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Park, Jungeun; DiNapoli, Joseph; Mixell, Robert A.; Flores, Alfinio – International Journal of Mathematical Education in Science and Technology, 2017
This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual…
Descriptors: Mathematics, Mathematics Instruction, Mathematical Models, Equations (Mathematics)
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López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael – International Journal of Mathematical Education in Science and Technology, 2016
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
Descriptors: Equations (Mathematics), Semi Structured Interviews, Undergraduate Students, Calculus
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Debnath, L. – International Journal of Mathematical Education in Science and Technology, 2013
This article deals with a short historical introduction to determinants with applications to the theory of equations, geometry, multiple integrals, differential equations and linear algebra. Included are some properties of determinants with proofs, eigenvalues, eigenvectors and characteristic equations with examples of applications to simple…
Descriptors: Equations (Mathematics), Geometry, Calculus, Algebra
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Spindler, K. – International Journal of Mathematical Education in Science and Technology, 2007
This paper introduces a concept of differentiability for functions in several variables which has a very natural definition and shares all the properties one expects of a notion of differentiability, but is shown to be weaker than the usual concept of differentiability defined as local linearizability. The exact connection between the two…
Descriptors: Calculus, Concept Mapping, Definitions, College Mathematics