Constructivist teaching of ‘Image formation due to reflection from a plane mirror’ - a probe into students’ learning through activity based learning

Constructivist teaching of ‘Image formation due to reflection from a plane mirror’ - a probe into students’ learning through activity based learning

1. K. Mody*, D. D. Gulwade, S. D. Ghodke

 Pillai’s Journal of Education Research and Technology July-Sept 2 (3) (2013)

Department of Physics, V.E.S. College of Arts, Science and Commerce,  Sindhi Society, Chembur,           Mumbai 400 071, INDIA

Abstract: In trying to overcome problem of undergraduate students in their conceptual understanding in basic physics, we have developed some simple activities. In this article we present our observations about how students think and progress in their understanding of formation of image due to reflection at the surface of a plane mirror through such activities.

These days students who join undergraduate course in physics in college affiliated to Indian Universities are demotivated and lack self-confidence as they have missed opportunity due to not qualifying for professional courses. These students also have poor understanding  and comprehension of concepts although have knowledge of facts and formulae. In other words, they have achieved first objective of Bloom’s taxonomy (knowledge) but are no where near to higher objectives (comprehension, application, analysis, synthesis and evaluation)(Bloom 1980).

To overcome this problem and bridge the gap between students’ existing state and desired state we have developed supplementary programme using methods of PBL (problem based learning) which can be classified as constructivist. (Pradhan 2009 a, b). This can also be considered as activity based learning.

These students have been taught through traditional methods. As per Redish(1996) traditional model of teaching basic physics has following characteristics:

1. It is content oriented.
2. It has 3-4 hours of lecture and 1-0 hours of problem solving recitation per week.
3. If there is a laboratory, it will be 2-3 hours and “cook book” in nature; that is, students will go through a prescribed series of steps in order to demonstrate the truth of something taught in lecture or read in the book.
4. The instructor is active during the class session while students are passive during the class period (atleast during lectures, and often during recitation).
5. The instructor expects the student to undergo active learning activities outside the class section, in reading, problem solving etc.

We all have found these methods to be ineffective for cognitive development. To overcome these difficulties, following are the suggestions made:

1. 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.

2. 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.

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

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

5.  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.

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

 To implement these suggestions an active engagement class is recommended  which is to have following characteristics:

1. The course is student oriented.
2. What students are actually doing in class is the focus of the course.
3. Laboratories in this model are of ‘discovery’ type; that is, students are guided to obsrve phenomena and buid for themselves the fundamentral idea via observation.
4. The course may include explicit training in reasoning.
5. The student is expected to be intellectually active during the class.

The primary aim of learning in undergraduate and/or +2 is to develop capacity to construct knowledge (rather than mere transmission from teacher to student) with reasonably good conceptual understanding, and learners are expected to develop foundation as well as expertise in the subject. Furthermore, students should acquire skills/expertise through constructivist approach wherein they will be prepared to face more challenging tasks in a subject/area of higher level learning. Conventional learning model remain far away from realizing the primary goal of learning. There have been consistent efforts in Physics Education research to develop interactive engagement learning methods for effective learning.

Students’ learning depend on their conceptions. Large amount of literature in Physics Education research (PER) is based on various facets in physics namely Force concepts, electricity and magnetism, Newton’s laws, and thermodynamics, etc. However, there have been fewer efforts in areas such as geometrical optics. The present work is to probe in to students’ learning of concept of reflection at a plane surface and construct their own knowledge in reflection at a plane surface in geometrical optics.

The group of students who was undergoing this learning module were First year undergraduate students who are supposed to have gone through all basic courses of physics in general and  specifically optics that is focus of present research. Furthermore, the present module is based on some very basic concepts that they have been introduced and taught in schools and at +2 level through conventional classroom.

Students learn about laws of reflection at a plane surface that (i) incident ray, reflected ray and normal to the surface all lie in the same plane and (ii) angle of incidence is equal to angle of reflection. Teacher can teach this experimentally using pin and mirror and constructing ray diagram. These days it is easy to demonstrate using simple LASER torch. Having established this, students can be asked or shown construction of position of image due to point object using laws of reflection and two or more rays. 

Problems:

1.      Construct a ray diagram showing formation of image of a point object due to a plane mirror.

2.      Construct image of an extended object due to plane mirror (say ‘P’)

3.      Construct image of a point objects due to two perpendicular mirrors

4.      Minimum height of a plane mirror needed to see image of yourself.

Observations for Problem 1.

1. One of the student thought that ray will penetrate the mirror and pass through it. The representative diagram drawn by a student is provided below.

