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Why Statistics Is Not Mathematics and Why We Should Care About

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Why Statistics Is Not Mathematics and Why We Should Care About
Why Statistics is Not
Mathematics and Why We
Should Care About
Teaching Statistics
What is Statistics?

Statistics is a science in my opinion, and it
is no more a branch of mathematics than
are physics, chemistry, and economics; for
if its methods fail the test of experience –
not the test of logic – they are discarded.
- John Tukey, 1962
Statistics in Industry

Statistical thinking is a philosophy of
learning and action based on the following
fundamental principles:



All work is a system of interconnected
processes.
Variation exists in all processes.
Understanding and reducing variation are
keys to success.
- The American Society for Quality
Statistics is a Mathematical Science

We use the singular is and not the plural are to
emphasize that statistics is a field of study, not
just a bunch of numbers.
 We use mathematical as an adjective because
although statistics certainly makes use of much
mathematics, it is a separate discipline and not a
branch of mathematics.
 We use the noun science because statistics is
the science of gaining insight from data.
- From “Some Important Comparisons between Statistics and Mathemaics, and Why Teachers Should
Care” by Rossman, Chance, and Medina (2006).
Statistics is NOT a Branch of
Mathematics

The book A History of Mathematics
(second edition by Carl B. Boyer and
Uta C Merzbach) is the classic onevolume history of mathematics.
Statistics is not even mentioned in
the comprehensive index.
Statistical Thinking vs. Mathematical
Thinking

Mathematics is, by and large, a
deterministic way of thinking and the way
mathematics is taught in schools in
America entrenches students into a
deterministic way of viewing the
quantitative world around them.
Statistical Thinking vs. Mathematical
Thinking

Statistics is, by and large, a probabilistic
or stochastic way of thinking.
Why is this important?
Statistical Thinking vs. Mathematical
Thinking

Science entered the nineteenth century
with a firm philosophical vision that has
been called the clockwork universe… By
the end of the nineteenth century, the
errors had mounted instead of
diminishing… By the end of the twentieth
century, almost all of science had shifted to
using statistical models… Popular culture
has failed to keep up with the scientific
revolution.
- David Salsburg “The Lady Tasting Tea” (2001)
Statistical Thinking vs. Mathematical
Thinking

Statistics has its own tools and ways of
thinking, and statisticians are quite insistent
that those of us who teach mathematics
realize that statistics is not mathematics,
nor is it even a branch of mathematics. In
fact, statistics is a separate discipline with
its own unique ways of thinking and its own
tools for approaching problems.
- J. Michael Shaughnessy, “Research on Students’ Understanding of Some Big Concepts
in Statistics” (2006)
Statistical Thinking vs. Mathematical
Thinking

Mathematical thinking is deductive: the
inference of particular instances by
reference to a general law or principle.
“General to specific”
Statistical Thinking vs. Mathematical
Thinking

Statistical thinking is inductive: the
inference of general laws from particular
instances.
“Specific to general”
Why Should We Care About
Teaching Statistics?

1983 report A Nation at Risk listed the primary
ingredients of mathematics education as follows:
The teaching of mathematics in high school should
equip graduates to




Understand geometric and algebraic concepts;
Understand elementary probability and statistics;
Apply mathematics in everyday situations; and
Estimate, approximate, measure, and test the
accuracy of their calculations.
Why Should We Care About
Teaching Statistics?

The Principles and Standards for school
Mathematics (NCTM, 2000) states the
following five major content strands that
are essential for school mathematics (k12):





Number and operations
Algebra
Geometry
Measurement
Statistics and probability
Why Should We Care About
Teaching Statistics?

The NCTM also recommends that
statistics and probability occupy
approximately 20% of the curriculum
(based on time) at each grade level from
kindergarten to 12th grade.
Why Should We Care About
Teaching Statistics?

2004 report Ready or Not: Creating a High
School Diploma That Counts from the American
Diploma Project lists the following quantitative
competencies needed for high school graduates
to succeed in postsecondary education or in
high-performance, high-growth jobs centers:




Number Sense and Numerical Operations
Algebra
Geometry
Data Interpretation, Statistics and Probability
Why Should We Care About
Teaching Statistics?

The Principles and Standards for school
Mathematics (NCTM, 2000) states that
instructional programs from
prekindergarten through grade 12 should
enable all students to –


formulate questions that can be addressed
with data and collect, organize and display
relevant data to answer them;
select and use appropriate statistical methods
to analyze data;


develop and evaluate inferences and
predictions that are based on data;
understand and apply basic concepts of
probability.
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