Physics Teaching and Learning Through Problems
Bulletin of Indian Association of Physics Teachers, 1 (12) (2009)
H. C. Pradhan
HBCSE,
TIFR, V. N. Purav Marg, Mankhurd,
Mumbai –
400 088
A. K. Mody
V. E.S. College of Arts, Science and Commerce, Sindhi
Society,
Chembur,
Mumbai – 400 071
The existing scenario in physics teaching and
learning:
One of the complaint from teachers of all
sciences is voiced succinctly in the joint report by all the distinguished
science academies in the country, Indian Academy of Science, Indian National
Science Academy and National Academy of Science in India notes (Resonance Dec
2008): ‘most students who join the science stream as undergraduates are
neither willing to nor capable of finally taking up an academic career (R&D
and/or teaching)’.
Clearly all the
academies are dissatisfied about quality of students. This demands urgent
efforts to improve the situation.
Way out for Physics teaching and learning:
We tried one such effort. This was based on a
non-traditional approach at teaching basic physics through problem solving to
build capacity of undergraduate students.
By capacity in context of Physics, we mean
capability of comprehension of knowledge, its application, analysis and
synthesis. The mode of building capacity that we have adopted is problem
solving. Thus in operational terms, we consider capacity as problem
solving ability.
What does problem solving achieve
in Physics?
1.
Problem/s makes students appreciate/justify theory.
2.
Problems teach students how to exploit symmetries:
physical, geometrical, abstract mathematical.
3.
Problems of interdisciplinary type/ introducing higher
level facts through problems using lower level physics.
4.
Order of magnitude calculation type problems give them
some insight into importance of values.
5.
Open-ended problems make them think critically and be creative.
6.
Problems illustrate applications.
7.
Problems to strengthen mental abilities. This allows
them to comprehend theories at higher level better.
8.
Once students can correlate principles, observations
and other physical quantities, their grasp of experimental techniques
automatically gets enhanced.
9.
As noted by Brownstein(2001)(on Wikipedia), learner
should constantly be challenged with tasks that refer to skills and knowledge
just beyond their current level of mastery. This will capture their motivation
and build on previous success in order to enhance the confidence of the
learner.
10. In preface to his famous
lecture series, Nobel laureate physicist Richard Feynman(1991) has noted, ‘I
think one way we could help students more would be putting more hard work into
developing a set of problems which would elucidate some of the ideas in the
lectures. Problems give a good opportunity to fill out the material of the
lectures and make more realistic, more complete, and more settled in the mind
the ideas that have been exposed’.
Our
Experiment:
We have designed
and conducted a capacity building course using basic physics for undergraduate
students by selecting special problems and following Reddish(1994)
termed them as touchstone problems, although we have used them in
different sense than Redish.
By a touchstone problem we mean a problem which satisfies more than one
of the following criteria.:
(i)
A problem which incorporates basic principle/s
(ii)
A problem which is attractive enough or is rich in
context
(iii) The
problem should be sufficiently difficult but not too difficult to put students
off.
(iv) The problem should require steps that are not
mechanical but involve some decision making
(v)
The problem should have a reasonable goal
(vi) The
problem should guide students to comprehend the topic and/or application.
Example:
An elevator ascends with an upward acceleration of 1.2
m/s2 . At the instant its upward speed is 2.4 m/s, a loose bolt
drops from the ceiling of the elevator 2.75m from the floor. Calculate
a)
the time of flight of the bolt
from the ceiling to the floor of the elevator.
b)
the displacement and the
distance covered by the bolt during the free fall relative to the elevator
shaft. (Irodov 1988)
Mechanism of problem solving:
If a touchstone problem is difficult, it can be broken up in to parts. We
have developed auxiliary problems corresponding to each part. Auxiliary
problems or smaller problems to comprehend the touchstone problem is the
technique we are using. The students are guided to solve these auxiliary
problems, so that they are able to comprehend the touchstone problem as a whole
and solve it.
This also involved (1) guiding students to create appropriate
visualization or mental picture or (2) pointing to them the precise auxiliary
problem (3) creating cognitive conflict with their misconception or (4)
involving them in a reflective metacognitive discussion so as to
arrive at a strategy to solve the problem.
The following are the smaller or auxiliary problems
used.
1.
The nucleus of Helium atom (a- particle) travels along the inside of a straight hollow tube 2.0 m
long, which forms part of a particle accelerator.
a.
If one assumes uniform
acceleration, how long is the particle in the tube if it enters at a speed of
1000 m/s and leaves at 9000 m/s?
b.
What is its acceleration during
this interval?(Halliday 2005)
2.
