Young Mathematicians: Mathematical Inquiry in the Early Years at ISP

Written in collaboration with Elsie Pinard and Allison Bryan, Reggio-Inspired and PYP Educators

In our Early Childhood Foundations (ECF) classrooms at ISP, we believe children are not passive recipients of mathematical rules, but capable, competent mathematicians who naturally seek to decode their world. Guided by the IB Primary Years Programme (PYP) framework and inspired by the Reggio Emilia approach, our young learners don't view math as an isolated, abstract subject. Instead, they use it as a powerful, dynamic lens to research, question, and explore the world around them.

The Environment as the Third Teacher: Fostering Mathematical Inquiry
Our classrooms are intentionally curated with open-ended, natural materials, mathematical provocations, that invite deep conceptual thinking. The beauty of our approach lies in the fluid blend of playful inquiry and intentional, research-driven instructional strategies. We don't just teach math; we co-construct it alongside our students, treating their natural curiosity as the driving force of our curriculum.

“When a child poses a question, we meet them at that moment to scaffold their thinking, offering meaningful challenges that push both our three-year-olds and six-year-olds to dive deeper. By connecting these concepts to real-life applications, like engineering block structures or surveying a class to gain data, math becomes a functional tool rather than an abstract concept. This empowers our students to take true ownership of their learning and see themselves as capable problem-solvers.”

Elsie Pinard, ECF Educator

From Rhythms to Structures: The Continuum of Algebraic and Numerical Thinking
At ISP, we intentionally map out learning progressions to meet children exactly where they are, transforming spontaneous observations into rich, conceptual research by pairing hands-on experiences with precise mathematical terminology.

 

• For our 3 and 4-year-olds: Inquiry begins through a multi-sensory exploration of structure and rhythm. Rather than just identifying simple, static patterns, our youngest researchers investigate the underlying pattern of repetition and translate it across different languages of expression. A child might analyze a visual pattern of natural loose parts (such as pinecone, leaf, pinecone, leaf) and translate that exact algebraic structure into an auditory rhythm (clap, stomp, clap, stomp) or a physical movement sequence. Through this hands-on translation, children learn to predict what comes next, troubleshoot anomalies when a pattern breaks, and articulate rules of change and repetition using their own authentic, developing vocabulary.
   
• For our 5 and 6-year-olds: This foundational pattern-seeking naturally matures into an understanding of numerical patterns and mathematical structure. Utilizing the architectural layout of the 100s chart, our oldest ECF learners discover that our number system is built on predictable, repeating geometric patterns where numbers systematically increase by 1s horizontally and 10s vertically.
   

When counting for larger sets of objects, children apply this structural awareness to organize and count materials efficiently in groups of 2s, 5s, or 10s.

Our students then take this concept of skip-counting and visualize it spatially using open-ended manipulatives to build arrays (equal rows and columns of objects), which forms the direct conceptual foundation for multiplication. Conversely, they experiment with partitioning these same groupings into equal shares, planting the early seeds for division.

Furthermore, instead of merely memorizing equations, our 5- and 6-year-olds delve into decomposing and composing numbers up to 10 and beyond. They discover that a single number can have multiple pairs of "partners," systematically discovering that a group of 10 can be broken down into descending pairs (such as 10+0, 9+1, 8+2, 7+3, 6+4, and 5+5). By arming students with precise vocabulary, such as decompose, compose, sequence, and systematic, we empower them to explain their mathematical logic with confidence.

Building a Foundation for Lifelong Learning
By embedding daily numeracy experiences, math-focused literature, and rich, tactile problem-solving into our curriculum, ISP students develop something far more valuable than rote memorization: they develop a mathematical mindset. They leave ECF viewing themselves as confident problem-solvers who can decipher patterns, analyze structures, and communicate their mathematical thinking to the world.

“I love watching children transfer their classroom discoveries into brand-new settings. When a child uses manipulatives to solve a problem systematically during play, and then spontaneously applies that same pattern logic to a game on the playground, we see true learning consolidation in action.”

Elsie Pinard, ECF Educator