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Response to ‘Statistics à la Mode’

1 February 2012 1,475 views 2 Comments
The following is written by members of the Special Interest Group of the Mathematical Association of America in response to the article “Statistics à la Mode,” which was published in the November issue of Math Horizon’s Aftermath column. In the Aftermath column, Meg Dillon, mathematics professor at Southern Polytechnic State University, discussed the difficulty she experienced teaching an introductory statistics course as a mathematician.
    SIGMAA Members
    Brian Gill, Seattle Pacific University

      Andrew Zieffler, University of Minnesota

        Nancy Boynton, SUNY Fredonia

          K. Scott Alberts, Truman State University

            Patricia Humphrey, Georgia Southern University

              John McKenzie, Babson College

                Michael A. Posner, Villanova University

                A statistics course may indeed be one of the most important courses a student takes. Arthur Benjamin concluded his Ted Talk by saying, “Instead of our students learning about the techniques of calculus, I think it would be far more significant if all of them knew what two standard deviations from the mean means.” As more and more data are collected, the future will belong to those who can make sense of it. In fact, Hal Varian—Google’s chief economist—said in an interview with McKinsey Quarterly (January, 2009), “The sexy job in the next 10 years will be statisticians.”

                Statisticians have many tools at their disposal to help make sense of data, including mathematics. Statistics, however, is not a subfield of mathematics. Like economics and physics, statistics uses mathematics in essential ways, “but has origins, subject matter, foundational questions, and standards that are distinct from those of mathematics” (Moore, 1988, p. 3). David Moore, statistics educator and former president of the American Statistical Association, gives the following four compelling reasons why statistics is a separate discipline from mathematics:

                • Statistics does not originate within mathematics
                • The aims and foundational controversies of statistics are unrelated to those of mathematics
                • The standards of excellence in statistics differ from those of mathematics
                • Statistics does not participate in the inter-relationships among subfields that characterize contemporary mathematics

                Statistics exists because of the need for other disciplines to examine and explain variation in their data. As such, any introductory statistics course would be remiss if it did not put data at the center of the curriculum. In fact, the recommendation of a joint committee of the American Statistical Association and MAA to discuss the curriculum in elementary statistics reflected this viewpoint: “Any introductory course should take as its main goal helping students to learn the basics of statistical thinking” (Cobb, 1992, p. 5). Statistical thinking includes the need for data, the importance of data production, the omnipresence of variability, and the quantification and explanation of variability. These views were echoed in the Guidelines for Assessment and Instruction in Statistics Education (GAISE) and endorsed by the ASA in 2005.

                The focus in a course with the goal of promoting this kind of thinking should not be on the mathematics, but rather the “intellectual framework that makes sense of the collection of tools that statisticians use and encourages their flexible application to solve problems” (Cobb, 1997, p. 815). It is not that mathematics and probability have no place in such a framework, but rather that they are not the focal point. Ideas of design, inference, and reasoning about uncertainty all have a more prominent role in the introductory statistics curriculum. The CUPM Curriculum Guide (2004) (p. 38) says, “The fundamental ideas of statistics, such as the omnipresence of variability and the ability to quantify and predict it, are important subjects that can be studied without sophisticated mathematical formulations. In particular, the notion of sampling distribution—which underlies the concepts of significance testing and confidence interval—is challenging enough on its own to justify a first course in statistics.

                Statistics has data and inference at its core, and as Moore (1988) so pointedly declared, “It is unprofessional for mathematicians who lack training and experience in working with data to teach statistics” (p. 3). The important part of Moore’s statement is not that mathematicians should not teach statistics, but rather that experience working with data is crucial for a teacher of statistics. It would be no more advisable to have a poet teach calculus than it would be to have a person with no data experience (be they a mathematician, economist, or psychologist) teach a statistics course. In each case, the person lacks the scholarship necessary to be taken seriously. To teach effectively in any field, one needs to understand more than just subject matter. It also requires a deep understanding of the methods that practitioners in that field use to approach problems. In teaching statistics, it is important for students to experience data and the methods of statistics (not only mathematics).

                A course (or more) in probability and a course in mathematical statistics would help most people’s understanding of statistics, along with the 2–3 other courses in basic and intermediate statistical methods. However, only a select few students will take five courses in probability and statistics in their college career. Then, the question becomes which course to take. We think most statistics educators agree that if you have to choose only one, a course in statistical thinking would supersede one in probabilistic thinking.

