Learning Before Knowing: Reflections on Teaching, Struggle, and Leadership - Manika Pandey

Assignment 1: Learning Through Struggle in the Classroom

“Struggle, when designed purposefully, prepares the mind for deeper learning.” — from the chapter on Struggle Before Instruction

There’s a Maths lesson from my teaching days that still stays with me because it quietly reshaped the way I look at learning.

I walked into the classroom that day fully prepared. My explanations were structured, my examples carefully chosen, and I was confident that I would finally make fractions look simple and logical. I spoke, demonstrated, and checked for understanding. The students nodded politely, but their eyes told a different story. They weren’t resisting; they were just… lost. And no amount of explaining seemed to bridge that gap.

The next day, I made a small but powerful shift. I didn’t begin with rules or steps. Instead, I gave them a slightly messy pizza-sharing problem—one that didn’t have an obvious starting point. Then I stepped back and said just one word: “Try.”

What followed was beautiful chaos. Students debated, drew rough diagrams, made incorrect assumptions, crossed things out, and tried again. There were disagreements, laughter, frustration, and sudden “aha” moments. The room was noisy, but alive with thinking. They were struggling, but this time the struggle belonged to them.

When I finally introduced the formal method, something was different. The explanation landed. It wasn’t just heard—it was understood. The students weren’t memorising steps; they were making connections. The method answered questions they had already asked themselves.

That lesson taught me something deeply important: learning doesn’t begin with perfect clarity. It begins with uncertainty, curiosity, and the courage to attempt something without knowing the outcome. A little discomfort doesn’t block learning—it invites it.

Since then, I’ve learned to trust the power of well-designed struggle. Because when students wrestle with ideas before being taught, understanding doesn’t just arrive—it stays.

Assignment 2: The Power of Prior Knowledge in Teaching

“Learning builds on what learners already know—or think they know.” — from the chapter on Activation of Prior Knowledge

During a classroom observation, I once watched a Grade 7 Maths lesson begin with algebraic expressions on the board. The teacher was confident, and the content was correct, but the students looked as though they had been dropped into unfamiliar territory. Their eyes followed the symbols, but their minds hadn’t arrived yet.

After the lesson, we sat down and talked—not about pace or classroom control, but about starting points. As we unpacked the lesson together, the teacher slowly realised something important: the students already had pieces of the puzzle. They knew patterns. They had worked with numbers and symbols. They had met variables before. But none of that had been called into the room before algebra was introduced.

What struck me most was how much students carry with them every day—half-formed ideas, prior experiences, small misunderstandings, and quiet confidence from earlier learning. When that knowledge isn’t activated, new concepts don’t settle. They hover, disconnected, with nothing solid to hold on to.

This experience reinforced a belief I now strongly hold as an academic head: lessons don’t begin with teaching; they begin with remembering. A quick recall question, a familiar example, a short conversation, or even asking students to explain what they already know can make all the difference. It warms up the brain and gives new learning somewhere to belong.

Because when prior knowledge is acknowledged and activated, learning doesn’t feel like a leap—it feels like the next natural step.

Assignment 3: Awareness, Reflection, and My Leadership Journey

“Recognising what we don’t know is the beginning of meaningful learning.” — from the chapter on Awareness and Metacognition

When I stepped into the role of Academic Head, I quietly assumed that experience would make things feel familiar and almost predictable. I believed that years in the classroom would prepare me for most situations. But leadership has a way of gently—and sometimes not so gently—challenging those assumptions.

Very soon, reality set in. Teachers asked thoughtful questions I didn’t always have immediate answers to. Parents raised concerns that revealed gaps I hadn’t noticed. There were moments when I realised I had misunderstood certain Cambridge guidelines and had to pause, revisit, and relearn. None of this felt comfortable. In fact, it felt unsettling at first.

This chapter helped me see those moments differently. It reminded me that awareness is not about self-doubt; it’s about self-observation. Noticing what I didn’t know, where I went wrong, or what I had assumed too quickly wasn’t a sign of weakness. It was evidence of growth.

I began to watch my own thinking more carefully, question my decisions, and reflect on why I chose certain paths over others. Over time, I understood that leadership is not about being flawless or having every answer ready. It is about being willing to pause, reflect, and adjust.

The days when things went slightly off track taught me far more than the days when everything ran smoothly. Those small missteps shaped my leadership mindset, strengthened my judgment, and deepened my empathy. They reminded me that meaningful learning—whether in classrooms or in leadership—always begins with awareness.

Assignment 4: Emotions as a Part of Learning and Leading

“Emotion fuels thinking—it doesn’t distract from it.” — from the chapter on Affect

There was a week that completely drained me—harsh words from a senior, a complaint from a parent, and teachers stressed about deadlines. By the end of the week, I felt like everything was slipping out of my control.

This chapter made me rethink the role of emotion. When a child gets frustrated with a maths problem, that frustration means they care. When I felt overwhelmed in school, it was because I wanted to do well.

Emotions aren’t obstacles; they are signals. Understanding this made me calmer, more empathetic, and more grounded as a leader.

Assignment 5: Bringing Meaning to Chaos — The Art of Assembly

“Learning becomes complete when ideas are gathered, refined, and made coherent.” — from the chapter on Assembly

Earlier in my leadership journey, I believed that being capable meant getting things right the first time. When decisions didn’t land as expected, or situations unfolded differently than I had planned, I took it personally. I saw mistakes as shortcomings—something to correct quickly and quietly.

Experience changed that belief.

There were moments when my judgment needed revisiting, when my communication could have been clearer, and when I had to admit that I didn’t fully understand a situation before responding. Those moments were uncomfortable, but they were also honest. And they taught me more than any smooth, successful day ever could.

Over time, I stopped fearing mistakes and started learning from them. Each misstep sharpened my awareness, softened my responses, and widened my perspective. I became more patient with others because I had learned to be patient with myself. I began listening more deeply—not just to words, but to intent, hesitation, and unspoken concerns.

Today, my leadership is shaped less by authority and more by empathy. I don’t aim to appear flawless; I aim to be thoughtful, reflective, and open to growth. The lessons that mattered most didn’t come from getting everything right, but from pausing, reflecting, and choosing to grow stronger each time something went wrong.

That is the kind of leader I’ve grown into—not perfect, but grounded.

Ms. Manika Pandey
Academic Head 
Sunbeam International, Varuna

Learning Through Struggle: A Reflective Study of Productive Failure and Personal Transformation - KRITIKA SRIVASTAVA

Assignment 1- From Failure to Finding Purpose: A Reflective Case Study on Learning Through Struggle

1. Introduction

Failure often discourages learners, but productive failure shows that initial struggle can lead to stronger outcomes. Her story reflects this principle. Despite repeated setbacks in banking examinations, she continued trying, learning, and evolving. Her turning point came when she realised that failure was not the end, but the beginning of a new direction—education.

2. Background

Her repeated examination failures did not make her weak; instead, they taught her resilience, discipline, and reflection. Much like students in productive failure settings, she grappled with challenges, explored possibilities, and questioned her abilities. This struggle pushed her to discover a career where her strengths truly belonged—teaching.

3. Turning Point: Learning Through Struggle

Entering the B.Ed programme became her experiment with hope. She studied with full dedication, not with fear but with curiosity—just as productive failure encourages learners to explore before receiving formal instruction.

Her emotional struggle, confusion, and early mistakes became powerful learning moments.

The outcome was remarkable:

She topped the B.Ed. examination and confidently cleared interviews in reputed schools.

Her success was not despite failure—it was because she engaged deeply with it.

4. Reflection

Her journey revealed that:

• Struggle builds deeper understanding.

• Failure, when reflected upon, creates clarity.

• Confidence grows when one learns from mistakes rather than avoids them.

• Reinventing oneself is possible at any stage.

Her life mirrors the core message of the Productive Failure model: initial confusion leads to long-term mastery.

5. Conclusion

Today, she stands as proof that meaningful learning and personal growth often begin with failure. Like students who benefit from productive failure, she converted her struggles into strength, her doubts into determination, and her setbacks into a new identity.

She rewrote her story—not by avoiding failure, but by embracing it.When I first introduced division to my Class 3 students, many were confused. They mixed it with subtraction and multiplication and were unsure what “equal groups” really meant. Instead of correcting them immediately, I followed Manu Kapur’s idea of Productive Failure, where initial struggle is not a problem—it is a powerful pathway to deep learning.

Assignment 2-Embracing Productive Failure: How Struggle and Reflection Lead to Personal and Professional Growth

As Kapur states, learners should be allowed to “grapple with the problem before being shown how.”

Productive Struggle: The Confusion Stage

I gave the students simple division tasks such as 12 ÷ 3. Their incorrect attempts created curiosity. Just as Kapur notes, failure is not the opposite of learning; it is the beginning of it.

