Introduction
I am delighted that I have been invited to deliver a speech at this conference on statistics in the beautiful, historic and culturally rich city of Isfahan. It is an honour to be amongst my colleagues representing internationally recognised universities and organisations, which are actively involved in the education and practice of such a significant topic.
Back in 1974, immediately after completion of my mathematics high school diploma at Alborz High School in Tehran, I undertook a course in a very strange subject. It was referred to as "Statistics". Although very closely associated with mathematics, it was something which I had never come across even during my Alborz College education. I gradually came to grips with the subject, became very interested in it and finally ended up teaching aspects of it at tertiary level.
The purpose of today’s talk is to review different phases of statistics education over the years and explore ways of popularising the concept of statistical thinking and image construction in this fascinating field.
Methods of Teaching
and Learning statistics
Several years ago when electronic devices such as advanced calculators and computers were not readily available, there was an emphasis on teaching and learning mathematical procedures to produce results. As noted by Stockburger (1996) a great deal of importance was placed on how to do the calculations rather than a reasonable insight into what they were doing.
Learning and using relevant formulae manually was an important part of education in statistics and electronic devices were only used on very special occasions in the classroom.
I remember having the opportunity to use a large and heavy looking calculating machine for calculating Standard Deviation in one of the mathematics labs of my college in England back in the 1970’s. I have never forgotten my successful attempt at putting my punched Fortran cards together and receiving an output for my Standard Deviation value the day after submission.
The advent of portable electronic calculators made it possible for students of statistics to partly shift their focus from number crunching procedures to application.
Gradually computers became much more user-friendly and offered the user a suite of programs to handle some of the more advanced routines. Therefore, the computer software available influenced modern methods of teaching and learning statistics. As a result, more and more social scientists became interested in using statistics as a tool.
The use of technologies associated with modern computing also help in reinforcing the concepts, mainly in terms of making teaching and learning processes more interactive and allowing learners to sit in the driver’s seat and steer towards their goals. Therefore, modern computing can and will play an important role in popularising statistics and in promoting the idea of statististical thinking amongst many different groups of people. The following figure illustrates different phases that teaching of statistics has undergone. They include the number crunching approach, the use of the computer as a "black box" and the user-friendly modern multimedia computer phases.
It is a proven fact that, regardless of the background of the scholar, any scholarly activity requires the use of statistics as one of its main tools. Statistics may be regarded as a "master key" which will open many doors to the researcher.
Therefore, it is important to approach the teaching of statistics in such a way that meanings and concepts are conveyed to the learner and at the same time the learner is not frightened and put off as soon as he encounters obstacles.
A very effective way is to adopt a constructivism-based approach to teaching and learning. As we now believe that students construct their own knowledge, with guidance from teachers, many teachers are offering students resources which encourage their independent exploration of the materials provided (Berge and Collins, 1995). Jedege (1992) claims that constructivism (as it is termed) does not view knowledge as a fixed entity and recognises that it is not transferred from one knower to another. It is therefore important that learners be actively engaged with the instructional materials to construct their own meanings through an “interpretive process, which unravels their world in a personally meaningful way”.
Allowing learners to engage actively in the use of real and interesting data will also encourage them to grasp concepts quickly and relate them to real applications. Takis (1999) adopts an interesting approach in teaching some of the commonly used statistical techniques such as the Chi-Square test. In this approach, data (passenger information) from the 'Titanic' tragedy is used by students to explore relationships such as class and survival rate.
Whether constructivism in education is teaching, or learning based as suggested by Clements (1997), I believe in the benefits of active learning and guiding the learners to find out for themselves rather than "holding their hands" and giving them all the information in a passive manner. Let me introduce an analogy here. Suppose someone wishes to learn rock climbing and he has a very limited amount of time. The instructor can either push the climber to the top of the cliff;
or the learner can be guided by the instructor and learn how to climb the rock right from the beginning.
It is interesting to note that the concept of guiding and leading the learner to find out the solution or the right answer to a problem was also discussed by Plato (the ancient scholar) almost 2400 years ago. If we analyse Plato’s famous “dialogue” Meno, we will realise that Socrates demonstrates to Meno how a mathematically ignorant person solves a geometrical problem through a controlled guidance procedure rather than being told directly.
