PSTET 2026
Mathematics / गणित
7-Day Bilingual Study Course
Content (15 Qs) + Pedagogy (15 Qs) — दोनों equal importance
7
Days
30
Exam MCQs
15+15
Content+Pedagogy
100+
Practice Qs
गणित paper की special बात: 30 में से 15 questions Content (actual maths — calculations, formulas, problems) और 15 questions Pedagogy (teaching methods, Bloom's taxonomy, diagnostic test, etc.) से आते हैं। दोनों halves equally important हैं — pedagogy को ignore मत करें!
Content — Actual Maths
Ratio, HCF/LCM, SI, Geometry, Algebra, Fractions — solved examples with steps
Pedagogy — Teaching Maths
Bloom's Taxonomy, NCF 2005, Diagnostic Test, Teaching Methods, Dyscalculia
Bilingual Notes
Hindi + English — हर concept दोनों भाषाओं में समझाया
Worked Examples
Step-by-step solutions — exact PSTET 2024 question types
Daily Quiz
10 MCQs हर दिन — Content + Pedagogy mix
30-Q Mock Test
15 Content + 15 Pedagogy — timed, real exam feel
Exam Analysis
PSTET 2024 — Maths Paper Analysis
गणित परीक्षा विश्लेषण — 9 papers, 2024
📐 Content Topics (15 Qs)
- Ratio & Proportion — ★ 9/9 papers
- Number System (Place Value, Operations)
- Fractions & Decimals — ★ Important
- HCF & LCM
- Simple Interest & Percentage
- Algebra (Linear equations, simplification)
- Geometry (Triangles, Angles)
- Mensuration (Area, Perimeter)
- Symbol Interchange problems — ★ 7/9
- Mean, Median, Mode basics
🏫 Pedagogy Topics (15 Qs)
- Bloom's Taxonomy (Cognitive domain) — ★★
- NCF 2005 — Maths curriculum — ★★
- Teaching methods (Inductive, Deductive) — ★★
- Diagnostic Test & Remedial Teaching — ★★
- Dyscalculia — learning disability
- Micro-teaching (controlled practice)
- Evaluation methods (Formative, Summative)
- Objectives of teaching maths
- Abacus & TLM in maths
- Mathematical language & concepts
Most Important from Content side: Ratio questions — almost EVERY paper had 4-6 ratio problems. Symbol interchange (+ means ÷ type) — appears in 7/9 papers. HCF questions with ratios also very common.
Most Important from Pedagogy side: NCF 2005, Bloom's Taxonomy, Diagnostic Tests, Teaching Methods. These 4 topics alone can give you 8-10 pedagogy marks.
Most Important from Pedagogy side: NCF 2005, Bloom's Taxonomy, Diagnostic Tests, Teaching Methods. These 4 topics alone can give you 8-10 pedagogy marks.
Study Plan
7-Day Maths Study Plan
7 दिन की योजना — Content + Pedagogy दोनों की तैयारी
| Day | Content Topic | Pedagogy Topic | Focus |
|---|---|---|---|
| Day 1 | संख्या पद्धति Number System — Place Value, Operations, Fractions | Objectives of Teaching Maths + NCF 2005 | Fractions + NCF 2005 = most asked |
| Day 2 | अनुपात, LCM, HCF Ratio, Proportion, HCF, LCM | Bloom's Taxonomy — 3 Domains + 6 Cognitive levels | ★ Ratio = 9/9 papers! Bloom's = pedagogy staple |
| Day 3 | ज्यामिति एवं क्षेत्रमिति Geometry — Triangles, Angles, Area, Perimeter | Teaching Methods — Inductive vs Deductive | Triangle angle sum + Heron's formula |
| Day 4 | साधारण ब्याज, लाभ-हानि, प्रतिशत Simple Interest, Profit-Loss, Percentage | Diagnostic Test + Remedial Teaching in Maths | SI formula + Diagnostic test importance |
| Day 5 | बीजगणित एवं पैटर्न Algebra — Linear Equations, Symbol Interchange | TLM, Abacus, Micro-teaching, Dyscalculia | Symbol interchange = 7/9 papers! |
| Day 6 | सांख्यिकी — Mean, Median, Mode | गणित शिक्षाशास्त्र — Full Pedagogy Revision | Pedagogy heavy day — 15 marks here |
| Day 7 | पूर्ण समीक्षा + 30-Q Mock Test | Formulas sheet + all pedagogy key points | |
Day 1 of 7
Number System + Objectives of Maths
Place Value · Fractions · Decimals · NCF 2005 · Objectives of Teaching
संख्या पद्धति + गणित शिक्षण के उद्देश्य
🎯 Learning Objectives
- Place value (स्थानीय मान) — 5-digit numbers समझना
- Fractions — proper, improper, equivalent, operations
- Decimals — fractions to decimals conversion
- Objectives of teaching Maths — Cognitive, Affective, Psychomotor
- NCF 2005 के मुख्य recommendations for Maths
📖 Part A — Content: Number System ★ Foundation
Place Value / स्थानीय मान
हिंदी
English
स्थानीय मान (Place Value): किसी अंक का मान उसकी position पर depend करता है।
Example: 47,352 में 7 का स्थानीय मान = 7,000
Example: 47,352 में 7 का स्थानीय मान = 7,000
Place Value: The value of a digit depends on its position.
In 47,352 → 7 is in thousands place → its place value = 7,000.
Face value of 7 = always 7 (regardless of position).
In 47,352 → 7 is in thousands place → its place value = 7,000.
Face value of 7 = always 7 (regardless of position).
