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Funding was provided by the McCormick Tribune Foundation and the Harris Foundation.
Math Education:
Promoting Young Children's Understanding
of Math Concepts
Friday, October 28, 2005
Rubloff Auditorium at Loyola Water Tower Campus
25 East Pearson Street, Chicago, Illinois
About the Symposium
Rethinking Early Mathematics Education:
Children, Curriculum, and Pedagogy
Herbert P. Ginsburg, Ph.D.
Early mathematics education is currently a topic of considerable concern.
American children’s school mathematics performance, especially that of
low-income and minority children, is relatively poor when compared with the
performance of children from East Asia. Research suggests that mathematics
education beginning in early childhood can help to remedy this situation, but
uncertainties about early childhood mathematics education abound. Can young children
really learn abstract mathematics? What mathematical topics are appropriate for
young children? Is it appropriate to implement a mathematics “curriculum”
at this age level? How should early mathematics be taught?
Dr. Ginsburg provided an overview of recent studies showing that young
children’s “everyday mathematics” is widespread, and often competent and
even abstract. Children enjoy playing with mathematics, including
school mathematics. He gave examples from a new mathematics
program — Big Math for Little Kids — showing that early childhood
mathematics education needs to be pervasive and deep, and that a curriculum
is required to help organize young children’s learning in this area.
He also argued that adults need to take a strong role in teaching early
mathematics, though little is known about appropriate pedagogy for early education.
Herbert P. Ginsburg, Ph.D., is the Jacob H. Schiff Professor of Psychology and
Education at Teachers College, Columbia University. His research interests
include the development of mathematical thinking (with particular attention
to young children and disadvantaged populations) and the assessment of cognitive
function. He has conducted basic research on the development of mathematical
thinking, and has developed mathematics curricula for young children, tests of
mathematical thinking, and video workshops to enhance teachers’ understanding
of students’ mathematics learning. Currently he is engaged in creating a model
video-based course in early childhood mathematics education; he is exploring
how hand-held computer technology can be used to help teachers assess
children's mathematical knowledge; and he is participating in an evaluation
of the Big Math for Little Kids mathematics program.
Bringing Meaning to Numbers:
How Children Pull the Pieces Together
Kelly S. Mix, Ph.D.
Download Dr. Mix's Presentation
(14MB PowerPoint file)
To most adults, numbers seem straightforward. “Three” means
three. But to those faced with explaining numbers to children,
the complexity of these words and their referents becomes quite
apparent. For one thing, we cannot point out a quantity the
same way we can point out a dog or a cookie. Numbers do not
refer to things. They refer to abstract ideas — properties of
sets that hold true no matter what items the sets contain.
In addition, number concepts involve many component parts,
including one-to-one correspondence, object recognition, numerical
equivalence, labeling sets, and counting. Each of these components
can at first be tightly tied to specific situations and each develops
along its own trajectory. Indeed, young learners face unique
obstacles as they master each piece, and a major challenge of early
childhood is the integration of these pieces into a stable number concept.
Dr. Mix reviewed research on early childhood number concepts to (1)
outline the components of mature number concepts; (2) describe the emergence
of these components in specific contexts; (3) discuss everyday experiences
and play activities that advance their development; and (4) examine the
way children use language and similarity to bring the pieces together.
Her talk highlighted the basic mechanisms of number concept formation,
as well as individual differences in the way this development unfolds.
Kelly S. Mix, Ph.D., is associate professor of educational psychology
and director of the Early Childhood Learning and Concepts Lab at Michigan
State University. Her research focuses on the development of numerical
equivalence, counting, and math concepts in infancy and early childhood.
She is co-author (with Janellen Huttenlocher and Susan Cohen Levine) of
the book, Quantitative Development in Infancy and Early Childhood,
published by Oxford University Press. She received the 2002 Boyd McCandless
Award from APA for early career contributions to research in developmental
psychology. She is currently completing a series of case and microgenetic
training studies, in collaboration with Arthur Baroody, that is funded by the
Spencer Foundation.
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