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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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2. Background
2.1 Brief description of the mathematics teachers’ background
First we present a brief outline of the background of the mathematics teachers’ content knowledge. The mathematics teachers can be classified under three categories: (1) teachers who majored or minored in mathematics in their undergraduate days; (2) teachers who were from engineering courses; and (3) teachers who were not from mathematics or engineering background.
With reference to the mathematics teachers who majored in mathematics in their undergraduate days : as they were taking university mathematics courses, many of them did not have contact with concepts in mechanics, relative velocity in particular, especially if their second teaching subject is not physics.
The second group of mathematics teachers, who were from engineering background, might have sufficient exposure with mechanics in their engineering courses. However, a talk with a few of my teacher trainees in National Institute of Education showed that they were not exposed much to the concepts involving kinematics leading to relative velocity.
The third group of mathematics teachers, who were from non-mathematics and non-engineering background, had virtually no experience with mechanics concepts in their undergraduate days.
It is no wonder that many mathematics teachers in schools might have difficulties with kinematics concepts and relative velocity. This was supported by the survey on the inservice teachers’ misconceptions in kinematics (see Toh, 2005)
2.2 Teachers’ Pedagogical Content Knowledge
Current
research has shown that what teachers know has a direct impact on the quality of
students learning (see for example Muijs and Reynolds, 2000; Wenglinsky, 2000;
Ling et al, 2006). Teachers must be able to anticipate the possible errors and
misconceptions that their students might have for each of the different topics
in the syllabus (for example, Chua & Wood, 2005). Only by the
anticipating of the pupils’ possible misconceptions can teachers be able “to
use a number of different strategies and how to coordinate between strategies
depending on the teaching context” (Abd Rahman N, 2004). It is also equally
important that the teachers’ own misconceptions of the various topics in the
syllabus (for example, see Toh, 2005 on misconceptions in kinematics) must be
rectified.
It is recognized that in order to teach well, a mathematics teacher must know a great deal of mathematics (Usiskin, 2001), on top of having a thorough mastery of the content knowledge of the material in the existing mathematics curriculum. The types of mathematics knowledge that a mathematics teacher needs to know are discussed in detail with examples by Usiskin (2001).
In specific to relative velocity, a mathematics teacher should have a good grasp of the following subtopics (Toh, 2004)
1. Concepts in vectors and kinematics (including familiarity of using i-j notation and column vector notation for displacement, velocity and acceleration)
2. Basic concept and definition involving relative velocity
3. On crossing a river (involving one moving object)
4. Concept of relative velocity and the replacement displacement of two moving objects
5. Relative velocity and the problems of interception of two moving objects
6. Relative velocity and the problems of closest approach.
According to Usiskin (2001), a teacher needs to know more content knowledge than their pupils; this knowledge includes generalization and extension from what is required in the syllabus. Thus, even though the problem of closest approach (item 6 above) is not required in the O-Level curriculum, teachers are expected to have a sound content knowledge on this (Toh, 2004).
2.3 Pupils’ Difficulties in Learning Science related concepts
According to Driver (1983), pupils’ interpretation of science concepts is often at odds with the scientists’ views. Pupils’ preconceived ideas influence them to interpret new learning experiences, and it is exactly these preconceived ideas serve as barrier for their future progress. To quote Driver (1983) exactly:
“...... all its experiences of pushing, pulling, lifting, throwing, feeling and seeing things stimulate the ability to make predictions about a progressively wider range of experiences. By the time .......... it has already constructed a set of beliefs about a range of natural phenomena. In many cases, these beliefs or intuitions are strongly held and may differ from the accepted theories which science teaching aims to communicate.”
Thus, effective teaching should involve teaching that entails teaching strategies that take into account these pupils’ misconceptions due to preconceived ideas. These strategies should also emphasize conceptual understanding instead of rote learning (Abd Rahman N, 2004).
