MISCONCEPTIONS IN MECHANICS

Anne Droogan, St Michael’s Grammar School, Lurgan and Ken Houston, University of Ulster, Jordanstown.

Introduction

This paper reviews some of the research on mechanics teaching and the misconceptions that 'A' level students have regarding mechanics and modelling. These ideas should help teachers to challenge students' alternative conceptions and improve their understanding of mechanics.

Research has shown that students bring to the classroom their own intuitive ideas about the physical world. These ideas may have been deduced from personal experiences or even from what they have read or seen on television. Whenever these ideas are misconceptions teachers should try to ensure that they are challenged and discussed immediately, otherwise students will find it very difficult to understand completely the processes and modelling in the physical world.

Successful learning of mechanics depends on three aspects which are,

a) being able to understand the principles involved,

b) being able to cope with mathematics,

c) being able to relate these two aspects to everyday life.

It has been demonstrated that some students can cope very well with the mathematics involved but they are not able to relate their knowledge to everyday life. These students have probably been successful by learning techniques which solve a problem, but they have not really understood the principles involved.

Some of this research had been conducted by Berry and Graham (1990, 1991, 1992), Jagger (1988) and Trowbridge and McDermott (1980, 1981). Their work revealed that there were misconceptions in the students' understanding of mechanical concepts, in particular, velocity, speed, acceleration and force. While dealing with the concepts of velocity and speed, some students used a position criterion to determine speed, while others either associated ‘being ahead’ with ‘being faster’ or believed that when one object catches up with another object and is along side it they both have the same speed. In dealing with acceleration a similar misconception to the above was found, i.e., some students used a position criterion to determine acceleration. Others either associated the direction of acceleration with the direction of motion or thought that increasing speed also meant increasing acceleration. Regarding the concept of force, some students postulated a force in the direction of motion in order to sustain motion. Others thought that force was proportional to velocity rather that force was proportional to acceleration. It was also obvious that students inserted forces onto diagrams from habit rather than on the basis of understanding. The ideas discussed below may help to develop a teaching strategy which addresses these weaknesses.

The topics considered were:- Motion in a Horizontal Circle, Motion of a Particle in a Vertical Circle and Simple Harmonic Motion. The literature suggests two approaches that could be adopted: the use of concept questions, (which Berry and Graham had recommended), and the use of experiments. The aims and objectives of our study were as follows:-

• To use equipment and concept questions to introduce the main concepts in a topic.
• To determine how useful equipment was in teaching mechanical concepts and ideas.
• To find out if by the use of concept questions and equipment the students had a clearer understanding of the mechanical ideas and principles.
• To discover if through these two approaches, the students were able to overcome their misconception and false ideas.
• To use discussion and group work as a method of trying to overcome any problems the students encountered.

Methodology

The method of introducing a concept was mainly by the use of an experiment along with an appropriate worksheet. Some of the worksheets were based on similar experiments taken from the book 'The Teacher’s Guide to the Leeds Mechanic Kit'. The worksheets were not all intended to be 'mathematical' as we wanted the students to write down what they had observed or thought and not to get 'bogged down’ with algebra. At all times, emphasis was placed on what the students were discussing and what explanation they had written.

Motion in a Horizontal Circle.

For Motion in a Horizontal Circle, an experiment based on the 'Conical Pendulum' was used. The worksheets were structured in a way to allow the students to comment on what they noticed or observed. Very little algebra was involved. Below is a sample of some of the questions which the students were required to answer while carrying out the experiment:-

• What assumptions are being made when setting up this model?
• If the string has tension T, in what direction does T act?
• Is the bob moving with constant acceleration?
• What force cause the acceleration?
• In the equation cos a= g /L w², what happens to a as w increases?

Motion in a Vertical Circle.

For Motion in a Vertical Circle, a 'loop the loop track' was used along with appropriate worksheets. (This experiment, in particular, was found to be very worthwhile and beneficial for the students.) Again, here are some of the questions on the worksheets:-

• Explain the motion of the marble as it moves along the track.
• What forces act on the marble as it moves along the track?
• When the marble leaves the track, describe with the aid of a diagram, its motion.
• What assumptions are being made when setting up this model?
• Which of the following affect the minimum value of h, where h is the vertical height of the marble in the loop, a) mass of the marble, b) size of the marble, c) radius of track?

