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Language of Mathematics — REET Notes

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This page covers REET maths-pedagogy's 'Language of Mathematics' topic — why maths is called a language, how everyday language relates to mathematical vocabulary and symbols, and the role of language in word problems are explained with simple examples. This topic is included in the maths-pedagogy syllabus for both REET Level 1 and Level 2, so understanding the right strategy for teaching vocabulary in the classroom matters.

  • 0 questions in REET 2024 (syllabus-based notes)
  • Teacher-training level
  • 7 min read
Verified 17 September 2026 · Source: BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

How this topic is asked in REET

No direct question on 'Language of Mathematics' was found in the REET 2024 paper records, yet it's included in the official BSER maths-pedagogy syllabus under the section on the nature of mathematics. This topic focuses on why mathematics' own symbols, vocabulary and sentence structure function like a 'language', and on how teachers should connect this to children's everyday language. The notes below are based on the syllabus wording and established pedagogical principles — no imagined 'previous question' has been used.

Why mathematics is called a 'language'

Mathematics is often called 'a language' because it too has its own vocabulary (sum, difference, product, quotient), its own symbols (+, −, ×, ÷, =, <, >), and its own grammar-like rules (such as the order of operations), which let it express ideas with remarkable precision and brevity. Just as a spoken language has rules of sentence structure, mathematical expressions also follow a fixed order and meaning when symbols are written down.

The mathematical language has three big characteristics — precision (every symbol has exactly one fixed meaning), conciseness (even complex ideas can be written in small symbols) and universality ('2+2=4' means the same thing wherever in the world it's written, no matter what spoken language the reader speaks). This universality is exactly what sets mathematics apart from other subjects.

Everyday language and mathematical language

Everyday phraseMathematical operation/symbol
adding, combining, altogether+ (addition)
taking away, less, left over, remaining− (subtraction)
times, of (e.g. 1/4 of 5)× (multiplication)
sharing equally, splitting into parts÷ (division)
is equal to, is the same as=
more than, greater than>
less than, smaller than<

Teachers should teach this mapping explicitly in class, because an incorrect connection here is exactly what causes the most common mistake in word problems.

The contribution of the Indian numeral system

The number-writing system used across the world today is called the 'Hindu-Arabic numeral system', because its foundation — the place value system and the concept of zero (0) — was developed in India and later reached Europe through Arab mathematicians. This is a direct historical example of how universal the language of mathematics is — the very same numeral system is used today by speakers of almost every language, in almost every country.

The role of language in word problems

Many students know how to calculate, but still can't solve word problems, because the real challenge lies in 'translating' everyday language into the correct mathematical operation, not in the calculation itself. For example, take 'a basket has 24 apples, 8 of them were given away, how many are left' — the sentence first has to be recognised as subtraction (24−8), and only then does the correct answer follow.

This challenge is even bigger for children studying through Hindi medium while also grappling with English mathematical terms (like sum, difference, product), or whose home language (mother tongue) differs from the school's language of instruction. In such cases, a teacher's role isn't limited to teaching the operation — it extends to building a bridge between language and mathematics.

Major types of mathematical notation

Mathematical symbols can be broadly grouped into four categories — numerals/numbers (0-9, and building larger numbers using place value), operation symbols (+, −, ×, ÷), relation symbols (=, <, >, ≠), and symbols related to shape/measurement (like ∠ for an angle, π for the circumference-to-diameter ratio). Each group has a fixed, universal meaning that cannot be changed — this fixedness is exactly what sets mathematical language apart from everyday spoken language, where the same word can carry several different meanings.

It's important for a teacher to understand that children first learn the language of numbers (counting, number recognition), and only gradually move towards the language of operation and relation symbols — so any new symbol should not be introduced directly in symbolic form; it should first be introduced through concrete objects and pictures.

Using this in the classroom

SituationWhat the teacher should do
Teaching a new mathematical word (like 'sum')First connect it to a concrete example and an everyday sentence (like 'putting two things together'), then introduce the symbol and the formal word
Getting students to solve a word problemFirst have the student restate the sentence in their own words, then ask 'which operation is hidden here' — this practises the translation from language to maths
Teaching children studying maths in a second languageExplain mathematical vocabulary by connecting it to words the children already know in their familiar/mother tongue, rather than skipping translation altogether
Making sure symbols (+, −, =) are understood correctlyHave children read symbols out loud in sentences repeatedly (like reading '=' as 'is equal to'), so they don't come to see it merely as a signal to 'write the answer next'

A trick worth remembering

Before solving any word problem, remind students of three steps — 'read, recognise, then write': first read the sentence carefully, then identify the operation hidden inside it (+, −, ×, ÷), and only then write the mathematical expression. This order emphasises understanding the language before the calculation, which prevents the most common mistakes.

Practice questions

Question 1

Why is mathematics called a 'language'?

  1. Aक्योंकि यह केवल संख्याओं का विषय है
  2. Bक्योंकि इसमें कोई प्रतीक नहीं होता
  3. Cक्योंकि यह केवल अंग्रेज़ी में ही पढ़ाई जाती है
  4. Dक्योंकि इसके भी अपने प्रतीक, शब्दावली व नियम होते हैं जिनसे विचार सटीक रूप से व्यक्त होते हैं

Explanation

Mathematics has its own vocabulary, a system of symbols and sentence-structure-like rules, all of which let ideas be expressed with precision, and this is exactly why it is called a 'language'.

Question 2

How would '3 more than 5' be written in mathematical language?

  1. A3 − 5
  2. B5 × 3
  3. C5 + 3
  4. D5 − 3

Explanation

The phrase 'more than' signals addition, so '3 more than 5' means 5+3.