A helicopter ascending with a
uniform vertical velocity of 5 m/s was used to drop food packets for people
marooned in a flooded colony. If the packets reach the ground in 10 s, find the
height of the helicopter when packets hit the ground.
3.
In above problem 2, what if the
packets were dropped by stationary helicopters? In this case what would be time
of flight?
4.
A particle is projected from
the top of a tower upward with initial speed u, reaches the ground after time t1
. The same particle projected downward with the same sped reaches the ground
after time t2 . Show that if the particle is just dropped will reach
the ground in time Öt1t2 .
In this case auxiliary problem 1
helps student overcome inertia of solving problems. Problem 2 and 3 helps
student learn about how to chose initial speed and its effect on time and
trajectory and problem 4 helps students realise effect of initial speed on
displacement.
Students were asked to solve
problems and no formal
teaching of the basic principle was carried out as in a conventional class. Students were not shown any
method of solving problem but based on their own previous knowledge and based
on the books made available to them they solved the problems. They actually
learned physics through solving problems.
The teaching method and
strategy varies from problem to problem and depends on the area of physics
being covered by the problem. It also varies with needs of the individual
student and also involves on the spot creating activity for student to help
develop insight into the physics and the process they are going through to
cater to individual difficulty and need. This strategy has proved very
effective in building capacity and have motivated students to pursue physics
seriously.
Here the instructor played the
role of a facilitator and helped learners to develop their own understanding of
concepts. The learning environment was designed to support (through books made
available and guided interventions) and challenge (through problems and counter
questions) the learner’s thinking. Thus learning became an active process where
the learners learned to discover principles, concepts and facts themselves.
Students learned by building upon knowledge they already possessed
themselves and guided interventions were used to correct errors, which crept in
their understanding. Students were not given answers to any questions, but were
guided (using interventions like auxiliary problems, counter questions,
cognitive conflicts) to converge to the answer themselves.
The course was conducted during April after
students were through with their second term examinations and it was not a part
of their main curriculum and did not influence their assessment. Thus, the
course was supplementary in nature, in the sense that it did not
interfere with their regular college term, and supplemented their regular
physics studies. Such a course can be run by any college teacher in physics for
his/her students and is therefore replicable anywhere in the country. The entire course was conducted covering
topics from basic physics with similar problems. The
choice of topics, time which can be devoted to each topic depends on situation
from year to year on need basis. Most of the problems required one or
more of the above-mentioned strategies to be used. The problems were of the
level of standard textbook ‘Fundamentals of Physics’ by Halliday, Resnik and
Walker (2005) and Young (2004). The problems were chosen from the textbooks
mentioned, competitive exams like JEE (Joint Entrance Exam for admission to
Indian Institute of Technologies), Physics Olympiads and some were specially
designed to achieve the purpose. It should be noted
here that there is no unique choice of touchstone or auxiliary problems.
Instructor can choose as per his/her convenience based on the above mentioned
criteria.
Testing Effectiveness of
the problem solving course:
To test the effectiveness of the
course, we conducted a pre-, a post- and a retention test before the course,
after the course and about two months after the course respectively.
We found that the average test
score in the post-test was greater than that in the post-test to a high level
of significance. The score in the retention test was statistically not
different from that in the post-test. Thus, this method is found to build
capacity of students to do basic physics with a significant amount of
retention.
We also observed improvement in
behaviour, belief and motivation level of students. Overall the course succeeded
in changing the belief of students from ‘I can not’ to ‘I can’ and from
‘Physics is difficult’ to ‘I see the correct way to learn Physics’.
Suggestion:
A capacity building course based
on problem solving such as the one we reported above can certainly be conducted
as a supplementary course during vacations in our colleges. Further, the method
can also be adopted even during the regular college terms via tutorials. We
need to revive tutorial system and adopt it to problem solving, especially for
teaching basic physics.
References:
1.
Joint Science Education Panel (IASc, INSA, NASI), “A
position paper”, Resonance 13 (12) 1177 – 1190 (Dec 2008)
2.
R. P. Feynman, R. B. Leighton and M. Sands, The Feynman
Lectures on Physics, (Narosa Publishing House, New Delhi 1991)
3.
Edward F. Redish, “Implications of cognitive studies
for teaching Physics,” Am. J. Phys. 62 (9), 796 - 803 (1994)
4.
I. E. Irodov, Problems in General Physics MIR
Publication (1988)
5.
Halliday, Resnick and Walker, Fundamentals of Physics
by 6th Ed., John Wiley & Sons (2005)
6.
Young and Freedman , “Sears and Zeemansky’s
University Physics,” 11th Ed., Pearson Education (2004)
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