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

**(grades 9-12, page 300)**

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