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The
Parasitism of Mathematics in Physics Learning
ABSTRACT
This
work attempts to identify some areas in which opportunities for better mutual
relationship, rather than parasitism, between mathematics and physics in the
actual learning activities to reducing students’ cognitive load also educators’
difficulties managing their teaching.
Keywords
: curriculum; mathematics;
learning; physics;
Published
on INA-Rxiv, Paper DOI: 10.31227/osf.io/tyehj
INTRODUCTION
Mathematics
is not a science from physicist and physics educator point of view, in the
sense that it is not a natural science. The test of mathematics validity is not
experiment. Peoples must, incidentally, make it clear from the beginning that
if a thing is not a science, it is not necessarily bad. For example, love is
not a science. So, if something is said not to be a science, it does not mean
that there is something wrong with it; it just means that it is not a science.[1]
The
most remarkable relationship between mathematics and physics a great intimacy.[2]
Mathematics has been described as “an essential tool for physics”,[3]
while physics has been described as “a rich source of inspiration and insight
in mathematics”.[4] Considerations about mathematics being the
language of nature can be found in the ideas of the Pythagoreans: the
convictions that “numbers rule the world”.[5] Then two millennia
later were also expressed by Galileo Galilei, “the book of nature is written in
the language of mathematics”.[6] Before giving a mathematical proof
for the formula for the volume of a sphere, Archimedes used physical reasoning
to discover the solution by imagining the balancing of bodies on a scale.[7]
Richard Phillips Feynman said that the real reason what mathematics doing in a
physics is, “the subject is enjoyable, and although we humans cut nature up in
different ways, and we have different courses in different departments, such
compartmentalization is really artificial, and we should take our intellectual
pleasures where we find them.”[8]
Based
on historical trajectory from the seventeenth century, many of the most
important advances in mathematics appeared motivated by the study of physics.[9]
This continued in the following centuries, although in the nineteenth century
mathematics started to become increasingly independent from physics.[10]
The creation and development of calculus were strongly linked to the needs of
physics: There was a need for a new mathematical language to deal with the new
dynamics that had arisen from the work of scholars such as Galileo Galilei and
Isaac Newton.[11] During this period there was little distinction
between physics and mathematics.[12] As an example, Isaac Newton
regarded geometry as a branch of mechanics.[13]
As
time progressed, increasingly sophisticated mathematics started to be used in
physics. The current situation is that the mathematical knowledge used in
physics is becoming increasingly sophisticated, as in the case of superstring
theory.[14] The interrelations between physics and mathematics led
professional mathematicians who were also interested in mathematics education
to strongly advocate teaching mathematics in a way more closely related to the
physical sciences.[15]
I
happen to be a mathematics educator who came as a physics education background,
that puts me in a difficult position just because these all informations.[16]
As a undergraduate physics educator teaching mathematics,[17] my
opinion about contemporary relation of physics and mathematics linear with
Freeman John Dyson, “I am acutely aware of the fact that the marriage between
mathematics and physics, which was so enormously fruitful in past centuries,
has recently ended in divorce.”[18] But, this divorce may happen to
the ‘new’ mathematics that started after 1920. Before 1920, the ‘old’
mathematics which is used in engineering and science developed to a large
extent, for example in the design of radar antenna systems, in determining the
position and orbits of the satellites, also in the most esoteric forms of
theoretical physics as well.[19] So, ‘old’ mathematics is still
enjoyable subject for me to teach in school, from primary, secondary, even
tertiary.
To
not go too far, I will continue with an attempt to identify some areas in which
opportunities for better mutual relationship between mathematics and physics in
the actual learning activities to reducing students’ cognitive load also
educators’ difficulties managing their teaching. It’s now being missed in
current Indonesia curriculum for secondary school, that make mathematics is
parasitism to physics learning. This case happen since lower secondary
education that typically with a more subject-oriented curriculum when students
entrance algebra. Mathematics, however, heavily obstacling physics learning
since upper secondary education with an increased range of subject streams when
educator using calculus to explain phyisics.
full text coming soon depended on my mood
WORK
CITED
[1]
Feynman, Richard Phillips. (2013). the relation of physics to other sciences.
In The Feynman Lectures on Physics, Volume I. California
Institute of Technology. URL: http://www.feynmanlectures.caltech.edu/I_03.html
[2]
Bailly, Francis; & Longo, Giuseppe. (2011, March 04). Mathematics and
the natural sciences: the physical singularity of life, p. 149. World Scientific.
