Day 1 – Numbers and Patterns

Dr. Waqas Ali Azhar

The first day of the Mathematics Teachers' Training Workshop was themed around "Numbers and Patterns," and I had the pleasure of facilitating the sessions. We began the day with brief introductions, followed by an engaging discussion on the challenges that teachers face in their classrooms every day.

It was inspiring to hear everyone openly share their experiences. Some of the key challenges highlighted by the participants included students being unable to study outside the classroom because many have to work after school, teachers not being up to date with the new curriculum, the lack of professional development opportunities, single teachers having to teach too many courses and classes, the declining attention span of students, the growing impact of AI, language barriers, the lack of connections between mathematics and real-world problems, the absence of mathematics laboratories, and the constant time constraints that make it difficult to conduct engaging classroom activities.

To set the tone for the workshop, we watched a short video by Steven Strogatz on Mathematical Exploration, which beautifully highlighted the importance of exploration, curiosity, and innovative teaching in the mathematics classroom. This naturally led us into exploring several pedagogical strategies, including Think–Pair–Share, through activities such as Number Jumble. My goal throughout the day was to introduce participants to low-threshold, high-ceiling activities—tasks that every student can begin, yet which naturally lead to deeper mathematical thinking. One such activity was the classic Tower of Hanoi, where the entire room enthusiastically explored the puzzle before gradually building layers of increasingly challenging questions around it.

As the day progressed, we experienced a variety of mathematical activities. We explored place value by making numbers using beads representing units and tens, investigated different ways of constructing numbers through combinations of consecutive integers, tackled the famous Locker Problem, and enjoyed strategic thinking through The Factor and Multiple Game and The Nim Game.

One of my favourite moments of the day came when I posed what appeared to be a simple question: Suppose you visit a pizza shop and order a 9-inch large pizza. The shopkeeper instead offers you two 5-inch medium pizzas for the same price. Are you at an advantage or a disadvantage? Almost everyone confidently answered that it was an advantage—only to discover, after some mathematical reasoning, that they were actually at a disadvantage. It was a wonderful reminder of how intuition can sometimes be misleading and how mathematics helps us uncover the truth. We also discussed fascinating problems such as the famous Dido's Problem, encouraging participants to appreciate the beauty and history behind mathematical thinking.

The final part of the day was dedicated to collaborative lesson presentations. Participants worked together in small groups to prepare and present a short classroom activity in their own teaching style. Watching these presentations was one of the highlights of the day.

Ms. Farah Irfan presented an engaging activity on the perimeter of two-dimensional shapes. Ms. Aliya introduced a fun "Who Am I?" activity based on three questions to identify a quadrilateral. Mr. Aimal Khan and Mr. Ghulam Mustafa creatively presented the perimeter of a "Gol-Matol" circle. Ms. Naureen Tariq and Ms. Afshan Zafar discussed fractions and different approaches to adding them. Mr. Saad Khalid demonstrated effective ways of visualizing data using graphs and histograms, while Ms. Raniya Ilyas concluded the presentations with a series of exciting mental mathematics challenges for everyone in the room.

These were wonderful presentations that reflected not only creativity but also the passion and dedication these talented teachers have for mathematics and for their students.

Overall, it was a fascinating day filled with fun, learning, excitement, thoughtful discussions, and meaningful sharing of experiences. I am deeply grateful to every participant for their enthusiasm, openness, and willingness to learn from one another. Their energy made the first day truly memorable, and I look forward to the exciting journey that lies ahead over the coming days.