Friday, February 21, 2014

Supplemnetary Programme for Capacity Building of Physics Undergraduate Students



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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