NIOS : Online Contact Pgm. 25.10.2026 Session - 4 : Pedagogy of Mathematics

Summary

The session covers Lessons 3 and 4 of Pedagogy of Mathematics, focusing on mathematical communication and effective ways to teach mathematics at the primary level. Its central message is that children learn mathematical ideas more meaningfully when teaching begins with familiar experiences, hands-on exploration, discussion, and reflection, and then gradually moves toward pictures and symbols.

Lesson 3: Mathematical Communication

Data handling

Data can be introduced through children’s everyday lives rather than through abstract examples or overly large sets of numbers.

• Collect familiar data: For example, the number of people in each student’s family, the distance from home to school, the number of boys and girls in a class, or the types of vehicles in the neighbourhood.
• Organize the data: Raw data can be difficult to interpret. Arrange it in a useful order, such as ascending or descending order, or group it by category.
• Represent the data: Use pictographs or tally marks. Pictures and icons can make numerical information more accessible to young learners, provided the symbols clearly match what they represent.
• Interpret the data: Ask children to read a pictograph and answer questions such as which category has the most or least, how many items there are altogether, or how much two quantities differ.
• Develop questions: Children should practise creating their own questions from a chart or pictograph, not just answering questions about the data.
• Use mathematical vocabulary: Reinforce terms such as more, less, most, least, equal, group, total, and count in different contexts.

The sequence of collecting, organizing, representing, and interpreting data helps develop analytical and problem-solving skills. Real-life contexts can also make numbers feel less abstract and reduce children’s anxiety about mathematics.

Visualization and spatial thinking

Children develop an understanding of space by noticing objects, their shapes, positions, and directions.

• Use a reference point when describing position: A location makes sense in relation to another object or place. For example, “above the table” uses the table as a reference point.
• Build spatial vocabulary: Have children describe positions and directions, and practise reading or drawing simple maps. A classroom or school map might use a familiar feature, such as the entrance, as its reference point.
• Explore shapes with real objects: Let children handle, identify, combine, sort, and arrange objects to discover shapes and make patterns.
• Distinguish shape from structure: Shape refers to a geometric form; structure concerns the material an object is made from. For example, a triangle may be made from paper, clay, or cement.
• Explore patterns and symmetry: Encourage children to look for patterns in flooring, clothing, walls, and other surroundings, and to investigate symmetry in bodies, flowers, and leaves.
• Connect 2D and 3D forms: Opening a box and examining its flattened surfaces can help children see how a three-dimensional object relates to two-dimensional shapes.
• Introduce maps as visual representations of space: Use familiar maps—such as classroom, school, neighbourhood, or transport maps—to discuss location, direction, and relative distance. Begin with comparisons such as “nearer” and “farther” rather than exact measurements.

The lesson’s case study contrasts a hands-on approach, in which children explore objects and discover shapes, with an approach that begins by explaining abstract shape concepts. The speaker recommends giving children opportunities to explore first, while the teacher introduces accurate mathematical language and concepts when appropriate.

Lesson 4: Teaching and Learning Approaches

Experiential learning

Experiential learning involves both hands-on activity and reflection. Teachers can encourage reflection by asking thoughtful questions about what children did and how they reached an answer.

The session describes four connected stages:

1. Concrete experience: Let children work with physical materials and experience a concept directly.
2. Reflection: Ask children to explain their process, consider what happened, and discuss their reasoning.
3. Abstract conceptualization: Help children recognize the general mathematical idea beyond the particular materials or example. For instance, addition is the joining of quantities, not merely the combining of two particular kinds of objects.
4. Active experimentation: Give children opportunities to apply the idea in a new setting, such as adding objects at home or solving a different kind of problem.

Where possible, complete the stages as a learning cycle. Moving to an answer too quickly—or teaching a standard written algorithm before children understand the concept—can leave gaps in learning.

Experience–Language–Picture–Symbol (ELPS) approach

The ELPS sequence moves from concrete experience toward abstract mathematical notation:

• Experience: Children handle and manipulate objects, such as sticks, stones, buttons, or leaves.
• Language: They describe what they are doing using familiar language, with mathematical vocabulary introduced and reinforced gradually.
• Picture: They represent the experience through drawings, images, or diagrams.
• Symbol: They move to numbers, signs, and formal procedures once they understand what the symbols represent.

For example, children might group sticks into bundles of ten, discuss the groups, view a drawing of the bundles, and then represent the quantity symbolically. Teachers should keep earlier stages connected as children progress and return to objects or pictures if symbolic notation is confusing.

The four-block approach

The session presents four parts that can structure a mathematics lesson:

1. Mathematical talk: Begin with conversation, stories, rhymes, riddles, puzzles, or games that connect to children’s existing experiences and prompt curiosity.
2. Skill teaching: Teach the target idea in a clear sequence, moving from concrete materials to visuals and then to symbols or procedures.
3. Skill practice: Reinforce learning through varied problems, examples, contexts, reasoning, demonstrations, or peer teaching. Practice should involve variation, not just repetition of the same exercise.
4. Mathematical games: Use board games, card games, traditional games, physical activities, or digital games where available. Games can make learning enjoyable and provide opportunities for problem-solving, cooperation, and healthy competition.

A possible lesson structure might include 5–10 minutes of mathematical talk, about 20–25 minutes of teaching, roughly 15 minutes of practice, and a concluding game. These timings are suggestions; the key principle is to include all four elements.

Additional Guidance for Teachers

• Choose suitable manipulatives: Materials should be safe, age-appropriate, affordable, engaging, and inclusive. Everyday classroom or environmental materials can work; specialized equipment is not essential.
• Focus on children’s reasoning, not only their answers: When an answer or written method is incorrect, identify whether the underlying concept is understood and whether the difficulty lies in how it was represented. Use discussion and reflection to determine what support is needed.
• Adapt textbooks to children’s contexts: A textbook is a resource, not a complete teaching plan. Teachers can connect its examples to local experiences or create classroom activities, such as a small fair, to make unfamiliar topics meaningful.
• Connect concepts across lessons: Data, shapes, patterns, maps, and number work can reinforce one another. Combining these ideas supports a more connected understanding of mathematics.

Speakers and Sources

• Professor Jyoti Sharma — Guest presenter from the Cluster Innovation Centre, University of Delhi; led the discussion on mathematics pedagogy.
• Ashish — Host and session facilitator.

Educational frameworks and materials referenced: the Experience–Language–Picture–Symbol (ELPS) approach; Bruner’s learning stages; the National Education Policy; the National Curriculum Framework for the Foundational Stage; and NCERT materials, including an example involving the Surajkund Mela.