The word “algorithm” is getting a lot of air time these days. Between references to “The Algorithm” used by YouTube, Facebook, or other social media and online entertainment platforms and “use the ____ algorithm to solve these problems” instructions on your child’s math homework, you’re probably already sick of this word.
The word’s been around much longer than you might think. In the past several decades, it was a term primarily used in computer science. But it’s even older than that.
In short, an algorithm is a group of steps and actions followed in a repeatable order. Algorithms get us from a starting point (“inputs”) to a desired end (“outputs”). Usually the inputs and outputs are data or information, especially in modern times, but algorithms might be used in creating physical objects such as in woodworking, manufacturing, food service, or lots of other places.
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Why Algorithms
Algorithms are useful and powerful in their ability to create reliable, predictable outcomes. Moreover, algorithms can be taught to people of all different skill levels, as well as to machines and computers. Algorithms increase the reliability and predictability of outcomes with minimum effort. They can be used for both good, bad, and well-meaning-with-unexpectedly-poor-results (as discussed in Weapons of Math Destruction by Cathy O’Neill — affiliate link).
Algorithms are often (not always) an efficient way of performing a task. Sometimes, as in many of the “traditional algorithms” of arithmetic, this efficiency is gained while sacrificing transparency and understanding.
Algorithms in Modern Math Class
In math class, your child might be taught a variety of algorithms. Some of them (such as the area model) may confuse you because they are different than the algorithms you were taught. The methods that tended to be taught from the 1980s through the early 2010s are now often referred to as the “Traditional Algorithm[s]”. Your child will learn these in school as well.
Before your child is taught the traditional algorithms, they will be encouraged to explore and discover numbers and develop a sense of how our numbers work. Ultimately, this “play” time with numbers will develop a deeper appreciation of how and why chosen algorithms do work, how to choose which one to use, not to mention how to program a machine to perform the algorithm more efficiently than most humans ever could.
The few algorithms the children are taught in the early days of a math concept are chosen to build this support of numeracy systems, a familiarity with how numbers work, and connections between the current topic and previous ones. It is important not to skip this part of the learning and exploration. Algorithms without a strong foundation are easily forgotten. With a strong underlying understanding, algorithms are not only more easily remembered, but are more easily re-created when forgotten.
Examples of Math Algorithms
Any process that is a set of rules or procedures in math class is an algorithm. This includes, but is not limited to,
- long division,
- order of operations,
- factoring using the ac-method,
- FOIL,
- carrying and borrowing,
- factor trees and factor ladders,
- cross-multiplying to solve proportions,
- multiplying by the reciprocal (in fraction division),
- slope formula for a line.
Why Have Algorithms in Math Class Changed?
When I was in school, calculators existed for arithmetic, but graphing calculators were brand new. We certainly did not walk around with powerful computing tools in our pockets at all times. When my parents and grandparents were children, it was important that humans knew how to reliably, accurately, and efficiently calculate sums, differences, products, and quotients. While cash registers had basic arithmetic functions, the human worker still needed to do quite a lot of arithmetic themselves even in everyday life. The “traditional algorithms” had high importance as an efficient, consistent way that humans across the globe could learn, do, and agree on the results.
Today, we walk around with powerful computing machines in our pockets. And on our store counters. And in our cars (does yours estimate your gas mileage for you?) And throughout our homes: even our microwaves now perform simple addition processes when you hit the “30 seconds” button in the middle of a session! These machines beat almost all humans in both accuracy and efficiency of arithmetic, no matter how well the human knows various algorithms.
However, there’s still a human element in that reliability piece. We still need to be able to recognize when the cashier types in a wrong number and asks us to pay the wrong total. We still need to recognize when we make our own calculator typos. We still need to make quick judgment calls where it might be rude or too slow to pull out these calculating machines. At least a few of us even need to be able to program these algorithms into the machines.
Being able to estimate is thus exceedingly important both then (for speed) and now (occasionally for speed, but mostly for tests of reliability and accuracy of results). In order to use estimation, a sense of numeracy, or the basic ways the numbers are related and the number system works, is crucial. Before the days of calculators everywhere, basic numeracy was gained in the course of everyday operations: shopping, skip counting while skipping rope, rhythms that made cooperative manual labor just work better, and much more. Now, a lot of those experiences are either no longer parts of our lives or are supplemented by machines and computers.
Further, we now know that a heavy emphasis on speed, rote memorization that feels pointless, and heavy algorithmic testing yields high stress, anxiety, loss of learning, and hatred of math class. Many of us in what I might call the “sandwich generations,” where computers were shrinking and becoming more available, experienced the worst of these effects. I don’t know about you, but I don’t wish those on any of today’s children.
So modern mathematics teaching and learning must focus first on numeracy, and second on algorithmic calculations. (In their podcast “The Harmful Effects of Algorithms,” Build Math Minds discusses in more detail why this is important.) The problems and strategies your child brings home are firstly focused on building that sense of numeracy. Some of those strategies still qualify as algorithms, as they do involve a step-by-step process of getting from a starting point to a goal. Other strategies ask for a more exploratory, playful, and/or creative approach, allowing for a deep sense of numeracy to develop as different number relationships are discovered along the way.
Your child will be taught the same algorithms you were taught. Eventually. In the meantime, be patient and explore these numeric ideas with them. Bring your sense of playfulness and discovery, and keep that magic of numbers and learning alive for your child as long as possible. The more you can do this, the more they (and you!) will uncover about numbers, and the better they will understand and remember the algorithms when they do learn them.
You’ve Got This!
