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Asia-Pacific
Forum on Science Learning and Teaching, Volume 6, Issue 2, Article 7
(Dec., 2005) Tin -Lam TOH On in-service Mathematics teachers' content knowledge on kinematics
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Asia-Pacific
Forum on Science Learning and Teaching, Volume 6, Issue 2, Article 7
(Dec., 2005) Tin -Lam TOH On in-service Mathematics teachers' content knowledge on kinematics
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Introduction
Anecdotal evidence during my school attachment of the past few years in the various schools has shown that many Mathematics teachers in the secondary schools, especially those teachers who do not teach Physics or Applied Mathematics as their second or third teaching subject, might not have a sound concrete understanding of kinematics concepts. This can also be clearly seen from my personal interaction with some secondary school students. Many of the students tend to have the opinion that the physics taught in Mathematics (which the students refer to the practical graphs section of Mathematics syllabus) is somewhat conceptually different from the physics that they learnt in their science subjects (which they refer to the kinematics section of the Newtonian Mechanics of their Physics syllabus) in their curriculum.
In the Mathematics O-Level syllabus before the year 2001, all kinematics problems were classified under the section on Practical Graphs in the chapter of Graphs. Here the students were required only to extract information and perform computation based on either the displacement-time graph or the velocity-time graph. The students must be able to obtain numerical values of the distance traveled, speed, velocity or acceleration without much concern or interpretation needed of the moving particle. In short, students were required merely to perform simple computations to obtain their answers without much qualitative knowledge of the motion of the particle. Practically in all the related examination problems, the particles being considered are always moving in one dimension along a straight line without changing direction. This is a good illustration that mathematics teachers are basically teaching the practice of routine skills rather than mathematical problem-solving (see, for example, Andrews P., 2002), mainly driven by the format and structure of the examinations.
To make matters worst, under such setting, the knowledge of kinematics of one-dimensional motion could even be wrongly generalized to two-dimensional motion. For example, a particle moving with constant speed along a straight line without reversing its direction of travel experiences zero acceleration. One might wrongly generalize to two-dimension that a particle moving with constant speed experiences zero acceleration, even though the direction may not be kept constant (for example, in the case of circular motion with constant speed).
I surveyed a collection of the Practical Graph questions found in the Mathematics examination questions set by the local secondary school teachers in the year end examinations of the past few years for the Elementary Mathematics syllabus. It is evident that many teachers did not even indicate that the moving particles whose motion graphs are shown are moving along a straight line (which they must assume in solving the question)! This shows that the teachers might have treated the statement "the particle is traveling along a straight line" without realizing the related kinematics concepts in motion in higher dimensions.
In the new Additional Mathematics syllabus recently introduced in 2001, more intensive knowledge of kinematics concepts is required of both the teachers and students. This is especially true with the introduction of the topic Relative Velocity into the Additional mathematics syllabus. Mathematics teachers' vague or inaccurate knowledge of kinematics is no longer sufficient to teach the content of this chapter.
As many local in-service teachers did not have sufficient subject content knowledge of Relative Velocity in specific and kinematics in general, I was tasked to design a series of mathematics content workshops for the teachers to "top-up" their subject content knowledge. While it is important that teachers are able to take into account pedagogical considerations in their teaching and how to enhance students' understanding through the use of Instructional Technology (for example, Toh, 2003) or to motivate their students, it is of immediate importance and top priority that teachers themselves have a sound subject content knowledge of this topic and the foundational knowledge of kinematics. In the process of planning suitable materials for the workshops, I felt it necessary to have an understanding of their subject content knowledge of kinematics. This motivated me to conduct a survey on their subject content knowledge of kinematics.
This paper reports the result of the survey conducted on a group of twenty six in-service teachers from different schools in Singapore. This paper begins with a background, discussion of the method of survey, followed by results and discussion. Hopefully the finding of this study could be useful for any future planning of in-service courses to help Mathematics teachers to be better equipped in teaching kinematics related topics in the Mathematics syllabus.
Copyright (C) 2005 HKIEd APFSLT. Volume 6, Issue 2, Article 7 (Dec., 2005). All Rights Reserved