Common Mistake: एक बच्चा 482 को "four hundred eighty two" पढ़ता है लेकिन 40082 लिखता है — यह place value की misconception है।
PSTET Classic Q: A child reads 482 correctly but writes 40082 → This shows misconception about place value in the process of subtraction/writing. Not just a "mistake".
Fractions / भिन्न
| Type / प्रकार | Definition / परिभाषा | Example |
|---|---|---|
| Proper Fraction उचित भिन्न | Numerator < Denominator (अंश < हर) | 3/4, 2/7, 5/9 |
| Improper Fraction विषम भिन्न | Numerator ≥ Denominator (अंश ≥ हर) | 7/3, 9/4, 5/2 |
| Mixed Number मिश्रित संख्या | Whole number + proper fraction | 2¾, 3½, 5⅔ |
| Equivalent Fractions समतुल्य भिन्न | Same value, different numerator/denominator | 1/2 = 2/4 = 3/6 = 4/8 |
| Simplest Form सरलतम रूप | HCF of numerator and denominator = 1 | 4/6 → 2/3 (÷2) |
Worked Example — Fraction Operations
Find: 3/4 + 2/3 − 1/6
हल करें: 3/4 + 2/3 − 1/6
1
Find LCM of 4, 3, 6 = 12
2
Convert: 3/4 = 9/12 | 2/3 = 8/12 | 1/6 = 2/12
3
Calculate: 9/12 + 8/12 − 2/12 = 15/12
4
Simplify: 15/12 = 5/4 = 1¼
✅ Answer: 5/4 or 1¼
📐 Key Formulas — Number System
Fraction to Decimal: divide numerator ÷ denominator
Decimal to Fraction: place over 10/100/1000 → simplify
1/2 = 0.5 | 1/4 = 0.25 | 3/4 = 0.75 | 1/5 = 0.2 | 1/8 = 0.125
💡 इन्हें याद रखें — PSTET में directly convert करने के questions आते हैं
📖 Part B — Pedagogy: Objectives of Teaching Maths ★ Important
| Objective Type | Hindi / हिंदी | Examples in Maths |
|---|---|---|
| Cognitive / संज्ञानात्मक | ज्ञान, समझ, application, analysis | Solving equations, understanding proof, applying formulas |
| Affective / भावात्मक | Attitude, appreciation, values towards maths | Developing interest in maths, reducing maths anxiety |
| Psychomotor / मनोगात्मक | Physical/skill-based — drawing, constructing | Drawing geometric figures with compass/ruler, using abacus |
| NOT an objective ⭐ | "Educational" is NOT one of the 3 domains of objectives. PSTET directly asks this — answer = "Educational" is not an objective of teaching maths. | |
📖 NCF 2005 — Mathematics Recommendations ★ Must Know
हिंदी
English
NCF 2005 के according NCERT Maths textbooks लिखी गई हैं।
यह most frequently asked pedagogy fact है।
यह most frequently asked pedagogy fact है।
Present NCERT Maths textbooks are written keeping in mind the recommendations of NCF 2005 (National Curriculum Framework 2005). NOT NPE 1986 or CBSE syllabus.
NCF 2005 की मुख्य बातें Maths के लिए:
• Maths should connect to daily life
• Child-centred learning
• Problem-solving approach
• Fear of Maths कम करना
• Maths should connect to daily life
• Child-centred learning
• Problem-solving approach
• Fear of Maths कम करना
Key NCF 2005 principles for Maths:
• Mathematics should be meaningful, not just procedural
• Children should construct knowledge themselves
• Contextual learning from daily life
• Remove math phobia / anxiety
• Mathematics should be meaningful, not just procedural
• Children should construct knowledge themselves
• Contextual learning from daily life
• Remove math phobia / anxiety
Curriculum का शब्द Latin भाषा से आया है।
"Curriculum" is derived from Latin
"Curriculum" is derived from Latin
The word "Curriculum" is derived from the Latin language (from "currere" meaning "to run").
PSTET Pattern: "Present NCERT Mathematics textbooks are written keeping in mind the recommendation of ___?" → Answer = NCF 2005. यह directly आया है।
Mathematical concepts development order: Experiences (III) → Drawing pictures (I) → Symbolic representation (II) → Language (IV) = III, I, II, IV
Mathematical concepts development order: Experiences (III) → Drawing pictures (I) → Symbolic representation (II) → Language (IV) = III, I, II, IV
📌 Key Takeaways — Day 1
- Place value ≠ Face value. Face value of any digit is always that digit itself.Common student error: reading correctly but writing wrong = place value misconception
- Fractions types: Proper (3/4) | Improper (7/3) | Mixed (2¾) | Equivalent (1/2=2/4)LCM method for adding/subtracting fractions — always find common denominator first
- 3 objectives of teaching Maths: Cognitive + Affective + Psychomotor"Educational" is NOT one of the objectives — PSTET directly asks this!
- NCERT Maths textbooks = NCF 2005 recommendation (NOT NPE 1986)"Curriculum" word = derived from Latin language
- Concept development order = Experiences → Pictures → Symbolic → Language (III, I, II, IV)
Day 2 of 7
Ratio, HCF, LCM + Bloom's Taxonomy
Ratio · Proportion · HCF · LCM · Bloom's 3 Domains · 6 Cognitive Levels
अनुपात, समानुपात, HCF, LCM + ब्लूम का वर्गीकरण
🎯 Learning Objectives
- Ratio — same unit में convert करके simplify करना
- Proportion — 4th proportional, mean proportional
- HCF और LCM — prime factorization method
- Bloom's Taxonomy — 3 domains और Cognitive के 6 levels
- Who classified each domain जानना
📖 Part A — Ratio & Proportion ★ 9/9 Papers — Most Asked!
