Problems of Teaching

Problems of Teaching Mathematics at Primary Level

Overview

Teaching mathematics to young children (Classes I–V) presents unique challenges that every aspiring primary teacher must understand. This topic appears regularly in UTET Paper I under the Mathematics Pedagogy section, testing your awareness of real classroom difficulties and appropriate solutions.

The problems range from abstract nature of mathematical concepts to resource constraints in schools, from math anxiety among students to inadequate teacher preparation. Understanding these challenges is crucial because UTET expects teachers who can identify problems and apply remedial strategies. Questions typically ask you to identify a teaching problem from a classroom scenario or suggest appropriate solutions.

Mastering this topic requires you to think from both perspectives—why students struggle with mathematics and why teachers find it difficult to teach effectively at the primary level.

Key Concepts

• Abstract nature of mathematics creates a fundamental barrier—young children think concretely, but math deals with symbols, numbers, and operations that have no physical form they can touch or see directly.
• Math anxiety is a real psychological barrier where fear of mathematics prevents students from engaging with the subject, often transmitted unknowingly by teachers or parents who themselves fear math.
• Language of mathematics differs from everyday language—words like "difference," "product," "table," and "volume" have specific mathematical meanings that confuse children who know only their common usage.
• Cumulative nature of mathematics means gaps in foundational concepts (place value, number sense) create cascading failures in later topics—a child weak in subtraction cannot learn division.
• Individual differences in mathematical readiness within a single classroom force teachers to manage children at vastly different levels simultaneously.
• Rote learning tradition persists where teachers emphasise memorising tables and procedures without building conceptual understanding, leading to mechanical learning.
• Lack of concrete materials in many schools prevents teachers from using manipulatives (blocks, counters, shapes) essential for primary math instruction.
• Disconnect from daily life occurs when textbook problems feel artificial and children cannot see why mathematics matters in their world.

Key Facts

Five teacher-side problems to remember:

1. Insufficient content knowledge in mathematics itself
2. Lack of training in activity-based methods
3. Pressure to complete syllabus over ensuring understanding
4. Inability to diagnose specific student difficulties
5. No exposure to child psychology and developmental stages

Five student-side problems to remember:

1. Weak pre-number concepts (seriation, classification, conservation)
2. Difficulty transitioning from concrete to abstract thinking
3. Poor number sense and estimation skills
4. Fear of making mistakes in mathematics
5. Limited vocabulary for mathematical communication

Worked Examples

Example 1: Identifying the Core Problem

Question: A Class III student can recite multiplication tables perfectly but cannot solve "If one packet has 6 biscuits, how many biscuits in 4 packets?"

Analysis:

• Step 1: The child has memorised tables (rote learning present)
• Step 2: Cannot apply 6 × 4 = 24 to a word problem
• Step 3: This indicates lack of conceptual understanding of multiplication as repeated addition or grouping
• Core Problem: Emphasis on procedural knowledge without building conceptual foundation
• Solution: Use concrete objects—actually show 4 groups of 6 items before connecting to multiplication

Example 2: Classroom Scenario

Question: In a Class II classroom of 45 students, the teacher wants to teach "greater than" and "less than" using number cards. What problems might she face?

Analysis:

• Large class size makes individual attention impossible
• Insufficient number cards for all students
• Cannot observe each child's understanding
• Discipline issues when children handle materials
• Time constraint—activity takes longer with large groups
• Key Problem: Resource and class-size constraints prevent activity-based learning
• Practical Solution: Group work with 5–6 children sharing one set, peer learning

Example 3: Diagnosing Student Difficulty

Question: A student writes 32 + 45 = 68. What is the likely problem?

Analysis:

• Correct answer should be 77
• Student got 6 in tens place (3 + 4 = 7, but wrote 6)
• Student got 8 in units place (2 + 5 = 7, but wrote 8)
• Diagnosis: Possible place value confusion—adding units to tens or careless column alignment
• Teaching Problem: Place value concept not firmly established before teaching addition
• Remediation: Use place value charts, bundling sticks, and expanded notation

Common Mistakes

• Blaming only students for failure → Recognise that teaching methods, resources, and curriculum design contribute equally to learning difficulties.
• Assuming all children learn at same pace → Accept individual differences; use differentiated instruction and flexible grouping rather than one-size-fits-all teaching.
• Skipping concrete stage to save time → Always move through concrete → pictorial → abstract sequence; shortcuts create permanent gaps.
• Treating math anxiety as laziness → Understand that anxiety is psychological; create safe classroom environment where mistakes are learning opportunities.
• Over-reliance on textbook exercises → Supplement with real-life problems, puzzles, and games; textbook alone cannot build mathematical thinking.
• Testing only final answers → Evaluate the process and reasoning; a child with correct method but calculation error needs different support than one with wrong concept.

Quick Reference

• Primary math teaching fails most when it prioritises procedures over concepts.
• Math anxiety often originates from teachers and parents, not from mathematics itself.
• Concrete-Pictorial-Abstract (CPA) sequence is non-negotiable at primary level.
• Large class size and lack of TLM are the most common resource-related problems.
• Language barrier doubles difficulty—teach math vocabulary explicitly.
• Formative assessment helps identify problems early; summative assessment comes too late.