But we wouldn't make them master mechanical skills, like how to factor trinomials or how to add complex fractions, since these computations can be done quickly and accurately with the calculator. First we would need to teach our students how to use the calculator. We would give them real-world problems and show them how the calculator can be used to solve those problems. We would explain the meanings of algebraic expressions and equivalences, and we would teach them how to set up and then solve equations with the calculator. One argument is that students should know how to manipulate algebraic expressions, solve equations, and draw graphs in case they get a job that requires such skills.
Companies use computers to do complicated, mechanical tasks.
And certainly they use calculators, too. Another argument is that student who do not know the algorithms won't be able to progress to higher-level courses like calculus. The argument goes on. The problem is that we must have realistic expectations. Many of us believe that it is necessary for our students to acquire some arithmetic skills without relying on a calculator and that it is necessary for our students to develop some proficiency at factoring and simplifying algebraic expressions, solving equations, and graphing functions without using calculators.