International Conference on Trends in Physics Education        

Tokyo, August, 1986

 

 

ＮＥＷ ＳＣＩＥＮＣＥ ＥＤＵＣＡＴＩＯＮ：

ＴＨＥ ＣＯＮＣＥＰＴＳ ＯＦ ＩＮＥＲＴＩＡ ＡＮＤ ＦＯＲＣＥ

 

　　　　　　To avoid the Aristotelian misconceptions

　　　　　　

 

Yoji Iida

Nagoya Kogei High School, Nagoya, Japan

 

§ �T  Investigation on the recognition of the concepts of inertia and force

§ �U　Analysis of students' common-sense views of nature

　　 (1) Common-sense views of nature backed up by experience

　　 (2) Analysis of students' common-sense judgments

　　　　　 Why do they draw  a “moving force”?

§ �V　Approach to overcome  a “moving force”

　　 (1) The law of inertia supported by the principle of relativity

　　 (2) The principle of force

§ �W　Force to change direction and linear motion of inertia

　　 (l) Analysis of students' wrong judgments

　　 (2) Development of lessons with “Monkey hunting”as the key point

Materials

       Chief problems and experiments in lessons　

                               

§�T Investigation on the recognition of the concepts of inertia and force　      

　　   　   

The investigation was carried out by giving the written tests to Japanese high school and college students. The subjects consisted of 39l in all and classified into three groups; 171 second year technology high school students who had not had mechanics, ll4 first year national university technology students and l06 first year national technology college students. They were examined on April, June, and July in l983 respectively. There was no significant difference between the results obtained from the college and university students. They have already studied mechanics in high school and are said to do fairy well.

 

The questions taken for the investigation consist of three types of items.

　　Type l: Inertia and force in the given direction

　　Type 2: Force to change direction and linear motion of inertia

　　Type 3: Trajectories of bodies

in the diagram shows high school students and

college students.

A correct response is marked with ＊

 

 

　　Type l: Inertia and force in the given direction

 

From the following results of Question 1 ~ 7 it is concluded that high school students who have not started studying mechanics have striking misconceptions about the motion of a body such F∝V as Aristotle thought.

 

In comparison with high school students, college students were not so bad. But only ll% of the national university technology students and l4% of the national college technology students gave a correct answer to all those questions. It may be mentioned that there were very few who had a proper understanding of mechanics and then got into college.

 

The results also seem to give a good example showing that every student cannot understand mechanics properly without making any conscious effort to dispel the Aristotelian view of nature. The responses given by college students apparently indicate how they were educated in high school, though said to be fairly bright students at that time.

 

 Question l

Draw ○ if the following expression is correct or × if it is not. “Some kinds of forces are acting on a stone gliding on the level surface of the ice. One of them always acts forward”

 

The result of qes.1

As many as 70% of the high school students thought a force always acts forward.

 

 Question 2

A car continues in  uniform motion in a straight line. There are forces acting upon the car. A is a driving force. B is a force which impels it backward, such as air resistance or frictional force.

　　 a. A<B

　　 b. A=B

　　 c. A>B

 

The result of qes.2

More than 70% of the high school students thought that a force acting on forward is greater.

 

 Question 3 　　　　　　　　　　　　

A ball is dropped on point O and follows the path shown below. Draw arrows of the forces acting on the ball in the positions A,B,C,D, and E. Neglect air resistance or frictional force.

 Question 4 　　　　　　　　　　　　

Draw the forces acting on the pendulum swinging in the direction of the arrow. Neglect air resistance.

 

The result of qes.3, 4

l7l high school students in all who had not had mechanics yet gave an incorrect response. Only 39% of the college students selected the correct one in Ques.3. Between 70% and 90% of the high school students were mistaken, drawing an arrow of the force acting forward.

 

 Question 5

A disk is gliding on the level ice. Draw ○ if the following force acts on it or × of it doesn’t.

　　 a. The gravity acting on the disk.

　　 b. The frictional force or air resistance impeding the motion of the disk.

　　 c. The force to maintain the forward motion of the disk.

　　 d. The inertial force caused by the inertia of the disk.

　　 e. The force of the disk reacted upward by the ice.

