Thoughts
Calculators and Math
There is a debate about calculators – whether they help by taking away the difficulty of calculating and allowing focus on the problem, whether they are just a neutral tool, or they are damaging.
I am strongly of the third view: I know (not believe) calculators to be damaging, but not in the obvious way most of the discussion is about.
The usual argument against calculators is that students don’t practice arithmetic and similar basic skills, which are important to have. That might or might be right, but it is not the real issue and problem.
The real problem lies in how we solve problems.
Solving problems can be described as a navigation exercise. We start at point A, the problem description or information we have, and try to reach point Z, the solution. However, we don’t “just go” but plan our trip, and only after knowing what roads we’ll take we start. When we are planning, if we don’t have a map for parts of the area, we freeze; we stop and don’t start the trip because we don’t want to get stuck in the middle without knowing where to go.
The same is when we do mathematical exercises and problems. If we cannot see the path, we freeze and just “don’t start.” In fact, I teach, and it is in the Word Problems book, how to solve problems even in such situations. That is why “calculation ability” is important.
When students are not able to calculate in their mind, they don’t see the path to the solution. They don’t have a map for parts of the path, and therefore, they freeze, and just not start. Often, teachers translate it as coming from lack of knowledge of the subject matter, or a psychological element that has to be overcome with “instilling confidence,” or just “s/he is not good at math.”
Often, the solution is much, much simpler: making sure they can calculate.