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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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Results
The response of the in-service teachers were collected and are summarized in the fourth and the fifth columns of the Table 3 below. The second column gives the correct answer to the corresponding question in Table 2 and the third column states the correct reason for the answer of each of the questions.
Not necessarily true when the object does not travel in the same direction throughout
An object traveling with non-zero acceleration may not be traveling with the same direction, hence it may have an acceleration Displacement of a particle indicates the position of the particle, not the distance it travels. It is possible that an object traveling with minimum velocity may be traveling the fastest.
It is not true if the object is not traveling in the same direction. Acceleration should be defined as the rate of change of velocity with respect to time, not "increase"
The sign of velocity indicates the direction it is traveling, not the increase in speed.
Displacement indicates the position, not the rate of change of speed The statement follows from definition The statement follows from definition
It can be proved that the speed equals the magnitude of its velocity. There is no statement that the particle travels in the same direction throughout Velocity is a vector quantity, hence the direction needs to be stated Table 3: Summary Results of the Teachers' Response
There were four participants who responded with FALSE for Question 1 but substantiated their answers with wrong reasons, hence as mentioned in the preceding paragraphs these responses were classified under "Wrong Response". Since air resistance is not known, the teachers felt that it was not possible to conclude that the particles travel with any acceleration.
From the data collected above, the top four questions with the greatest number of wrong response were Question 1 (96% wrong response), Question 5 (88% wrong response), Question 12 (88% wrong response) and Question 2 (85% wrong response). The four questions with the greatest number of correct response were Question 10 (100% correct response), Question 11 (96% correct response), Question 13 (96% correct response) and Question 9 (92% correct response).
Verbal Response
During a casual talk after the survey with four participants, three of the participants mentioned that they had never encountered mathematical problems involving motion in two dimensions in their teaching career. That was the reason why they had responded to the questions with only one dimensional motion in mind. Most likely they had forgotten the further knowledge of kinematics which they had learnt in their undergraduate days.
One participant mentioned with regard to Question 12 that he was used to computing acceleration as the gradient of the speed-time graph. He had not taken into consideration that the particle might not be traveling in the same direction throughout the motion. He further added that he would not know how to handle the case of non-uniform direction.
Copyright (C) 2005 HKIEd APFSLT. Volume 6, Issue 2, Article 7 (Dec., 2005). All Rights Reserved
