statistics in E-learning environments is presented.
The following ways in using E-learning in the mathematical statistics field are emphasized: learning from feedback, observing patterns, seeing connections, working with dynamic pictures, exploring data and teaching the computer by writing code.
Details on preparing a statistics course are given.

3. I. INTRODUCTION
Statistics represents a special branch of mathematics dealing with the collection, analysis, interpretation and presentation of data.
Summarizing data by descriptive statistics plays an important role in every practical project.
Moreover, dealing with uncertainties is possible by inferential statistics. These two topics belong to applied statistics.
The mathematical statistics provides the theoretical basis of the field.
The aim of this paper is to describe a structure of an on-line course on Mathematical Statistics at Higher Education Level and implementation approaches in order to contribute in adding real value when comparing against classical textbooks / learning.

4. II. ICT AND STATISTICS
In order to produce a good E-course, which increase the quality of teaching and learning in classrooms, or at distance, the following ideas can be considered:
The E-course will be an environment providing opportunities to make conjectures test and modify them, according to the learning from feedback principle.
The environment will support the making and justifying the generalizations by successive increasing the size of the samples (observing patterns).
The changing of representations will be supported for a better understanding of the connections between representations (seeing connections).
Generation and editing of images describing the geometrical structure of data, or of different entities during data analysis is required also (working with dynamic images).
The environment will permit data interpretation and analysis in order to work with real data (exploring data).
Inserting formulas or code to be interpreted by environment will be supported (teaching the environment).

5. An E-course in statistics
The main chapters of the course will address:
The basics of statistics (descriptive statistics, inferential statistics, sampling, variables, percentiles, measurement, distributions, and linear transformations)
Graphing (charting) distributions (histograms, frequency polygons, box plots, bar charts, line graph, etc.)
Distribution summarization (measuring central tendency, mean and median, variance, additional measures, effect of transformations, etc.)
Bivariate data description (Pearson correlation, properties and computing aspects)

6. The main chapters of the course will address (also)
Basic of probability theory (conditional probabilities, uniform distribution, binomial distribution, the Bayes’ Theorem etc.)
Normal distribution (standard normal, approximations, properties)
Sampling distributions (of the mean, difference between means, Pearson’s correlation, proportion)
Estimation (degrees of freedom, characteristics of estimators, confidence intervals)
Logic of hypothesis testing (significance testing, type I and type II errors, one- and two-tailed tests, interpreting results)

7. The main chapters of the course will address (also)
Testing means
The power of a test
Prediction (at least linear regression)
ANOVA (one- and multi-factor)
Chi square (distribution, one-way tables, contingency tables)

8. Further considerations
The environment will include case studies and different calculators (or searching through tables).
Moreover, the style and presentation will be considered to permit navigation (meaningful buttons, access to the Table of contents, etc.), understanding (minimum text but maximum information), and progress in learning (considering pedagogic factors, formative evaluation etc.), contiguity (between text and simulations), using meaningful data for demos, self-monitoring (personal reflection and self-assessment)

9. III. WAYS OF IMPLEMENTATION
There are many ways to implement an On-line course in statistics with respect of the above requirements. The most common solutions are:
E-books and on-line books supporting: navigation, understanding, progress in learning and interactivity (including bookmark creation, notes insertion).
Wiki books developed in a collaborative manner.
Dedicated website making use of special routines (CGI, servlets, applets etc.).
Specialised software supporting also e-learning/e-assessment, but also independent experimentation.

10. Further considerations on implementation
On-line books are different from books stored in different formats: PDF, DJVU, DocBook etc. Of course, PDF format admits searching, TOC organisation, link recognising. But such formats are not able to support simulation. They are quite statically. On-line books have to be dynamic.
Electronic textbooks even developed according to the three-dimensional model developed in don’t satisfy the requirements as contiguity, demos and self-monitoring availability.
Wiki books can be integrated in the largest collection of open-content textbooks. At this moment there are available more than 100 books on Mathematics: All open-content resources can be used to create not only a textbook, but approximately an on-line book.

11. Case studies (1)

12. Case studies (2)

13. Case studies (3)
When creating dedicated proprietary websites then Web-programming techniques will be used to implement communication between user and the website, to provide data processing for files sent by user, etc. Simple versions are based only on applets and pre-established data sets. This is similar with a textbook having solved exercises. The user doesn’t have the possibility to insert code, or formulas. However, a client-server version can meet all requirements.
Not only graphical elements and simulations play an important role in learning mathematics, and statistics too. Playing relevant games (statistical games) is a good approach to feel statistics. This is why images, sound, and video are important for good on-line learning/teaching statistics.

14. Conclusions
There are many ways to design an On-line course in statistics.
We reviewed the state of the art in the field and presents some ways of implementing such a course.
The course will be available for students enrolled at Spiru Haret University, Faculty of Mathematics and Informatics, under the Blackboard Platform.

15. Thank you!
Questions?