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A Mathematics Curriculum for the Gifted and Talented

A mathematics program for the gifted and talented should provide for the diverse needs of individuals and a changing society as well. With the impact of information technology, the nature of knowledge is shifting. Schools must adjust or face obsolescence. Actually, many (most) schools will not change, in my judgment, and thus our youth will be &dquo;miseducated.&dquo; The curriculum being used in schools today was developed for an industrial society and requires major restructuring to prepare children for a future where computers will be the major tool for all areas of work and thought. In an industrial society, it is assumed that work will be done by machines being controlled by man. Many repetitive tasks are required. In the present informationbased society, the focus is on access and transmission of information. Many routine tasks will be performed by automated machines, freeing workers for more interesting and varied tasks. Furthermore, in almost every aspect of life the computer is a tool for thought and work. The present curriculum was developed for a society very different from the present; it is time changes were made. During this century, the demands of an industrial society led to the rise in influence of behavioristic psychology on American education. Within the past few years there has been a surge of interest in cognitive psychology with emphasis on motivation, attention, thought processes, and other patterns of human cognition. While behavioristic approaches are appropriate for certain types of knowledge such as skill leaming, programs for the gifted must break out of rule-oriented instruction. The gifted are capable of mathematical achievement many times greater than we see in today’s schools under existing curriculum. For example, sixth graders are capable of performing at the level of many university courses. Through several talent search programs, sixth-, seventh-, and eighth-grade pupils are taking the Scholastic Aptitude Test (SAT). Often, gifted and talented children in these grades score above the national average for college-bound seniors. The gifted are often blocked from rapid advances in conceptual thought by the almost exclusive emphasis on skill leaming. The bright child can become mired in the details of skill acquisition and never experience the thrill of soaring with intellectual ideas. We must reorient the mathematics curriculum with attention to principles and concepts. Skill acquisition can be achieved quite efficiently when seen from a perspective of problem solving and application. In today’s schools, children expect to apply a rule. All of their experience has lead them to this expectation. Children think, &dquo;What am I expected to do with this task?&dquo;, rather than focusing on the important ideas and relationships involved. This can be overcome only by changing content and approaches. In a recent study, we found that by studying problem solving, sixth-grade children can break out of such a rule orientation (problem solving is what you do when you don’t know what to do). In the study (Wheatley & Wheatley, 1982), children learned heuristics for solving nonroutine problems. They worked in small groups to solve