                                                                                                                                                               

The result of qes.5

 

There were only 24% of the high school students and 52% of the college students who answered correctly. Note more than 1/2 of the high school students believed in the force to maintain a forward motion or the inertial force caused by inertia. As many as 34% of the college students maintained the inertial force to be existent.

 

 Question 6 　　　　　　　　　　　

If a stone falls freely from the height between one and two meters, what kind of force will act on it?

Select the correct one from four options.

　　 a. The gravity is a constant force and there is no force but the gravity.

　　 b. The gravity is increased gradually and there's no force but the gravity.

　　 c. The gravity is a constant force and the upward“remain force” is reduced gradually.

　　 d. The gravity is a constant force and the “falling force” acts on the stone and is increased gradually.

 

 

The result of qes.6

 

Only 5% of the high school students answered the gravity is a constant force. High school students who thought there are gravity and  falling force" amounted to 53%. More than 30% of the college students were mistaken on this problem.

 

 Question 7

At what speed will the cart go, ignoring frictional force, if it is pulled with constant force continually?

　　 a. The cart continues in its state of constant speed.    

　　 b. The cart initially accelerates and then moves with constant speed.

　　 c. The cart continues accelerating.

 

The result of qus.7

　

 

There were as many as l/2 of the high school students who selected b' saying that the cart initially accelerates and then moves with constant speed. l/4 of them and only 63% of the college students selected ‘c' saying that the cart continues accelerating.

 

　　Type 2: Force to change direction and linear motion of inertia

 

From the following results of Question 8 ~ 10, no correct response was given at all by high school students. The college students who answered to these questions completely correctly were only 3% out of national university technology students and 5% out of the national technology college students.

College students who are said to do fairly well were so much mistaken that there must have been some substantial errors in mechanics education they had in high school days. It is very important to teach that a force must be applied to a body to change its direction in uniform motion. This is what Newton meant in his theory of mechanics.

 

 Question 8

A pendulum swings. When it is at the lowest position as shown below, which is greater, tension T of a string or gravity W?

　　 a. T>W

　　 b. T=W

　　 c. T<W

 

The result of qus.8

Only l3% of the college students gave the correct response T>W. The result was surprisingly bad. This result was inferior to that of the high school students(l5%).

 

 Question 9

If a car turns at constant speed, additional force will act upon it, differing from the case of a car's traveling in a straight line. Select the correct one from four options. The observer stands on the ground.

 

The result of Qes.9

The college students giving the correct answer amounted to a smaller percentage than 50%. As many as 60% of the high school students answered ‘b'. Perhaps they answered the question as they felt themselves shaking right when it made a left turn. Of course the response was correct on condition that they as observers were on the car, but it is a serious problem that they maintained the response in spite of staying on the ground. 

 

 Question 10

Suppose a body is moving in uniform circular motion. Which force is in reality acting on it? The observer stands on the ground.

 

The result of qus.10

　

Only about 40% of the college students gave a correct response. No one of l7l high school students did. Almost all errors were caused by their thinking that when a body continues in circular motion, a force acts forward. There were over 90% of them selecting a, b, c, and d.

Additionally, more than 80% who selected a, b, e, and f believed that inertial force acts on a body. Even college students answered that there are forces acting in the forward and outward direction of motion, amounting to nearly 40%.

 

　　Type 3: Trajectories of bodies

 

To convince students of the existence of laws by providing demonstration experiments with them is indispensable to forming the concepts of force and inertia.

 

 Question 11 　　　　　　　　　　　　

The car moves in uniform motion. When it is abeam of an electric pole, a stone is thrown horizontally at the pole out of the car window. What kind of path will the stone follow?

Suppose the throw is a success.

　　 a. The stone will hit the pole (to position A).

　　 b. The stone will travel ahead of the pole (to position B).

　　 c. The stone will travel backward and land behind the pole

　　　　(to position C).

