Math and Active Thinking in Grade 2
Excerpt from a recent letter from Daichi Hirata, grade 2 class teacher, to the parents of grade 2
There is a striking difference between how our work in language arts and math is brought in a Waldorf school because of the inherent difference between these two subjects.
Our language, both spoken and written, is based on human conventions, and over the course of hundreds and thousands of years it has been enriched but also muddied in its form. Thus in our work with language arts, our primary aim is to strengthen our relationship to our language so that the students feel drawn to learning the conventions of the written word.
Mathematics, which essentially is a science of things that have patterns and regularity, has a logical order and a universal quality that stretches across all cultures. Thus in our work with numbers and patterns, we invite children into active thinking.
One of the ultimate goals of education is for students to learn how to think independently, flexibly, and creatively. Starting in the early grades, our work with math gives us an incredible opportunity to develop these different qualities of thinking. My goal for this block is rather simple; to explore the concept of place value, and revisit and rediscover the operation of division and multiplication.
My intention is to offer a math problem everyday that gives us the opportunity to “make sense of” and “figure out” the problem as a group.
Last week, I began by telling them a story of a large group of woodsmen who had worked tirelessly all summer, hauling logs down from the mountain and milling them into lumber. As the winter approached, they decided they should count the fruits of their labor. But as they had so many pieces of lumber, they would get confused or lose their place when they counted by ones. The woodsmen decided they needed to figure out ways to group them, so that they could keep better track as they counted up. Then I presented to the class a large heap of nearly 1,500 pieces of lumber (popsicle sticks) and gave them, just as the woodsmen, the task of accurately counting them all.
Children worked in groups of three or four, taking a large handful from the heap to begin counting and organizing their share. As expected there were different ways in which groups decided to organize their pile. I gave each group time to share their ideas, and we all counted their pile using their method of grouping. We found that some groupings such as by 2s took a long time; other grouping such as by 20s were difficult to track for most children once it got into the hundreds; and grouping by 10s seemed both efficient and reasonably easy to count. With this problem we gradually but actively began moving towards constructing our understanding of place value. Using this approach, my hope is that the children see math as an active process that is flexible, creative, imaginative, and requiring cooperative learning.