## Plus Four — The Role of Statistics in Mathematics Education

We’ve all been reading and hearing about this … statistics is critical in modern society (in a ‘world of uncertainty’, as some people say). Some argue that all students should take an introductory statistics course in college, while others argue that some statistics be included in a general education course. One of the latest blog writings on this is from Kevin Carey (see http://chronicle.com/blogs/brainstorm/everyone-should-learn-statistics/46353)

There are fundamental differences between statistics and ‘other areas’ of mathematics. [I put ‘other areas’ in quotes because I question an equivalence between statistics and mathematics as scientific endeavors.] In most ways, statistics is a laboratory science based on logic used to support or refute claims in an argument. Some specialties in mathematics are much like this, though those specialties do not normally show up in community college mathematics programs.

What is unsettling about an emphasis on statistics as a ‘better math requirement’ is that statistics supports methodologies based on getting better results … not just on properties of measurement. Ever heard of “plus 4 confidence intervals”? The ‘plus 4’ method is used for creating proportion confidence intervals; see http://www.math.metrostate.edu/mike/Course/Fa2006/ConfidenceIntervals.pdf for some background. Essentially, an arbitrary adjustment is made to the sample size (n+4) and to the success outcome (p+2); this adjustment provides confidence intervals that are judged to be more appropriate. As you can see, the ‘plus four’ procedure results in a success outcome closer to 50% for use in the confidence interval; there is no scientific basis given for doing this at all … we could use ‘plus 2’ or ‘plus 6’, why ‘plus 4’ (besides the circular argument of producing the results we want)?

In developmental mathematics, we spend a lot of time (traditionally) on “percents”. In statistics, percents are usually a proportion statement (when used as a measurement); overall, however, percents are a label (as in ‘95% confidence interval’). A transition from the mathematical percent (calculation based) to the statistical (a label) is difficult for students. Before you mis-interpret, let me add … I teach a course where we use both types of percents (in quantitative reasoning), and I think that this is good for students.

I have no problem with considering statistics part of quantitative reasoning; in fact, I can not envision teaching a quantitative reasoning course without significant coverage of statistics. What I object to, or at least question, is the presumption that statistics is an alternative to mathematics in general. Mathematics, in general, is applied theories about quantities where consistent meanings and interpretations are essential; in mathematics, our work is constrained by whether the results are consistent with established knowledge and theory. Statistics … a wonderful field of study … is more flexible in its methodologies; competing theories with differing results are accepted and expected in statistics. For some students, statistics (a lot) is what they need. For most, however, not so much.

We should not use statistics as the only general education ‘math’ course for a global audience. Even algebra and calculus have a role in general education.

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