BCIS Class of 2022 alumni Chris Sha, currently majoring in applied mathematics at Columbia University, shares his thoughts on the importance of mathematics teaching.

The purpose of teaching math is to change the way we think and how we perceive the world around us. Learning math changes the way we see stuff, it creates a mindset of modeling, a mindset of taking a real-world problem and creating objective, scientific and abstract models. I think that’s really important regardless of whatever type of work you later pursue.

Welcome to the homepage of Chris: chrissha0104.github.io

At BCIS Chris studied Mathematics (Higher Level) in the IB Diploma Programme and he reflects,  “the DP math curriculum covers way more than AP maths. This is important because the different types of math we learn in high school is so fundamental, and it gives students more opportunity to see what they are really interested in. This gives students a striking advantage because learning more math subjects creates a smoother transition to university math later on. Learning across all math research areas in high school will better prepare students to dive into a specific area later.”

Chris recalls a mathematics research paper that he undertook during high school. “Roller coasters are undeniably the star entertainment people could find in an amusement park. The physics here is simple - the transfer of potential energy into kinetic energy. However, many amusement park lovers like me are not satisfied with the maximum speed experienced on the roller coaster. Hence, the purpose of this investigation is to explore the optimal slope of a brachistochrone curve which could minimize the time required to travel between two distinct points.”

When Chris completes his bachelor’s degree at Columbia University, he is planning to study a PhD in AI. “Choosing to study math rather than computer science, then transitioning to computer science later might be a longer and more difficult route, but the foundation that math builds is distinctly different than that of computer science. If we are to fundamentally improve a computer algorithm it is very reliant on mathematics.”

We have all studied mathematics at school, and yet people’s experiences, memories and expectations vary significantly. When mathematics is taught well, it can excite and engage students and encourage them to experiment. Conversely, it can instill anxiety, leading students to believe they are “not good at math”. Each of us knows someone who loves and excels in mathematics and someone else who loathes and continues to struggle with it. Somewhere on that spectrum lie our own personal lived experiences of math education and our hopes for our children’s experiences. 

When we think of mathematics, we automatically think of numbers, but mathematics is so much more. Math is about thinking, sorting, noticing patterns, making comparisons, describing the environment, estimating, as well as counting, naming shapes, measuring and building. In our increasingly interconnected world, where people speak, read and write a multitude of languages, mathematics provides a universal language that unites us all. Mathematics helps us make meaning of our world, explaining patterns and relationships, and enabling us to predict the future.

At BCIS we teach all students to think mathematically, fostering a positive attitude and developing a growth mindset where students believe they can and want to succeed. High quality mathematics learning and teaching begins with our youngest 2 year-old Toddlers and continues through to Grade 12 graduation and beyond. Research shows a clear correlation that building a strong foundation for mathematical understanding in kindergarten provides one of the strongest indicators for future educational success.

At BCIS Early Childhood Center (ECC), deep foundations of mathematical learning are laid as children are exposed to important mathematical concepts through play, activity and conversation. Every child is different, each bringing their own rich and diverse experiences on which our teachers build mathematics learning. Through skillful observations and interactions, ECC teachers identify every child’s unique strengths and create intentional, personalized learning experiences that connect students’ prior mathematical knowledge with their individual cultural, linguistic and home experiences. ECC teachers capitalize on the joy and wonder that youngsters naturally bring to their learning, cultivating and extending their mathematical sense and interest, ensuring each child’s confidence, competence, and interest in mathematics flourishes.

Dan Zhu, Coordinator of the International Baccalaureate (IB) Primary Years Programme (PYP) in our ECC, explains, “Many children may know how to count from one to ten, or even more, but they may not fully grasp the practical significance of these numbers in everyday life. In cooking games, children need to ensure accurate measurements of time and ingredients, involving mathematical concepts of measurement and counting. In pretend-play games, students prepare food and then ensure it is distributed evenly among all participants. This involves concepts of division and fractions in mathematics. In the building area, students may engage in construction while learning concepts of height, length, and stability. They need to think about how to use different shapes to build a stable structure, and if it's unstable, they need to think about how to improve it. Teachers encourage students to ask questions, contemplate solutions, and emphasize mathematical concepts in their own language. This approach aligns with the clear cognitive requirements for mathematical development at each stage, further analyzing and planning for future learning, laying a solid foundation for later IB mathematics studies.”