Hands-On Discovery Using Rajma Seeds

To turn confusion into understanding, I provided rajma seeds and cups.

Students shared 12 seeds among 3 cups.

They experimented, shifted seeds, made mistakes, and corrected themselves.

Finally, they discovered that each cup gets 4 seeds.

They also learned that division means making equal groups.

This hands-on exploration made division visible and meaningful.

Storytelling for Deeper Clarity

I narrated a short story about Raju the farmer planting seeds in equal rows. Through this story, students connected division to real life, reinforcing the idea of equal sharing and grouping.

Learning Division Properties Naturally

Through manipulation and play, students discovered:

• Division as equal sharing

• Dividend = Divisor × Quotient

• Dividing by 1

• Dividing by the same number

These concepts were not memorised—they were experienced.

Outcome

By the end of the lesson, students could:

• Explain division confidently

• Use objects to show equal groups

• Understand division properties

• Solve sums with meaning, not fear

Their learning journey reflected Kapur’s key insight:

“Let students struggle first. Teaching after struggle leads to stronger and deeper learning.”

- KRITIKA SRIVASTAVA, Sunbeam Annapurna

Overcome Stage Fear Through Productive Failure - Anushree Agarwal

 

Good School Assignments by Manisha Khanna

The journey highlights how confidence develops through consistent support, patience, and meaningful opportunities for productive struggle. With the teacher acting as a mentor, guide, and motivator, she gradually overcame stage fright, gained confidence in her speaking abilities, and became more expressive in class. This transformation demonstrates that confidence cannot be directly taught; it is carefully built through encouragement, structured practice, and a nurturing learning environment that empowers students to find their voice.

Anushree Agarwal

Integrated Approaches to Teaching Mathematics Through Exploration and Productive Failure - Prachi Pandey

Assignment 2

Teaching Perimeter and Area to Grade 5 Through Hands-on Learning

Abstract

This paper presents my real classroom experience while teaching the topic of Perimeter and Area to Grade 5 students. I used hands-on activities, real-life examples, and group work to make students understand the concept deeply. The experience showed that when learners explore, measure, and discuss on their own, they not only enjoy Mathematics but also develop a strong conceptual foundation.

1. Introduction

Teaching Mathematics to young learners is always a creative challenge. Students often find topics like perimeter and area confusing when taught only through formulas. I wanted my students to understand these ideas in a fun, practical way. So, I decided to design an activity that would help them experience the difference between “boundary” and “space inside” using real objects and materials from their daily life.

2. Classroom Context

This experience took place in my Grade 5 Mathematics class of 30 students. The topic was “Perimeter and Area of Rectangles and Squares.” I had noticed earlier that students easily memorised formulas but mixed up when to use which one. For example, some students calculated the area when the question asked for the perimeter.

To help them, I planned a hands-on learning activity using chart paper, rulers, and graph paper, so that they could measure, calculate, and visualize the concepts themselves.

3. The Experience

I began the lesson by asking:

“If we want to put a fence around our school ground, are we finding the perimeter or the area?”

Students shouted different answers. I didn’t correct them immediately. Instead, I divided the class into groups and distributed rectangular paper sheets and rulers.

Each group had to:

1. Measure the length and breadth of their rectangle.

2. Find the perimeter by adding all the sides.

3. Find the area by multiplying length × breadth.

As they worked, I noticed that some groups got confused, some debated the right formula, and others started comparing their results. I allowed them to explore and make mistakes. After 15 minutes, we discussed their findings on the board.

They were surprised to see that two rectangles could have the same perimeter but different areas. This curiosity led them to understand why both concepts are related but not the same.

Later, I gave them graph paper to draw rectangles and count squares to find the area visually. The visual approach made the idea much clearer.

Finally, I related it to real-life examples:

Perimeter → fencing a playground, border of a notebook.

Area → painting a wall, laying a carpet on the floor.

By the end of the session, most students were confidently using both terms correctly.

4. Reflection and Learning

This experience taught me that students learn better when they explore first and are taught later. Letting them discover through trial and error helped them retain the concept longer.

I also realised that:

• Concrete learning builds strong understanding: Manipulatives and measurements helped students connect abstract formulas to real life.

• Active participation improves memory: Students remembered the formulas better because they found meaning in them.

• Group work encourages learning from peers: Children explained and corrected each other’s mistakes in simple language.