📐 Ratio Rules / अनुपात के नियम
Ratio = a : b = a/b (both in SAME unit)
Always convert to same unit before finding ratio
Simplest form: divide both by HCF
⚠️ सबसे common mistake: units same किए बिना ratio निकालना। Always convert first!
Worked Example — Ratio (Units must match)
Find ratio of 75 paise to 4 rupees
75 पैसे से 4 रुपये का अनुपात ज्ञात करें
1
Convert to same unit: 4 rupees = 400 paise
2
Ratio = 75 : 400
3
HCF of 75 and 400 = 25. Divide: 75÷25 = 3, 400÷25 = 16
✅ Ratio = 3 : 16
Worked Example — Ratio (Time units)
Find ratio of 360 months to 2.5 years
360 माह से 2.5 वर्ष का अनुपात
1
Convert 2.5 years to months: 2.5 × 12 = 30 months
2
Ratio = 360 : 30. Divide by 30: 12 : 1
✅ Ratio = 12 : 1
Worked Example — Greatest Ratio
Greatest ratio among 2:3, 5:7, 75:120, 40:25
1
Convert each to decimal: 2/3=0.667 | 5/7=0.714 | 75/120=0.625 | 40/25=1.6
✅ Greatest = 40:25 (only one greater than 1)
📖 HCF & LCM ★ Important
HCF / महत्तम समापवर्तक
LCM / लघुत्तम समापवर्त्य
Definition: दो या अधिक संख्याओं का सबसे बड़ा common factor
Use: Simplifying fractions, dividing things equally
Use: Simplifying fractions, dividing things equally
Definition: Smallest number divisible by all given numbers
Use: Adding/subtracting fractions, finding common time
Use: Adding/subtracting fractions, finding common time
Example: HCF of 12 and 18
12 = 2²×3 | 18 = 2×3²
HCF = 2×3 = 6
12 = 2²×3 | 18 = 2×3²
HCF = 2×3 = 6
Example: LCM of 12 and 18
12 = 2²×3 | 18 = 2×3²
LCM = 2²×3² = 36
12 = 2²×3 | 18 = 2×3²
LCM = 2²×3² = 36
PSTET Type — HCF with Ratio
HCF of three numbers is 12 and their ratio is 1:2:3. Find the largest number.
तीन संख्याओं का HCF 12 है और उनका अनुपात 1:2:3 है। सबसे बड़ी संख्या ज्ञात करें।
1
Numbers = 12×1, 12×2, 12×3 = 12, 24, 36
2
Largest = 36
✅ Largest number = 36
📖 Part B — Bloom's Taxonomy ★ Pedagogy Must Know
Benjamin Bloom (1956) ने Educational Objectives का taxonomy दिया। 3 domains हैं। Cognitive domain में 6 levels हैं जो lower order से higher order thinking की तरफ जाते हैं।
| Domain / डोमेन | Classified By / वर्गीकरण | Focus / केंद्र |
|---|---|---|
| Cognitive / संज्ञानात्मक | Bloom (1956) | Thinking, knowledge, understanding — सोचने की क्षमता |
| Affective / भावात्मक | Krathwohl (1964) | Feelings, attitudes, values — भावनाएं |
| Psychomotor / मनोगात्मक | Simpson / Harrow | Physical skills, motor abilities — शारीरिक कौशल |
| Level | Cognitive Domain Level | Hindi | Example in Maths |
|---|---|---|---|
| 1 (Lowest) | Knowledge / ज्ञान | याद करना | Recall formula of area of triangle |
| 2 | Comprehension / बोध | समझना | Explain why area = ½ × b × h |
| 3 | Application / प्रयोग | उपयोग करना | Solve: area of triangle with b=6, h=4 |
| 4 | Analysis / विश्लेषण | विश्लेषण करना | Compare different methods of solving |
| 5 | Synthesis / संश्लेषण | नया बनाना | Create a new problem using the concept |
| 6 (Highest) | Evaluation / मूल्यांकन | निर्णय करना | Evaluate which solution method is best |
PSTET Direct Questions:
"Cognitive domain objectives classification किसने दिया?" → Bloom
"Affective domain को subgroups में कब divide किया?" → Krathwohl, 1964
"Domains of Educational Objectives की संख्या है?" → 3 (Three)
"SOLO stands for?" → Structure of Observed Learning Outcome
"Cognitive domain objectives classification किसने दिया?" → Bloom
"Affective domain को subgroups में कब divide किया?" → Krathwohl, 1964
"Domains of Educational Objectives की संख्या है?" → 3 (Three)
"SOLO stands for?" → Structure of Observed Learning Outcome
📌 Key Takeaways — Day 2
- Ratio — ALWAYS convert to same unit first before calculating9/9 papers में ratio आया — यह मत छोड़ें। 75 paise : 4 rupees = 75:400 = 3:16
- HCF with ratio: Numbers = HCF × ratio parts. (HCF=12, ratio=1:2:3 → 12, 24, 36)LCM = for adding fractions | HCF = for simplifying fractions
- 3 Domains: Cognitive (Bloom, 1956) | Affective (Krathwohl, 1964) | PsychomotorCognitive domain के 6 levels: Knowledge → Comprehension → Application → Analysis → Synthesis → Evaluation
- SOLO = Structure of Observed Learning Outcome
- Greatest ratio: convert to decimals and compare. Ratio > 1 means numerator > denominator.