Ensuring a smooth transition from ECC to BCIS Elementary School (ES), the IB PYP provides a continuous curriculum framework. Mathematics concepts and ideas are wide ranging and intricately connected. ES teachers connect mathematical concepts across the curriculum and challenge students to develop mathematical thinking. Building on the strong mathematical foundations laid in the ECC, ES teachers employ inquiry-based teaching and learning strategies, personalizing experiences that strengthen students’ numeracy, problem-solving and reasoning processes. When students focus on problem solving rather than on “getting the right answer” they understand that making mistakes helps them to learn. Focusing on problem solving, and using mistakes as an opportunity, encourages students to try again, to approach the problem in a different way, and promotes a growth mindset. 

Grade 4 homeroom teacher and G4 team leader, John Herse elaborates, “We approach math education by focusing on building conceptual knowledge reinforced through collaboration, open-ended tasks, and discussion. Opening a task with a question allows students to try and, equally important, fail while getting gentle guidance from their partners, groups, and teachers. We encourage students to think about applying skills and concepts in a situation with possible real-life implications rather than a series of routines and pen-and-paper equations that reinforce rote memorization. 

We organize math teaching by working on boosting math attitudes and making it an enjoyable and accessible subject. For example, drawing conclusions and creating connections between decimals, percentages, and fractions to manipulate their value, their diverse usages, and applying these concepts into activities, projects, vernacular, and using the concept to apply it in diverse problem-solving tasks. This concept-based approach allows students to draw connections between tasks utilizing critical thinking and pattern making strategies to find answers.”

In Grades 6 to 10, the IB Middle Years Programme (MYP) builds naturally on from student learning experiences in the PYP. BCIS Secondary School (SS) mathematics teachers challenge and support all students to master fundamental math skills and concepts, incorporating technology tools and resources to enhance understanding, while personalizing so students can inquire deeply into areas of particular interest. Working independently and collaboratively, students explore concepts through questioning, investigation and projects, developing communication and teamwork skills and strengthening conceptual understanding as they explain ideas to their peers. Recently, Grade 9 students explored the concept of Geometry (Trigonometry) and used their mathematical understanding, critical thinking and problem-solving skills to design a ramp for various locations around campus to enhance accessibility for students in wheelchairs. 

But mathematics learning in Secondary School is not limited to mathematics class. Global Citizenship at BCIS empowers students to engage as citizens in an interconnected world. It provides an awareness and understanding of local and global issues, sustainable development, and the differences and commonalties of others. Mathematics is as powerful a tool for global understanding and communication in SS as it is in ECC and ES, empowering students to make sense of the world and solve authentic, complex problems. Mathematical thinking, problem solving and reasoning are deeply embedded across the SS curriculum. Whether studying forces of nature (meteorology, climate change, earthquakes etc), population and migration trends, economic development, scientific growth and decay, the spread of contagious diseases, coding, architecture, engineering or graphic design, students apply mathematical thinking and concepts to gain a deeper understanding of global issues. Mathematics teachers collaborate with teachers of other subjects to ensure that exploring authentic global contexts deepens students’ understanding of mathematics and of our world. 

In the final two years of high school at BCIS, students can choose to study IB Diploma Programme (DP) Mathematics courses at standard or higher level, or to study Mathematics in our bespoke BCIS IDEATE Program, depending on their preferred future directions and areas of major study at university. BCIS Head of SS Mathematics, Patrick Kitsao, explains, “BCIS is dedicated to providing MYP level mathematics learners with the necessary support to excel in DP and IDEATE mathematics courses. Through a comprehensive curriculum, experienced teachers, additional resources, and a collaborative learning environment, we ensure that students develop the knowledge, understanding, and intellectual abilities required for success.” 

ECC PYP Coordinator, Dan, reminds us that mathematics is everywhere. “The key lies in ensuring our teachers have sufficient expertise to understand children's mathematical development and guide them in observing and documenting their thought processes. We engage in collaborative lesson planning and professional discussions, asking ourselves: what have I observed in the children? What does it mean? Where can I guide them next? How can I assist them in a way that aligns with their progress? We then proceed to plan the curriculum, considering how arranging certain elements in the classroom can stimulate their thinking. It truly tests the teachers' capabilities, but they are all highly professional early childhood educators and they are all doing an excellent job!”

Grade 4 PYP teacher, John adds, “As the world is ever-evolving, especially with the introduction of AI technologies, we are intent on being flexible in providing students diverse opportunities to reinforce critical thinking and knowledge-building in mathematics to prepare students for whatever the future may hold.”

Wherever your learning journey may take you, BCIS alumni Chris’ former DP math teacher and Head of SS Mathematics, Patrick, proudly states, “Our goal has been, and will always be, to ensure that every student has the opportunity to excel in mathematics and achieve their full potential.”