Entering the Child's Mind
"You know why we study children?" the man answered. "We try to find out how they learn math so that we can help them learn math if they have trouble."
The man was Herbert P. Ginsburg, the new Jacob H. Schiff Professor of Education at Teachers College, and his answer to the first grader's question sums up much of his research over the last 25 years.
Ginsburg has been analyzing children's mathematical thinking since early in his career and, in recent years, he and his students have been developing techniques for the cognitive clinical interview, a process by which an adult can discuss the thinking process with a child.
The professor, who has served on the TC faculty since 1985, is now completing two books, Entering the Child's Mind: The Cognitive Clinical Interview in Psychological Research and Practice (forthcoming from Cambridge University Press) and Learning What Children Know About Math: The Teacher's Guide to Flexible Interviewing in the Classroom (coauthored with TC graduates Susan F. Jacobs and Luz S. Lopez).
The book for teachers speaks to the essence of teaching, Ginsburg and his coauthors say. To teach effectively, it is important for the teacher to understand what the child means when she says that two rows of objects both have the "mostest". It is important for the teacher to know why the child believes you can't take a big number from a small one. It is important for the teacher to discover what the shy child is really thinking or why the student from a different culture refuses to answer a question.
Ginsburg, his students and TC graduates who studied with the professor are working to develop and disseminate new techniques for cognitive interviews. The flexible form of the interview takes 20 to 30 minutes and calls upon the adult teacher, parent or researcher to pay close attention to the child.
In this kind of intervention, the interviewer is not so much interested in whether children are getting right or wrong answers to math problems, Ginsburg points out. The interviewer is trying to understand the child's thinking process. A knowledge of that thinking can lead a teacher to move away from mathematics as rote memorization in which children are called upon to get the right answer in the shortest possible time with the least possible amount of thinking.
Ginsburg wants children to think more about math problems and proposes that such thinking can involve using objects or even the most basic calculator of all: fingers.
Many children first learn to add by counting on their fingers, but may actually hide their fingerwork, as if they were somehow cheating.
"It's okay to use your fingers," Ginsburg and his colleagues tell children. "Put your hands on the table and show me how you do this. Tell me out loud what you are doing."
Ginsburg and his students are now working in a daycare center on Manhattan's West Side, interviewing and observing low-income children to try to understand their real mathematical competence.
We are working with the staff members at the center and with the parents too, Ginsburg said. We are showing them just what kind of ability these children have. Many of the parents have become excited because they had never noticed that their kids are so competent with numbers.
Ginsburg is also inviting other TC faculty members to join his group in researching disadvantaged children and their education. This collaboration is being supported by a grant from the College's Trustees.
The Jacob H. Schiff Professorship at Teachers College was established in 1921 by a gift from Felix M. Warburg to honor the memory of Schiff, Warburg's father-in-law. Warburg and Schiff were both leading bankers, and Warburg was a Trustee of TC. Ginsburg is the sixth Jacob H. Schiff Professor. The fifth was A. Harry Passow, who held the professorship until his retirement in 1991. Professor Passow died on March 28.
Ginsburg, who earned his bachelor's degree at Harvard University and his master's degree and Ph.D. in developmental psychology from the University of North Carolina, was on the faculty at Cornell University, the University of Maryland and the University of Rochester before coming to Teachers College.
He is the author of several books, including Piaget's Theory of Intellectual Development (with S. Opper), The Myth of the Deprived Child: Poor Children's Intellect and Education and Children's Arithmetic: The Learning Process.previous page