Sometimes, Always, Never

Three activities produced by Susan Wall are designed to provide the opportunity for students to explore the concepts involved and to highlight any misconceptions by discussing whether the statements presented can sometimes be true, are always true or can never be true.

Algebra: students are presented with a statement such as (x-4)²= x²-8x-16 and have to say whether they think this statement can sometimes be true, is always true or can never be true. The important part of the activity is to require students to give full explanation of, and justification for, their answer.

Trigonometry: is the same activity as the algebra activity using different statements. Students are presented with a set of statements appropriate to their stage of learning. Some of the statements will be familiar such as sin²(x) + cos²(x) = 1, whilst others involving sec and cosec may only be met later in the course.

Complex numbers: is once again the same activity. This time the statements all concern properties that may or may not be exhibited by complex numbers for example, if all the coefficients in an equation are real then the equation has a real root. As well as justifying their answer students are encouraged to give examples to support their argument.