 

The result of qus.11

 

Question 12

Ball A is launched straight at target B and B freely falls simultaneously. Select the correct one from three options.

        a. A fails to hit B.

        b. A never fails to hit B.

        c. Hitting a target depends upon initial speed or angle at which it is launched.

 

The result of qus.12

 

 　

 

“Monkey hunting”is very well-known. Very high percentage of the high school students answered that initial speed or angle at which a ball is launched will condition hitting a target. Hence the success of this experiment left a deeper impression upon the students.

 

 

　§�U Analysis of students’ common-sense views of nature  

 

　　(1) Common-sense views of nature backed up by experience

 

After the mechanics class I once requested the students to ask themselves what made them get into the Aristotelian, common-sense view of nature. As a result it was found that they have had good experience for maintaining their common-sense views. Though they have not originally learned the Aristotelian ideas, they cannot help thinking of a force which always acts forward. Experiential and common-sense views of nature are grounded so strongly on their mind. So they get more and more easily into these views unless they have a conscious effort to acquire a scientific way of seeing phenomena.

Students' thinking reported are presented as follows.

 

        When I am on the ground, the sun, the moon, and the stars look to be in motion and I have no sensation of motion. Is it wrong of me to think just as Aristotle did? I myself never feel the earth is going around. Reason differs from feeling.      Because man is endowed with reason, we realize the earth's motion.

 

        Rest is the state of being still and uniform motion is the act of moving at constant speed. It follows that there is great difference between two factors. Yet, what a fun and a wonder the arrows of the forces show the same direction!

 

        We think in the way Aristotle did. This may be derived from a self-centered idea. As the intention to  move" causes the movement of our body, I can't convince myself that uniform motion is the same as rest, which I have been often told, considering to put myself into motion.

 

These are reasons why most of students think in the way Aristotle did.

 

        I never feel the earth is moving. What looks to be in motion are the sun, the moon, and the stars.

 

        There is an apparent difference between motion and rest.

 

        If a force doesn't act on a body, no motion will result. Hence it doesn't appear to me that a body moves by nature.

 

        If a force acts on a body, motion will result and if it does not, no motion will. The world of experience we are living in is real.

 

        When we drive a car at constant speed, gasoline is used. It　will stop if the accelerator is released.

 

        A star is one thing and the earth another. I don't think they　are the same.

 

The attitudes of the students aren't inconsistent with our actual　experience. So it is natural that their thinking by feeling and experience should lead to the Aristotelian view. The non-Aristotelian view is rather improper to them. When they meet a phenomenon inconsistent with their feeling or experience, they will not accept it at its full value. Although they must admit there is reason in the phenomenon, it is full of a wonder to them. They are compelled to give up their own feeling or experience to select a reasonable response. This is why they say “wonder."

 

        Why in the world should I follow Aristotle's way of thinking? Because my feeling will not allow to accept anything but such thinking. Every thing lies in motion. Though the earth is moving, we can't feel it. However, it is a wonder that rest belongs to uniform motion.

 

        I have no sensation of moving. If my body were in motion, I would wonder at it naturally.

 

        I can't give up common sense. I think common sense is most likely to tell the truth. I find I come back to the theory of Aristotle soon even after I have learned Galileo in class. Common sense is so strongly rooted on my mind. I could not achieve a firm grasp of mechanics in the time Aristotle or Galileo lived.

 

        Common sense has been rooted on my mind for ten years or so. We should make a considerable effort to give up the thinking of Aristotle. We will not be able to succeed in understanding the reasonable theory of Galileo unless we dispel the Aristotelian view.

 

　　　(2) Analysis of students' common-sense judgments

　　　　　Why do they draw “a moving force"?

 

As is evident from the results of the questions, a force acting forward" first comes to most of all students' mind. Now it is apparent that the misunderstanding is grounded so strongly through their experience that it is impossible for them to overcome it so easily. What is their criterion by which they make a drawing of “a force acting forward"? Their statements consist of three important points (Figure l). 

