Perhaps you’ve heard someone make the claim that “math is a language.”
Maybe you’ve made that statement yourself because you truly believe it.
On the other hand, you might never have considered the idea before. No matter which of these describes you, it's a question math educators should think about since the answer is bound to affect how we approach effectively teaching math and mathematical discourse.
In considering whether math is a language, we first need to ask, “What exactly defines a language, and does math meet these criteria?
One common way to define language is a system of communication that conveys ideas and concepts.
Another way to think about language is by considering its component parts. A language has vocabulary, the basic units of meaning (words or symbols), and grammar, the rules for using the vocabulary.
A language also has syntax, the structured order in which these symbols are arranged to convey meaning. These components work together to allow the communication of ideas.
On careful consideration, most of us would agree that math fits this definition.
Consider equations. They are a kind of mathematical sentence, concisely expressing relationships and properties. Let’s take a simple example.
2 + 3 = 5
We have a vocabulary, including numbers (2, 3, 5) and symbols (+,=). We also have rules of syntax and grammar that dictate what is allowed and how the meaning can change with changes in syntax. Consider the following change to our example.
3 + 2 = 5
This equation, or “sentence,” is still “grammatically correct,” even if it has a slightly different meaning. Now, let’s try something else.
2 + 5 = 3
Although this version seems to follow the rules of syntax, it is not "grammatically correct.”
This is precisely how language works. Let’s try this with a simple English sentence.
Red and green are colors.
This sentence is syntactically and grammatically correct. We’ll make a small change.
Green and red are colors.
This one is slightly different but still correct.
Red and colors are green.
Once again, although we are following the rules of syntax, the sentences do not convey a logically correct idea.
It’s clear that math possesses many of the hallmarks of language, so what are the implications of this conclusion for math education?
By recognizing math as a language, we can better choose and implement appropriate teaching and intervention strategies to foster deeper comprehension and fluency in numerical expression.
But to truly harness the power of math as a language, we must first understand its intricacies and nuances.
As we delve deeper into the complex relationship between mathematics and language, we discover an intriguing interaction between these two seemingly different ways of thinking.
Natural languages and mathematics both have distinctive structures and communication modalities, but they also share fundamental syntactic, semantic, and practical considerations.
By drawing connections between math and language, we can take advantage of the human brain’s natural facility for language.
If human brains are wired for language, and math is a language, then there’s no reason for anybody to make the claim, “I’m not a math person.”
The very fact that you can use language to make that claim shows that you are, in fact, a math person.
The ties between math and science are numerous and strong. Math is often called ‘the language of science,’ and with good reason.
Math gives scientists a common framework for explaining, evaluating, and forecasting natural phenomena. In all scientific disciplines, including physics, chemistry, biology, etc., mathematical concepts like functions, equations, and statistical models are indispensable resources.
For example, Newton's laws of motion are mathematically expressed in physics to predict how objects will move. Differential equations are used in population growth models in biology to comprehend ecological dynamics.
Math acts as a universal language, bridging disciplinary boundaries to facilitate more profound discoveries and improved communication within the scientific community.
Many of what we call laws in science are basically mathematical equations.
Perhaps the most famous example of this is Newton’s law of universal gravitation, the law that describes the force of gravity between any two objects in the universe.
What might look complex at first is actually pretty simple.
Mathematically, the equation is made up of some multiplication and division (allowing that squaring is just multiplying a number times itself).
Looking at it as a sentence that describes gravitational attraction, what does it tell us?
“The force of attraction (F) depends on (=) the mass of the two objects we’re looking at (M & m), the distance between them (r), and some other number, the gravitational constant (G).”
Starting with that basic idea, communicated through the language of math, we can derive other ideas and express them in simple language.
“If the mass of either object (M or m) gets bigger, the force of gravity (F) gets bigger.”
“If the distance between the objects (r) gets bigger, the force of gravity (F) gets smaller.”
The connection between the math and the words is clear. Understanding one helps us understand the other. We’re basically translating from one language to another.
Math is frequently referred to as the "universal language," a tool that transcends linguistic and cultural barriers.
Its basic concepts are universally applicable and offer a basis for mutual comprehension and communication.
The meaning of the equation E=mc^2 remains the same whether we’re in Houston or Hanoi. Because of this universality, math is a language we can use to communicate with others around the world.
Experts agree that should we encounter intelligent life beyond our solar system, math offers our best chance as a viable form of communicating with them.
Here on this planet, in our classrooms, math as a universal language promises more tangible and immediate benefits.
Students new to the country and struggling with English frequently do better in math class since, no matter where they come from, that part of the world still uses the concepts of numbers, addition and subtraction, multiplication and division, etc.
Students who struggle with verbal communication for other reasons also can often be “reached” through the language of math.
Acknowledging math as a language creates exciting new possibilities for both communication and education.
Math, with its own vocabulary, grammar, and syntax, can express complicated ideas accurately in ways that are understandable to kids and adults across language, cultural, and even cognitive barriers.
Understanding math as a language anyone can speak helps teachers and students alike overcome the very common resistance of those who believe they are not “math people.”
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Perhaps you’ve heard someone make the claim that “math is a language.”
Maybe you’ve made that statement yourself...
