Disclaimer: I am not anti-calculator. Calculators are genuinely useful and they have an important role to play in academics as well as human progress. Furthermore, for various reasons, such as a dyscalculia diagnosis, some students have been granted an accommodation that allows them to always have access to a calculator for schoolwork, tests, and standardized exams. I am not advocating for these students to abandon the accommodation they are entitled to. I am simply making the case that any student will benefit from regularly practicing math without a calculator.
Math classes have changed during the past few decades. Boring, black-and-white textbooks have been replaced with more colorful ones. Rote memorization has been replaced with exploration and intrigue whenever possible. The newer textbooks favor real-world numbers for which the arithmetic is difficult. Calculators have become more complicated and much more prevalent.
All of this is well and good so long as nothing needs to be memorized and so long as calculators are always allowed. Since we now live in a high-tech world, complete with Google, smartphones, and fancy graphing calculators, it’s easy to see why math classes have shifted in this direction.
But in the spring of 2016, the College Board launched the newest version of the SAT. For over one third of the math questions on the new SAT, no calculators are allowed. Given the direction math classes have gone in recent years, it should come as no surprise that the #1 thing we hear from our students about the new SAT is that the no-calculator section is very hard.
To be fair, this isn’t entirely about calculators. Both of the new SAT’s math sections cover higher-level content than the old SAT did. Students are expected to know nearly everything from Algebra I, Geometry, and Algebra II in addition to the fundamentals from the lower levels of math’s inverted pyramid. In terms of math content, the bar has been raised. The new SAT, in short, is harder.
But it’s especially harder for students who don’t have their math facts memorized. If you have to struggle with arithmetic, the no-calculator section is brutal. After all, the exam isn’t testing arithmetic; it’s testing higher-level math skills and problem-solving. If you have to spend a great deal of mental energy crunching the numbers, you won’t have enough brainpower or time leftover to solve the test’s harder problems. You’ll be slower and less agile because you’re weighed down by excess cognitive load.
You might be surprised how common it is for a student to be doing well in high school math classes but to be simultaneously lacking knowledge of fraction operations, how to set up proportion problems, or how to decode a word problem. To a certain extent, the SAT has always punished students for forgetting these skills. Now it also punishes students for struggling with addition, subtraction, multiplication, and division. Many students have chosen not to memorize their math facts, and now they’re paying for it. Others once had their math facts memorized, but have since forgotten them through lack of practice, in a classic case of use it or lose it.
Because the brain is like a bunch of muscles, any skill we don’t use regularly weakens. If we never use the skill, it atrophies. If you always wear a brace on your wrist, your wrist will become weaker. If you always ride your bike with training wheels, you’ll never develop balance. If you always use a calculator, you’ll forget how to do math without one.
Students who wish to do well on the new SAT will have to go back to basics and put in some time working on the fundamentals. The prospect of devoting time to working on old math is particularly hard to stomach during the schoolyear because there is so much new content to learn, which makes summer the ideal time to work on this goal.
It is possible, however, to make significant progress on the basics while you’re learning higher-level content. You simply have to find opportunities to practice the basics while you’re doing your homework. Essentially, this means choosing to do problems the hard way. Not necessarily every time, but whenever you could do a problem without a calculator, that’s an opportunity to practice the basics. It will make your math homework take slightly longer, but you’ll be killing two birds with one stone. Do it the hard way.
The SAT isn’t likely to change again for many years, and it will take a long time for the school system to shift in such a way that helps students tackle the new exam. So that leaves you. You’ll have to change. You’ll have to choose to help yourself.
Title Image: Creative Commons Public Domain. Courtesy of Pixabay. https://pixabay.com/en/calculator-math-mathematics-988017/. Text added.