Constructivism applied to physics teaching for capacity building of undergraduate students

Constructivism applied to physics teaching for capacity building of undergraduate students

University News, 47 (21) 4-10, (2009) 

H. C. Pradhan

Centre Director

HBCSE, TIFR, V. N. Purav Marg, Mankhurd

Mumbai – 400 088

Tel: (022) 25562132

e-mail: hcp@hbcse.tifr.res.in

A.  K.  Mody

Lecturer (SG)

V. E.S. College of Arts, Science and Commerce, Sindhi Society

Chembur, Mumbai – 400 071

Tel: (022) 25227470

e-mail: atulmody@gmail.com

We report on a Supplementary Programme of Capacity Building for Physics Undergraduate Students, which we have developed and implemented using a constructivist approach.  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 ‘touchstone’ problem, around which supplementary problems are woven. The course was given to about 30 undergraduate physics students from different colleges in Mumbai. It was four weeks in duration and the students met for about seven hours per day for six days a week.  The results, which are presented, were quite encouraging.  The course may serve as a model of capacity building for science students. This may result in better manpower inputs to research and professional institutions in sciences and work towards catering to a need currently severely 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 (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)’.

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 conducted a supplementary capacity building course for students of affiliated colleges of Mumbai University studying in first year and second year B.Sc. This course was conducted with a constructivistic approach and is expected to 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 during vacation without disturbing the regular schedule.

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.

Characteristics of a constructivistic approach are discussed in details by Neeru Snehi (2008 ). She has emphasized the need to orient teaching along the constructivism. As an Indian college set up does not support in its regular schedule, innovative teaching methods of this kind we conducted a supplementary programme to try it out. Following is the characteristic as listed by Snehi. These are not presented in hierarchical order.

·         Multiple perspectives and representations of concepts and content are presented and encouraged.

·         Goals and objective are derived by the students or in negotiation with the teacher or system.

·         Teachers serve in the role of guides, monitors, coaches, tutors and facilitators.

·         Activities, opportunities, tools and environments are provided to encourage metacognition, self analysis –regulation, -reflection and awareness.

·         The student plays a central role in mediating and controlling learning.

·         Learning situations, environments, skills, content and tasks are relevant, realistic, and authentic and represent the natural complexities of the ‘real world’.

·         Primary sources of data are used in order to ensure authenticity and real-world complexity.

·         Knowledge construction and not reproduction is emphasized. It takes place in individual contexts and through social negotiation, collaboration and experience.

·         The learner’s previous knowledge constructions, beliefs and attitudes are considered in the knowledge construction process.

·         Problem-solving, higher order thinking skills and deep understanding are emphasized.

·         Errors provide the opportunity for insight into student’s previous knowledge constructions.

·         Exploration is a favoured approach in order to encourage students to seek knowledge independently and to manage the pursuit of their goals.

·         Learners are provided with the opportunity for apprenticeship learning in which there is an increasing complexity of tasks, skills and knowledge acquisition.

·         Knowledge complexity is reflected in an emphasis on conceptual interrelatedness and interdisciplinary learning.

·         Collaborative and cooperative learning are favoured in order to expose the learner to alternative viewpoints.

·         Scaffolding is facilitated to help students perform just beyond the limits of their ability.

·         Assessment is authentic and interwoven with teaching.

The key idea of constructivism came from distinguished cognitive psychologist, Jean Piaget(1972). According to these ideas, children construct their knowledge. They are not ‘taught’ but they ‘learn’. Edward Redish (1996) has explicitly summarised these ideas through four principles, which we present below. Redish had teaching and learning of Physics in mind.

Principle 1:The Constructivistic Principle

Students “construct” their ideas and observation—pulling together what they see and hear into a “mental model”.  Piaget called this a ‘Schema’.

A mental model(Redish 2004) is an association pattern of cognitive elements that fit together to represent something. Typically one uses a model to reason with or calculate from by mentally manipulating the parts of the model in order to solve some problem.

