Part I: Mathematics Everyday and Everywhere
Part II: Mathematics Content for Young Children

Welcome to Mathematics for the Curious

   I have no special talents. I am only passionately curious. — Albert Einstein   

Young children are natural mathematicians. They are passionately curious as they explore, experiment, and ask an endless stream of questions: What is the biggest number? How much does the sky weigh? How far is the moon? How much water is in the ocean? How many grains of sand are there in the world?  Offering opportunities for young children to learn mathematics gives them new ways to understand their world and provides them with the tools they need to explore, test new ideas, and answer their own questions. The early childhood educator plays a key role in helping children see the mathematics all around them, creating a culture for mathematical thinking, and exploring alongside children.

Help children see the world through a mathematical lens

Long before entering first grade, prekindergarten and kindergarten children already possess strong intuitive notions of pattern, shape, magnitude, and number, and they use these notions naturally during play (Seo and Ginsburg 2004). Teachers, childcare workers, and parents play a key role in orienting children’s attention to the mathematics in their play by structuring occasions to bump into the mathematics that is all around them. When teachers and caregivers recognize the mathematics in spontaneous activities, promote exploration and invention, prompt predictions, conjectures, and reflection, ask questions, and challenge intuitive notions, children begin to see the world through a mathematical lens. 

Create a culture of mathematical thinking

Young children go about their early explorations and playful work with confidence. They will build structures with blocks only to have them topple over, and then rebuild them again and again in ever more sophisticated ways. Children roll balls, toy cars, and other objects down improvised ramps to see how far the objects go. If the objects tumble off steep inclines or stall on low ramps, children make adjustments to their structures. Adjustments and reconstructions are not seen as errors, but rather are part of the natural process of testing out ideas and eliminating the ones that do not work. Given the opportunity, children will bring the same positive dispositions to their learning and doing of mathematics. 

Explore alongside children

Early educators are instrumental in creating a culture of mathematical thinking and promoting positive dispositions toward mathematics. For this to occur, teachers and caregivers must also see themselves as mathematicians. They must be willing to explore and experiment alongside children and to display curiosity in both the mathematics and the children’s mathematical thinking. They need to ask questions that prompt predictions, conjectures, and generalizations such as, I wonder what will happen if . . . ? What makes you think that . . . ? Is there another way we can find out? How can we solve the problem another way?