Simple Harmonic Motion.

For S.H.M. the students carried out an experiment involving masses oscillating vertically on an elastic spring. Again the worksheets concentrated on the students writing down their observations and explaining in words what they noticed. Only after the observations and relationships between the appropriate variables were discussed was algebra introduced. Some of the questions on the worksheets were:-

• When the mass is oscillating is the position of the central point the same as the position in which the mass would hang in equilibrium?
• Set the mass in motion and find the period, T, of the oscillation.
• As the mass moves in the downward direction from the equilibrium position, explain in words what happens to its displacement, x.
• As the mass moves in the downward direction what do you think happens to its velocity and acceleration?

Throughout the teaching of these three topics regular discussion between the pupils and the teacher was encouraged. Many concept questions were asked in order to challenge the students misconceptions and make them rethink their incorrect ideas. Students were encouraged to write in words what they observed as it is felt that this method of approach helps the students to obtain a clearer understanding of the particular concept, or equation, and what it represented.

Reflection

After having reviewed and analysed these two methods of approach in the classroom, we found that they did work in practice. The students enjoyed the practical approach and discussing the principles involved. The use of concept questions throughout the teaching of a topic proved vital for the students and the teacher. This type of question encouraged the students to think about what was happening and more importantly why it was happening. However, there were certain students who still had problems when they were asked to answer a typical 'A' level question. These students were able to set up the model (unlike on previous occasions) and label the forces correctly in an appropriate diagram. They were also, on most occasions, able to form the equations but when it came to the algebra or a 'twist' in the problem, their understanding was limited.

Groupwork tends to be used quite often at G.C.S.E. level and rarely at 'A' level, which is a pity. We believe that this type of approach is very worthwhile, in particular for the less able students, as the more able students were able to explain the idea behind the concept involved. Groupwork also led to further interesting questions which the students had proposed. The practical work provided 'hands-on' experience for the students and allowed them to discuss what was happening. It also allowed the students to 'test out' their beliefs, for example, if the marble (during Motion in a Vertical Circle) was released from a height of 2r, would it complete the loop? Surprisingly some students were not able to answer this question correctly.

There were limitations and some drawbacks to the practical approach. The main ones were obviously time and resources. As we all know, time is of the essence, as there is a syllabus to cover. However, we would strongly recommend the use of concept questions and allowing the students time to write down what a particular equation actually meant. We would advise the use of practical work where possible as the students should get 'hands-on' experience on some occasions during their course.

RECOMMENDED BOOKS.

MEW GROUP, Exploring Mechanics : Teachers Book, John Berry, Centre for Teaching Mechanics, Plymouth University.

The Teacher's Guide to the Leeds Mechanics Kit, Mechanics in Action Project (Leeds), School of Mathematics, The University of Leeds, Leeds, LS2 9JT.

REFERENCES

Berry, J. and Graham, T. (1990) Sixth form Students' Intuitive Understanding of Mechanics Concepts, Teaching Mathematics and its Applications, 9 (2), 82-90.

Berry, J. and Graham, T. (1991) Using concept questions in teaching mechanics. International Journal of Science Education, 22 (5), 749-757

Berry, J. and Graham, T. (1992) Sixth form Students' Intuitive Understanding of Mechanics Concepts: Part 2, Teaching Mathematics and its Applications, 11 (3), 106-111.

Jagger, J. (1985) A review of the Research into the Learning of Mechanics, Studies in Mechanics Learning, edited by A. Orton, University of Leeds.

Trowbridge, D.E. and McDermott, L.C. (1980), Investigation of student understanding of the concept of velocity in one dimension, American Journal of Physics, 48 (12), 1020-1028.

Trowbridge, D.E. and McDermott, L.C. (1981), Investigation of student understanding of the concept of acceleration in one dimension, American Journal of Physics, 49 (3), 242-253.

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