Mental models have the following properties (Redish 1994)

(1)    They consist of propositions, images, rules or procedure, and statements as to when and how they are to be used.

(2)    They may contain contradictory elements.

(3)    They may be incomplete.

(4)    People may not know how to “run” the procedures present in their mental models.

(5)    Elements of mental model do not have firm boundaries. Similar elements may get confused.

(6)    Mental models tend to minimize expenditure of mental energy. People will often do extra physical activities- sometimes very time consuming and difficult- in order to avoid a little bit of serious thinking.

Principle 2: The Context Principle

It is reasonably easy to learn something that matches or extends an existing mental model. This follows from what Piaget called ‘process of assimilation’.

     This has two corollaries.

(i)           It is hard to learn something we do not almost already know.

(ii)         Everything we learn is learned via interpretation within a “context”.

It follows from context principle that much of our learning takes place step by step. Placing a thing in a context familiar to students makes it easy to grasp it. For this, we also use examples and analogies. For example, in electrostatics we use example of water stored at heights to explain concept of electric potential difference.

Principle 3: The Change Principle

 It is very difficult to change an established mental model substantially. This follows from what is referred to by Piaget as ‘accommodation principle’.

It is a well known misconception that heavy object falls faster than lighter one. A student once said that we know this because Galileo dropped a penny and feather from the top of leaning tower of Pisa and the penny hit first. This is an example of how difficult it is to change the existing model.

   

 Two of the consistent observations of this research are:

(i)     Reading and listening to lectures are, for most students, ineffective ways of     

      changing their mental models.

(ii)     One effective way of changing a mental model is “cognitive conflict”.

For example, if the student in the above mentioned example of Galileo’s experiment at leaning tower of Pisa is actually shown two objects of different masses falling together, it would create conflict between his observation and mental model. This is known as cognitive conflict. It becomes easy to change mental model once the student is exposed to this conflict rather than simply presented the correct information..

There are many situations where knowledge does not come with assimilation. New models have to be formed or substantial changes have to be made in existing models. A teacher’s role here is to create conducive opportunity for students to build a right model. This is where teacher acts as a facilitator.

For example, learning algebra does not come as a natural extension of arithmetic learnt earlier. This becomes a major stumbling block for students. No amount of listening or reading help here. One needs to develop essentially new schemas for learning algebra which are different from those which students have acquired while learning arithmetic earlier.

Principle 4: The “Distribution Function” Principle or Individuality Principle

Since individuals construct their own mental states based on their own experiences and personal makeup, different students have different learning styles and responses.

Two corollaries are:

(i)   There may not be a unique answer to the question: “What is the best way to teach a subject?”

(ii)   Our individual experiences have little relevance to how to best teach our students.

To these principles, which follow from Piagetian constructivism, we wish to add two more principles based on more recent versions of constructivism. One is based on what are called metacognitive strategies. Metacognition refers to cognition of cognition, knowing of knowing, that is ability to reflect on one’s own knowledge and thereby to monitor and control one’s own learning. It is found that students are considerably benefited, if they are given opportunities to reflect on their learning even at the level of primary school.

One of the important classroom practices that follow from this is to ask students to express orally or on the blackboard, the solution to a problem that they have solved or in general what they have thought. While communicating what one has done, one is used to organize one’s knowledge, reflect on it and make corrections if necessary and so on.

Principle 5: Communication Principle

Learning something is also being able to communicate it.

Another principle that we wish to add is based on social constructivism. Social constructivism in education is largely attributed to Vygotsky and Bruner. Our reasoning is as follows:

Learning takes place in a certain cultural environment which operates at various levels like: the subject, the curriculum, learning as a whole, the classroom, the school, the community and so on. Every subject has its rules, symbols, procedures, concepts, themes, ways of thinking, its perspective, and so on, largely specific to itself. In a class room, though each student is different, students learn together. It is not enough that the teacher is a facilitator, who creates learning opportunities for the learners, but something more. The teacher becomes a leader-co-learner who leads the learner through the environment of learning. Through what goes on (cultural mediation), a student internalizes, becomes integrated with, the culture. The teacher in this sense serve as an enculturator.

