Summer 2026 President's Message Leading with Curiosity: Developing Number Sense and Unleashing Mathematical Creativity

As I reflect on classrooms across California, I am continually struck by the brilliance students bring to mathematics when they are given the space to think, explore, and create. In this issue of our journal, we center on two deeply connected ideas: developing number sense and unleashing students’ mathematical creativity. These are not separate goals; they are intertwined, each strengthening the other.

We often hear the terms number sense, number fluency, and number flexibility. But how do these actually develop? They do not come from memorization alone. They grow through experience, play, and rich opportunities to take numbers apart and put them back together again. When students are invited to decompose, recombine, estimate, and reason, they begin to understand numbers as meaningful and dynamic rather than fixed or rigid.

True number sense means students can approach numbers in multiple ways. They use different representations, visual models, number lines, equations, and stories. They try out strategies, revise their thinking, and make connections. One student may see 24 as 20 and 4, another as three groups of 8, and another as 25 minus 1. Each perspective offers insight. Our role is not to narrow those approaches, but to elevate them.

There are so many powerful ways we can nurture this thinking in our classrooms. Here are a few strategies that consistently support the development of number sense:

• Number Talks: Short, daily conversations where students mentally solve problems and share strategies. These build flexibility, confidence, and communication.

• Open-Ended Tasks: Problems with multiple entry points and solutions invite creativity and allow students to use numbers in ways that make sense to them.

• Games with Purpose: Simple games (like making target numbers, card games, or dice challenges) create joyful repetition and strategic thinking.

• Visual Models: Using tools such as ten frames, arrays, and area models helps students “see” numbers and operations.

• Estimation Routines: Activities like “Which is closer?” or “About how many?” develop reasoning and help students trust their intuition about numbers.

When we consistently provide these kinds of opportunities, we send a powerful

message: mathematics is not about getting the one right answer as quickly as possible; it is about making sense of ideas.

At the same time, we must recognize that number sense is not built only within the walls of a classroom. Students come to us with rich mathematical knowledge shaped by their families, communities, and lived experiences. Long before formal schooling, children are engaging with numbers in meaningful ways. A young child counts their toys as they clean up, divides snacks evenly among siblings, or notices who has “more” or “less.” In the grocery store, they may compare prices or help estimate a total. These are powerful early experiences of quantity, comparison, and reasoning.

As students grow, these experiences become even more complex. A middle school student saving money for something important is engaging in budgeting, addition and subtraction, and even proportional reasoning. Another student helping cook at home may double or halve a recipe, working with fractions in a real and tangible way. Others may track time, manage schedules, or notice patterns in sports statistics or music rhythms. These everyday moments are not separate from mathematics; they are mathematics.

The California Mathematics Framework reminds us to honor these assets and to design

learning that builds from them. As the framework states, “Students’ cultural and linguistic backgrounds, experiences, and ways of knowing are resources for learning mathematics.” This perspective challenges us to see students’ lived experiences not as peripheral, but as central to meaningful mathematical understanding. The framework also emphasizes that “Engaging students in reasoning, sense-making, and problem solving supports deeper understanding than focusing on procedures alone.” These ideas align directly with our goal of developing number sense through exploration and creativity.

Families also play a vital role in nurturing number sense. Supporting mathematics at home does not require worksheets or formal lessons. It can look like playing simple card or dice games, talking about numbers during daily routines, or asking questions like, “How did you figure that out?” Families can encourage children to explain their thinking, notice patterns, and stay curious. Even small moments, counting steps, comparing quantities, and estimating time, build confidence and reinforce that mathematics is everywhere.

One of the most beautiful aspects of this work is recognizing that children often see numbers differently from adults. While we may default to efficient algorithms, students bring fresh and sometimes unexpected approaches. A student might solve 18 + 17 by thinking, “18 + 2 is 20, and then I have 15 more,” while another might double 17 to get 34 and adjust from there. These strategies are not misconceptions; they are evidence of sense-making. When we honor them, we validate students as thinkers.

And this is where identity becomes so important. When students are given the freedom to explore numbers flexibly, they begin to see themselves as mathematicians. They develop confidence in their ideas. They take risks. They explain, justify, and revise. They experience autonomy, the sense that they can figure this out. This is at the heart of mathematical creativity.

As educators, we have the opportunity to create environments where this kind of learning thrives. When we shift from telling to listening, from showing to wondering, we open the door for students to bring their full selves, their experiences, their cultures, and their ideas into mathematics. In doing so, we not only build stronger number sense, but also cultivate curiosity, agency, and joy.

Let us continue to create classrooms where numbers are explored, not just computed; where ideas are shared, not just evaluated; and where every student knows they belong as a mathematician, both in school and beyond.

With appreciation,

Hilda Villarreal Wright

California Mathematics Council

State President

California Department of Education (CDE). 2023. Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve (Mathematics Framework). Sacramento, CA: CDE.