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Textbook Coding  
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Cognitive Behavior  
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> >  Background:
Five textbook series, CME, CPMP, Glencoe, IMP, and UCSMP have been examined, scoring each and every question for the mathematical concepts involved as well as the "Cognitive Behavior" required to address the question in the context in which it appears in the textbook. A total of 52,767 questions have been scored, each by two people who met and discussed any discrepancies in their assessments.  
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> >  The graph below addresses how to summarize the three types of Cognitive Behavior: Knowing, Applying, and Reasoning. The three corners of the plot represent each of the Cognitive Behaviors: Knowing, Applying, and Reasoning. Each side of the triangle represents 0% for the opposite corner and the corner itself is 100% for that feature. To help characterize the triangle in terms of the more familiar pie charts, the background of small pie charts shows the underlying "Landscape" of how the triangle portrays the proportions. It also allows you to read off approximate values for a position in the chart since there is a row for each 10% change in proportion. There is also a pie in the center of the triangle, representing equal proportions for all three.
Here is a narrative highlighting some observations which this presentation makes particularly accessible: Each textbook series is represented in the plot by a pie chart with its position consolidating across all texts as well as one for each of the up to three volumes in the series, represented by .1, .2, .3 in the label. From the plot, showing 17 pie charts, their location on the plot shows, for example, that CPMP consistently involves more reasoning and that the "orbit" of the series starts with a comparative emphasis on reasoning, shifting towards knowing in year 2 and then moving to applying in year 3. Glencoe and UCSMP have very little reasoning and move from knowing to applying from book 1 to book 2. CME, in contrast, moves away from applying and knowing towards more reasoning in going from year 1 to year two. All textbooks in all series devote more than half of their questions to Applying.
 
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 DickFurnas  20090918
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