Using Mathematical Concepts to Decipher Languages

By Christa Bedwin

In mathematics, exercises and activities help students to systematically build on what they already know. Through a step-by-step approach, students develop math skills and understanding, and eventually, the procedural ‘how’ evolves into the conceptual ‘why.’

In the same way, language study in natural, practical situations, like travel to foreign countries or even frequent visits to ethnic neighborhoods or restaurants, can provide opportunities for breakthroughs. Basic understanding of foreign language grammatical concepts eventually gives way to natural conversations—opening a new world of possibilities.

Let’s say you’re in Italy and you walk into a coffee shop for a cup of coffee and to ask for directions. If you ask about paying for coffee when it’s delivered to you, you would likely try to put together the words from a pocket dictionary, “I + pay,” to form “io pagare?” without even trying to sort out the grammar.

The server might reply, “Dopo, dopo,” while making calming body motions. Most Italians use a lot of body language and gestures that reinforce their spoken words. You and your students would pick up that “dopo” means “later.” Or, the server might say, “Si, adesso,” and with body language make it clear he would like to be paid now.

Next, you ask for directions but don’t quite understand his reply. So when you head hesitantly out the door, the store owner might say, “Aspette, aspette,” which you understand by his hand gestures to mean you should wait. The owner likely wants to walk out the door with you and show you the directions on the street.

If you were to consult a textbook to determine what learning just took place, the answer would be problem-solving using visual, social and contextual clues. Ben fatto!

The English language has Latin, Germanic and Greek influences, making it easy to learn many foreign words.There are also similarities in grammatical structure with other languages.

To begin identifying the similarities, get an introductory language CD. While driving in the car, start with a few basic words that can be easily picked up. Then, watch your students progress to patterning, problem solving and communication skills.

Identifying Patterns in Foreign Languages

An easy example of recurring patterns in other languages can be found by introducing yourself. This is usually one of the first things a native and foreigner do in conversation. Through this exercise, students will build flexible thinking as they put together the combination of potential words, then compare and contrast the words in different languages.

In English, we usually say: “My name is Jill.” But we can also say: “I’m called Jill.” Or a bit more awkwardly: “I’m named Jill.” Compare to…

French: “Je m’appelle Jill.” (Me, I’m called Jill.)

Spanish: “Me llamo Jill.” (I’m called Jill.)

Italian: “Mi chiamo Jill.” (I’m called Jill.)

Did you notice the similarities in the look and sound of “named,” both llamo and chiamo?

Figuring out the Unknown Variables in a Foreign Language Sentence

When your students learn a new language, they must learn vocabulary and the structure of the language. That includes the order of words, how verbs are conjugated and how nouns are pluralized.

Once your students grasp the structure, they will develop the skill of using known words to guess the meaning of unknown words. Remember our math example? It’s a process similar to finding the unknown number “X” in algebra.

You’ll soon watch your students improve their speed in this game as you travel and learn. And, the neural connections and skills they develop will last much longer than the trip and will carry over into other skills at home.

Let’s look deeper into learning new words that fit in sentences where you expect, which is called decoding logic. For example, let’s say your students learned two tiny things about French:

The pronouns: je (I singular), tu (you singular), nous (us), vous (you plural).

“Est-ce que” in front of something forms a question.

When you meet someone in a hotel, the person might ask: “Est-ce que vous aller au restaurant ce soir?” It looks complicated written out, but your students’ flexible brains will process this in a snap.

The more they practice, the faster they will pick up more words. It’s incredible what a few weeks of trying to communicate in a foreign language will do for your students’ skills.

Here are the steps their brain might go through to decode this phrase.

1. One of the words—restaurant—is the same as the English word. That’s handy and happens a lot..
2. Chop up the code and decode the pieces you know.

“Est-ce que | vous  | aller au |  restaurant |  ce soir?”

| you (plural) | …Unknown1 | restaurant | …Unknown2

Okay, we know it’s a question because it starts with “est-ce que.” And, they’re talking about all of us and the restaurant.

Your students already know three of the five pieces!

3. Because we know the sentences in French follow the same structure as English, we can guess without much thought that Unknown1 is a verb. What would we do? We’d go to the restaurant. Okay! That must mean “aller” means “go” and “au” means “to the.” That can be confusing, which is perfect for further learning. This “cognitive dissonance,” as educators call it, will send curious kids straight to their language lesson to figure out why “au” is two words here.
4. What would come after “restaurant?” Probably a time. You can pick up what time they are talking about by looking at the context of the conversation. In this case, the Unknown2, “ce soir”, means “this evening.”

When your curious students look at their phrase book again, they will find other time phrases such as matin, midi, après-midi and nuit (morning, noon, afternoon and night).

This overall process captures the benefits of homeschooling. Students in a traditional French class will waste countless hours learning simple words like “ce” and “au” vs. “a le” that can be difficult to assimilate and remember.

However, in our travel-based, problem-solving learning environment, those little words fall into place on their own in real-world practice. The desire to get the words right in the company of others is a fantastic motivator for students. This will drive them to their book to find (and remember!) the right way to use what they learned.

3 Ways to Apply Math to Language Learning at Home

If you are not planning an international field trip, your family can still benefit from applying math to language learning. Here are some fun homeschool activities to try with Google Translate.

1. Look up lists of Latin words and compare to their English, French, Italian and Spanish equivalents.
2. Race to see who can be the first to find five very similar words in two to three languages. Explore which subject areas are most likely to have similar words.
3. Help your students make charts of equivalent words in an area of their own interest. If they choose a modern field such as computers, have them identify English words that are used throughout many languages. If they choose an historical period centered on ships, have them look up the etymology (word history) of a few key words or phrases. This could easily lead to an exciting study of various trade routes and empires that caused languages to mix throughout history.

Endless adventures at home and abroad await in the exploration of foreign languages. Applying math principles to the learning of languages will help get you well underway.