In the dialogue Socrates conducts his geometrical experiment on one of Meno’s retainers who was totally ignorant of mathematics.
In this experiment, Socrates asks the boy to determine the dimensions of a square which is exactly twice as large as a given square (say, abcd). The boy, eventually, after a series of questions, finds out that the correct solution is obtained by constructing the square (twice as large as abcd) on a diagonal (say, ac) of the given square.
Even if learning is only the recovery of the pre-existent knowledge in the human soul, as Socrates argues, it can be passed on from teacher to learner by simply guiding the learner to find out for himself.
The Use of Anecdotes
and Analogies in Teaching Statistics
The use of anecdotes and analogies in explaining concepts is also an effective way of teaching. I often ask my students to think about a scenario in which a layperson asks them to explain (obviously in a language they can understand) what they are studying at university. There are three alternative ways of answering this hypothetical question:
1. Answer by using the technical jargon and totally confuse the poor friend who may courteously keep nodding his head to indicate an understanding,
2. Tell the person that it is not possible to describe it in a few words, or
3. Use an anecdote or analogy to convey the message in as few words as possible and in an interesting manner.
It is obvious which alternative will be attractive for our layperson who does not have a great deal of experience in the field but is keen to find out about it.
For instance, if I am asked by a layperson what is meant exactly by statistics, I will refer to the following Old Persian saying: “Mosht Nemouneyeh Kharvar Ast (translated: a handful represents the heap).
This brief statement will describe, in one sentence, the general concept of inferential statistics. In other words, learning about a population by studying a randomly chosen sample from that particular population can be explained by using an analogy similar to this one.
Chanter (http://science.ntu.ac.uk/rsscse/ts/bts/chanter/text.html) presents an interesting collection of anecdotes and analogies used in the teaching of statistics. According to Chanter an old favourite is the person with his head in a fridge and feet in an oven who is said to feel ‘quite comfortable’ on the grounds that his average temperature is normal.
Another favourite is the story of two soldiers who congratulate each other on the grounds that, on average, they hit the enemy target. They both miss the target by
equal distances; one misses it to the left and the other to the right!
These types of anecdotes are very effective in conveying the message to the learners that one cannot simply quote an average without indicating the variability.
Friedman, Halpern and
Salb, (1999) present an anecdote which can teach students an important lesson
on choosing a representative sample. It
also conveys the message that in a survey sample, the number of respondents is
not the important factor, but the percentage of the respondents should be
considered. In this anecdote,
“Professor Klutz” claims that based on his survey, 30% of Americans have been
abducted by aliens from other planets! 
If students examine Professor Klutz’s survey carefully, they will find out that two million questionnaires were sent out and 100,000 people responded. Although 100,000 is a reasonably large figure, it is only 0.05 percent of two million! So, the message about the difference between the response numbers and response rate would become quite clear to a learner of statistics.
As is demonstrated throughout this paper, I have taken things one-step forward and added the medium of image to presentation of the concepts, anecdotes and analogies. Therefore, by designing and drawing and presenting these special illustrations in conjunction with our text or verbal description, we are moving closer to having a 'multimedia' method of presentation.
Such basic, non-computerised multimedia presentation will be
more interesting for learners. They
will learn and remember the concepts and, in future, one quick look at the
images will prompt the whole story and logic.
After all, human beings receive, decipher and store information using
different senses.
The use of Multimedia in Teaching Statistics
For an effective and successful lecture, a lecturer must utilise a number of different forms of media in its delivering. For instance, audio is used when a lecturer enters a lecture room and starts talking to the students. Text is used when a reference to a section of a book is made. When an image is placed on the overhead projector or drawn on the board, and the lecturer starts explaining various features by moving their hands or the pointer over it, an attempt to make 'animations' is simulated. If a student stops the lecture, requests for a repeat or asks further questions, the lecturer would respond accordingly. We may refer to this feature as interactivity. More effective interactivity would, obviously, be a two way one in which both teacher and learner may respond to each other's requests.