• Mistakes are valuable: Instead of being afraid of errors, students learned through them—making failure truly productive.

5. Conclusion

This classroom experience was a reminder that Mathematics can be joyful when taught through activity and exploration. My students not only learned how to calculate perimeter and area but also understood when and why to use them. As a teacher, I felt proud watching them discover answers on their own. It strengthened my belief that real learning happens when children are allowed to do, think, and reflect.

Assignment 3

Title:

Learning Through Struggle: The Role of Safe Failure in Teaching Measurement

Abstract

This research explores how allowing students to experience productive failure—safe and guided struggle—enhances their understanding of the concept of Measurement. Conducted with Grade 4 students, the study examined how emotional safety and reflection after mistakes improved problem-solving ability, motivation, and confidence. Findings revealed that when students are encouraged to attempt problems before direct teaching, their conceptual clarity and participation increase significantly.

Introduction

Measurement is an important part of mathematics that connects directly to real-life experiences. Yet, many students struggle with unit conversions and practical understanding.

According to Manu Kapur’s theory of Productive Failure, learners develop deeper conceptual understanding when they are allowed to explore, make mistakes, and reflect on them before formal instruction.

This paper demonstrates how creating emotionally safe learning spaces helped students understand and apply conversion rules such as SBD (Smaller to Bigger – Divide) and BSM (Bigger to Smaller – Multiply).

Objectives

1. To study the impact of guided struggle on students’ understanding of Measurement.

2. To promote emotional safety and reduce fear of mistakes.

3. To build problem-solving confidence and resilience among learners.

Methodology

Participants: 25 students of Grade 4.

Topic: Measurement (length, weight, and capacity).

Procedure:

• Students were given practical problems such as estimating the capacity of bottles or comparing object lengths without prior teaching.

• They attempted conversions on their own and made observations.

• Later, I introduced the rules of conversion:

SBD Rule (Smaller to Bigger – Divide): Divide by 10, 100, or 1000 depending on the unit steps.

Example: 1000 g ÷ 1000 = 1 kg.

BSM Rule (Bigger to Smaller – Multiply): Multiply by 10, 100, or 1000.

Example: 2 m × 100 = 200 cm.

Students practised conversions using real-life examples and reflected on where they went wrong earlier.

Data Tools:

• Observation of engagement and participation.

• Student reflection sheets.

• Pre- and post-formative assessment on Measurement concepts.

Findings

• Students initially confused the direction of conversion but became confident after understanding the SBD and BSM rules.

• Discussions of mistakes made them more alert and motivated.

• Conceptual understanding and test scores improved significantly.

• Students could relate conversions to daily life (e.g., litre–millilitre in kitchen, metre–centimetre in the classroom).

Conclusion

Allowing safe struggle before teaching concepts in Measurement helps students think critically and connect learning with real life. When emotional safety and reflection are part of classroom culture, failure becomes a bridge to understanding rather than a barrier. The use of SBD and BSM rules gave them a clear and simple method to remember conversions.

Assignment 4

Title:

Activating Prior Knowledge: A Key Understanding to Decimals

Abstract

As a mathematics teacher, I have often noticed that students struggle to grasp the concept of Decimals, especially when they fail to see its connection to what they already know—whole numbers and fractions. This research explores how activating students’ prior knowledge before teaching decimals makes learning smoother, more meaningful, and long-lasting. The findings show that when students recall and relate their existing knowledge, they not only understand decimals better but also participate more confidently in class.

Introduction

While teaching decimals in Grade 5, I realized that many children find it abstract and confusing. They often mix up tenths and hundredths or fail to understand the value of digits after the decimal point. I understood that instead of directly teaching the topic, it was more effective to begin by activating their prior knowledge—the understanding they already had about place value, fractions, and real-life examples like money or measurements.

This approach is supported by Manu Kapur’s concept of Productive Failure, where students are encouraged to explore and make sense of new concepts through their existing understanding, even if it includes initial errors.

Objectives

1. To connect the topic of decimals with students’ prior understanding of whole numbers and fractions.

2. To make learning more meaningful by linking it to real-life examples.

3. To help students gain confidence and actively participate through discussion and reflection.

Methodology

Class: Grade 5

Topic: Decimals

Duration: 3 periods

Before introducing the topic, I started with a simple discussion:

• Have you seen prices like ₹25.50 or marks like 8.25 out of 10?

• What do you think the dot (.) means?

