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The roles of cognition and metacognition were examined in the mathematical problem-solving behaviors of students as they worked in small groups. As an outcome, a framework that links the literature of cognitive science and mathematical problem solving was developed for protocol analysis of mathematical problem solving. Within this framework, each behavior is categorized by heuristic episode and cognitive level. Data were obtained from videotapes of six small groups of seventh-grade students (N=27), who attended a middle school in Queens (New York City), as they worked together to solve a mathematical problem. Three coders viewed each tape in 1-minute intervals. Watching one or two students in the group, the coders assigned one of the following episodic categories and cognitive levels: (1) read (cognitive); (2) understand (metacognitive); (3) analyze (metacognitive); (4) plan (metacognitive); (5) explore (cognitive or metacognitive); (6) implement (cognitive or metacognitive); (7) verify (cognitive or metacognitive); (8) watch (undetermined cognitive level); and (9) listen (undetermined cognitive level). Explicitly delineating the role of metacognition and cognition within the heuristics of problem solving gives researchers and mathematics teachers a tool to evaluate problem solving. Implications for cooperative group processes and classroom assessment are discussed. Three figures and one table contain the study data. The framework that was developed is outlined. (Author/SLD)

1Boy Crusoe

By Allan Eric

Also published as" A Yankee Crusoe" . A 15 year old hard working and studious farm boy finds the lure of adventure on the seas as a merchant seaman more than he can resist. This is his story. " I was born in a little town in the State of Maine, near the close of the Civil War. My boyhood life did not differ materially from that of the average farmer's son in the remote country districts of New England--except, perhaps, that I read more and thought more. Hard work on the rugged soil, two terms each year in the little yellow country schoolhouse, a day's fishing now and then filled the early years of my life full to over-flowing. " What he gets is enough excitement and adventure to overflow his wildest dreams. How he experiences disaster and uses his wits and knowledge to overcome every problem makes for a great read. - Summary by Phil Chenevert