Transfer of structural math knowledge to physics is difficult for students. While research suggests various improvement techniques, enhancing parallelism of algebraic structures used in physics to those studied in mathematics courses seems underrepresented. This paper proposes an alternative way of introducing wave functions as a set of parametric equations. Research shows that the mathematical underpinnings of the mechanical wave function are problematic for students. As seen from the math perspective, there can be several drawbacks that likely impede scientific analysis and interpretation of the wave function:
y(x,t)=Acos(2πλx2πTt).
1.
Ricardo
Karam
and
Mauricio
Pietrocola
, “
Recognizing the structural role of mathematics in physical thought
,” in
Contemporary Science Education Research: International Perspectives
, edited by
M. F.
Tasar
and
G.
Caķmakci
, pp.
65
76
(
Pegem Akademic
,
Ankara
,
2010
).
2.
Andrzej
Sokolowski
,
Understanding Physics Using Mathematical Reasoning: A Modeling Approach for Practitioners and Researchers
(
Springer Nature
,
Cham
,
2021
).
3.
Erin M.
Kennedy
and
John R. de
Bruyn
, “
Understanding of mechanical waves among second-year physics majors
,”
Can. J. Phys.
89
,
11
(
2011
).
4.
Syllabus of Calculus 1
, https://canvas.harvard.edu/courses/20490/assignments/syllabus, accessed June 1, 2021.
5.
James
Stewart
,
Lothar
Redlin
, and
Saleem
Watson
,
Precalculus
(
Nelson Education
,
Toronto
,
2016
).
6.
Douglas C.
Giancoli
,
Physics: Principles with Applications
, 6th ed. (
Prentice-Hall
,
Upper Saddle River, NJ
,
2005
).
7.
Andrea A.
DiSessa
, “
Toward an epistemology of physics
,”
Cognit. Instr.
10
,
105
225
(
1993
).
8.
Physics Simulations
, https://phet.colorado.edu/en/simulation/masses-and-springs, accessed June 10, 2021.
9.
Physics Simulations
, https://phet.colorado.edu/en/simulation/wave-on-a-string, accessed June 5, 2021.
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