Students began sharing examples from shopping, fuel prices, and scorecards. I then asked them to relate these to fractions (e.g., 0.5 as ½ or 0.25 as ¼).

This discussion helped me assess what they already knew and identify misconceptions.

After this, I formally introduced decimals—explaining tenths, hundredths, and thousandths using a place value chart and real-life examples like money and measurements.

Students practised writing decimals, converting them into fractions, and representing them on number lines.

We ended with a reflection where students wrote what new ideas they had formed and what they already knew before.

Findings

• Students were able to connect decimals with familiar contexts like money and fractions.

• Misconceptions such as “0.05 is greater than 0.5” reduced significantly.

• Participation increased because the lesson started with what they already understood.

• The class became more interactive, and students showed more confidence in expressing their thoughts.

Teacher’s Reflection

This activity reminded me how important it is to start where the learner is. When I allowed students to recall their previous knowledge and share experiences, they became more involved and curious.

Activating prior knowledge not only helped in understanding decimals but also developed their reasoning and problem-solving skills.

As a teacher, I learned that connecting lessons to students’ lived experiences and past learning is the foundation of meaningful teaching.

Conclusion

Activating prior knowledge transforms the classroom into an engaging and thinking space. In the topic Decimals, it made students feel capable and confident, reducing their fear of mistakes.

Learning became more than memorising—it became connecting, reflecting, and discovering.

As a teacher, I realised that before introducing any new concept, it is essential to unlock what students already know.

Assignment 5

Title:

Task Design Matters: Enhancing Collaboration and Discussion in Simplification

Abstract

As a mathematics teacher, I observed that while students in Class 5 could perform basic operations, they often got confused while solving mixed-operation problems in the chapter Simplification. This research explores how thoughtful task design and collaborative discussion can improve understanding. Inspired by Manu Kapur’s concept of Productive Failure, I redesigned activities to encourage exploration, peer discussion, and self-correction before formal explanation. The results showed a significant increase in student engagement, conceptual understanding, and confidence.

Introduction

In traditional math classes, students are often given direct exercises for Simplification, like:

25 + 5 × 2 − 10 ÷ 5,

without being encouraged to think why they must follow the order of operations (BODMAS).

I noticed that students applied rules mechanically without truly understanding them.

To address this, I implemented task-based learning where students explored simplification problems through collaboration and guided struggle.

As Manu Kapur suggests, when students are allowed to face initial confusion and collaborate to solve challenging tasks, their eventual understanding becomes deeper and more meaningful.

Objectives

1. To improve students’ understanding of the BODMAS rule through well-designed collaborative tasks.

2. To enhance group discussion, reasoning, and explanation during problem-solving.

3. To analyse how productive struggle supports learning in Simplification.

Methodology

Class: Grade 5

Topic: Simplification

Duration: 2 periods

Procedure:

1. I began by giving students a real-life situation:
   “Ravi has ₹25, buys 3 pencils costing ₹5 each, and then gives ₹10 to his friend. How much money is left?”
   Students were asked to write and solve this as a mathematical expression.

2. Most students wrote different expressions and got varying answers. I did not correct them immediately.

3. In groups of 4, they discussed their reasoning, compared answers, and tried to find out why results were different.

4. After the discussion, I guided them towards the correct approach using BODMAS, connecting it to their earlier work.

5. Students then solved a set of progressively challenging problems (task ladder)—from simple mixed operations to multi-step word problems.

6. Finally, students reflected on what they learned through group work and self-discovery.

Findings

• Initially, only 30% of students could solve mixed-operation problems correctly.

• After collaborative discussion and teacher facilitation, accuracy improved to 85%.

• Students began explaining why multiplication or division must come before addition or subtraction.

• They became more confident and curious about the logic behind the rule rather than just memorising it.

Teacher’s Reflection

I realised that the key to learning Simplification was not in repetition, but in how tasks were designed. When problems were real, slightly challenging, and open for discussion, students naturally collaborated and thought critically.

Allowing them to first struggle and debate helped them internalize the logic of BODMAS. I shifted from being an instructor to a facilitator—guiding reflection rather than giving answers.

Conclusion

This study reaffirmed that Task Design Matters. When students engage in collaborative exploration before instruction, they construct knowledge meaningfully.

Through productive struggle and peer discussion, learning becomes active, deep, and joyful.

In the context of Simplification, this approach transformed confusion into clarity and hesitation into confidence.

Prachi Pandey
Sunbeam School Indiranagar