Rethinking the introductory college course

Goals for rethinking:

  • Build a highly integrated set of technical concepts and methods that inform the reasoned interpretation of data.
  • Demonstrate that statistical thinking is a useful component of critical thinking.
  • Support the development of decision-making skills.
  • Develop literacy in data computing.
  • Crack open the lid on the “black boxes” that will be widely encountered in professional and civic endeavors. Examples: machine learning, databases.

Constraints:

  • Keep it novel, motivating, interesting, and accessible to a broad range of college-level students; both those

    1. who have or have not developed algebra skills,
    2. who have or have not had AP statistics
    3. who have or have not had calculus
    4. who have or have not been introduced to technical computing.

  • Draw on lessons learned from the last 50 years of teaching introductory statistics.

    • minimize algebra

  • Avoid unnecessary duplication of statistical concepts that have migrated into high-school and even earlier.

  • Avoid the “GATC trap,” where a pre-technological definition of calculus leads to a high

Citizenship

“The great body of physical science, a great deal of the essential fact of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex worldwide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.”—H.G. Wells (1903) Mankind in the Making.

Jessica Utts (2003) “What educated citizens should know about statistics and probability” The American Statistician 57(2)

“There are of course many important topics that need to be discussed in an elementary statistics course. For this article, I have selected seven topics that I have found to be commonly misunderstood by citizens, including the journalists who present statistical studies to the public. In fact researchers themselves, who present their results in journals and at the scientific meetings from which the journalists cull their stories, misunderstand many of these topics.”

  1. When it can be concluded that a relationship is one of cause and effect, and when it cannot, including the difference between randomized experiments and observational studies.
  2. The difference between statistical signicance and practical importance, especially when using large sample sizes.
  3. The difference between finding “no effect” or “no difference” and finding no statistically significant effect or difference, especially when using small sample sizes.
  4. Common sources of bias in surveys and experiments, such as poor wording of questions, volunteer response, and socially desirable answers.
  5. The idea that coincidences and seemingly very improbable events are not uncommon because there are so many possibilities.
  6. “Confusion of the inverse” in which a conditional probability in one direction is confused with the conditional probability in the other direction.
  7. Understanding that variability is natural, and that “normal” is not the same as “average.”