Today’s educational culture encourages students to express all of their thought processes on paper. Both AP exams and classes like physics require students to explicitly list all equations and calculations step by step.
While this culture may help students identify errors and prove their understanding of the material, it kills a valuable skill: mental math, calculations done in the head without the usage of pencils, calculators or other aids.
Furthermore, the prevalence of the calculator creates a situation in which students often prefer to rely on technology rather than on their minds when solving arithmetic problems.
As a result of this shift away from mental math, students not only miss out on basic advantages such as increased speed and the ability to make on-the-spot calculations, but also fail to receive major cognitive benefits such as a heightened number sense, mathematical comprehension and memorization skills.
Performing arithmetic through mental computation promotes the development of number sense, or a strong understanding of numeric relationships and the effects of operations on numbers. The possession of strong number sense ultimately leads to higher mathematical achievement.
According to a study by St. Catherine University, mental computation encourages the incorporation of multiple strategies to solve problems accurately, efficiently and flexibly. The strategies include varying methods of grouping and manipulation of numbers to help solve the problem both easier and quicker.
For example, instead of using traditional arithmetic to add 318 and 119 by starting with the ones place, then the tens place and hundreds place, mental computations add 320 with 120 and then simply subtract 3.
A study by the Rochester Institute of Technology supports the assertion that mental computations build a stronger number sense, finding that mental calculation strategies develop a better understanding of the number system, number relationships and even develop greater mental flexibility.
The development of strong number sense has vast effects on students, and according to a research paper published on the U.S. National Institutes of Health’s National Library of Medicine, students with strong number sense obtain greater overall mathematical success and often perform better at both written calculations and applied problem solving.
Not only does mental computation improve number sense and mathematical comprehension, it also keeps the brain healthy and reduces the risk of memory loss by keeping the brain active. Just as physical exercise builds a strong body, mental exercise also builds a strong brain.
Based on multiple studies published by the Public Library of Science and U.S. National Institutes of Health’s National Library of Medicine regarding dementia risks and cognitive training, Everyday Health recommends mental math as one of the best ways to boost brain memory.
Mental math also exercises the working memory, a system for processing and manipulating information over short periods of time, by juggling around numbers and equations in the short-term memory.
According to “Cognitive Psychology: Mind and Brain” by Edward E. Smith and Stephen M. Kosslyn, applications of working memory range from predicting various sequences of possible chess moves to remembering driving instructions until certain landmarks are reached.
In addition, larger working memory capacities predict higher general intelligence in the form of IQ tests and even faster speed at which skills like computer programming are learned, according to the textbook.
While showing all work has important merits, mental math holds great potential for higher student achievement and health.
Students should not always rely on writing everything down and using their calculators, but rather maximize their usage of mental math outside of tests and quizzes to ensure a healthier, smarter life through improved memory and mathematical comprehension.