More than Numbers: Math in the Early Childhood and Elementary Grades

By Kathryn Bauman-Hill, Early Childhood and Elementary Head

In my experience as an elementary student, learning math was solely focused on numbers. Yet our students in the Early Childhood and Elementary levels at Capitol Hill Day School experience a much deeper understanding of the whys behind the numbers.

I have a few very vivid memories of math from my early school experience. One memory is of memorizing a multiplication facts table in my bedroom in 3rd Grade. It was an isolated exercise, unlike the investigative approach we value at Capitol Hill Day School, where students explore patterns and relationships to deepen understanding. Rather, I sat on my bed reviewing the facts over and over until I committed them to memory. Later, I remember explaining to a classmate how to complete the division algorithm by memory without discussing place value or the logic behind breaking numbers into equal parts. It was a robotic set of steps we performed to get a correct answer. 

A humbling moment came on my first day at a new school in 8th Grade. Confident in my memorized facts and procedures, I was thrown when I didn’t recognize a new (to me) symbol: a dot (.) used for multiplication instead of an x. Equations I once solved with ease suddenly seemed unfamiliar. Too proud to ask, I spent two days inferring before finally asking my teacher for clarification. That small shift unlocked the equations, but it made me realize that mental flexibility had never been part of my math experience.

What I lacked in each of these experiences was what I later came to value as a math instructor and recognized as crucial in developing strong math students. These same items are prioritized by the National Council for Teaching Mathematics (NCTM) in math instruction: 

• Presenting math tasks that promote reasoning and problem solving
• Investigating patterns and relationships
• Increasing procedural fluency based on a deeper conceptual understanding
• Facilitating meaningful mathematical conversations
• Purposeful questioning to encourage deeper student thinking and analysis
• Encouraging productive struggle and a growth mindset 
• Reflecting and critiquing one’s work

At Capitol Hill Day School, students see the importance of connections in math and interpret how ideas build upon one another as they move between grade levels. Mastering different elements of number sense helps students to decipher equations and the process beyond an algorithm. Students learn to synthesize larger numbers as they extend collections of numbers that make ten (3+7=10; therefore, 30+70=100). Students also use place values to break down more complex multiplication and division problems. Patterning can become a tool to help with repeated addition, leading to a deeper understanding of multiplication facts.

Through collaborative conversations, students enhance their reasoning skills and justify the steps of solving a problem. They discuss various strategies that help them arrive at a solution and gain flexibility in problem solving. Writing skills are interwoven as students share their answers in thorough explanations that express each step of the process. They are encouraged to engage in and move through productive struggle, where persistence in greater challenges is celebrated and coached through rather than avoided.  

Executive functioning skills are built within the math practices at Capitol Hill Day School.  Teachers encourage students to work through the impulse of quickly finding an answer, something highly prioritized in my elementary experience, by taking their time to solve problems and explain their step-by-step process. This strategy also helps build working memory as they document each level of thinking, which identifies any misconceptions. Students can then self-monitor their understanding as they work with more complex problems. Developing ways to organize their ideas on a page improves accuracy as one tracks their mathematical journey.  

Join Us! | More Than Numbers: Math in the EC & Elementary Grades
We invite you to join us for a deeper look into the ways we teach math at the Early Childhood and Elementary levels on Thursday, April 10th at 9:00 a.m. We hope to see you there to learn more about how instruction today compares to your personal experience.