Mathematics for Teaching Category: Calculus

Category: Calculus

Variables, Constants and Parameters

Whether a mathematical notation is a variable,  parameter, or constant depends on what you mean by it. If you intend to represent the value of a quantity whose measure varies within a situation, then you are using that notation as a variable. If you intend to represent the value of a quantity whose measure is the…

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Teaching the derivative function

Most Grade 10 syllabus do not yet include the concept and calculation of derivative. At this level, the study of function which started in Year 7 and Year 8 on linear function is simply extended to investigating other function classes such as polynomial function to which linear and quadratics belong, the exponential function and its…

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Prerequisite knowledge for calculus

This post describes foundational reasoning abilities and mathematical knowledge students need to develop before beginning a course in calculus. 1. Covariational reasoning This type of reasoning involves recognition of two quantities that are changing together. A student who considers how two quantities in a dynamic situation change together is said to be engaging in covariational…

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Application of the Discriminant

The discriminant of a quadratic equation, ax2 + bx + c = 0 is D = b2 – 4ac. If D>0, the quadratic equation has two distinct roots; if D<0, then the equation has no real roots; and, if D=0, the we have two equal roots. Let’s apply it in the following problem. What is…

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8 Different Ways to Think of the Derivative

In his paper The Transition to Formal Thinking in Mathematics, David Tall presents W.P. Thurston’s seven different ways to think of the derivative: Infinitesimal: the ratio of the infinitesimal change in the value of a function to the infinitesimal change in a function. Symbolic: the derivative of x^n is nx^n−1, the derivative of sin(x) is cos(x), the…

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