Counting Up, Counting on Each Other: Constructivism in Early Childhood Math

posted by Alisa Algava ‘08, leader of a small Hudson Valley progressive school

To know the world, one must construct it.  ~Cesare Pavese

Walking into a math group last week at my school, I saw a group of first, second, and third graders deeply engaged in trying to figure out how many days there are until the annual Spring Show.  The challenge was to determine the number of days between two dates in different months using the evidence in front of them.  Without a calendar, they were using all they had learned the week before about months in the year and the number of days in each month to solve “story problems” that related to their real life experiences.  Some of these mathematicians counted up from April 17 (that day) until they reached May 7 (the night of the big performance).  Others wrote tally marks for the entire month of April and then crossed out 17 days and counted how many were left.  Ben, a second grader, realized that he could subtract 17 from 30 and then add the 7 days in May.  Once he shared that realization, everyone decided it was now “easy” to solve these problems.  And, thankfully, there were so many more problems to be solved!

This is what we do in real life.  We are rarely given every bit of information we need – we infer, draw on prior knowledge, and, when necessary, do additional “research” to solve the problems we encounter, whether we are paying bills, scheduling a vacation, or figuring out how many bags of flour we need to triple a batch of cookies. While subtraction and addition were important tools these learners used, the real thinking happened when they were deciding how to solve the problems with the limited information they had.

But even more important (and interesting to me as someone who loves learning and loves seeing other people learn) is the fact that these six, seven, and eight year olds constructed their own understanding of how to solve these calendar problems. Anita, their teacher, purposefully didn’t tell them what to do or how to do it, even though she knew the steps that would get them to the right answer.  Instead, they tried many different strategies, each of which worked for each learner.  They shared their various approaches and listened to each other’s explanations.  Ultimately, these learners discovered on their own that using subtraction and addition would make the process quicker and easier.

Constructivism is a theory of learning that explains how human beings generate knowledge and meaning from direct experience.  We learn by doing, not by being told what to do.  The teacher is a facilitator, and learning happens through an active, social process in which children are challenged to reach just beyond their immediate comfort levels or abilities.  Through this process, they acquire new skills and a deeper conceptual understanding of all they encounter.  (Dewey and Piaget and Vygotsky are some of the great thinkers who provided inspiration for the founding of this school in 1963.)

And by the way, I’m so looking forward to seeing all of our mathematicians-turned-actors in the amphitheater when the “curtain goes up” and the Spring Show begins, exactly 13 days from today!  (That’s 30-24+7.)

Alisa Algava graduated from Bank Street’s Leadership for Educational Change program in December.  For the past 14 years, she has taught and learned in public, private, and charter schools in NY, NJ, and RI.  She has written a handful of postings in the past three months about her experiences leading and learning in a small progressive school.  Alisa loves learning.  She loves moderating The Alumni Blog. And she really loves her nephew.

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