Methods of Teaching Mathematics

Overview

Methods of Teaching is a core pedagogy topic in TS TET Paper I and Paper II Mathematics sections. It tests your understanding of how to effectively teach mathematical concepts to children—not just what to teach, but how to make learning meaningful and lasting.

This topic carries significant weightage because TET assesses your readiness to be a classroom teacher. Questions typically ask you to identify the most appropriate method for a given situation, distinguish between inductive and deductive approaches, or recognise characteristics of activity-based learning. Mastering this topic requires understanding the philosophy behind each method, its classroom application, and when to use which approach.

The three pillars you must know are: activity-based learning (learning by doing), problem-solving method (learning by thinking), and inductive-deductive methods (learning by reasoning). Each serves different purposes and suits different types of mathematical content.

Key Concepts

**Activity-based learning** centres on hands-on experiences where children manipulate objects, conduct experiments, and discover concepts through doing rather than passive listening.

**Problem-solving method** develops higher-order thinking by presenting students with unfamiliar situations that require applying known concepts in new ways—it follows the steps: understand → plan → execute → verify.

**Inductive method** moves from specific examples to general rules (particular → general). Students observe patterns in multiple examples and then formulate the underlying principle.

**Deductive method** moves from general rules to specific applications (general → particular). The teacher states the formula or rule first, then students apply it to solve problems.

**Inductive method is discovery-oriented** and builds conceptual understanding; deductive method is **verification-oriented** and saves time but may lead to rote learning.

**Child-centred methods** (activity-based, inductive, problem-solving) align with NCF 2005's vision of constructivist learning where children build their own understanding.

**No single method is universally best**—effective teachers combine methods based on topic complexity, student readiness, and available time.

Formulas / Key Facts

| Method | Direction | Teacher's Role | Student's Role | Best For | |--------|-----------|----------------|----------------|----------| | Inductive | Examples → Rule | Facilitator | Active discoverer | New concepts, younger children | | Deductive | Rule → Examples | Instructor | Applier | Practice, revision, older students | | Activity-based | Concrete → Abstract | Organiser | Doer/explorer | Primary stage, abstract concepts | | Problem-solving | Problem → Solution | Guide | Thinker/solver | Application, higher classes |

**Key facts to remember:**

Inductive method follows the psychological order of learning (how children naturally learn).
Deductive method follows the logical order of subject matter (how textbooks are organised).
Activity-based learning uses TLMs (Teaching-Learning Materials) like Dienes blocks, fraction kits, geoboards.
Problem-solving method was advocated by John Dewey and follows his reflective thinking model.
NCF 2005 recommends moving from concrete to abstract—this supports activity-based and inductive approaches.
Polya's four steps of problem-solving: Understand the problem → Devise a plan → Carry out the plan → Look back.

Worked Examples

**Example 1: Inductive Method — Teaching "Sum of angles in a triangle = 180°"**

Step 1: Ask students to draw three different triangles (acute, obtuse, right-angled).

Step 2: Students measure all three angles in each triangle using a protractor.

Step 3: Students add the angles for each triangle and record: Triangle A = 60° + 70° + 50° = 180°; Triangle B = 90° + 45° + 45° = 180°; Triangle C = 120° + 35° + 25° = 180°.

Step 4: Students observe the pattern—all sums equal 180°.

Step 5: Teacher helps students generalise: "The sum of interior angles of any triangle is 180°."

*This is inductive because students moved from specific observations to a general rule.*

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**Example 2: Deductive Method — Teaching the same concept**

Step 1: Teacher states the rule: "Sum of angles in a triangle = 180°."

Step 2: Teacher demonstrates with one example on the board.

Step 3: Students solve problems: "If two angles are 65° and 75°, find the third angle."

Solution: Third angle = 180° − 65° − 75° = 40°.

*This is deductive because students started with the rule and applied it to specific problems.*

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**Example 3: Problem-Solving Method — Area application**

Problem: A farmer has 24 metres of fencing. What dimensions of a rectangular field will give maximum area?

Understand: Perimeter = 24m, find length and breadth for maximum area.

Plan: If perimeter = 2(l + b) = 24, then l + b = 12. Try different combinations.

Execute: l=1, b=11 → Area=11; l=2, b=10 → Area=20; l=4, b=8 → Area=32; l=6, b=6 → Area=36.

Look back: Maximum area = 36 sq.m when l = b = 6m (a square).

*Students discover that a square gives maximum area for a given perimeter—this builds problem-solving skills.*

Common Mistakes

**Confusing inductive and deductive** → Remember: Inductive = "I observe many examples first" (Examples → Rule); Deductive = "Definition/rule comes first" (Rule → Examples).

**Thinking activity-based means any classroom activity** → Activity-based specifically means hands-on manipulation of concrete materials, not just answering questions or group discussion.

**Believing deductive method is always inferior** → Deductive method is efficient for revision, time-constrained situations, and mature learners. The error is using it exclusively for introducing new concepts to young children.

**Forgetting the verification step in problem-solving** → Polya's fourth step (Look back) is essential. Students often skip checking whether their answer makes sense.

**Assuming one method fits all topics** → Different content requires different methods. Teaching place value needs concrete materials (activity-based); proving a theorem suits deductive approach; discovering patterns suits inductive approach.

Quick Reference

**Inductive = Specific → General** (discovery-based, psychological, time-consuming but lasting)

**Deductive = General → Specific** (application-based, logical, quick but may encourage rote learning)

**Activity-based = Concrete → Abstract** (hands-on, uses manipulatives, ideal for primary classes)

**Problem-solving = Polya's 4 steps** (Understand → Plan → Execute → Verify)

**NCF 2005 favours** child-centred, activity-based, and constructivist approaches

**Best practice**: Combine inductive for concept introduction + deductive for practice and consolidation

Methods of Teaching