While students try to lean new knowledge, they need help. The teacher provides the necessary cognitive and cultural setting which is referred to as scaffolding. Vygotsky refer to a zone of proximal development. It is the distance between the actual developmental level as determined by individual problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers. Scaffolding helps students advance into their zone of proximal development. It is important to recognize that social constructivism, while recognizing learning as an individual process, underscored the importance of teachers, peer group, parents and others, the social milieu in learning.

Principle 6.  Principle of scaffolding and Enculturation

     While students are trying to develop new knowledge, they need scaffolding and enculturation.

Implications of the cognitive Principles for Physics Teaching:

·         We have to be concerned that our students not only “have” the material but that they “make sense of it” and can use it effectively.

·         If we are going to make deep changes in the way our students think, we are going to have to help them confront their incorrect beliefs.

·         We must find new ways to help students understand concepts that they do not naturally build.

·         We must find ways to actively engage students who learn differently than we do. (Redish 1996,2004)

·         It is equally important to give students opportunity to communicate what they have learned. This means over-viewing the entire structure of the subject, seeing linkage within the subject and with outside, monitoring one’s process of learning and reflecting on what one has to learn.

·         We must also give peer learning, students learning from each other, its due place in learning.

Methods of constructivist approach include three well-known approaches as per literature.

1.      Situated or context based learning.

2.      Cognitive apprenticeship.

3.      Problem solving.

Third approach, through problem solving is more practicable in a college set up. Problem solving brings to bear essentially reasoning about the subject. Problem solving is scaffolding/building up higher objectives of learning. As per Bloom (1980), these objectives are, comprehension, application, analysis and synthesis. Doing science itself in a way is problem solving.

    James Ross as quoted by Radhamohan (2002), defines problem-solving as an educational device where by the teacher and the pupils attempts in a conscious, planned, purposeful manner to arrive at an explanation or solution to some educationally significant difficulty.

 

According to the famous mathematician, George Polya (1962), ‘Solving a problem means finding a way out of a difficulty, a way around an obstacle, attaining aim that was not immediately understandable. Solving problem is the specific achievement of intelligence, and intelligence is the specific gift of mankind: Solving problem can be regarded as the most characteristically human activity.’

According to Risk,T.M. as quoted by Radhamohan, problem solving may be defined as planned attack upon a difficulty or perplexity for the purpose of finding a satisfactory solution. Risk further elaborates that problem-solving procedure is a process of raising a problem in the minds of students in such a way as to stimulate purposeful, reflective thinking in arriving at rational solution.      

The above definitions of problem solving indicate that problem solving is an activity which involves stimulating purposeful, reflective thinking in students when they attempt to arrive at rational solution. The teacher creates learning opportunities through properly selected problems and leads the learner through the environment of learning. In the process, which can be termed as cultural mediation, a student internalizes, becomes integrated with, the culture of the subject. Thus teaching students through problem solving becomes a constructivistic activity.

As noted by Hoyle (1992), teaching is characterized in term as of helping learners to bring within their individual capability that for which the previously required assistance, and a major role for either a teacher or a more capable peer is that of providing the cognitive “scaffolding” to support this transition. Such scaffolding comes from a deeper understanding of the problems encountered and the possession of conceptual frame works of which the learner is as yet only dimly aware. All the evidence so far is that the process of assisting the learner through the zone of proximal development requires interaction with a teacher and/or capable peers, even when interactive learning resources are used.

We decided to use a course, so that it gives time long enough to cover necessary objectives. This was done covering basic physics as all the higher-level concepts are constructed upon principles learned in basic physics. Therefore we designed and conducted a course aimed at capacity building of undergraduate students in physics via a supplementary programme, consisting a problem solving along the line of constructivist principle. Our effort can be largely termed as ‘scaffolding’ in a Vygotskian way. We found this approach to be effective and practicable.

