Becoming
a Teacher of Statistics
Portfolio
by
Susan Sexton
Probability and Statistics for Secondary
Teachers
STAT 6070
University of Georgia
Fall 2007
Instructor: Christine Franklin
Recommendation 3: Emphasize statistical literacy and
develop statistical thinking.
Utts, J. (2003). What educated citizens should know about statistics and probability. The American Statistician, 57(2), 74–79.
Abstract:
Much has changed since the widespread introduction of statistics courses into the university curriculum, but the way introductory statistics courses are taught has not kept up with the changes. This article discusses the changes, and the way the introductory syllabus should change to reflect them. In particular, seven ideas are discussed that every student who takes elementary statistics should learn and understand in order to be an educated citizen. Misunderstanding these topics leads to cynicism among the public at best, and misuse of study results by policy-makers, physicians, and others at worst.
Utts
addresses the need for students to leave statistics courses with knowledge and
understanding of the key statistical ideas. Most early introductory statistics
courses emphasized computation without providing students opportunities to
Òintegrate information from study design to final conclusions in a meaningful
wayÓ (p. 74). Utts argues that even though many students who study statistics
will not actually perform computations when they enter their field of work they
will, no doubt, encounter statistical presentations in their everyday lives.
These encounters include Òstudies conducted and analyzed by others, published
in journals, and reported by the mediaÓ (p. 74).
Utts
provides seven key statistical topics that statistics students should encounter
and have been found Òto be commonly misunderstood by citizens, including the
journalists who present the statistical studies to the publicÓ (p. 74). UttsÕ
discussion of these seven topics aligns with the Guidelines for
Assessment and Instruction in Statistics Education (GAISE) recommendation that
charges statistics teachers to Òemphasize statistical literacy and develop
statistical thinkingÓ (GAISE, 2005, p. 7). In the GAISE report, statistical
literacy is defined as Òunderstanding
the basic language of statistics (e.g., knowing what statistical terms and
symbols mean and being able to read statistical graphs), and understanding some
fundamental ideas of statisticsÓ (GAISE, 2005, p. 7).
The
seven topics identified by Utts are: (1) understanding when a cause and effect
relationship exists, (2) the difference between statistical significance and
practical significance, (3) the difference between not finding an effect and
the power of the study, (4) bias that can occur in surveys, (5) understanding
that coincidences are not so coincidental, (6) understanding that conditional
probability and its inverse are not equivalent, and (7) knowing that normal is
not equivalent to average. Within each topic, Utts provides at least one
example to illustrate the misconception or misuse of the topic by the media,
researchers or an individual of the general public.
Utts
acknowledges that there are many statistical topics covered in a statistics
course. However it is the seven that she has identified that she has found Òto
be so prevalent that it is likely that millions of people are being mislead by
themÓ (p. 78). Having the ability to interpret and critically analyze
statistical reports is crucial for the development of statistical literacy.
Furthermore, while Utts points to the necessity of the average educated citizen
to understand these topics, she has found that those who use statistics in
their own research (i.e. Ph.D. candidates) have also demonstrated a lack of
critical understanding of these statistical ideas within their personal field
of work.
Utts
provides ways for statistics teachers to incorporate these seven topics into
their teaching of other statistical ideas and concepts. For example, she
identifies the topics that discuss statistical significance and effect and
power (topics (2) and (3)) as naturally corresponding with the topic of Type 1
and Type 2 errors. Connecting statistical ideas is powerful for the statistics
student and can provide avenues to develop or enhance their statistical
thinking. The GAISE report defines statistical thinking as Òthe type of
thinking that statisticians use when approaching or solving statistical
problemsÓ (GAISE, 2005, p. 7). A student who possesses statistical thinking and
statistical literacy will be less likely to be misled by the information
presented in their everyday life. Thus Utts deems it necessary to discuss the
statistical concepts and topics as they might be encountered in the media. She
explains, ÒOne lecture explaining the difference between an observational study
and a randomized experiment, and the role of confounding variables in the
interpretation of observational studies would do more to prepare students for
reading the news than a dozen lectures on statistical inference proceduresÓ (p.
78).
References
GAISE College
Report. (2005). Guidelines for Assessment and Instruction in Statistical Education
College Report. Alexandria, VA: American Statistical Association, http://www.amstat.org/education/gaise.
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Summaries and Reflections