Peer instruction to address alternative conceptions in Einstein's special relativity

Alvarez-Alvarado, Manuel S.; Mora, Cesar; Cevallos-Reyes, Cesar B.

doi:10.1590/1806-9126-RBEF-2019-0008

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Articles • Rev. Bras. Ensino Fís. 41 (4) • 2019 • https://doi.org/10.1590/1806-9126-RBEF-2019-0008 copy

Peer instruction to address alternative conceptions in Einstein's special relativity

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

In education, decades have been spent investigating what kind of beliefs and attitudes students may have in relation to learning. The relevance of these lies on the implications that it brings concerning students' alternative conceptions. This research focuses on the inclusion of Peer Instruction (PI) as a methodology to address the alternative conceptions in Einstein's special relativity. PI was selected since there is evidence that it has an impact on the academic performance of the students, however, concerning the topic of relativity, it has not been previously proposed. Alternative Conception Einstein's Special Relativity Test (ACESRT) is proposed to determine students' alternative conceptions. The sample for this study consisted of 25 high school students from Ecuador. In none of this level, students study Einstein's special relativity, nevertheless, in the current year a special course with senior students (picked randomly) was open in which the topic was considered in their academic curriculum. In the first lecture, the students filled a survey to get a notion of their beliefs and attitudes. Then a pre-test (ACESRT) take place, with a view getting information of alternative conceptions that students may have. Later, lectures following PI were given. At the end, to measure PI impact on students' attitudes, beliefs and alternative conceptions the students filled again a survey, followed by post-test (ACESRT). The results were statistically analyzed, and they reveal that PI has a strong impact on students' beliefs and attitudes. Furthermore, the methodology has the potential to address the alternative conception in concepts related to the topic Einstein's special relativity.

Keywords:
Attitudes; Alternative Conceptions; Beliefs; Peer Instruction; Special Relativity

Belief	Questionnaire propositions
Learning the concepts of physics without giving much interest to the mathematical part	5. I must remember as many facts, laws and equations as possible in Einstein's special relativity.
	29. To get good grades in physics you must understand the ideas and remembering the facts
	33. Mathematics is not the main difficulty in learning physics, it is the theory itself.
The knowledge should be given by the instructor	8. Discussing Einstein's special relativity ideas with other students does not help me understand them.
	15. The instructor should listen to the class opinions.
	16. The instructor should explain each topic in detail.
	20. My understanding in Einstein's special relativity mainly depends on how well I am taught by my instructor.
	21. In a lecture session, I take notes by writing down exactly what the instructor says and what he writes on the board.
	22. I prefer to practice with the exercises that are similar to the examples given by the instructor.
Learning for the development of experiments	13. Laboratory work in Einstein's special relativity is relevant for me.
	14. Experiments help me to understand Einstein's special relativity.
	35. The main purpose of laboratory work is to verify physics concepts and laws.
Application and connection with the world	1. I don't want to study Einstein's special relativity because it is not relevant in my life.
	2. I want to study Einstein's special relativity because it helps me to understand the world.
	11. Physics instruction must relate to everyday experiences, so we can see how it affects us in our daily lives.
	36. Learning Einstein's special relativity is very important for the development of technology.
Grades are more important than to learn	9. I just want to get a good grade and I am not interested in understanding Einstein's special relativity ideas.
	26. If I work hard I will get good grades in physics.
	30. I must be an obedient student in class to get good grades.

Attitude	Questionnaire propositions
Confidence in the construction of his own knowledge	3. I have been required to study Einstein's special relativity by other people.
	7. It is important that I try to make sense of Einstein's special relativity concepts and really understand them.
	10. Lecturing and giving notes are not the most important activities in the Einstein's special relativity lecture, since I can read and understand in a better way the theory involved in the topic of study
	19. I need to learn by myself without the guidance from the instructor.
Personal and professional motivation	4. Studying Einstein's special relativity will help me with my career.
	24. Physics is a subject not only for people who studies engineering, since it can be applied to different areas of the sciences.
	34. In a lecture I prefer examples applicable to different careers
Positive interest in learning	6. Passing exam is not my biggest concern about studying Einstein's special relativity, since I want to learn because is interesting.
	12. I need some opportunities to discuss Einstein's special relativity ideas with my classmates to help me understand physics.
	18. The instructor should let us work on problems and exercises in small groups to help us learn physics.
	25. If I remember more facts and laws related with special relativity, then I will be able to develop different problems in the topic.
	31. I always have some questions to ask or discuss with the instructor.
Effort in learning	17. The Einstein's special relativity lectures should be enjoyable.
	23. I use my own words to summarize concepts from texts and lectures in Einstein's special relativity topic.
	27. If you are not a clever student you but if I put effort I will get good grades in physics.
	28. Success in studying physics depends more on effort than ability.

