How Learning Maths and a New Language are Interlinked

How Learning Maths and a New Language

The Abstract

Language as a concept is also a universal constant, without which no society on earth could function, and although there is staggering variation in languages, a language like English is also arguably one of the most universally applicable. It is based on a set of (largely) simple principles, lacks complex gendered nouns, is based on the Roman alphabet so its symbols correlate well with the phonetic pronunciation, and it is the 2nd-most spoken language in the world behind only mandarin, with around 983 million speakers worldwide. But did you know that your likelihood of being proficient at learning a new language is likely to be linked to your proficiency in the universal language of mathematics?

If you were under the impression that the two disciplines of maths and languages were mutually exclusive, then you wouldn’t be alone. After all, they’re two distinctly separate subjects and are taught as such. One seeks to quantify and explain phenomena like structure, space, change (over time, distance, altitude, pressure, and so on), and of course quantity. Language is a form of either written or verbal communication that takes the form of a structure with complex rules and peculiarities. On the surface, they don’t sound like two peas in a pod. That is, however, until you realise that both maths and language involve some similar frameworks.

Firstly, both require the use and the understanding of abstract thoughts and thought processes in order use them. For example, the differences between the pronunciation of the “A” sounds between the words apple, amoral, articulate, and amazing, are impossible to explain simple by knowing the how the letter “A” sounds; knowing how these are pronounced is a matter of understanding context, as is understanding the meaning abstract nouns like “love”, “hate” or “anger”. Similarly, formulating a mathematical theory to explain the workings of the physical world requires application of abstract logic and theorising about the intangible. It is even argued that learning maths in the abstract - https://scienceblogs.com/notrocketscience/2008/04/24/when-learning-maths-abstract is superior to real or literal.

At its most basic, if you cannot understand the meaning of a word – let’s take “love” as an example – then it is impossible to consistently utilise it in a sentence and in everyday conversation. If you dislike someone, but say that you “love” them, then you do not understand the meaning of the word “love”. Similarly, if you see the number 5 yet cannot understand what it means, then you cannot know that it is comprised of 3+2, or that 20-15 equals this number. To the uninitiated, love and 5 are as abstract as each other, but knowing their meaning allows the prospective linguist or maths enthusiast to utilise them properly.

A Matter of Patterns, Logic, and Deduction

Perhaps the strongest correlation between the two disciplines is seen when looking at how they both utilise logical patterns in order to present the information they are designed to communicate to the learner. So rather than simply dumping a textbook in front of students and asking them to memorise dozens of complex equations, there is evidence that teaching in the abstract - https://www.whizz.com/blog/abstract-concepts-better-teaching-maths/ allows for more efficient learning. This is because abstract principles are more transferrable than specific ones and allow the learner to apply them to a variety of problems – whether in language or mathematics.

The easiest way to represent this is through an example of the use of pattern recognition, as well as simple logic and finally some deduction to seal the deal. The problem:

An energy company charges $120 per month for 200 Kilowatt Hours of Energy, with an additional fee of $2 per additional kilowatt hours that exceed the 200-kilowatt monthly limit.

This sentence contains a subject and an object (with object being the kilowatt hours and the subject being the energy company); these are two principles within the English language that are taught at its most basic level. Similarly, the above can be represented as an equation:

C = 120 + 2k (where C represents the total monthly cost to the customer, and k represents the number of kilowatt hours that exceed the monthly limit of 200 kilowatts)

Even though the separated sentence looks different to the equation, they are both valid explanations of the relationship between energy usage and the price of the energy used per month. In order to take advantage of the abstract being more useful for learning than the concrete/specific, one would therefore not simply memorise the above equation, but the relationship between the different objects/subjects within. The very same applies to the learning of the English language as demonstrated so eloquently by Andrew Biggs - https://andrewbiggs.com/ who uses this logic to teach people a variety of languages.

I Before E, Except After C (Except When It’s Not)

Of course, when drawing comparisons between learning languages and learning mathematics, many will be made uncomfortable by the tremendous wealth of exceptions contained in most of the frameworks of many languages on this planet. In English, you are taught that “an” is to prefix any word beginning with vowel and “a” is to prefix a word beginning with a consonant. However, one would always say “I’ll be the in an hour”rather than “a” hour, directly violating what many are taught.

However, these kinds of unusual exceptions and imperfections also exist in mathematics. Though Pi is a mathematical constant, its digits stretch to the millions, and so is most often abbreviated to 3.14159. Similarly, attempting to estimate the areas of irregular shapes involves the monte carlo integration, which utilises random numbers in its calculations. Therefore, mathematics and languages share similar peculiarities and exceptions within their frameworks.

It’s In the Brain

Finally, it has also been observed that the learning of second languages may directly affect how the brain processes language and mathematics. Being bi-lingual not only has benefits such as slowing down the progress of dementia, but being able to utilise and differentiate between two or more different language frameworks can also allow the brain to apply these changes to the frameworks, rules, and exceptions of mathematics. These observations follow from the well-researched observation of the basal ganglia’s role in language development - http://www.ens.fr/agenda/role-basal-ganglia and use of the knowledge/frameworks surrounding languages. These relationships have also been shown to have direct correlation to the rules that govern various mathematical concepts.