### 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…

### Three ways to teach math algorithms or procedures

It is a bunch of procedures. That’s how people perceive algorithms are. And they are right. Algorithm has been defined as 1) “step-by-step procedures that are carried out routinely”; 2) “a precisely-defined sequence of rules telling how to produce specified output information from given input information in a finite number of steps”. It is no…

### 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…