The formula triangle and other problems with procedural teaching in mathematics

Students often express dislike of mathematics, even when they seem competent
at it. They are often taught shortcuts for untangling mathematical problems; however, these
shortcuts can bypass understanding and diminish a student’s ability to recognise when an answer
looks correct and when it does not. Using the examples of the formula triangle and a method
for subtraction, it is shown that the mathematical steps to solve problems must be thoroughly understood before they are used, to lead to the understanding of short routines. Only then will students become confident in their answers.