INSIDE THE CLASSROOM: MATH

Ariana Vlachos, kindergarten teacher, Brownsville Ascend L ower School, Brooklyn

In kindergarten, the majority of mathematics instruction focuses on numbers up to 20. Kindergarteners learn to count well beyond 20, of course, but the most rigorous aspects of the curriculum involve composing and comparing smaller numbers.

Kindergarteners l earn that numbers can be decomposed, or broken apart — not just into individual units, but into two (or more) sets of whole numbers. This is one of the most important concepts they grasp during this year, and we use a variety of activities, routines, and games to help students explore all of the different ways to decompose numbers up to 20.

The more they work with these numbers, the more efficient their strategies become. For example, rather than always starting from 1 and counting each item in a group, students learn that they can “count on” from any number. They also start to internalize number pairs and combinations, which they use to solve a variety of problems quickly. Well before students learn the addition and subtraction symbols, they have spent several weeks performing these operations.

Many of our lessons at Ascend revolve around a compelling real-world problem, or “number story.” At the beginning of the lesson, I share the story problem in an engaging way to get students excited about being “math detectives.” Then, to ensure understanding of the task, I ask three students to repeatepeat the story to the class.

For example, I told my students the following story: Keisha had 6 seashells. Later that day, she found 10 more seashells. How many seashells does Keisha have alll together?

I gave each student paper, al,pencil, and counting cubes so thatd they could work independently. The beauty of this task is that there is no single wayay for the students to go about solving thehe problem. It is up to them, as eager mathematicians, to think flexibly about all thethe strategies that could help them.

I circle the room, noting students’ stratrategies, and have quick conferences withwith individual students in which I use careareful questioning to address their miscon-conceptions or elicit their thinking. Throughough these conferences, I select three studentsdents to share their work with the rest of the class, making sure that multiple strategies are showcased.

In this lesson, one student solved the problem by creating a set of 10 cubes and a set of 6 cubes. He then counted the cubes in both sets starting from 1. Another student drew a group of 10, then simply counted on from 10 using individual units.

The distinctions may seem subtle, but these strategies indicate the kind of flexible, conceptual thinking we aim to nurture in our students. What’s so interesting and fun about teaching math in this way is that you get to see how students’ minds are working in different, and often very creative,c ways.