1. A Study on the Misconceptions of Average Velocity
Conference of Asian Science Education
February 20-23, 2008
Kaohsiung, Taiwan
A Study on the Misconceptions of Average Velocity
from Teaching and Learning Approaches
邱韻如
Yun-Ju Chiu
General Education Center
Chang Gung University
Taoyuan,Taiwan

2. Taoyuan
Chang Gung University
Taipei
Kaohsiung
Welcome to Taiwan！

3. A Study on the Misconceptions of Average Velocity
from Teaching and Learning Approaches
Abstract: This paper addresses some factors which will make students confused in class when they are learning the definition of the average velocity. I will also explain how to use suitable examples to help students understand the concepts of average velocity.

4. Outline I have not enough time to present all of these,
Therefore, I will present these.

5. The definition of average velocity
What’s wrong?
The definition of average velocity

6. The definition of average velocity is
There is a similar conception ,average speed
What is the difference between velocity and speed ?
Let me show you an example!

7. From Kaohsiung to Taipei
The distance from Kaohsiung station to Taipei station by HSR is 345 km.
It needs 90 minutes to take HSR.
Displacement≒280km
The average speed is
資料來源：維基百科
What is the average velocity?
The displacement from Kaohsiung station to Taipei station is 280 km.
The average velocity is
Which is more meaningful? 230km/hour or 187 km/hour?

8. Velocity and Speed Are they the same?
What is the different between them?

9. Velocity : 速度(su du)
Speed : 速率(su lu)
For people who speak English, speed is commonly used in daily language, and velocity is seldom used outside of textbooks. But for people who speak Chinese, it is contrary.
In Taiwan daily life, we use 速度(su du) in spoken language, but the Chinese textbooks translate 速度(su du) with velocity, which is seldom used in English daily life.
I drew a comic to show clearly.

10. 速度(su du)和速率(su lu)， 哪一個比較常聽到？
Velocity or speed, which is commonly used in daily life？
速度(su du)和速率(su lu)， 哪一個比較常聽到？
速度 (velocity)
速率( speed)
速度。
I don’t know what is 速率？
speed 。Velocity is seldom heard outside of Physics books.
速度。
I have never heard 速率. 速度
speed
speed 速度 速度
Physics
Teacher
College
Student
Adult
American
English
Teacher
High School
Student
Junior
High School
Student
English
Teacher
Elementary
Student
They speak/teach English.
Taiwanese

11. What is the difference between speed and velocity?
(Textbook)
It seems that they are the same？！
Teacher said
But some textbooks call it 速率
vector,
with direction
scalar,
without direction
Average
velocity
Average speed
速度(su du)
速率(su lu)
速度 includes direction.
速率 don’t include direction.
速度 means how fast.速率…I have no idea.
速度is associated with displacement，速率 is associated with distance.
速度，I don’t know!
速率，what’s that?
7th grade
Student
Student who doesn’t
majors in Science
9th grade
Student
Student who
majors in Science
Elementary
School Student

12. The mismatch of daily language and textbook language
In English dictionary, velocity and speed are almost the same.
In Chinese dictionary, 速度 and 速率 are almost the same.
For people who speak English, speed is commonly used in daily language. For people who speak Chinese, 速度 is commonly used.
The Chinese textbooks translate speed with the Chinese word 速率(su lu), which is seldom used in Chinese daily life. That is to say, we use the Chinese word 速度(su du) in our spoken language to mean speed but in our textbooks it means velocity.
No wonder students get confused in class !
MSN Dictionary explain velocity：
speed：the speed at which something moves, happens, or is done.
rate of change in position：a measure of the rate of change in position of something with respect to time, involving speed and direction.
According to the etymology :
The word velocity comes from 15th century Latin. Science literature of the 11th ~18th century were written in Latin. This is why we represent velocity and speed both with v.

13. From Kaohsiung to Taipei
The distance from Kaohsiung station to Taipei station by HSR is 345 km.
It needs 90 minutes to take HSR.
Displacement≒280km
The average speed is
The displacement from Kaohsiung station to Taipei station is 280 km.
資料來源：維基百科
Is it meaningful?
The average velocity is
The result of this example is
“the magnitude of velocity does not equal speed.”
Don’t you feel a little strange?
What’s this all mean?

14. Understanding instantaneous velocity as a limit
The instantaneous velocity is indeed the average velocity
in a minute time interval.

15. When the time interval is divided into very narrow sections, the displacement will be very close to the distance.

16. From Kaohsiung to Taipei
The distance from Kaohsiung station to Taipei station by HSR is 345 km.
It needs 90 minutes to take HSR.
Displacement≒280km
The average speed is
The displacement from Kaohsiung station to Taipei station is 280 km.
資料來源：維基百科
Can it represent how fast the HSR is?
The average velocity is
It’s too long!

17. The definition of average velocity is not strange
The definition of average velocity is not significant when the distance or time interval is long. Therefore, the examples that emphasis the difference between the distance and the displacement is not suitable when teaching the definition of average velocity.
We must use some examples to help students understand in what situations the distance will approach to the displacement.
But, on the contrary, teachers in Taiwan teach the definition of average velocity by using examples to emphasis the difference between the distance and the displacement.

18. Some examples emphasis the difference between distance and displacement
Example 5: Traveling from Taipei to Hualien
Example 1: Problem with a turning point
One-dimensional problems
(back and forth)
two-dimensional problems
Example 2: The yo-yo problem
Example 6: Running in a playground 10 12 9 6
Example 7: The second hand problem
Example 3: The rolling down problem

19. Implications for instruction
The examples that emphasis the difference between the distance and the displacement is not suitable when teaching the definition of average velocity.
From what I’ve seen in Taiwan, many teachers do not think these examples stated previously are unsuitable. They let their students practice them again and again because these examples are in the textbooks and have appeared in the national entrance examinations.
Implications for instruction
To teach the concept of average velocity, teachers must understand the mismatch of daily language and textbook language will make students confused.
Teachers must select suitable examples to help students understand what situations the distance will approach to the displacement.

20. Is the difference between speed and velocity only defined by whether direction is involved or not?
Are the magnitudes of velocity and speed the same after all?
Conclusion
These questions will be easier to understand by categorizing motions into three types.
In one-way straight motion, it makes no difference what the magnitudes of average velocity and average speed are. So it is meaningless to teach this concept using one-way straight motion examples.
You can ask the average speed of a back and forth one-dimensional motion, but it is not suitable to ask the average velocity in this situation. If this situation is used to emphasize average velocity to students, it will confuse them.
Two-dimensional examples are suitable to help students understand what situations the distance will approach to the displacement.

21. Thank you very much Enjoy the Lantern Festival! Yun-Ju Chiu 邱韻如
Today is the Lantern Festival,
an important traditional Festival in Taiwan and China.
Thank you very much
Enjoy the Lantern Festival!
Yun-Ju Chiu 邱韻如
2008/2/21