
Children's Understanding of Math:
Teaching, Learning, and the Brain
How do children learn math? Is a "number sense" hard-wired in the brain? What difference does teaching make?
This symposium examines how biological factors, such as the development and organization of the brain, and environmental factors, notably the way children are taught mathematics, affect the emergence of number skills. Recent behavioral and brain-imaging studies as well as cross-cultural studies of classroom teaching shed new light on how children develop mathematical proficiency and how teaching strategies improve mathematics learning.
The Developing Brain: Is There a Number Sense?
Stanislaus DeHaene, Ph.D.
Recent experimental advances have clarified how children develop numerical understanding and how this understanding is organized in the adult brain. Research indicates that a specific area of the brain is associated with knowledge of numbers and their relations. In addition, behavioral studies in infants and animals have revealed number perception, discrimination, and elementary calculation abilities.
Dr. DeHaene proposes that a non-verbal number sense or quantity system enables us to interpret the number domain and to have intuitions about numbers. During development, this early understanding of quantity becomes progressively linked to conventional representations of numbers. However, some children experience difficulty with numerical understanding because of specific dysfunctions. Educational strategies informed by psychological and neuroscience studies of number processing could offer help in circumventing or rehabilitating those deficits.
Dr. DeHaene has been Research Director at INSERM (the French equivalent of the U.S. National Institutes of Health) since 1989. Widely published and honored, he currently heads the research team studying cerebral bases of human cognitive functions within INSERM, located at the Service Hospitalier Frederic Joliot in Orsay, France.
Cross-Cultural Findings: Reflections on Teaching Mathematics and How to Improve It
James W. Stigler, Ph.D.
The Third International Mathematics and Science Study (TIMSS) was the first ever to videotape a national sample of classroom teaching, and it did so in three countries: Germany, Japan, and the United States. Although it was observed that teachers within each culture tended to follow a script specific to their culture, teaching practices differed dramatically across cultures. There were other differences as well, most notably in the level and kind of mathematics instruction across the three countries.
As a cultural activity, teaching is learned implicitly, hard to see (for an insider), and hard to change. Reforms intended to change a particular feature of teaching often fail because other factors act to prevent the change from taking place. Among the three countries, Japanese teaching appears to have changed the most markedly in the last 100 years. The mechanism of change may lie in "lesson study," a unique form of teacher development activity that is widespread in Japanese schools and that might be supportable within the culture of U.S. schools for teaching mathematics.
Dr. Stigler has been Professor of Psychology at UCLA since 1991, following eight years on the University of Chicago faculty. The author of two books and the recipient of numerous awards, he is best known for his observational work in classrooms and for pioneering the use of multimedia technology for the study of classroom instruction. Dr. Stigler is currently the Director of the TIMSS video series.
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