 

(�@) Students have the misconception that motion differs from rest completely.

This is an almost undeniable fact for them. They intend to apply the misconception to every mechanical phenomenon.

　　　

(�A) Assuming that motion is different from rest, students must seek a reason for it from their experience.

Now let's take a concrete example of a car.

 “There are no cars traveling without any fuel."

 “No one can imagine that a car originally moves without any force."

 “The state of a car's traveling can be realized with some force being applied to it."

 

In other words, students try to grasp the current motion of the car, including the previous state (from start to motion).

 

They don't completely err in their judgment. Everyone knows that there must be a force to change a car from start to motion; a car at rest will never move without fuel supplied to it.

 

But students believe the idea can extend easily to uniform motion, so they interpret the first applied force as a force as it is or the previously acted force turns into “a remain force" reduced, “an impressed force", “a moving force" or “impetus."

 

What gives us the most trouble is  a moving force." Students believe that it isn't an ordinary force to cause a spring to deform its shape or to change motion but a force to maintain its motion. They will not be able to give up this idea without being convinced the concept of force; force deforms or accelerates a body.

 

 “Impetus" possibly gets to Ft = mv.

 

(�B) A body in motion will stop naturally without any frictional forces if it is left as it is.

 

The misconception indicates that a body cannot move without anything being exhausted and must be supplied with anything to maintain its motion.

“A body lies in being at rest. It is natural that a moving body stops." (static view of nature)

        “Motion is reduced because of a body's weight".

        “No motion of a car results without any fuel applied to it"

and so on.

 

 

　　§�V Approach to overcome “a moving force”     　

 

What steps should be taken to dispel the misconception “a moving force," after analysis of all the results? In my class I have tried to do so with“Galileo's  principle of relativity,” “the principle of force," and “the atomistic view of nature." Good results seem to have been obtained in my own way, though not sufficient for that. I am going to explain how to do something fundamental before informing you of my practical instruction including experiments.(Figure 2.)

 

   (1) The law of inertia supported by the principle of relativity.

 

(�@) To dispel the misconception “the alternative of motion or rest.”

To do so, experiments in dropping or launching a body out of a vehicle in uniform motion are made, accompanied with the introduction of the Galileo’s principle of relativity as a practical fact and students are taught “There is no mechanical difference between uniform motion and rest."

 

(�A) “It is unbelievable that a body moves originally if it is left as it is.”

To avoid the misconception the experiments mentioned above may be also helpful. That is, students are reluctant to admit that “A ball released on the vehicle is moving forward without applied force."

 

The wrong frame of belief that an applied force turns into “a moving force” will be broken through the introduction of relative motion.

 

(�B)  “A moving body will stop naturally if it is left as it is.”

This misconception can be overcome in this way. After students have admitted the results of the experiments to be real, they must also agree “In the horizontal direction, the ball moves just as fast as the vehicle.” The acknowledgement of the principle of relativity leads to that of the law of inertia.

 

The introduction of the principle stimulates students to get free from the frame of common sense completely. Apparently it collides with students' experience or feeling. Now that this is an undeniable fact, however, students must admit it by reason, even if it is a wonder.

 

To admit the principle of relativity - rest is mechanically equivalent to uniform motion –this is just a good example showing feeling or experience is not to be relied upon. We don't feel the earth moving though it is actually. This may be thought to be a wonder.

 

 

 

   (2) The principle of force (F∝a)

 

On the other hand, to avoid  a moving force" it is necessary to have the clear concept of force.

 

(�@) Mechanical phenomena such as motion should be understood not by F∝v (the alternative of motion or rest) but by F∝a(the alternative of uniform motion or non-uniform motion).

 The principle of force"; force changes motion.

This is demonstrated by a simple experiment.

 

(�A) Most students hold that  When forces are balanced, there is no motion."

In this case, too, they need to be explained uniform motion is mechanically equivalent to rest, including a simple experiment. If resultant force is 0 ( or no force acts ), a body continues in its state of motion (in uniform motion).　(Figure 3.)