Day 3 of 7
Geometry + Teaching Methods
Triangles · Angles · Area · Perimeter · Inductive vs Deductive · Abacus
ज्यामिति एवं क्षेत्रमिति + गणित शिक्षण की विधियाँ
🎯 Learning Objectives
- Triangle types — by sides और by angles
- Triangle angle sum property (180°)
- Area and Perimeter of basic shapes
- Euclid — Father of Geometry जानना
- Inductive vs Deductive method of teaching Maths
- TLM — Abacus, 3D resources for geometry
📖 Part A — Geometry / ज्यामिति ★ Important
Father of Geometry = Euclid (यूक्लिड) — Greek mathematician. "Elements" book में geometry की foundations लिखीं।
Father of Mathematics (broadly) = Pythagoras
"Mathematics" word coined by = Pythagoreans
Father of Mathematics (broadly) = Pythagoras
"Mathematics" word coined by = Pythagoreans
| Triangle Type | By Sides (भुजाओं के आधार पर) | By Angles (कोणों के आधार पर) |
|---|---|---|
| Equilateral / समबाहु | All 3 sides equal | All angles = 60° |
| Isosceles / समद्विबाहु | 2 sides equal | 2 base angles equal |
| Scalene / विषमबाहु | All 3 sides different | All 3 angles different |
| Acute / न्यूनकोण | — | All angles < 90° |
| Right / समकोण | — | One angle = 90° |
| Obtuse / अधिककोण | — | One angle > 90° |
📐 Key Geometry Formulas
Sum of angles in a triangle = 180°
Area of Triangle = ½ × base × height
Heron's Formula: A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
Area of Rectangle = length × breadth | Perimeter = 2(l+b)
Area of Square = side² | Perimeter = 4 × side
Circle: Diameter = 2r | Area = πr² | Circumference = 2πr
💡 Triangle angles sum = 180° — इस property पर based questions बहुत आते हैं
PSTET Type — Angle Problem
In a triangle, two angles are 50° and 40°. Find the third angle.
एक त्रिभुज में दो कोण 50° और 40° हैं। तीसरा कोण ज्ञात करें।
1
Sum of all angles = 180°
2
Third angle = 180° − 50° − 40° = 90°
✅ Third angle = 90° → This is a Right Triangle!
Important Geometry Facts
Key Points
वृत्त (Circle): केंद्र (Centre), त्रिज्या (Radius), व्यास (Diameter = 2r)
Circle: Centre is equidistant from all points on circle. Diameter = longest chord = 2 × radius.
सममित आकृति (Symmetry): Line of symmetry = आकृति को दो equal halves में बाँटती है
Symmetry: Square has 4 lines, Rectangle has 2, Equilateral triangle has 3, Circle has infinite lines of symmetry.
3D objects की geometry: Tennis ball (sphere), Cylindrical rod (cylinder), A room (cuboid) — इन्हें use किया जाता है geometry समझाने के लिए
Resources for 3D geometry: Tennis ball (sphere), Room (cuboid), Cylindrical rod. All can be used to explain 3D geometry — PSTET says "All of the above"
📖 Part B — Teaching Methods / शिक्षण विधियाँ ★ Pedagogy
| Method | Hindi | How it works | Maths Example |
|---|---|---|---|
| Inductive Method ⭐ | आगमन विधि | Specific examples → General rule. Child discovers pattern. Observation → Generalization | Show 3+5=8, 7+5=12, 9+5=14 → Child discovers "adding 5 pattern" |
| Deductive Method | निगमन विधि | General rule → Specific examples. Teacher gives formula first. Criticized: mechanical practice, little attention to meaning. | Teacher gives formula, students apply. Rote-learning tendency. |
| Analytic Method | विश्लेषण विधि | Start from unknown (what to find) → work backwards to known | Given area, find side of square: A=s² → s=√A |
| Synthetic Method | संश्लेषण विधि | Start from known → reach unknown. Opposite of analytic. | Given side, find area: s=5 → A=25 |
| Heuristic Method | खोज विधि | Student discovers by themselves with minimal guidance | Let child figure out area formula by counting squares on graph paper |
Deductive Method is criticized because: (1) teaches grammar in isolated way (2) little attention to meaning (3) practice is often mechanical → Answer: All of the above (given options). यह directly PSTET 2024 में था।
Teaching aids most used in: Arithmetic (not Algebra, not Calculus). TLMs are most practically used in Arithmetic teaching.
Teaching aids most used in: Arithmetic (not Algebra, not Calculus). TLMs are most practically used in Arithmetic teaching.
📖 Abacus & TLM in Mathematics
हिंदी
English
Abacus (अबेकस): Decimal addition सिखाने के लिए "learning by doing" का best tool। Class III में decimals का addition — Abacus most suitable teaching activity है।
Abacus: Best TLM for teaching decimal operations in Class III using "learning by doing" method. Directly in PSTET 2024.
गणित में TLM (Teaching Learning Material) सबसे ज़्यादा: Arithmetic (अंकगणित) में use होता है। Concrete materials — counters, number lines, shapes।
TLM most used in: Arithmetic — concrete objects make abstract number operations tangible for young children.
