Supplementary Programme for Capacity Building
of Physics Undergraduate Students
Physics Education, 26 (2) 93-98, (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
We report on a Supplementary
Programme of Capacity Building for Physics Undergraduate Students, which we
have developed and implemented. The
programme, run as an intensive vacation course, is aimed at developing
students’ knowledge of basic physics through problem solving. The strategy was to build for each topic
covering basic physics a central ‘touch stone’ problem, around which
supplementary problems are woven. Inputs for the strategy also come from the work
by Allen Shoenfeld.1 The four
weeks long course was given to about 30 undergraduate physics students from
different colleges in Mumbai. The results, which will be presented, were quite
encouraging. The course may serve as a
model of capacity building for science students, which may result in better
manpower inputs to research and professional institutions in sciences and work
towards fulfilling an acute need currently felt in the country.
A 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: ‘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)
2’.
Thus there is a genuine need for building up
motivation and confidence of undergraduate students in science subjects in the
whole country. The way to do this is through capacity building efforts. We have
developed a course that will serve as a model for such efforts. Further, it
will provide a practical model, as it is a supplementary course, supplementing
the regular studies in the college and is conducted without disturbing the
regular schedule.
We have identified what is required by way of content
and instruction in a programme meant to build ‘capacity of undergraduate
physics student’. It is not practical to conduct such a programme during the
regular term work of the college and therefore has to be supplementary, i.e.,
additional to the term work and not conflicting with it. We term the programme
as ‘Supplementary Programme for Capacity Building in Physics’.
Our model to build capacity is through
problems. Arons3 has noted that a quick and casual assertion of the
character of interaction (or phenomenon) destroys a significant learning
experience for the student and marks the loss of a valuable pedagogical
opportunity. He suggested way of asking questions or posing problems in which
students have to decide what to calculate and interpret result. He felt that
such an approach would greatly improve student’s learning, comprehension and
intellectual self-confidence. This can be considered as Aron’s description of
Capacity.
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.
Choice of Problems:
We have tried to incorporate these ideas in
selecting our special problems for the course designed and following
Redish4 termed them as touchstone problems.
By 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) 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.
We have
formulated the course on the lines of a problem-solving course run by
Schoenfeld1 for undergraduate students in mathematics. We used
primarily problems similar to or based on those in the textbooks by Halliday
and Resnick5 and Sears and Zeemansky6. Some problems have been taken from JEE and
Physics Olympiad exams and some have specially been designed for the purpose. Our
choice of problems was also based on years of experience of working with
students and knowledge of their strength and weaknesses.
Redish7
has used as touchstone problems many elementary problems that illustrate basic
idea of the topic. On the other hand we have used as touchstone problems ones
that for any topic cover the methodology and all possible concepts involved
with the formalism of that topic that follows one or more criteria mentioned
above. This is because students we deal with already had an exposure to basic
Physics course during their class XI and XII.
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. 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
involves (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.
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.8
Tasks involved
in this problem are:
1. To identify the reference frame. In this case students
can work with either of two different frames: (1) elevator and (2) ground based
(what problem specifies as elevator shaft).
2. To specify value of velocity, acceleration and
displacement using proper sign convention in each frame.
3. To realize that time is same (Galilean invariant) in
both the reference frames.
4. To be able to understand the difference between distance
traveled and displacement.
As can be
seen this problem satisfies all the criteria of a Touchstone problem and gives
a thorough picture of use of Kinematical equations that are to be used for
motion with constant accelerations.
The smaller problems,
which could lead them to understand this, require: students to know which equation to be used
and how to use it, difference between distance and displacement. How to choose
initial value of a quantity and to make a choice of proper sign.
The following are the smaller 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?5
This problem is just an
introductory type and involves identifying quantities their sign and use of
proper kinematical equations. A general tendency of a novice problem solver is
to give more importance to unnecessary details. In this problem students tend
to worry about helium nucleus instead of focusing on kinematical aspects. In
that sense problem serves to put students on the track.
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.
The purpose of this problem no.2 and 3 is to make
students understand choice of initial speed.
At this stage
students make mistake with initial speed. A question as to what is the height
of the helicopter when packet was dropped makes them realize their mistake.
3. In P(2) what if the packets were dropped by stationary
helicopters? In this case what would be time of flight?
Students here realize importance of initial
speed and its effect on time.
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 speed reaches the ground after time t2.
Show that if the particle is just dropped will reach the ground in time Öt1t2.
This problem was chosen to make students
realize effect of initial speed on displacement. Also to realize that in all
three motions displacement is same although distance traveled differ.
The course
was conducted before the summer vacation. Student’s progress throughout the
course, their progress, qualitative change in their behaviour, attitude and
most importantly their belief have been noted. In addition a pre-test,
post-test and retention test were conducted to test students’ progress and
effectiveness of the method used. It should be noted that at no stage any
formal teaching was carried out. Pre-test was conducted before the course and
post-test was conducted at the end of the course. One-day preparation break was
given before the post-test. The retention test was conducted after the summer
vacation was over and normal course work had started. All the indicators,
qualitative and test result indicated effectiveness of the problem solving
approach with the kind of problems chosen. The test results are as shown below.
Result
Summary:
The following histogram shows comparison of pre- and post-test performance. As can be seen, the pre-test distribution is skewed to the right. Post-test distribution shows all the peaks shifted to the right indicating progress made by students due to the treatment given. Also note that the post-test distribution is more normal. Even the top two students’ performance has improved.