 

　　　 ΣF=0　←→　a=0　(v=const)　　c≠0 uniform motion

　　　　　　　　　　　　　　v=c    

　　　　　　　　　　　　　　　　　　　c=0　rest

 

In this way students need to recognize that rest belongs to uniform motion.

 

(�B) Students very often consider “a moving force” as an attribute of a body in motion, which may be refer to momentum or kinetic energy.

Hence “force isn't an attribute of a body, but acts on it.”

What deforms or accelerates a body is defined as force.

Thus the concept of force should be defined. Additionally, other concepts such as inertial mass, momentum and kinetic energy should be explained in contrast to force. 　　　　　　　　　　　　　　　　　　　　　　　　　　　

Inertia isn't a quantitative concept but a qualitative phase of inertial mass. But the concept is very important in clarifying the role of inertial frame of reference (which conditions the formation of Newtonian mechanics) in the principle of relativity.

 

  

 

 

　　§�W  Force to change direction and linear motion of inertia

 

　　 (1) Analysis of students' wrong judgments in Type 2

 

Students' misconceptions in Type 2 are classified into three chief criterions.

 

(�@)  When a car makes a turn, centrifugal force will act."

This is a very popular statement used in our daily life. It is true that a person on a car feels inertial force, but students interpret it as a force belonging to circular motion, irrespective of their observation system.

 

(�A) “A car turns with forces balanced.” or

     “There is no acceleration in uniform circular motion.”

What leads them to the criterions is that they recognize a body's orbit is already given. The form is principle.

 

(�B) Students think “a moving force” exists in the direction of motion.

 

Why do they sympathize with such miserable misconceptions? The reason for (�@) is that inertial force is so popular among students that educators have not taught cautiously it is a force occuring only on non-inertial frame of reference. The reason for(�A) is that it is not completely understood by students that “A shape of motion is formed by force”.

Force changes direction as well as speed. Without any force, neither speed nor direction will not change. The teaching was not completely restricted to only direction". See §2 and 3 regarding the reason for (�B).

 

 

　 (2) Development of lessons with “Monkey hunting”as the key point.

 

There are some reasons why lessons are developed with “Monkey hunting” as the key point.

 

(�@)The following facts are not self evident to students.

The motion of a thrown body is the resultant motion which is composed of a uniform motion in the direction of the first velocity and a uniformly accelerated motion in the vertical direction. Two motions are independent of each other. The trajectory of a body is parabolic.

 

There are only ll% of the high school student in Question l2, believing that a bullet will hit a target because they are not accustomed to grasp the path of it according to scientific law. If the experiment makes a nearly complete success of hitting a target, a scientific law will win more confidence of students.

 

It will be evident that the experiment actually demonstrates the resolution and composition in motion. Also evident that educators must not put their own interpretation on the matter.

 

(�A)It can be easily shown through the experiment that gravity impedes uniform motion and a parabola results. I'll give an outline on which a lesson is developed as shown below.

 

 

Such development will help to understand that there is acceleration in the inward direction of circular motion and to recognize that parabolic motion is substantially relative to circular motion.

 

There is no need telling terrestrial motion from celestial motion. Finally it is to be desired that students should understand those motions are produced by linear motion of inertia and force to change direction.

 

 

 

＜Materials＞                   

      　　　 Chief problems and experiments in lessons

 

�T  The law of inertia   The principle of relativity

 

 Problem l-l

With a ball in his hand, a boy is riding on the bicycle at almost constant speed. He brings a ball just above the white line drawn on the ground and then releases it. Where will it land on the ground, if it falls freely from the height of l.25m?

　　Expectations:

　　　a. Back of the white line.

　　　b. On the line, far back of the bicycle.

　　　c. A head of the line, at the same position as the bicycle.

　　　d. In other places.