📌 Key Takeaways — Day 3
- Father of Geometry = Euclid | "Mathematics" word = coined by PythagoreansTriangle angle sum = 180°. If two angles known, third = 180 − sum of two
- Heron's formula: s = (a+b+c)/2, Area = √[s(s-a)(s-b)(s-c)]Area of triangle = ½ × base × height — simpler formula for right/given height triangles
- Inductive = Specific→General (examples first) | Deductive = General→Specific (formula first)Deductive method criticized: mechanical, little meaning, isolated practice — ALL of these
- TLM most used in Arithmetic | Abacus = best tool for decimal addition (Class III)3D geometry resources: Tennis ball, Room, Cylindrical rod — all are valid
Day 4 of 7
Simple Interest, Percentage + Diagnostic Test
SI Formula · Profit-Loss · Percentage · Diagnostic & Remedial Teaching in Maths
साधारण ब्याज, लाभ-हानि, प्रतिशत + निदानात्मक परीक्षण
🎯 Learning Objectives
- SI formula — Principal, Rate, Time की calculation
- Amount = Principal + SI
- Profit-Loss percentage formula
- Percentage problems — finding X% of Y
- Diagnostic Test importance in Maths (3 uses)
- Remedial Teaching — best feedback strategy
📖 Part A — Simple Interest / साधारण ब्याज ★ Important
📐 Simple Interest Formulas
SI = (P × R × T) / 100
Amount (A) = P + SI = P(1 + RT/100)
P = (SI × 100) / (R × T) | R = (SI × 100) / (P × T) | T = (SI × 100) / (P × R)
P = Principal (मूलधन) | R = Rate per annum (वार्षिक दर) | T = Time in years (वर्षों में समय)
PSTET Type — Find Rate (SI)
A sum amounts to ₹6300 in 2 years and ₹7875 in 3 years 9 months at SI. Find the rate.
एक राशि साधारण ब्याज पर 2 वर्षों में ₹6300 और 3¾ वर्षों में ₹7875 हो जाती है। वार्षिक दर ज्ञात करें।
1
3 years 9 months = 3.75 years. SI for 3.75−2 = 1.75 years = 7875−6300 = ₹1575
2
SI per year = 1575/1.75 = ₹900
3
SI for 2 years = ₹1800. So P = 6300−1800 = ₹4500
4
R = (SI × 100)/(P × T) = (1800 × 100)/(4500 × 2) = 20%
✅ Rate = 20% per annum
📖 Percentage / प्रतिशत
📐 Percentage Formulas
X% of Y = (X/100) × Y
Profit% = (Profit / CP) × 100 | Loss% = (Loss / CP) × 100
SP = CP × (1 + Profit%/100) | SP = CP × (1 − Loss%/100)
CP = Cost Price (क्रय मूल्य) | SP = Selling Price (विक्रय मूल्य)
PSTET Type — Proportionality
Which number should be added to each of 2, 7, 10, 25 so they become proportional?
प्रत्येक संख्या 2, 7, 10, 25 में कौन-सी संख्या जोड़ी जाए ताकि वे समानुपाती हो जाएं?
1
Let the number be x. Then: (2+x)/(7+x) = (10+x)/(25+x)
2
Cross multiply: (2+x)(25+x) = (7+x)(10+x)
3
50+27x+x² = 70+17x+x². So 10x = 20. x = 2
✅ Add 2 → 4, 9, 12, 27 → Check: 4/9 = 12/27 ✓
📖 Part B — Diagnostic Test in Mathematics ★ Pedagogy Important
हिंदी
English
Diagnostic Test (निदानात्मक परीक्षण) का महत्व:
1. शिक्षण में (In teaching)
2. परामर्श और मार्गदर्शन में (In counseling)
3. उपचारात्मक शिक्षण की व्यवस्था में (For remedial teaching)
→ तीनों सही हैं — All of the given options ✅
1. शिक्षण में (In teaching)
2. परामर्श और मार्गदर्शन में (In counseling)
3. उपचारात्मक शिक्षण की व्यवस्था में (For remedial teaching)
→ तीनों सही हैं — All of the given options ✅
Importance of Diagnostic Tests:
1. In teaching — to understand student's current level
2. In counseling and guidance — identify needs
3. For remedial teaching arrangements
→ All three = correct. PSTET answer = "All of the given options"
1. In teaching — to understand student's current level
2. In counseling and guidance — identify needs
3. For remedial teaching arrangements
→ All three = correct. PSTET answer = "All of the given options"
Diagnostic Test के लिए methods (PSTET Q):
• Case history or interview
• Clinical observation
• Informal testing
→ तीनों valid methods हैं। "None of the above" सही answer है (मतलब सब सही हैं)
• Case history or interview
• Clinical observation
• Informal testing
→ तीनों valid methods हैं। "None of the above" सही answer है (मतलब सब सही हैं)
Methods to obtain data for diagnostic test:
Case history/interview ✓ | Clinical observation ✓ | Informal testing ✓
→ PSTET: "Which is NOT a method?" → Answer = "None of the above" (all listed ARE valid methods)
Case history/interview ✓ | Clinical observation ✓ | Informal testing ✓
→ PSTET: "Which is NOT a method?" → Answer = "None of the above" (all listed ARE valid methods)
Best feedback after class test: Vikas 56 students को पढ़ाता है, 10-mark test लेता है। Immediate feedback के लिए best तरीका?
→ Each student checks their own answers (self-evaluation) — fastest and most effective for immediate feedback
→ Each student checks their own answers (self-evaluation) — fastest and most effective for immediate feedback
Most effective immediate feedback in Maths class test: Have students exchange papers and check each other, OR have them self-evaluate against correct answers displayed — immediate engagement with errors.