URL: https://books.google.com/books?id=7-dGHyIyI-AC&pg=PA149
[3]
Wagh, Sanjay Moreshwar; & Deshpande, Dilip Abasaheb. (2012, September 27). Essentials
of physics, p. 3. PHI Learning Pvt. Ltd. URL: https://books.google.com/books?id=-DmfVjBUPksC&pg=PA3
[4]
Atiyah, Michael (1990, Auguts 29). On the work of edward witten, p. 34. Proceedings
of the International Congress of Mathematicians, Kyoto, Japan, August
21-29, 1990, pp. 31–35. URL: http://bohr.physics.berkeley.edu/reinsch/phys105spr2014/files/Witten_Atiyah.pdf
[5] Assayag,
Gerard; Feichtinger, Hans G.; & Rodrigues, José-Francisco. (2002, July 10).
mathematics and music: a diderot mathematical forum, p. 216. Springer.
URL: https://books.google.com/books?id=bjsD8ClsFKEC&pg=PA216
[6]
Galilei, Galileo. (1894). le opere di galileo galilei: sotto gli auspici di
sua maestà il re d'italia – vi, p. 232. Firenze: Tipografia di G. Barbera.
URL: https://tools.wmflabs.org/wsexport/tool/book.php?lang=it&format=pdf-a4&page=Le_opere_di_Galileo_Galilei_-_Vol._IV
[7]
Mazer, Arthur. (2011, September 26). The ellipse: a historical and
mathematical journey, p. 5. John Wiley & Sons. URL: https://books.google.com/books?id=twWkDe1Y9YQC&pg=SA5-PA28
[8]
Feynman, Richard Phillips. (2013). Algebra. In The Feynman Lectures on
Physics, Volume I. California Institute of
Technology. URL: http://www.feynmanlectures.caltech.edu/I_22.html
[9]
Post, E. Jan. (1997, September). A history of physics as an exercise in
philosophy, p. 76. Westchester CA. URL: http://www22.pair.com/csdc/pdf/philos.pdf
[10]
Plotnitsky, Arkady. (2012, September 05). Niels bohr and complementarity: an
introduction, p. 177. Springer Science & Business Media. URL: https://books.google.com/books?id=dmdUp97S4AYC&pg=PA177
[11]
Newton, Roger G. (1997). The truth of science: physical theories and reality,
p. 125–126. Harvard University Press. URL: https://books.google.com/books?id=SzxsjN3t4i0C&pg=PA125
[12]
Gowers, Timothy; Barrow-Green, June; & Leader, Imre. (2010, July 18). The
princeton companion to mathematics, p. 7. Princeton University Press. URL: https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA7
[13]
Rowe, David E. (2008). Euclidean geometry and physical space. The
Mathematical Intelligencer, 28 (2): 51–59. DOI: https://dx.doi.org/10.1007%2FBF02987157
[14]
Gervais, Jean-Loup; & Sakita, Bunji. (1971, November 15). Field theory
interpretation of supergauges in dual models. Nuclear Physics B, 34 (2):
632–639. DOI: https://dx.doi.org/10.1016%2F0550-3213%2871%2990351-8
[15]
Lesh, Richard; Galbraith, Peter L.; Haines, Christopher R.; Hurford, Andrew.
(2009, December 15). Modeling students’ mathematical modeling competencies:
ictma 13, p. 14. Springer Science & Business Media. URL: https://books.google.com/books?id=Jj5tfi2594kC&pg=PA14
[16]
Setiawan, Adib Rifqi. (2018, May 19). Máthēmatnic: — catatan perjalanan. alobatnic.blogspot.com.
URL: http://alobatnic.blogspot.com/2018/05/mathematnic.html
[17]
Setiawan, Adib Rifqi. (2019, March 29). Máthēmatnic: pengalaman memandu
pembelajaran matematika. INA-Rxiv. DOI: https://dx.doi.org/10.31227/osf.io/fx7uw
[18]
Dyson, Freeman John. (1972, September). Missed opportunities, p. 635. Bulletin
of the American Mathematical Society, 78 (5): 635-652. URL: https://projecteuclid.org/euclid.bams/1183533964
[19]
Feynman, Richard Phillips. (1965, March). New textbooks for the “new”
mathematics, p. 15. Engineering and Science, 28(6): 9-15. URL: http://calteches.library.caltech.edu/2362/1/feynman.pdf