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Why Statistics is Not Mathematics and Why We Should Care About Teaching Statistics

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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

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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

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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).

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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 one- volume history of mathematics. Statistics is not even mentioned in the comprehensive index.

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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.

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Statistical Thinking vs. Mathematical Thinking Statistics is, by and large, a probabilistic or stochastic way of thinking. Why is this important?

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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)

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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)

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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”

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Statistical Thinking vs. Mathematical Thinking Statistical thinking is inductive: the inference of general laws from particular instances. “Specific to general”

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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.

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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 (k- 12): Number and operations Algebra Geometry Measurement Statistics and probability

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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 12 th grade.

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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

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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;

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develop and evaluate inferences and predictions that are based on data; understand and apply basic concepts of probability.

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