Remedial Teaching Cycle in Maths:
1. Diagnostic test दो → 2. Specific error identify करो → 3. Different method से reteach करो → 4. Practice दो → 5. Re-evaluate
Key: DIFFERENT method — same method repeat करना = same result
1. Diagnostic test दो → 2. Specific error identify करो → 3. Different method से reteach करो → 4. Practice दो → 5. Re-evaluate
Key: DIFFERENT method — same method repeat करना = same result
📌 Key Takeaways — Day 4
- SI = PRT/100 | Amount = P + SI. Find P, R, or T by rearranging.PSTET SI type: Find Rate given two different time amounts → find SI per year first
- Proportionality: cross-multiply and solve for unknown additionAdd 2 to each of 2, 7, 10, 25 → 4, 9, 12, 27 → proportional (4×27 = 9×12 ✓)
- Diagnostic test importance = Teaching + Counseling + Remedial = ALL threeMethods of diagnostic test: Case history, Clinical observation, Informal testing — ALL valid
- When exam is near: Teacher should complete syllabus by extra time in school (NOT call students home)
Day 5 of 7
Algebra + Symbol Interchange + Dyscalculia
Linear Equations · Symbol Problems · Patterns · Dyscalculia · Micro-teaching
बीजगणित, प्रतीक प्रश्न, अनुक्रम + अधिगम अक्षमता
🎯 Learning Objectives
- Symbol interchange problems — step-by-step approach
- Linear equations — one variable solve करना
- Number patterns — triangular and square numbers
- Dyscalculia — definition, symptoms, teaching strategies
- Micro-teaching — controlled practice system
- Gates के problem-solving steps
📖 Part A — Symbol Interchange Problems ★ 7/9 Papers!
Strategy / तरीका: Simply substitute the new meanings and calculate step by step using BODMAS.
Replace each symbol with its new meaning, then solve normally. अर्थ बदलो, फिर normal calculate करो।
Replace each symbol with its new meaning, then solve normally. अर्थ बदलो, फिर normal calculate करो।
PSTET Type — Symbol Interchange
If '+' means '−', '−' means '×', '÷' means '+', '×' means '÷', then find: 15 − 3 + 10 × 5 ÷ 5
यदि '+' का अर्थ '−', '−' का अर्थ '×', '÷' का अर्थ '+' और '×' का अर्थ '÷' हो, तो 15 − 3 + 10 × 5 ÷ 5 का मान?
1
Replace symbols: 15 × 3 − 10 ÷ 5 + 5
2
BODMAS: First × and ÷: 15×3=45 | 10÷5=2
3
Now: 45 − 2 + 5 = 48
✅ Answer = 48
PSTET Type — Interchanged Signs AND Numbers
Given interchanges: signs ÷ and ×, and numbers 3 and 2. Find: 14 × 3 ÷ 2
÷ और ×, तथा 3 और 2 आपस में बदलें। तो 14 × 3 ÷ 2 का मान?
1
Swap signs AND numbers: 14 ÷ 2 × 3
2
BODMAS (left to right): 14÷2=7, then 7×3=21
✅ Answer = 21
📖 Linear Equations / रैखिक समीकरण
Standard PSTET Algebra Pattern
Oranges fill 4 smaller boxes with 15 remaining. If small box holds x oranges, how many in large box?
एक बड़े डिब्बे से 4 छोटे भर जाते हैं और 15 बाहर रहते हैं। छोटे में x संतरे हों तो बड़े में कितने?
1
Large box = 4 × (small box) + 15 remaining
2
= 4x + 15
✅ Answer = 4x + 15
📖 Number Patterns / संख्या पैटर्न
| Pattern Type | Hindi | Sequence | Formula |
|---|---|---|---|
| Triangular Numbers | त्रिभुजीय संख्याएं | 1, 3, 6, 10, 15, 21... | n(n+1)/2 |
| Square Numbers | वर्ग संख्याएं | 1, 4, 9, 16, 25, 36... | n² |
| Cube Numbers | घन संख्याएं | 1, 8, 27, 64, 125... | n³ |
| Fibonacci | फिबोनाची | 1, 1, 2, 3, 5, 8, 13, 21... | Each = sum of previous two |
📖 Part B — Dyscalculia & Learning Disabilities ★ Pedagogy
हिंदी
English
Dyscalculia (डिस्केलकुलिया): संख्याओं और calculations में specific difficulty — NOT low IQ।
Class 4 का Karan को numbers और calculations में problem है → Dyscalculia।
Class 4 का Karan को numbers और calculations में problem है → Dyscalculia।
Dyscalculia: Specific learning disability in mathematics — difficulty with numbers, arithmetic operations, understanding mathematical concepts. NOT related to overall intelligence. Directly in PSTET 2024.
Pre-operational stage पर Piaget के अनुसार बच्चा क्या सीख सकता है?
→ केवल Numbers (संख्या) — basic counting
HCF/LCM, Mensuration, Factors — नहीं सीख सकता (abstract concepts)
→ केवल Numbers (संख्या) — basic counting
HCF/LCM, Mensuration, Factors — नहीं सीख सकता (abstract concepts)
In Piaget's Pre-operational stage (2-7 years): child can only learn Numbers (basic counting, recognizing numerals). NOT HCF/LCM, Mensuration, or Factors — these need concrete or formal operational thinking.
📖 Micro-teaching / सूक्ष्म शिक्षण
हिंदी
English
Micro-teaching = Controlled Practice की प्रणाली
एक छोटे group में, limited time में, specific skill practice करना।
एक छोटे group में, limited time में, specific skill practice करना।
Micro-teaching = A system of CONTROLLED PRACTICE (not uncontrolled, not wide topic, not extensive). Teacher practices one specific skill with a small group for a short time.