It is reasonable to assume that, without these different forms of media, a lecture (even on a very interesting topic) can appear lifeless and dry. So, really, a good lecture is a multimedia lecture. However, the term multimedia is generally used with a different connotation. It usually refers to an implementation of those different types of media (audio, text with links, video/animation) on a computer.
A multimedia system will make it possible for students to enjoy an interaction with a virtual teacher at their chosen pace. The virtuality of the instructor can even change to actuality by the communication features of the Internet! These features include E-mail, newsgroups and interactive chat facilities such as Microsoft Netmeeting. I often use Netmeeting to have an instant and interactive communication with my distance education students. These types of systems are ideal for those students who are studying in distance mode and cannot take advantage of the teacher/student interaction, which usually takes place within a classroom.
As suggested by Velleman and Moore (1996) " the main premise of the movement to reform instruction in the mathematical sciences is that students learn best by their own activity, rather than by passively receiving information." The validity of claims similar to this one has been proven to me by my own experience with multimedia teaching of statistics. I have adopted an approach, which I have named ‘TTAT’ (Total Technology Approach to Teaching). A ‘TTAT’ system which I developed for a mathematical subject won me the University of Southern Queensland's inaugural Award for Excellence in Design and Delivery of Teaching Materials in 1997.
One of the main features of this educational multimedia system is its ability to facilitate the teaching of statistical concepts via specially designed animations and simulations. This feature enables all students, regardless of their geographical location and means of interaction with the University, to enjoy that extra level of explanation which is usually conveyed during a traditional face-to-face lecture or tutorial.
For instance, the concept of the Binomial Theory is complemented by incorporating features which allow students to interact with the animations and investigate different situations. Similarly, the concept of Normal Approximation is supplemented with a specially designed animation, which provides that extra level of interactivity for students.
As explained earlier, the use of anecdotes and analogies has proven to be a very effective means of teaching complex concepts. Multimedia is ideal for capturing and delivering interactive animations and simulations, which represent various anecdotes and analogies.
One of my favourite analogies, which I developed for explaining the concept of complete and partial enumeration techniques, has been incorporated as an interactive animation into the system. The purpose of this analogy is to explain the concept of how we can become more selective in searching a problem space. This concept will help students to appreciate a variety of techniques and approaches in quantitative areas.
The analogy is based on a missing watch, which is assumed to be lost on Campus. As the problem space (the Campus) contains the solution, a complete enumeration by looking in every building is a possible method. In the animation an icon of an “eye” searches every possible location on the university campus until it finds it.
Alternatively, a more efficient way of partial enumeration is demonstrated by focusing only on the buildings visited during the day that the watch was lost. In the animation an icon of an “eye” searches only a selected sample of possible locations on the university campus until it finds it.
The student can interact with these animations by pausing, moving forward or backward in the animation to get to the desired positions until a satisfactory understanding of the concept is achieved.
Conclusions
Whether we choose to adopt the latest technology or maintain the traditional "chalk and talk" methods of teaching, we must bear in mind that we need to make teaching of statistics as interesting as possible for our students. There is no doubt that the misunderstood image of statistics as a dry subject should be re-built in the 21st century.
As suggested by Kettenring (1997) in a presentation entitled "Shaping Statistics for Success in the 21st Century" to the American Statistical Association back in 1997, image reconstruction of the field of statistics must be placed right at the top of the list.
I am always searching for books, which emphasise concepts and meanings, and present statistics as an interesting topic with the main purpose of popularising the subject. I recently came across the interesting title of Statistics for Poets by Berkowitz (1991) while I was searching the Internet for newly advertised books on statistics. I decided to review the book. The book covers most of the important topics included in an introductory book on statistics and presents them in an easy to understand manner. Its interactive nature, which invites and encourages the reader to participate in the learning process, is also a valuable feature.
The other book, which is worth a mention, is the classic titled Statistics Without Tears by Rowntree (1981). I have always been fascinated by the approach taken in this book. It certainly encourages statistical thinking without overwhelming the learner by Greek symbols and equations.
It is encouraging to learn that there are authors of books who have been making their contribution to statistics as a subject which can be learnt without pain by almost anyone.
I would like to conclude this paper by emphasizing the fact that statistics teachers (at all levels and capacities) will play an important role in popularising statistics and spreading the idea of statistical thinking.
References
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