Series
1: shows performance of students in
pre-test and
Series 2: shows performance of students in post- test .
We checked the difference
between the pre and post test scores of the students by Student’s t-test.
Since the same group took the tests, it was appropriate to use the correlation
group formula rather than the independent group formula :
where m1 = mean of pre-test scores

m2 = mean of
post-test scores
and sE = Standard error of the difference between
mean of two correlated groups
= 

where s1 = standard
deviation for the pre-test score
s2 = standard
deviation for the post-test score
N1 = number of students
who took pre-test
N2 = number of students
who took post-test
and r12 = coefficient of
correlation between the pre and the post test scores.
The table below gives the values
obtained.
Test |
Number of Students (N) |
Average Marks (m) |
Standard Deviation (s) |
Pre |
27 |
14.05 |
10.48 |
Post |
27 |
23.85 |
10.18 |
Difference
between the mean = 9.79
Correlation
between the tests = 0.739
Standard error (correlated group) of the difference =
1.438..
t = 6.812
It is
found that the t-value is significant at a level higher than 0.1%.
We have also
worked out the correlation between the post-test and the retention test. As
explained earlier, the retention test had to be held after a sufficiently long
duration after the post-test. The retention test had to be conducted in June
after the vacation and the college term work for the next academic year had
started. The students were from different colleges in Mumbai, and even some
were from a different subject. As a result only 14 students took the retention
test. Their motivation in taking the test seems to be somewhat affected due to
a long break in between. Some of the students were from other colleges which
may be one of the factor that could influence motivation as regular course work
had already begun. The mean score in the retention test (19.39) was lower than
the score in the post-test. The difference between the scores was statistically
insignificant and the correlation between the post-test and the retention test
was 0.814, which is quite high. These results indicate a fair amount of
retention.
Conclusion:
We carried out supplementary programme based on
meaningful problem solving. The effectiveness of the programme to teach physics
through meaningful problem solving was tested through pre-post test mechanism
and found significant improvement in students’ capacity as measured through
their problem solving ability.
References:
1. Alan
H. Schoenfeld: Mathematical Problem Solving (Academic Press,INC 1985)
2. Joint
Science Education Panel (IASc, INSA, NASI), “A position paper”, Resonance 13
(12) 1177 – 1190 (Dec 2008)
3. A.
B. Arons, “Phenomenology and logical reasoning in introductory physics course,”
Am. J. Phys. 50 (1), 13 - 20 (1982)
4. Edward
F. Redish, “Implications of cognitive studies for teaching Physics,” Am. J.
Phys. 62 (9), 796 - 803 (1994)
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)
7.
Cummings et al; in Understanding Physics : John
Wiley and Sons (2004)
8. I.
E. Irodov, Problems in General Physics MIR Publication (1988)
Paper appeared in: Physics Education, 26,
(2) 93-98, (2009)
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