2. Few students gave response that image will be at same point as that of object

3.      Questions posed: Will it depend on angle of view. They were able to ascertain a position of image but could not substantiate the answer with correct ray diagram.  The following figures exhibit their thinking, they have shown image but no relevance with the incident rays; incident rays are penetrating the mirror and rays starting from the image is shown. Most of them believed that rays from image (inside the mirror) comes out of the mirror. Image is formed inside the plane mirror and rays come from image.

4. Question was asked to students: Will ray get reflected from mirror or penetrate the mirror? This question helped them think about reflection. But they could not make use of laws of reflection. With what reference we measure angle of incidence and reflection helped them to make further progress.

5.      They could not make out how we see objects, what is a role of light in it and role played by reflecting surface. how we see things/objects? helped them to figure out rays would appear to come out from the image. Thereafter, they were able to draw the correct ray diagram. After completion of this problem, they were asked to work on problem 2.

Observations for Problem 2

1.      Could not draw the image of extended object ‘P’ even after working out image of point object; could not make out that the extended object may be treated as multiple point objects and each point will lead to an image.

Observations for Problem 3

1.      After posing a problem they were demonstrated the same using two plane mirrors perpendicular to each other. After, seeing three images, they gave responses

a)      Third image is because of image formed by image of one of the mirror due to one of the image.

b)      Third image is because of ray passing through the edge joining two mirrors

2.      In these ray diagrams, they have not made correct use of laws of reflection and they could not extend basics of image formation to the complex situation although they learned it before starting to work on this problem.

3.      Is there a change of left-right in all images? This question helped them to analyze and observe that one of the images is not inverted.

4.      Then were asked to probe a possibility of double reflection.

5.      The above questions and interventions made them to reach a correct ray diagram.

Observations for Problem 5

1. When we will be able to see image in mirror this was not clear to all students. That clearly means that they don’t know how we see objects. Importance of light and its reflection reaching eye. This in spite of doing above mentioned problems.
2. By posing a question when you will see image, helped them to understand that rays starting at object need to reach eyes.
3. 
   They were able to guess that height required is 3 feet but they had no idea why/how?

4. Difficulty was to draw ray diagram showing the conclusion that they pointed out correctly. They struggled to draw the ray diagram. What is angle of incidence and reflection. By posing a argument that angles are measured with normal, they used correctly laws of reflection. 
5. How to show that minimum height of mirror required i.e. h/2.( If height of a person is h.) They were able to show the same in diagram that requirement is h/2 but could not use knowledge of basic mathematics to arrive at conclusion.

We can categorise students responses to very basic concepts in optics under two categories: (i) false response born through their misconceptions and (ii) correct answers without any reasonable logical way to explain the answers. The students’ conceptions namely image formation due to a plane mirror is an example of the former and minimum height of mirror required to see image of a person of height h is h/2 belongs to the latter. These two are examples which establish the damage caused and misconceptions borne through conventional teaching.

Exposing students with an interesting and challenging problem have encouraged independent thinking ability and better understanding of the subject while solving these problems through constructivist approach. Students worked on these problems under interventions/scaffolding of instructor. This kind of approach helped students firstly to get rid of misconceptions and also to learn and construct knowledge while solving problems.

Following misconceptions or conceptual difficulty automatically got addressed while they were engaged in above mentioned activity.

1.      Many believed that light rays penetrate the mirror.

2.      Rays from image (inside the mirror) comes out of the mirror.

3.      Image is formed inside the plane mirror and rays come from image.

4.      Could not figure out role of reflection in formation of image of object.

5.      Laws of reflection and its correct implementation in ray diagram.

6.      They had no idea, how we see objects, what is a role of light in it and role played by reflecting surface.

7.      Could not lead to the image of extended object even after working out image of point object (Could not visualize an extended object as a collection of multiple point objects)

Conclusion: As described above, it was possible to help students construct their own knowledge of reflection beyond just facts and formule level through meaningful activity and problem. While students construct their knowledge observations as described above can be used for dynamic assessment (Mody 2011). In the light of this, the method described above turns out to be very effective and valuable.

Acknowledgement: We are thankful to those students who spend their time trusting us in doing meaningful activity and constructed their knowledge and simultaneously allowed us to record observation of their work.

References:

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

2.      Mody A.K. “On New System of Grading for Students’ Learning of Physics” Proceedings of Episteme-4, Macmillan India (2011)

3.      Pradhan H.C. & Mody A. K., ‘Constructivism applied to physics teaching for capacity building of undergraduate students’, University News, 47 (21) 4-10, (2009a)

4.      Pradhan H.C. & Mody A. K., ‘Supplementary Programme for Capacity Building of Physics Undergraduate Students’, Physics Education, 26 (2) 93-98, (2009b)

5.      Redish Edward F., New Models of Physics Instruction Based on Physics Education Reearch : Part I & II ‘Proceedings of the Deustchen Physikalischen Gesellschaft Jena Cenference (1996)’

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