                As educators, we need to do a better job of thinking about where we want our students to be at the end of a course and what crucial skills they need to get there. Understanding the conceptual framework of a hypothesis test or of inference from data, even without any probability theory (including even the central limit theorem through methods like a randomization test) is more useful in today’s data-driven world than predicting how many heads you might get when you flip a coin 100 times (although, again, the latter is helpful in understanding the former).

                It also should be clear that there are some mathematicians who are phenomenal teachers of statistics. It is not your degree that matters, but rather your knowledge in statistics and statistical pedagogy. Just as when a physicist teaches a mathematics course, a mathematician is teaching in a field different from their training when they teach a statistics course. To teach in a different field, one needs to understand the ways practitioners of that field approach problems and to have experienced the joy of making discoveries in that field. We need to convey to our students the excitement of solving problems using all the tools of statistics. It is wonderful to be teaching statistics in the 21st century because there are so many resources to help beginning and experienced statistics teachers. After the many years we have amassed teaching statistics, each of us continues to learn a lot every time we participate in a professional development experience.

                Each year, there are several events at the Joint Mathematics Meetings to help us all become better teachers of statistics. Many of these are sponsored by the SIGMAA on Statistics Education. Teachers of statistics should think about joining the SIGMAA on Statistics Education. The business meeting and reception is a good chance to get together with a nice group of statistics educators in an informal setting.

                Next summer, the MAA will sponsor a PREP workshop—Beyond Introductory Statistics: Generalized Linear and Multilevel Models—with Jim Albert and Brad Hartlaub.

                CAUSE (the Consortium for the Advancement of Undergraduate Statistics Education) sponsors a website with lots of useful information and a number of important professional development opportunities including the following:

                • Frequent webinars on statistics education that one can participate in (from your office computer) or watch at a later time
                • USCOTS (United States Conference on the Teaching of Statistics) in odd-numbered years
                • In May, CAUSE will sponsor an electronic conference, eCOTS

                All teachers of statistics should be familiar with GAISE, which includes recommendations for introductory statistics courses. In addition, there are several publications for teachers of statistics, including the following:

                Editor’s Note: The opinions expressed here reflect the views of the authors and not the SIGMAA on Statistics Education.

                References

                Cobb, G. W. 1992. Teaching statistics, in L. A. Steen (ed.) Heeding the call for change: Suggestions for curricular action, MAA Notes 22:3–23. Washington DC: Mathematical Association of America.

                Cobb, G. W., and D. S. Moore. 1997. Mathematics, statistics, and teaching. The American Mathematical Monthly 41(9):801–823.

                Moore, D. S. 1988. Should mathematicians teach statistics (with discussion)? College Math. Journal 19:3–7.

                Barker, W., D. Bressoud, S. Epp, S. Ganter, B. Haver, and H. Pollatsek. 2004. Undergraduate programs and courses in the mathematical sciences: CUPM curriculum cuide 2004.

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                2 Comments »

                • Christian P. Robert said:

                  I discussed this post a few weeks ago, finding the mathematician’s perspective rather naïve. But also the adverse reaction that statistics (as a field) had nothing to do in math (as a field).

                • Johann said:

                  I wanted to think about this idea of a eoscnd path to fellowship before responding. I was on the CAS Board of Directors when we set up the latest revision of our exam syllabus. The idea of separate paths to fellowship, which I had some sympathy for, was considered and soundly rejected. Given the scarcity of exam space, I see no point in trying to make significant additions to the statistics content on the exams. (My Bayesian MCMC proposal is short, and can replace other statistics material which is currently on the syllabus.)As about 10 of my 37 years as an actuary were spent working for statisticians, I have come to recognize that there are shortcomings in the statistical education of actuaries. In my current position, working in a predictive analytics group, I also see the shortcomings of statisticians when they attempt to do actuarial work. In our group we do fine, as we all talk to each other frequently and we do involve actuaries in other areas here at ISO.In general I think we train actuaries enough to appreciate statistical work, but we don’t train actuaries enough, in the era of computers and large data sets, to actually do what is now considered statistical work. Those actuaries that do modern statistical work, learn it either by on the job training, as I did, or by education beyond fellowship. As a profession, we should ask if we want to cede the statistical work to those more qualified, of to take in on ourselves. If we choose the latter, we should consider finding a way for the CAS to officially recognize this training, post fellowship (or perhaps post associateship). The CERA provides a precedent for such recognition.