Question	Alternative conception	Concepts in action	Theorems in action
1	Students may relate relativity with some Einstein's experiment	Epistemology	The history of the evolution of Physics give ideas for future research
2	Students may not conceive space-time as one thing	Space-time geometry	Einstein's special relativity is based on the Lorentz's transform
3	Students may have confusions with inertial and non-inertial frame	Inertia	Given an inertial reference system, a second reference system will be non-inertial when describing accelerated motion with respect to the first.
4	Students may not know the author of special relativity	Epistemology	The scientists inspire others to continue with the construction of knowledge
5	Students may think that the speed of light can vary	Light speed	Light is speed has a constant value no matter the reference frame
6	Students may believe that the equation $E = m c^{2}$ is one of the postulates of special relativity	Postulates of special relativity	The postulates relate basically the space-time and light and it does not mention the famous equation $E = m c^{2}$
7	Students may think that time is same no matter the reference frame	Time dilation	The time depends on the speed of the observer
8	Students may think that length of a body is not related with its speed	Space crunch	The length of a body depends on the speed of the observer
9	Students may present difficulties applying time dilation equation	Time dilation calculation	Recognize that the time for the observer who is not moving is greater than the one who is moving
10
11	Students may present difficulties applying space crunch equation	Space crunch calculation	Recognize that the length of a body that is moving is greater than the one who is not moving
12
13	Students may have confusion applying the concept of relativistic mass in classical equations	Relation of the classical equations with the relativistic ones	It is not just about to replace equations and use them without understanding the real meaning of them, especially with concept of relativistic mass
14	Students may not know how to relate in a graph the relativistic kinetic energy and the speed	Interpreting a chart	Interpreting the graph and recognizing the physical parameters involved allows us to establish an effective scheme to establish a strategy and thus initiate the resolution of the problem.
15	Students may think that there is no application of special relativity	Connection with the real world	The application of the theory is fundamental for the development of science

Statistical Values	Pre-test	Post-test
Participants	25	25
Mean	2.76	10.72
Median	3	12
Mode	3	12
Standard Deviation	1.8321	2.1893
Variance	3.3567	4.7933
Maximum	7	15
Minimum	0	6
Range	7	9

	$V a r i a b l e 1 (O_{1})$	$V a r i a b l e 2 (O_{2})$
Mean	2.76	10.72
Observations	25	25
Pearson Correlation	-0.0901645
t Stat	-13.3610218
t Critical one-tail	1.71088208
P(T<=t) two-tail	1.31064E-12
t Critical two-tail	2.063898562

Input
Normalized average of correct answer pre-test $\to θ_{p r e} = 0.20$
Normalized average of correct answer post-test $\to θ_{p o s t} = 0.77$
Normalized average of number of questions students answer correctly on the post-test and incorrectly on the pre-test: $θ_{p o s t} \cap μ_{p r e} = 0.10$
Normalized average of number of questions students answer incorrectly on the post-test and correctly on the pre-test: $θ_{p r e} \cap μ_{p o s t} = 0.23$
Output
$G = \frac{θ_{p o s t} \cap μ_{p r e}}{μ_{p r e}} = \frac{0.23}{0.27} = 0.85; L = \frac{θ_{p r e} \cap μ_{p o s t}}{θ_{p r e}} = \frac{0.10}{0.20} = 0.50; ω = \frac{θ_{p r e}}{1 - θ_{p r e}} = \frac{0.20}{1 - 0.20} = 0.25$
Learning Gain $g = G - ω L = 0.85 - (0.25) (0.50) \to g = 073$

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[1] ^*Correspondence email address: manuel.alvarez.alvarado@ieee.org.