Hi.
Welcome to my blog. I am a professional mathematician documenting my adventures in tutoring, outreach, and conference travel. Hope you have a nice stay!
Welcome to my blog. I am a professional mathematician documenting my adventures in tutoring, outreach, and conference travel. Hope you have a nice stay!
Calculators, as we now know them, have become the microwave of laborious computations. As early as the 1940’s at NASA, a calculator was a human who approximated the computations of logarithms, trigonometric functions, square roots etc. by hand. While watching the movie “Hidden Figures,” I cringed at the thought of having to manually approximate these values every time an irrational number crept into my work! Scientific calculators are to logarithmic, trigonometric, and irrational computations as indoor plumbing is to cooking, cleaning, and daily hygiene. Yes, I just compared decimal approximations of irrational numbers to water because they are essential to real-world mathematics. No, it was not hyperbole.
The power of the scientific calculator has removed hours of tedious computation time, and freed up the storage space of large tables of values. This does not even scratch the surface of the power of a graphing calculator!
So you see, calculators are designed for much more than the addition, multiplication, and division of integers. When students in Pre-Algebra and Algebra I are given calculators for addition and multiplication of integers, their arithmetic skills are weakened. Their memory of how to handle negative numbers fades, their “times tables” are all but erased.
I discovered this by observation of three different Pre-Algebra students enrolled at three different schools during the same semester. At the start of the semester, all three students were dealing with the same struggles and I worked with each of them one at a time. One of the students’ math teacher did not permit calculators while the others’ did. By the end of the semester, the student who did not use calculators was tackling long division with poise and accuracy. No longer did she hesitate before a quick multiplication or long division computation. As I watched her work, I realized that although some of the specific concepts of Pre-Algebra were still giving her pause, the necessary arithmetic was her sword and she was not afraid to wield it when needed! In contrast, the two students who were granted calculators reached for it for every single computation there was. Addition of a single digit positive number with a single digit negative number paralyzed them without the calculator. This inability to recall how to add negative numbers, was the result of over-reliance on calculators.
When is it okay for students to use calculators at school? At what point are calculators doing more harm than good? What do I do if my child’s Pre-Algebra teacher is letting the class use calculators all the time?
Observe your child. If your child is beyond 5th grade, observe them while they do their math homework from time to time. (One assignment is not enough to assess.) Are they using their calculators to compute things like: 5 + -13? Are they using their calculators to compute things like 12 x 31? If so, their arithmetic skills are weakening. Algebra I, Geometry, Algebra II all rely heavily on strong arithmetic skills. It will continue to hurt them on standardized tests (state tests, Pre-SAT, SAT, ACT, etc.) that have both calculator and non-calculator portions.
If this is the case with your child, how to you help your child develop their arithmetic skills? My first response is: PLEASE DO NOT RUIN THEIR MATH EXPERIENCE. Please don’t give them hours and hours of arithmetic exercises to do daily. However, incorporating some arithmetic exercises into their routine is helpful. Some helpful websites with interactive software and free math games are:
Incorporating 30 minutes of interaction on these websites 3-4 nights a week will help them reestablish the arithmetic footing they will need for what lies ahead. Perhaps even playing the games with your child or as a family challenge will help make the experience more enjoyable and feel less like painful, agonizing, dreadful work.
Teachers and school administration do their best to create policies for sound learning environments. Sometimes it is necessary for the sake of completing all course material for teachers to allow calculator use. This blog post is only a suggestion; a way to help keep your child on track and prepare for the next phase of learning.