    

We have tried selecting our special problems for the course designed and following Reddish(1994) termed them as touchstone problems. Although we have used them in different sense than Redish.

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.

Mechanism of problem solving:

If a touchstone problem is difficult, it can be broken up in to parts. Following Schoenfeld(1985) 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.

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)

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 travelled 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:  (i) students to know which equation to be used and how to use it, (ii) difference between distance and displacement (iii) 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?(Halliday 2005) 

             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 above problem 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 sped 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 travelled differ.

Observations:

(1) Students are not able to decide whether fall of the bolt should be taken as a free fall. Thus what is the acceleration of the ball? Is it ‘g’, more or less? To make students realize we considered an example of relative speed of two vehicles when they approach towards each other with 25 km/hr and 15 km/hr. Here we tried to guide students to create mental picture and apply this analogously to relative acceleration in our problem.

(2) Some students were confused. They arrived at relative speed of 10 km/hr. At this point we changed 15 km/hr also to 25 km/hr and created cognitive conflict as now the relative speed as students work becomes zero. This indeed worked and they realized their mistake and could come to the correct acceleration.

(3) Students faced confusion using proper sign convention.  This, we tried to clear using proper auxiliary problem. There was also question whether acceleration of bolt is g a? Eventually they agreed that it would be ‘g+a’. But the problem can be viewed from two different frames. One elevator and other ground based. Therefore they had to figure out as to what is the initial speed in each reference frame and what is the acceleration.? Here also they were directed to appropriate auxiliary problem. Next question was, how are times of flight in two frames related? For this we had to guide them to appropriate auxiliary problem.

(4) Finally they were asked to draw the motion as seen by each observer. They had difficulty in visualizing especially in ground-based frame, as that is where the bolt has initial non-zero speed. They had difficulty distinguishing between distance travelled and displacement, which was clarified using an example of motion along semicircle.

As mentioned above, students were asked to solve problem 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 entire course was conducted covering topics from basic physics with similar problems. 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 (2004) and Young (2004). Most problems were chosen from the textbooks mentioned, competitive exams like JEE (Joint Entrance Exam for admission to Indian Institute of Technologies) and Physics Olympiads. Some problems were specially designed as dictated by need.

Students’ learning was assessed through observation of their progress as shown by an example above as well as through pre-post test mechanism. In addition to test results the following observations indicated effectiveness of the course designed.

·         Direct feedback collected from students showed students appreciated the course.

·         Some sessions were monitored by colleagues who expressed satisfaction about students’ progress and the effectiveness of the method.

·         Many of the students (those who were in F.Y.B.Sc.) came back to go through similar course at a higher-level Physics. This shows that they really found the course beneficial. This indicates the effectiveness of the method employed.

·         Many of the students who had no clue as to what they would do after B.Sc. in Physics, were ready to face national level competitive exams for admission to post graduate courses.

·         Students who were indifferent to what was being taught in a formal class room, started showing interest and participated actively in the class after attending the course.

·         One of the students later admitted that she has decided to take teaching as a career and teach physics with this method as she found it very effective and that she really learned physics the right way.

Earlier she thought she was good in problem solving, which now she realised were merely mechanical or plug-in problems. The problems chosen for the course offered challenges and helped her understand concepts, which she did not understand earlier.

·         One of the other students was very critical of the course and about its effectiveness at the end of the course. During the vacation she participated in a competition organised by ISRO for undergraduate students and was successful. The competition involved solving some problems made available on ISRO website to undergraduate students and students were to solve and send their solutions to ISRO. After the result she personally came and thanked for the course and said that she realised that she was wrong about her initial reaction which she expressed at the end of the course and that she could succeed only due to the training received during the course.

