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

April 24, 2009 at 10:07 pm 3 comments

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

alisanephewTo 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 img_4563the 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.

Entry filed under: classrooms, constructivism, curriculum, dialogue, early childhood, integrated curricula, math.

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3 Comments Add your own

  • 1. Julie Diamond  |  May 14, 2009 at 12:21 pm

    I really like the description of children figuring out how to solve a calendar problem – a real problem, that’s solved as the children work together.
    About the photo accompanying the article: the drawings illustrating each month look computer-generated, in content and style. Why use computer graphics? What if we consistently have children illustate class signs, as part of their class work – they decide on appropriate imagery, and make the drawings? This too becomes a real problem… and the environment of the class is liberated from commercial imagery.

  • 2. Bank Street Alumni Blog  |  May 15, 2009 at 9:44 am

    Julie, I totally agree about the drawings/graphics that the teacher used in this experience and the importance of children being involved in creating imagery for the work they’re doing and problems they’re solving. This is an area that seems harder for some teachers than for others. Could specific, do-able examples and techniques for creating a kid-generated environment help? –alisa

  • 3. Julie Diamond  |  June 16, 2009 at 1:57 pm

    I think there is a way, exactly as you suggest: when people see kids’ work used in this way (schedule signs, titles for wall displays, labels, charts made by kids, illustrations for classroom rules) it’s powerful and inspiring. Other teachers see it and think, oh, of course, why not! We’ve been so brain-washed by commercial imagery, “cute” advertising pictures, etc. – and tend to assume this is the way to appeal to children… I think we can consciously find ways to make classroom images real, and connected to the children we teach, using photos, too, if children’s ability to produce representational drawings is limited.

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Some of Our Past Bloggers

Alisa Algava ‘08, leader of a small Hudson Valley progressive school
Gloria Arenson ’58, psychotherapist
Bill Ayers ‘84, UIC professor, Chicago
Fred Baumgarten ‘84, writer/musician/naturalist/father
Keith Berman '03, founder/president of Options for College and Bank Street’s LinkedIn moderator
David Bowles ’08 (SFC ’93), museum educator at the Rubin Museum of Art
Elena Canaras ‘07, Special Education teacher, Hawaii
Virginia Casper, Bank Street faculty member
Jim Clay ‘88, director of a Washington DC Quaker preschool
Mary DeCamp Cotterall ‘87, Reading Specialist, Michigan
Judy Coven ’77, retired public school teacher and former Antioch University faculty member
Leslie Day '93, adjunct instructor at Bank Street and author of Field Guide to the Natural World of New York City
Mary Louise (Molly) Day ‘76, Lab School teacher, Chicago
Liezel de La Isla ‘99, Prague International School teacher
Diane Trister Dodge '70, founder and president of Teaching Strategies, Inc.
Meghan Dunn ’08, 3rd grade teacher, Brooklyn
Steven Evangelista ’01, co-director Harlem Link Charter School, NYC
Janine Fetters ‘02, Senior Associate of Parent Engagement at NACCRRA
Dena Florczyk '88, middle school teacher and founder/director of The Nigerian School Project
Hollee Freeman '94, writes about parenting issues for the alumni blog and was featured on BSCAA's April 2012 Career Panel
Ellen Galinsky '70, is President and Co-Founder of Families and Work Institute and author of Mind in the Making: The Seven Essential Life Skills Every Child Needs
Joanne Ruvolo Gannett ‘84, Columbia College art history professor, Chicago
Joan Goldstein ‘67, sociologist and educator
Margot Hammond, Director of the Center for Early Childhood Professionals
Carol Hillman ‘67, early childhood educator, author, and Long Trip co-leader
Pam Jones ‘05, Bank Street advisor and instructor
Lee Klinger Lesser ‘87, trainer for the Parent Services Project
Preminda Langer ‘97, teacher trainer
Claire Milam ’97, life coach, Austin, Texas
Rabin Nickens ‘03, Speaker, Trainer and Educational Consultant
Beth Norford ‘89, consultant and former School for Children teacher
Susy Ogden ‘97
Marion Palm ‘95, Leadership in the Arts alum, writing tutor, poet and singer
Jessica Poser, assistant professor of art education at UIC, Chicago
Jesse Pugh '76, BSCAA President
Meg Rauen ‘06, former Chicago elementary school teacher, NY
Linda Reing, Bank Street Director of Alumni Relations
Rosalind Rothman '62, retired NYC teacher and guidance counselor
Kyla Ryman '92/'97, educational coach and consultant
Ariel Sacks ‘06, middle school teacher, Brooklyn, NY
Linda Appleman (Guidall) Shapiro ‘81, psychotherapist and author
Barbara Silver ‘80, literacy consultant and former NYC first grade teacher
Andrea Penny Spencer, former Associate Dean of Academic Affairs at Bank Street
Debbie Stone ‘84, former teacher/co-director of High Valley School
Rachel Theilheimer ‘74, chair of teacher education at BMCC/CUNY
Theodore Timpson ’05, founder/president of Young Spirit Foundation
Eleanor Traubman '95, is Editor in Chief of Creative Times, a blog which promotes NYC's performing, visual and literary arts
Allison Warren '08, new mom, recent grad, and early childhood teacher
Max Weinberg ‘03, Francis Parker School teacher, Chicago
Ted Wells ‘07, 4th grade teacher at The Park School, Brookline, MA
Tracy Wiessbrod ’03, kindergarten teacher and stay-at-home mom

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