Maths in the curriculum, the language of maths and community mathematics for CTET

A child can work out 23 − 15 in a second, yet stares blankly at "A child has 15 stickers. How many more are needed to make 23?" The arithmetic is the same. What has changed is the language, and whether the child can see the subtraction inside a sentence. Three headings in the CTET pedagogy syllabus meet here: the place of mathematics in the curriculum, the language of mathematics and community mathematics. Together they ask one question: how does school maths connect to the child's words and world?

This guide covers each heading, with the NCF 2005 background that the questions draw on, and ends with scenario questions and reasoning.

Why mathematics is in the curriculum

• Thinking: it develops logical reasoning, abstraction and problem solving. This is what the NCF 2005 position paper on teaching mathematics calls mathematisation, and it names it as the main goal. See the nature of mathematics.
• Life: money, time, measurement, shopping, cooking, travel and reading data.
• Other subjects: science, geography, economics and technology use it constantly.
• Habits of mind: precision, patience, checking and arguing from evidence.

The same position paper separates a narrow aim (useful numeracy) from a higher aim (the child's ability to think and reason mathematically), and warns that a curriculum focused only on the narrow aim leaves many children fearful of the subject.

How the curriculum is organised

• Spiral curriculum. Jerome Bruner argued that any subject can be taught in some honest form at any stage, and that ideas should be revisited at increasing depth. Fractions appear as "half a roti" in the early years, as equivalent fractions later and as operations in upper primary.
• Concrete to abstract, with experience before symbols.
• Linked to life and to other subjects, one of NCF 2005's guiding principles being to connect knowledge to life outside the school.
• Stage-appropriate emphasis. In the primary years the stress is on a positive attitude, number sense and spatial sense through games, puzzles, stories and activity. Upper primary brings the first real taste of abstraction through algebra and reasoning in geometry.
• Foundational numeracy. NEP 2020 made foundational literacy and numeracy by Grade 3 an urgent national priority, pursued through the NIPUN Bharat mission.

The language of mathematics

Mathematics has its own vocabulary, symbols and grammar. Each can block a child who is perfectly able to do the maths.

Vocabulary

Symbols and word order

• The same symbol has many readings: 12 − 5 is "12 minus 5", "take 5 from 12", "5 less than 12" and "the difference between 12 and 5".
• Word order can reverse symbol order: "5 less than 12" is written 12 − 5; "subtract 5 from 12" also starts with 12.
• The equals sign means "is the same as", not "the answer comes next". See algebra.

Word problems and the keyword trap

Children are often taught "more means add, left means subtract". It fails quickly.

Example. "A has 15 marbles. That is 6 more than B has. How many marbles does B have?" The word is "more", but the answer is 15 − 6 = 9.

Addition and subtraction problems come in different situation types, and children should meet all of them:

Teaching the language of maths

• Discuss words that have a special meaning in maths, and keep a class word wall.
• Ask children to retell a problem in their own words or act it out before solving.
• Ask children to write their own word problems for a given sum, such as 20 − 7.
• In multilingual classrooms, let children use their home language to talk through problems. NEP 2020 recommends the home language or mother tongue as the medium of instruction until at least Grade 5 wherever possible. See multilingualism.

Community mathematics

Community mathematics is the mathematics that people use in everyday work and life outside school: the vegetable vendor adding bills mentally, the tailor measuring cloth, the mason calculating bricks, the farmer measuring land in local units such as the bigha (which varies from region to region), the cook scaling a recipe, the weaver or rangoli artist creating symmetric designs.

Why it matters for teaching:

• It connects school maths to life, which makes it meaningful.
• It values the knowledge children bring from home, which matters especially for first-generation learners.
• It shows other correct methods. A vendor pricing 4 coconuts at ₹35 each may think "35 and 35 is 70, and 70 and 70 is 140", a doubling strategy that is quite different from the column method.
• It shows that maths is a human activity carried out by people in the child's own community.

Studies of child street vendors in Brazil, published as Street Mathematics and School Mathematics (1993), found that many children who calculated accurately while selling did much worse on the same sums written as school exercises. The lesson for teachers: school maths should build on this competence, not ignore it.

Classroom ideas: interview shopkeepers or parents about how they calculate; run a class market; collect local units of measurement and compare them with standard units; study patterns in local crafts and floor designs.

Scenario questions with reasoning

1. A child can compute 23 − 15 but cannot solve "A child has 15 marbles. How many more are needed to make 23?" The difficulty is mainly with: (a) subtraction facts (b) handwriting (c) memory (d) the language of the word problem
2. Children interview shopkeepers about how they calculate bills. This mainly helps to: (a) finish the syllabus faster (b) improve handwriting (c) connect school mathematics with daily life (d) prepare for board exams
3. Revisiting fractions in Classes 3, 5 and 7 at increasing depth reflects: (a) a spiral curriculum (b) a linear curriculum (c) rote learning (d) a subject-centred approach
4. A child explains a subtraction problem in their home language and gets it right. The teacher should: (a) insist on English only (b) accept it and help the child link it to mathematical terms (c) mark it wrong (d) ignore it
5. The word "odd" confuses some children in a maths lesson. The best response is to: (a) discuss its everyday and mathematical meanings with examples (b) avoid the word (c) punish inattention (d) move on
6. A child's parent, a carpenter, calculates lengths using a method different from the textbook's. In class, the teacher should: (a) tell the child the textbook method is the only right one (b) ask the parent to stop (c) ignore it (d) invite the child to share and compare both methods
7. Asking children to make their own word problem for 20 − 7 mainly develops: (a) neatness (b) speed of computation (c) the link between mathematical language and situations (d) memorisation

Answers and reasoning

1. (d). The computation is known; turning the sentence into a subtraction is the problem.
2. (c). This is community mathematics in action.
3. (a). A spiral curriculum returns to the same idea at deeper levels.
4. (b). The home language is a resource for thinking, and mathematical terms can be added on top.
5. (a). Words with two meanings should be discussed, not avoided.
6. (d). Community methods are valid and comparing methods deepens understanding.
7. (c). Problem posing makes children translate between symbols and situations.

What to do next

• List eight maths words with everyday meanings, like the table above.
• Write one word problem of each type (join, separate, combine, compare) for 13 − 5.
• Note three examples of community mathematics from your own neighbourhood.
• Continue with evaluation in mathematics.