·         One of the S.Y.B.Sc. student from the course won Gold Medal in National Graduate Physics Examination (NGPE-2008) conducted by Indian Association of Physics Teachers (IAPT).

·         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’.

To support this observation, we conducted a pre-, a post- and a retention test before the course, after the course and about two months after the course respectively.

The tests contained three parts: (a) Multiple choice questions, (b) Short answer questions, (c) Full-fledged problems.

The pre and post tests were designed to be equivalent. The corresponding items on pre-post and retention tests addressed the same subject content and involved the same principles although the context was different, so that the items were equivalent but not identical. The tests were validated by careful introspection and through evaluation of them by experts.

A group of additional students which was equivalent in academic record to the experimental group was given both the pre and post-test.

Result:

The pre-post score analysis of 27 students from various colleges of Mumbai who took the course showed that averaged student’s score in post-test was higher than the pre-test score. The difference between pre and post test score was statistically significant to high level (0.1%).It was found that control group pre-post test scores were not significantly different. This indicates that it was the treatment (course) which resulted in better performance of experimental group in the post-test thereby indicating the effectiveness of the problem solving course.   

                                   

Besides the quantitative statistical analysis, qualitative observations of students behaviour indicated positive changes. Number of students who earlier said ‘I can not’ changed their opinion to ‘I can’ and from ‘Physics is difficult’ to ‘I see the correct way to learn Physics’. On the whole therefore we could say that our capacity building course on basic physics was fairly effective with respect to its objective, i.e., Capacity building of students in basic physics.

References:

Books:

1.      Benjamin S. Bloom, Ed., Max D. Engelhart, Edward J. Furst, Walker H. Hill, David R. Krathwohl,  ‘Taxonomy of Educational Objectives, Vol. I, Longman Inc. (1980)

2.      Halliday, Resnick and Walker, Fundamentals of Physics by 6^th Ed., John Wiley & Sons (2005)

3.      I. E. Irodov, Problems in General Physics MIR Publication (1988)

4.      Jean Piaget, The Principles of Genetic Epistemology, Routledge & Kegan Paul (1972)

5.      Polya, How to Solve it, Doubleday, NY (1945)

6.      F. Reif: Understanding basic Mechanics, Wiley, New York (1995)

7.      Radhamohan : Innovative Science Teaching, Prentice Hall India 2nd Ed (2002)

8.      Alan H. Schoenfeld : Mathematical Problem Solving, Academic Press INC (1985)

9.      L S Vygotsky, Mind in Society: The Development of Higher Psychological Processes, Harvard University Press, Cambridge, Massachusetts (1978)

10.  Young and Freedman , “Sears and Zeemansky’s University Physics,” 11^th Ed., Pearson Education (2004)

Articles:

1.      C. Hoyle and R. Noss, “A pedagogy for mathematical microworlds,” Educ. Stud. Math. 23 (1)  31-57 (1992)

2.      Joint Science Education Panel (IASc, INSA, NASI), “A position paper”, Resonance 13 (12) 1177 – 1190 (Dec 2008)

3.      Edward F. Redish, “Implications of cognitive studies for teaching Physics,” Am. J. Phys. 62 (9), 796 - 803 (1994)

4.      Edward F. Redish, “New Models of Physics Instruction Based on Physics Education Research,” Proceedings of the Deustchen Physikalischen Gesellschaft Jena Conference (1996)

5.      Edward F. Redish, “A Theoretical Framework for Physics Education Research : Modelling Student Thinking,” Proceedings of Enrico Fermi Summer School Course : CLVI , Italian Physical Society, 1 – 63 (2004)

11.  Edward F. Redish and Richard N. Steinberg, “Teaching Physics : Figuring Out What Works,” Physics Today 52 (1) 24 – 30 (1999)

12.  Neeru Snehi : Improving Quality of Teaching-Learning in Higher Education: Constructivist Learning Approach, University News, 46 (04) 7-10, 2008

Paper appeared in:  University News 47, (21), pp4-10, May 25-31 (1009)