Question 3

What does the mathematical symbol '>' represent?

  1. Aजोड़
  2. Bसे बड़ा
  3. Cसे छोटा
  4. Dबराबर

Explanation

The symbol '>' means 'greater than', while '<' means 'less than'.

Question 4

The numeral system used worldwide today is called the Hindu-Arabic numeral system. Its foundation — place value and the concept of zero — is mainly credited to which origin?

  1. Aभारत में विकसित हुई अवधारणाएँ
  2. Bकेवल रोमन अंक पद्धति
  3. Cकेवल यूनानी गणितज्ञों की देन
  4. Dकेवल चीनी अंक पद्धति

Explanation

The place value system and the concept of zero were developed in India and reached Europe through Arab mathematicians, which is why the system is called the 'Hindu-Arabic numeral system'.

Question 5

To solve the word problem 'A basket has 24 apples. 8 were given away. How many remain?', what skill does the student need first?

  1. Aकेवल गुणा करना
  2. Bचित्र बनाना अनिवार्य है, अन्यथा हल नहीं हो सकता
  3. Cभाषा को सही गणितीय संक्रिया (घटाव) में पहचानना/अनुवाद करना
  4. Dकेवल संख्याएँ पहचानना, संक्रिया की ज़रूरत नहीं

Explanation

The first and most essential skill in solving a word problem is recognising which operation is hidden in the sentence — here, the words 'given away/left over' signal subtraction (24−8).

Question 6

The phrase 'sharing equally' is related to which mathematical operation?

  1. Aघटाव (subtraction)
  2. Bभाग (division)
  3. Cगुणा (multiplication)
  4. Dजोड़ (addition)

Explanation

Phrases like 'sharing equally' or 'splitting into parts' indicate the operation of division.

Question 7

What is the key characteristic of mathematical language that distinguishes it from everyday spoken language?

  1. Aयह केवल मौखिक बातचीत के लिए बनी है, लिखने के लिए नहीं
  2. Bयह हमेशा अस्पष्ट व अनिश्चित होती है
  3. Cइसका कोई निश्चित अर्थ नहीं होता, बोलने वाले पर निर्भर करता है
  4. Dयह सटीक, संक्षिप्त व सार्वभौमिक प्रतीकों पर आधारित है

Explanation

The defining feature of mathematical language is its precision, conciseness and universality — every symbol keeps a fixed meaning, wherever it's read, and whoever reads it, in whatever spoken language.

Question 8

What is the most suitable way to teach mathematical vocabulary (like 'sum', 'difference', 'product') in class?

  1. Aशब्द को ठोस उदाहरण व रोज़मर्रा की भाषा से जोड़कर सिखाना
  2. Bशब्दावली सिखाना आवश्यक नहीं, बच्चे स्वयं समझ जाएँगे
  3. Cकेवल शब्दकोश-जैसी परिभाषा रटवाना
  4. Dकेवल अंग्रेज़ी शब्द रटवाना, हिन्दी अर्थ न बताना

Explanation

Any new mathematical word should first be connected to a concrete example and everyday language, only then do the formal word and symbol stay meaningfully in memory.

Question 9

What is the correct meaning of the symbol '='?

  1. Aजोड़ करना है
  2. Bदोनों पक्षों का मान बराबर है
  3. Cप्रश्न समाप्त हो गया
  4. Dअगला चरण शुरू होता है

Explanation

The correct meaning of '=' is that the value of the expressions on both sides is equal — treating it merely as a signal to 'write the answer next' is a common misconception.

Question 10

For children learning mathematics in a second language (e.g. English maths terms in a Hindi-medium class), what should the teacher primarily do?

  1. Aअनुवाद से पूरी तरह बचना, ताकि बच्चे अंग्रेज़ी सीख लें
  2. Bकेवल पाठ्यपुस्तक की भाषा में पढ़ाना, कोई अनुवाद न करना
  3. Cगणितीय शब्दावली को बच्चों की परिचित/मातृभाषा से जोड़कर स्पष्ट करना
  4. Dशब्दावली की समस्या को नज़रअंदाज़ करना

Explanation

When mathematical vocabulary is explained by connecting it to children's familiar/mother tongue, the language barrier is reduced and children understand the concept better.

Frequently asked questions

How many questions come from 'Language of Mathematics' in the REET exam?+

No direct question from this topic was found on record in REET 2024, but it is included in the BSER maths-pedagogy syllabus, so preparing it shouldn't be skipped.

Why is mathematics called a 'language'?+

Because it too has its own vocabulary, symbols and grammar-like rules, which let ideas be expressed precisely, concisely and universally.

Where do children make the most mistakes in word problems?+

Most mistakes happen not in the calculation, but in recognising and translating everyday language into the correct mathematical operation — for example, always linking the word 'of' to multiplication without checking the context.

How does the Hindu-Arabic numeral system relate to the language of mathematics?+

Its foundation (place value and zero) was developed in India, and it's now used almost universally — this shows how the language of mathematics carries the same meaning across geographic and linguistic boundaries.

What are the main groups mathematical notation can be sorted into?+

Broadly, four groups — numerals/numbers, operation symbols (+,−,×,÷), relation symbols (=,<,>), and symbols related to shape/measurement (like ∠, π) — each with a universal, fixed meaning.

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REET Syllabus 2024

See the complete official REET Level 1 and Level 2 syllabus, subject-wise.

REET 2024 Solved Papers

Read the REET 2024 previous papers with answers and explanations.

Official Sources

  1. BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked