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At TC, psychologist Herbert Ginsburg has been working to empower a new generation of teachers with a different outlook.

If literacy is an area in which non-English speaking students are often unfairly stigmatized, mathematics presents an opposite conundrum: In U.S. schools, math—a universal language—has become something of a national phobia for teachers and students alike. 

At TC, psychologist Herbert Ginsburg has been working to empower a new generation of teachers with a different outlook.

Preservice teaching students who take Ginsburg’s course “The Development of Mathematical Thinking” often find themselves immersed in preschool classics such as Eric Carle’s Rooster’s Off to See The World. As the title suggests, one fine morning the hero sets out to explore. He is soon joined in rapid succession by two cats, three frogs, four turtles and five fish. Then, with night falling and no dinner or place to sleep, his new companions depart in reverse order. Left alone, Rooster, too, returns home to sleep on his own perch, where he dreams of the adventures that might have been.

In addition to teaching kids about animals (and, possibly, the tenuous nature of friendship), Carle’s book is also very much about math—and not just plain old counting. Recognizing patterns, from piano keyboards to days of the week, is a form of algebraic thinking, since kids must solve the pattern’s riddle by making predictions. 

Those truths have been vividly documented in a final project for Ginsburg’s class submitted by Regina Ferrin, who is earning a master’s degree in the College’s teacher preparation program in early childhood education. For her project, Ferrin videotaped a clinical interview she conducted with Tania (not her real name), a six-year-old Latina student. Thanks to a technology program employed in the class, clips of the interview appear in the paper as clickable footnotes. The clips show Tania performing several feats: accurately extending patterns of circles and triangles created by Ferrin; reestablishing patterns when Ferrin deliberately breaks them; and, when Ferrin reads the Carle story aloud, correctly predicting how many animals will appear on each page, confirming that she recognizes the book’s “growing pattern” of plus one.

Ferrin’s project is further evidence of the theory that Ginsburg—TC’s Jacob H. Schiff Foundation Professor of Psychology and Education—has been demonstrating for years: Children as young as 18 months have a sense of “everyday math” that can be developed both through play and more formalized teaching. In hundreds of videotaped clinical interviews, Ginsburg and his students have documented instances of children displaying their grasp of number operations, shape, pattern, cardinality (recognition that a number represents a definable quantity of things) and more (a word that, in itself, implies an understanding of quantity). 

Ginsburg has also co-authored a preschool curriculum called “Big Math for Little Kids,” written a number of landmark texts, and developed several technologies for assessment and teaching. Yet given the potential multiplier effect of each aspiring teacher who takes “The Development of Mathematical Thinking,” his teaching may turn out to be his greatest legacy.  

“I went into Herb’s course not liking math and thinking that I couldn’t teach it because I didn’t understand it,” says Ferrin. “I came out of it not only realizing I did understand it, but actually excited about it and recognizing its importance in everyday life in a way I never had before.”

The course syllabus alone, which ranges from works by Jean Piaget to a cross-cultural analysis of play titled Street Mathematics and School Mathematics, makes for a fascinating experience. But the clinical interviewing—supplemented by technology and pedagogy that enable students to study video, to refer within a paper to relevant clips, and to think deeply about them—is where everything really seems to come together. 

“I don’t like my students to talk in vague ideological terms, like, ‘It’s great to let kids construct knowledge,’” says Ginsburg, who co-authored a 2009 National Academy of Sciences study of math instruction for young children, and who last year was elected to the National Academy of Education. “I want them to integrate what they learn about kids, from observation, with what they read and with their own teaching skills. The ultimate goal is for them to understand each kid’s thinking so that they can teach better, and in a more personalized and effective way.”previous page