 

(Hint) When the bicycle remains at rest, the ball falls on the ground in 0.5sec from the height of l.25m. Supposing that it covers l8km/h(=5m/sec) constantly, it will have traveled at the rate of 2.5m per 0.5sec. The attachment of a speedometer to the

bicycle is preferable.

 

 Problem l-2

There is a cart with a device for launching a ball. When the cart is at rest, a ball is set to fall to the original pad of the cart after it has been launched straight upward. Where will the ball fall if it moves at almost constant speed?

　　Expectations:

　　　a: To the launching pad.

　　　b. Back of the launching pad.

　　　c. Ahead of the launching pad.

 

Expect, discuss and then make the experiment.

The following experiments are recommended to be made together.

　　　l. How does a ball bound, forward, backward or upward?

　　　2. Throw a ball upward or drop it on the white line while running at almost constant speed and check its path.

　　　3. While a cart equipped as shown in the right drawing moves at almost constant speed, turn off an electronic switch to drop a ball of metal. Where will it land?

　　　4. There are two balls of metal; one is for dropping and the other for launching.  Will they collide with each other when they follow their own path?

　　　5. Just a little before a cart goes into the tunnel, a ball is launched upward.  Will the ball land on the original place?                                                                              

 

 

Problem 2

The free falling motion of a ball and the motion of a bicycle are drawn below at each interval of 0.lsec. Draw in the figure the ball's positions at each interval of 0.lsec.

 

Fill the blank with a short expression.

        The ball falls quite the same way as (                   ) from the viewpoint   of a person on the bicycle.

 

 Problem 3-l

The drawing shows a cart, which was presented in the problem l-2, at each interval of 0.lsec. Supposing that a ball falls down to the launching pad of the cart 0.6sec after it was launched, draw in the figure the positions of the ball at the same interval. Note that when the cart stops, a ball is supposed to be launched and get down as the drawing shows.

After that, compare your drawing with a picture taken with a stroboscopic camera.

Draw a red line between the cart and a launched ball at each interval of 0.l sec.

Fill the blank with a short expression.

　　　The ball falls quite the same way as (　　　　　　　　　　 )

　　　from the viewpoint of a person on the cart.

 

 Problem 3-2

The cart decelerates after a ball was launched. In 0.6sec it moves halfway as far as it did. Draw the positions of the ball in the figure.

Draw a red line between the cart and a launched ball at each interval of 0.l sec.

 

 

�U　Parabolic motion.    “Monkey hunting”

 

《How to make a simultaneous launching pad》

 

l. Cut a veneer of 5mm thick into the shape shown in Figure l.

 

2. Cut small scantling according to the dimension shown below. As    Figure 2 shows, stick 　　 on the veneer and then fix them with a nail on the wrong side. 　　 guides a pecker to operate.

3. ■■■shows the pecker, fixed with a nail as shown in Figure 3.

　 It is placed in the guide 　　 so that it can slide right and left. Set scantling d' backward by half a size of the ball.

 

4. As Figure 2 and 4 show, scantling c is clamped at point O and turns around in touch with the pecker. A ring of gum is on the nails of the scantlings c and c'. Between them is a ball.

 

5.  Balls e and f are released by the pecker simultaneously from the device. A ball of metal is φ3cm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

《Method》

Attach the simultaneous launching device to a flat board and stand it vertically.

Make many trials of different slopes θ.

What kind of path will a ball follow as the board is initially leveled to the floor (θ=0°)and then the slope θ is increasing? (Fig.5)

Make the experiment, varying initial speed or angle α at which a ball is launched.                                                                                           

 

�V　Force and motion.

 

Experiment of  Question 7

Pull the cart, maintaining almost uniform stretch of the spring.

It is not easy to maintain it. But you will immediately find whether your prediction is correct. As shown in the drawing, the cart is easily pulled by a stick of about one meter long whose end is tied to the spring.

Experiment of  Question 2

 

Attach two springs (A and B), whose strength is of the same, to the front and rear of the cart.

Put it in motion at almost constant speed by pulling at the spring A, with a sand bag tied to the end of the spring B.