Abstract
Today, equations are one of the main linking points between mathematics and physics. This term describes a logical proposition concerning the equality between two expressions. This chapter will discuss and compare the mathematics and physics educational perspectives on the concept of equation.
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Notes
- 1.
The definitions of “equation” differ slightly depending on the source and especially the language. In English, any equality (like 1 = 1) is called an equation, while an equation (“équation,” see www.larousse.fr) in France has to have at least one variable (Marcus & Watt, 2012). Here we consider every equality to be an equation.
- 2.
For the case \(\left( {x + y} \right)^{2} = x^{2} + 2xy + y^{2}\) of the binomial theorem, 3 equations in particular are learned in Germany as “kept in memory,” so to speak.
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1.
\(\left( {a + b} \right)^{2} = a^{2} + 2ab + b^{2}\)
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2.
\(\left( {a - b} \right)^{2} = a^{2} - 2ab + b^{2}\)
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3.
\(\left( {a + b} \right) \cdot \left( {a - b} \right) = a^{2} - b^{2}\)
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1.
- 3.
- 4.
In addition, in physics, vector quantities—such as gravitational force F and gravitational acceleration g—are often represented in scalar form, but treated in vector form.
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Hohmann, S., Pielsticker, F. (2022). Comparison: Equations in Mathematics and Physics Education. In: Dilling, F., Kraus, S.F. (eds) Comparison of Mathematics and Physics Education II. MINTUS – Beiträge zur mathematisch-naturwissenschaftlichen Bildung. Springer Spektrum, Wiesbaden. https://doi.org/10.1007/978-3-658-36415-1_7
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