When Should Students be Introduced to Calculators? I am sure that this topic could spark an interesting debate. Well, I certainly have no interest in debating, but, I would like to bring to light, my professional belief on this topic, after working with math students for almost 20 years.
First, I would like to explain theoretical mathematics as doing math independent of the world. It uses reasoning, proof, and abstract concepts to establish truth upon truth. While things going on in the world around us may inspire a theoretical mathematician with new ideas, the study of theoretical mathematics does not depend on the world around us. So, some might argue that if math does not have a direct “real-world application”, then it is useless. This is not true since even applied mathematicians draw on theoretical mathematics to solve problems related to the the world.
Research has shown that students receiving more instruction in theoretical math do better overall because they build a mathematical foundation that will allow them to extrapolate math to other real-world situations. If math is just taught for a specific application, then the student will not be able to transfer that knowledge to another context. Theoretical mathematics does not change. It is simply, truth.
Now, let’s get back to the calculators! What is the purpose/role of calculators in mathematics? To make it simple, calculators are used to speed up extensive calculations involved in real-world problems. The problem is that students who haven’t developed a strong math foundation are using these calculators for much smaller calculations that they should be doing by hand, to strengthen their grasp of numbers, or even in their head in some cases. When students do computations by hand, they develop a feel for number patterns and a respect for mathematics. They build a foundation of mathematics that will be evergreen, and thus withstand the test of time and any changing technology.
Consider this example: I watched an advanced 9th grader go to her calculator to compute 105-90. A person with a strong sense of numbers would likely “mentally” compute this by knowing that from 90, it’s 10 more to 100 and then 5 more past 100 so the difference is just 10+5 =15. Once this skill is developed, it is certainly quicker to state this difference without a calculator! Just in case you think this example is too “complicated”, what about watching a student perform 13-9 on a calculator? That is not what a calculator was invented to be used for!
So, what am I suggesting? I am suggesting that calculators aren’t really needed until a student has a solid grasp of number sense. So solid, they won’t “forget” how to do basic arithmetic on all numbers, including integers, fractions, and decimals. So, when is this? Well, clearly it will vary from student to student, but in general, I would go as far as to suggest not allowing calculators until at least precalculus. And even then, limiting their use. Even the AP Calculus exam and the SAT have “no calculator” sections!
I say to all math teachers, let’s put the pencils in student’s hands and give them lots of paper and let them DO MaTh! There is no shortcut or tricks to learning math. Each student has to walk the road and allow their brain to make the connections.