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Asia-Pacific Forum on Science Learning and Teaching, Volume
7, Issue 2, Article 8 (Dec., 2006) Tin-Lam TOH A survey on the teaching of relative velocity and
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4. Pupils’ Learning Difficulties in Relative Velocity
From the feedback obtained, the pupils’ learning difficulties in relative velocity can be classified as the following categories:
4.1. Psychological Factor – Rosenthal Effect
This first factor raised by two of the heads of mathematics departments turns out as a little surprise to the author. Rosenthal effect is a form of self-fulfilling prophecy or experimenter bias in a social setting suggested by the psychologist Robert Rosenthal (1976).
According to these two heads of departments, their teachers have indicated that relative velocity is a challenging (or difficult) topic to the teachers themselves; this feeling towards the topic could have turned into nonverbal cues in their classrooms and consequently their pupils felt that this topic is difficult and hence were unwilling to spend extra time on this topic and at the same time did not heed the teachers’ advice on how to handle such questions.
Rosenthal effect could have been universal for all the topics in the syllabus; because the teachers personally find this topic difficult themselves, Rosenthal effect could have played a significant role in teaching relative velocity in contributing to the pupils’ learning difficulty in relative velocity.
Also, one of the heads of department further pointed out that the teachers might have instilled in the pupils that giving up this topic on relative velocity does not affect one’s chance of scoring good grades in Additional Mathematics provided one masters the other topics sufficiently well. This could also have affected pupils’ learning in this topic.
4.2.
Language of Relative Velocity
Many pupils have difficulty in interpreting the language of vectors, for example, the wind movement.
Example 1
| As an illustration given by one of the teachers, many pupils cannot distinguish between the case when “the wind is blowing along north” as contrasted to “the wind blowing from the north”. |
Example 2
| According to another teacher, many pupils and several teachers had difficulties in interpreting the direction of rain in the following information: “A man is walking along a horizontal road at 1.2 m/s. The rain is coming towards him and appears to be falling with a speed of 4 m/s in the direction which makes an angle of 60° with the horizontal.......” |
4.3. Related Science concepts
Most pupils who are not offering pure physics as another main subject have difficulty in understanding the technical terms involved in relative velocity. These concepts raised by the participating teachers are discussed below.
4.3.1 Velocity and Displacement
When both velocity and displacement, being vector quantities, can be represented in the standard i-j notation or the column vector forms, there is a great deal of confusion among students between velocity vectors and displacement vectors. Consequently the pupils are not able to use the information in solving the word problems.
Example 1
In a word problem when both displacements and velocities are given in i-j notations, the pupils have difficulties in interpreting the information. |
4.3.2
Physical Meaning of Relative Velocity
It is a common problem raised by the teacher participants and the students that there is a great deal of difficulty in distinguishing true velocity and relative velocity. Consequently, it becomes a rather difficult task for the pupils to translate the information into drawing a correct vector diagram.
Furthermore, it is difficult for pupils to visualize (and for teachers to explain) the concepts related to relative velocity, for example, the velocity of one object relative to another; the velocity of airplane in still air.
4.4 Difficulties related to Mathematics
While the above problems tend to occur across most pupils learning the chapter on relative velocity, the weaker pupils also have additional difficulties involving mathematics related items. Some of the problems that were mentioned by the teacher participants are listed below:
i. the use of angles formed by non-parallel lines, especially when the line segments (drawn) to represent the lines do not appear to intersect;
Figure 2: Students’ difficulties with angles between two nonintersecting line segments
ii. the conversion between vectors in i-j form and column vector form and the related concepts of vectors in kinematics form (e.g. the magnitude of the velocity vector gives the speed; the magnitude of the displacement vector yields the distance from the origin O);
iii. the use of bearings of locating positions;
iv. performing vector addition and subtraction by using vector diagrams; and
v. the use of sine and cosine rules in solving triangles.
Copyright (C) 2006 HKIEd APFSLT. Volume 7, Issue 2, Article 8 (Dec., 2006). All Rights Reserved.
