Benchmark 12E: Habits of Mind - Critical-Response Skills

• Notice and criticize arguments based on the faulty, incomplete, or misleading use of numbers, such as in instances when (1) average results are reported, but no the amount of variation around the average, (2) a percentage or fraction is given but not the total sample size (as in "9 out of 10 dentists recommend ..."), (3) absolute and proportional quantities are mixed (as in "3,400 more robberies in our city last year, whereas other cities had an increase of less than 1%"), or (4) results are reported with overstated precision (as in representing 13 out of 19 students as 68.42%). (1 of 6)
• Standard 3-4 page 143, Grades 9-12
Judge the validity of arguments
• Check graphs to see that they do not misrepresent results by using inappropriate scales or by failing to specify the axes clearly. (2 of 6)
• Standard 10-1 page 167, Grades 9-12
Construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations
• Wonder how likely it is that some event of interest might have occurred just by chance. (3 of 6)
• Standard 11-5 page 171, Grades 9-12
Describe, in general terms, the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed.
• Insist that the critical assumptions behind any line of reasoning be made explicit so that the validity of the position being taken whether one's own or that of others can be judged. (4 of 6)
• Standard 3-4 page 143, Grades 9-12
Judge the validity of arguments
• Be aware, when considering claims, that when people try to prove a point, they may select only the data that support it and ignore any that would contradict it. (5 of 6)
• Standard 3-4 page 143, Grades 9-12
Judge the validity of arguments
• Suggest alternative ways of explaining data and criticize arguments in which data, explanations, or conclusions are represented as the only ones work consideration, with no mention of other possibilities. Similarly suggest alternative trade-offs in decisions and designs and criticize those in which major trade-offs are not acknowledged. (6 of 6)
• Standard 10-1 page 167, Grades 9-12
Construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations