We found similar difficulties when we interviewed four high school seniors
(ages 17–18) who had just completed a yearlong course in probability and statistics
(Biehler, 1997; Konold et al., 1997). During the course, the students had frequently
used medians (primarily in the context of box plot displays) as well as means to
make group comparisons. However, during a postcourse interview in which they
were free to use whatever methods of comparison seemed appropriate, they seldom
used medians or means for this purpose. Instead, they tended to compare the number
of cases in each group that had the same value on the dependent variable. For
example, to decide if males were taller than females, they might inspect the sample
for all individuals who were 6 feet tall and argue that males were taller because there
were more males than females of that height. In making these comparisons, students
typically did not attend to the overall number of individuals in the two groups (in
this case, to the overall number of males vs. females). Other researchers, including
Cobb (1999) and Watson and Moritz (1999), have reported students using this same
“slicing” technique over a range of different problems to compare two groups.
We found similar difficulties when we interviewed four high school seniors(ages 17–18) who had just completed a yearlong course in probability and statistics(Biehler, 1997; Konold et al., 1997). During the course, the students had frequentlyused medians (primarily in the context of box plot displays) as well as means tomake group comparisons. However, during a postcourse interview in which theywere free to use whatever methods of comparison seemed appropriate, they seldomused medians or means for this purpose. Instead, they tended to compare the numberof cases in each group that had the same value on the dependent variable. Forexample, to decide if males were taller than females, they might inspect the samplefor all individuals who were 6 feet tall and argue that males were taller because therewere more males than females of that height. In making these comparisons, studentstypically did not attend to the overall number of individuals in the two groups (inthis case, to the overall number of males vs. females). Other researchers, includingCobb (1999) and Watson and Moritz (1999), have reported students using this same“slicing” technique over a range of different problems to compare two groups.
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We found similar difficulties when we interviewed four high school seniors
(ages 17–18) who had just completed a yearlong course in probability and statistics
(Biehler, 1997; Konold et al., 1997). During the course, the students had frequently
used medians (primarily in the context of box plot displays) as well as means to
make group comparisons. However, during a postcourse interview in which they
were free to use whatever methods of comparison seemed appropriate, they seldom
used medians or means for this purpose. Instead, they tended to compare the number
of cases in each group that had the same value on the dependent variable. For
example, to decide if males were taller than females, they might inspect the sample
for all individuals who were 6 feet tall and argue that males were taller because there
were more males than females of that height. In making these comparisons, students
typically did not attend to the overall number of individuals in the two groups (in
this case, to the overall number of males vs. females). Other researchers, including
Cobb (1999) and Watson and Moritz (1999), have reported students using this same
“slicing” technique over a range of different problems to compare two groups.
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