Gates ने Problem Solving के Steps:
Gates द्वारा problem solving के steps बताए गए हैं।
(Exact number: PSTET में directly आया है)
Gates द्वारा problem solving के steps बताए गए हैं।
(Exact number: PSTET में directly आया है)
Gates' Problem Solving Steps: Gates described steps of problem solving. The number of steps he gave is directly tested in PSTET. The exact number is 5 steps according to Gates.
📌 Key Takeaways — Day 5
- Symbol interchange: Replace symbols/numbers first → then apply BODMAS normally7/9 papers में आया — यह type practice करना बहुत ज़रूरी है। हर paper में 2-3 ऐसे questions होते हैं।
- Algebra pattern: Oranges = 4x + 15. "Remaining" = added outside the groupsLinear equation pattern: Set up equation first, then solve. Common PSTET approach.
- Dyscalculia = Maths-specific difficulty, NOT low IQ (Karan Class 4 wala question = Dyscalculia)Pre-operational stage (Piaget, 2-7 yrs) = only Numbers can be taught, not HCF/LCM
- Micro-teaching = Controlled Practice की system (not uncontrolled, not wide topic)
- Triangular numbers: 1,3,6,10,15 → n(n+1)/2 | Square numbers: 1,4,9,16,25 → n²
Day 6 of 7
Statistics + Full Maths Pedagogy
Mean · Median · Mode · Evaluation · Values of Maths · Mathematical Language
सांख्यिकी + गणित शिक्षाशास्त्र का पूर्ण पुनरावलोकन
🎯 Learning Objectives
- Mean, Median, Mode calculate करना
- Values of Mathematics — Utilitarian, Disciplinary, Cultural
- Mathematical language build करने के तरीके
- Evaluation — Broadest concept, bases of evaluation
- Triangular process of teaching — 3 focal points
- Place of Mathematics in curriculum
📖 Part A — Statistics / सांख्यिकी
📐 Mean, Median, Mode Formulas
Mean (माध्य) = Sum of all values / Number of values
Median (माध्यिका) = Middle value when arranged in order
Mode (बहुलक) = Value that appears most frequently
For even number of values: Median = average of two middle values
Mean, Median, Mode Example
Find mean, median, mode of: 3, 7, 5, 3, 9, 7, 3, 8
1
Arrange: 3, 3, 3, 5, 7, 7, 8, 9
2
Mean = (3+3+3+5+7+7+8+9)/8 = 45/8 = 5.625
3
Median (8 values, even) = (5+7)/2 = 6
4
Mode = 3 (appears 3 times, most frequent)
✅ Mean=5.625 | Median=6 | Mode=3
📖 Part B — गणित के मूल्य (Values of Mathematics) ★ Must Know
| Value Type | Hindi | Meaning | Example |
|---|---|---|---|
| Utilitarian / Practical | उपयोगितावादी मूल्य | Daily life में use — practical value | Calculating change, measuring, budgeting |
| Disciplinary | अनुशासनात्मक मूल्य | Develops systematic, logical thinking, discipline | Following steps, logical reasoning |
| Cultural | सांस्कृतिक मूल्य | Maths as part of human civilization — Vedic Maths | Aryabhata, Brahmagupta, Vedic Mathematics |
| Social | सामाजिक मूल्य | Cooperation, sharing, fairness through maths | Dividing resources equally |
| NOT a value ⭐ | Irrationalism (अतार्किकता) is NOT a major educational value of Mathematics — PSTET directly asks this! | ||
📖 Evaluation / मूल्यांकन — Key Concepts
हिंदी
English
सबसे व्यापक concept: Evaluation (मूल्यांकन) > Measurement (माप) > Examination (परीक्षा)
Evaluation includes measurement AND judgment.
Evaluation includes measurement AND judgment.
Broadest concept: Evaluation is the broadest and most comprehensive — includes Measurement (quantitative), Examination (specific test), and value judgment. Direct PSTET question.
Evaluation process का आधार: Objectives (उद्देश्य) — evaluation हमेशा objectives पर based होती है।
Basis of evaluation process: Objectives — all evaluation is tied to stated learning objectives. NOT teaching aids, lesson plans, or teaching alone.
Test item का Discrimination Power: 0.30 से कम होने पर test item low और high achievers में अंतर नहीं कर सकता।
Test discrimination: A test item CANNOT discriminate between low and high achievers when its discrimination value is lower than 0.30. Direct PSTET fact.
📖 Triangular Process of Teaching / शिक्षण की त्रिकोणीय प्रक्रिया
हिंदी
English
3 focal points: Teacher (शिक्षक), Pupil (छात्र), Contents (विषय-वस्तु)
Teaching Method शिक्षण की त्रिकोणीय क्रिया का केंद्र बिंदु नहीं है
Teaching Method शिक्षण की त्रिकोणीय क्रिया का केंद्र बिंदु नहीं है
3 focal points of triangular teaching process: Teacher, Pupil, Contents
Teaching Method is NOT a focal point — it's the process between the three, not a vertex. Direct PSTET question.
Teaching Method is NOT a focal point — it's the process between the three, not a vertex. Direct PSTET question.
📖 Mathematical Language / गणितीय भाषा
हिंदी
English
बच्चों में गणितीय भाषा की समझ कैसे बनाएं?
→ Daily life की भाषा से जोड़कर, concrete experiences से, और gradually abstract symbols की तरफ बढ़ाकर।
→ Daily life की भाषा से जोड़कर, concrete experiences से, और gradually abstract symbols की तरफ बढ़ाकर।
Building mathematical language: Start with everyday language, connect to concrete experiences, then gradually introduce formal mathematical symbols and terminology.
गणित का संबंध किन subjects से है?
Geography, Economics, Commerce, Life Sciences — सब से।
Geography, Economics, Commerce, Life Sciences — सब से।
Maths is a part of: Geography (statistics, maps) + Economics (data) + Commerce (calculations) = All three. Also closely linked to Life Sciences (statistics, measurements).
Topological Structure: Limit और neighborhood की concepts किस mathematical structure में हैं?
→ Topological Structure (संस्थानिक संरचना)
→ Topological Structure (संस्थानिक संरचना)
Mathematical structures with limit, neighborhood concepts = Topological Structure. Not algebraic, not order, not arithmetic structure.
Pedagogy Quick Hits — Direct Answers for PSTET:
• "Most desirable teacher quality?" → Explain difficult aspects as simply as possible
• "Teacher's function?" → Teaching and learning (not just teaching)
• "Math teacher function?" → Teaching and learning (D — "teaching and learning" always preferred over "just teaching")
• "Good learning habits — what's desirable?" → Firm determination and initiative of learner
• "Mathematics is a part of?" → Geography, Economics, AND Commerce (all three)
• "Most desirable teacher quality?" → Explain difficult aspects as simply as possible
• "Teacher's function?" → Teaching and learning (not just teaching)
• "Math teacher function?" → Teaching and learning (D — "teaching and learning" always preferred over "just teaching")
• "Good learning habits — what's desirable?" → Firm determination and initiative of learner
• "Mathematics is a part of?" → Geography, Economics, AND Commerce (all three)
📌 Key Takeaways — Day 6
- Mean = Sum/n | Median = middle value (arranged) | Mode = most frequentEven number of values: Median = average of 2 middle values
- Values of Maths: Utilitarian + Disciplinary + Cultural + Social. Irrationalism = NOT a value.Broadest concept: Evaluation > Measurement > Examination (Evaluation is most comprehensive)
- Evaluation basis = Objectives (not teaching aids, not lesson plans)Test discrimination < 0.30 = cannot differentiate low and high achievers
- Triangular process focal points = Teacher, Pupil, Contents. Teaching Method = NOT a focal point.Topological structure = limit and neighborhood concepts
- Maths is part of Geography + Economics + Commerce (all three)
Day 7 — Final
Full Review + Mock Test
All Formulas + All Pedagogy Key Points + 30-Q Timed Test
पूर्ण समीक्षा — Content + Pedagogy + Mock Test
📖 Formula Quick Reference Sheet
🧮 All Key Formulas
Ratio: Always convert to SAME unit first
HCF with Ratio: Numbers = HCF × ratio parts
SI = PRT/100 | Amount = P + SI
Triangle: Angle sum = 180°
Area of Triangle = ½ × b × h
Heron's: s=(a+b+c)/2, A=√[s(s-a)(s-b)(s-c)]
Mean = ΣX/n | Mode = most frequent | Median = middle value
Profit% = (Profit/CP) × 100
Symbol Interchange: Substitute → BODMAS
Triangular numbers: n(n+1)/2 | Square: n²
📖 Pedagogy Master Table — Direct PSTET Answers
| Question Type | Direct Answer |
|---|---|
| NCERT Maths books based on? | NCF 2005 |
| "Curriculum" word from? | Latin |
| Objectives of teaching Maths (3 types)? | Cognitive + Affective + Psychomotor ("Educational" is NOT) |
| Cognitive domain classified by? | Bloom (1956) |
| Affective domain classified by? | Krathwohl (1964) |
| Domains in Educational Objectives? | Three (3) |
| SOLO stands for? | Structure of Observed Learning Outcome |
| Micro-teaching is a system of? | Controlled Practice |
| TLM most used in? | Arithmetic |
| Abacus best for? | Decimal addition (Class III) — "Learning by Doing" |
| Pre-operational stage can learn? | Numbers only (not HCF/LCM/Mensuration) |
| Dyscalculia = ? | Numbers/calculation difficulty (NOT Dyslexia, Dysgraphia) |
| Father of Geometry? | Euclid |
| Triangular process focal points? | Teacher, Pupil, Contents (Teaching Method is NOT) |
| NOT a value of Maths? | Irrationalism |
| Broadest concept? | Evaluation (broader than Measurement or Examination) |
| Basis of evaluation? | Objectives |
| Discrimination < what value = bad item? | 0.30 |
| Inductive vs Deductive? | Inductive = specific→general | Deductive = general→specific |
| Deductive method criticized for? | All: isolated grammar, little meaning, mechanical practice |
| Most desirable teacher quality? | Explain difficult aspects as simply as possible |
| Diagnostic test importance? | All 3: Teaching + Counseling + Remedial teaching |
| Concept development order? | Experiences (III) → Pictures (I) → Symbolic (II) → Language (IV) |
| Maths part of? | Geography + Economics + Commerce (all three) |
Exam Strategy for Maths Paper:
Content (15 Qs): Ratio questions — always convert units. Symbol interchange — substitute first, BODMAS after. SI — find yearly SI first. Geometry — angle sum 180°.
Pedagogy (15 Qs): NCF 2005, Bloom's Taxonomy, Diagnostic Test, Teaching Methods — these 4 topics cover 8-10 marks. मत छोड़ें।
Content (15 Qs): Ratio questions — always convert units. Symbol interchange — substitute first, BODMAS after. SI — find yearly SI first. Geometry — angle sum 180°.
Pedagogy (15 Qs): NCF 2005, Bloom's Taxonomy, Diagnostic Test, Teaching Methods — these 4 topics cover 8-10 marks. मत छोड़ें।
Notes बंद करें। 30 minutes timer लगाकर सभी 30 questions attempt करें। No negative marking — सभी attempt करें।
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