Mathematical Practice
City: Multan
School: The Women University, and Govt. Muslim Girls High School
Dr. Nazir spoke about "Cultivating Virtues through Mathematical Practice" at The Women University, Multan. She highlighted how practicing math impacts us and the virtues it instills. The talk was interactive and drew many curious questions from young women pursuing MS and PhD degrees. They were urged to engage in math circles for school kids, emphasizing the role of math in shaping young minds to become better individuals.
Two math circles were conducted at Govt. Muslim Girls High School, Multan. During the first session, approximately 70 students in grades 6, 7, and 8 gathered with great enthusiasm to explore mathematics. We delved into the "Pigeonhole Principle" as our main topic but kicked off the session by discussing why they enjoyed math and their perceptions of numbers. One student expressed a liking for the power of 2, prompting a discussion about its significance. We explored sets and their subsets, posing a question about the number of subsets within a set containing just one element. This led us to discover how the power of 2 relates to the count of subsets in a finite set. To make things more engaging, we experimented with folding paper to see how many times it could be folded and related it to the power of 2. We also had fun guessing birthdays using algebraic tricks, sparking curiosity among the students. The core focus shifted to understanding the pigeonhole principle, demonstrated through a game of "Musical Chairs," which vividly illustrated its concept. We applied this principle to solve various problems, such as determining the minimum number of cards needed from a deck to guarantee specific card combinations and solving tiling problems using dominos. We even explored how on a sphere's surface, at least four out of five points will lie on the same closed hemisphere. The session was concluded by introducing algebraic questions where the pigeonhole principle could be applied, empowering the students to unlock these problems independently through playful experimentation.
In the second math circle session, around 100 enthusiastic grade 9 and 10 students joined, their excitement palpable as every seat in the auditorium was filled, and some students even sat on the floor to participate. This session centered on "Catalan Numbers" which commenced with the Skolem sequence of 1, 2, and 3. Students were challenged to discern its pattern, and a student was able to quickly decode it! We then extended the challenge to create a sequence using 1, 2, 3, and 4, which the students eagerly accomplished. To intrigue the students further, they were prompted to explore the concept for sequences up to 6, known as "Langford pairs." Next, we dived into counting "balanced parentheses," delighting the students as they explored various patterns up to 4 pairs of parentheses. We progressed to counting "Mountain ranges" and introduced Ballot Sequences, encouraging the students to find all possible sequences. We illustrated the nonintersecting shaking hands problem, visually engaging the students and later transforming it into a mathematical model, showcasing the beauty and problem-solving capacity of mathematics. Towards the end, two pivotal questions were introduced which linked these problems: how they related to each other and the connection to "Catalan numbers." After revealing that the sequences they explored were indeed Catalan numbers, the students were showed them the formula to verify their findings. Witnessing the students' joy and curiosity in discovering these magical connections in mathematics was truly remarkable.
To conclude the session, a book on Catalan Numbers by Stanley was showcased which encouraged them to explore further patterns, leaving them inspired to delve deeper into this fascinating mathematical realm.
We thank Dr. Zill e Shams and Dr. Kiran Batool from The Women University for their support and collaboration in the facilitation of these sessions. Their coordination was instrumental in making the events successful. We also extend our gratitude to Ms. Mah Talat, Principal of Govt. Muslim Girls High School, for her presence and encouragement to her students, urging them to participate in these engaging sessions. A special thanks to the dedicated school math teachers whose efforts shone through the enthusiasm and preparedness of their students. Their dedication to nurturing mathematical interest among their students is truly commendable and played a significant role in the sessions' success.
Here are some highlights from the event:
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