Monday, August 29, 2005
A small excursion into teaching techniques using the example of statistics
Statistics is fun if you know how to teach it
One of the most important things in teaching is to explain the students, why they should learn a specific subject or a specific idea, term etc. This applies for all subjects, all age categories and all levels of education.
Many years ago I was asked to teach Statistics at ERAU / Embry-Riddle Aeronautical University, Florida, USA /. I did not like statistics too much during my studies at VSE Prague, Czechoslovakia but I agreed. Usually, in order to explain what statistics is about, I used the following example:
Imagine you are a young man of 27 to 29 and you want to get acquainted to a young lady about 25 years old. There are specialized travel agencies who aimed at people in search for a partner. They organize every night three ships where they put people of fitting age together and let them talk, dance listen to music , eat and drink the whole night so that they can find out if they like each other. So you, as the young man go to such an agency and they ask you what age of a lad would be goof for you, you say you would like to learn a lady of 25 years of age. The lady at the teller in the agency says it is really terrific as just tonight on ship takes off where the AVERAGE age of ladies is exactly 25 years. So you are happy and buy the ticket for the ship and cannot await the evening as the ship takes off at 20:00. What is your surprise when you get on board and see that there are only grandmothers aged 48 with their granddaughters aged 2, the average age is 48 plus 2 divided by 2, which is exactly 25! So which of them would you prefer to get acquainted to: The 2 year old or the woman who might be your mother?????
Everybody can see that the AVERAGE number can be severely misleading, and exactly therefore there are statistical procedures which give us better grasp of the average number we want to understand, for example the standard deviation, and of course many others. Using these additional numbers we can better, much better understand what the average is telling us. Usually everybody can remember then that the average alone is not enough to base any judgements on but that we need some more numbers describing the reality more precisely.
This type of explanation makes the student aware of the danger of blind trust into average, and understands the necessity of Statistics and is prepared to learn.
The opposite example is the grades at school. Suppose there is a student with the average grade 1,4 on the scale from 1 /being the best/ to 5 /being the worst grade/. The question is. ”Is the student good or poor?” The correct answer is that the student is good because his average grade is closer to the grade 1 – being the best grade, and far away from the worst grade, 5. So the average grade of a student gives us a clear statement because we know the upper and lower boundaries, 1 and 5.
Compared to the example with the young man trying to get acquainted exactly this is the difference. The young man did not know the upper and lower age boundaries, but we know the boundaries when we speak of school grades.
In such a way it is possible to properly motivate the students by showing them what kind of benefit they can draw from learning the subject. This is possible for every subject. Only the teachers must think a bit. Basically, it is telling the students what is the stuff they are to learn good for.
Statistics is fun if you know how to teach it
One of the most important things in teaching is to explain the students, why they should learn a specific subject or a specific idea, term etc. This applies for all subjects, all age categories and all levels of education.
Many years ago I was asked to teach Statistics at ERAU / Embry-Riddle Aeronautical University, Florida, USA /. I did not like statistics too much during my studies at VSE Prague, Czechoslovakia but I agreed. Usually, in order to explain what statistics is about, I used the following example:
Imagine you are a young man of 27 to 29 and you want to get acquainted to a young lady about 25 years old. There are specialized travel agencies who aimed at people in search for a partner. They organize every night three ships where they put people of fitting age together and let them talk, dance listen to music , eat and drink the whole night so that they can find out if they like each other. So you, as the young man go to such an agency and they ask you what age of a lad would be goof for you, you say you would like to learn a lady of 25 years of age. The lady at the teller in the agency says it is really terrific as just tonight on ship takes off where the AVERAGE age of ladies is exactly 25 years. So you are happy and buy the ticket for the ship and cannot await the evening as the ship takes off at 20:00. What is your surprise when you get on board and see that there are only grandmothers aged 48 with their granddaughters aged 2, the average age is 48 plus 2 divided by 2, which is exactly 25! So which of them would you prefer to get acquainted to: The 2 year old or the woman who might be your mother?????
Everybody can see that the AVERAGE number can be severely misleading, and exactly therefore there are statistical procedures which give us better grasp of the average number we want to understand, for example the standard deviation, and of course many others. Using these additional numbers we can better, much better understand what the average is telling us. Usually everybody can remember then that the average alone is not enough to base any judgements on but that we need some more numbers describing the reality more precisely.
This type of explanation makes the student aware of the danger of blind trust into average, and understands the necessity of Statistics and is prepared to learn.
The opposite example is the grades at school. Suppose there is a student with the average grade 1,4 on the scale from 1 /being the best/ to 5 /being the worst grade/. The question is. ”Is the student good or poor?” The correct answer is that the student is good because his average grade is closer to the grade 1 – being the best grade, and far away from the worst grade, 5. So the average grade of a student gives us a clear statement because we know the upper and lower boundaries, 1 and 5.
Compared to the example with the young man trying to get acquainted exactly this is the difference. The young man did not know the upper and lower age boundaries, but we know the boundaries when we speak of school grades.
In such a way it is possible to properly motivate the students by showing them what kind of benefit they can draw from learning the subject. This is possible for every subject. Only the teachers must think a bit. Basically, it is telling the students what is the stuff they are to learn good for.
# posted by Dalibor @ 9:44 AM 
