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Cognitive Psychology Offers Solutions
for Teaching Challenging Math Concepts
If some children are failing miserably in school, it is not for lack of a solution, says Meir Ben Hur, an educator and mechanical engineer who is associated with the International Center for the Enhancement of Learning Potential in Jerusalem, Israel.
What we see in the classroom is a rudimentary way of teaching, Ben Hur, an educator trained in cognitive psychology, engineering and mathematics, told an audience at AAAS on 26 March. “Students are taught procedures, but the concepts are not understood.”
Ben Hur's talk, the first lecture in a series aimed at improving the teaching of mathematics, drew representatives from universities, federal agencies, professional organizations and school districts.
The title of the series is “Developing Productive Pathways Between Cognitive Science, Developmental Psychology and the Teaching and Learning of Mathematics and Science.” “The bottom line is that we are trying improve teaching and learning and to bring the disciplines of psychology and cognitive science to bear on the teaching of math and other content areas,” says Madeleine Long, AAAS program director for math and science education.
Educating Urban Children
Ben Hur said that his methods for improving teachers’ skills had been particularly helpful to impoverished children in urban areas. The need for addressing the learning gaps among urban children was made particularly clear in New York recently. The New York Times (28 March 2002) reported that black and Hispanic children, especially residents of urban areas, were found to have test scores in English and mathematics that were dramatically lower than those of Asian and white children. The report "mirrors similar findings nationwide," the Times reported. "The findings also show that black and Hispanic students continue to lag as they go through school and that in many cases the gap worsens," according to the article. “Students in inner-city schools don’t have the goals expressed by students from suburbia,” Ben Hur said in his lecture. “These differences in background make an enormous difference in their achievement scores.”
Teachers often fail to provide children with a sense that everything they are learning is part of something much bigger, Ben Hur said. “Something has to be gained in learning. The teacher has to communicate that the math problem is going to be valuable in the future.”
Poor children come to Kindergarten ill-prepared for learning, and the gaps grow larger over the years if they are not addressed when the children are young. “If you address the gap early, you can reduce the impact of the problem,” said Ben Hur. He adds that the solution is in retraining teachers so that they consider the needs of each child, and his or her ability to grasp a subject.
“There is a crisis in professional development. Teachers need time to reeducate themselves, and, unfortunately, most can’ take a sabbatical to refresh their knowledge. You have to understand the necessary tasks from a developmental point of view -- which task will be overwhelming and which is not, and you have to pace instruction so that it is appropriate to the child’s level.”
In working with students, teachers must be consistent and systematic, Ben Hur said. If they teach in a piecemeal fashion, development is never possible.
Among the problems a child might have is an inability to relate things to each other in space. The child might recognize an isoceles triangle, but not recognize it after it has been rotated to another position. The children are not prepared to be flexible, Ben Hur said. “If a child of a certain age cannot tell me where my right side is without turning himself around, we have a problem.”
Madeleine Long suggested that teachers should be trained differently. University programs are not looking at changes in mathematics and science, she said. “They're doing the same thing they've been doing for years. We need to think of ways to improve the service teachers are providing our children.”