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How teaching calculus might distort a view of statistics

Example of calculus-like problem … of a sort that I very rarely see in statistical work.

The scores on the SAT verbal test in recent years follow approximately the N(517, 112) distribution.

• What is the proportion of students scoring under 400?
• What is the proportion of students scoring between 400 and 550?
• How high must a student score to place in the top 10% of all students taking the SAT? State answer as a whole number.
• Using the empirical rule, what is the probability that a randomly [selected] SAT test will have a verbal score between 629 and 853?

Your priorities

• Top priority
  • 8 / 14 learn how to incorporate real data into classes (17 / 19) YES*
  • 7 / 14 learn about tools/technology (18 / 19) YES*
  • 7 / 14 learn new statistics teaching methods (18 / 19) YES*
  • 7 / 14 learn how to engage students (15 / 19) WE PLAN and HOPE*
  • 6 / 14 learning more about data science concepts (17 / 19) YES*
  • 6 / 14 learning to use R (14 / 19) IF YOU WANT*
  • 5 / 14 get ideas about modifying department curriculum (11 / 19) WE THINK SO*

All together, the 14 respondents have 58 “top” priorities!

✽ Will we cover this in the next two days?

Confidence

Only 4 / 19 were confident in developing data models.

Possible issues:

• what does “developing” mean?
• what does “models” mean?
• and, maybe, what does “data” mean?

Software vs by hand

• 1 / 19 – by hand
• 9 / 19 – by software
• 9 / 19 – by hand and also by software
• Nobody – by graphing calculator

Statistical theory

• 3 / 19 – algebra is the best method to express statistics, yet …
  • 10 / 18 – statistical concepts are intrinsically based in algebraic notation
• 5 / 19 – include theoretical probability distributions
• EVERYONE – The many methods covered in introductory statistics can be reduced to a small set of common principles.
  • What are those principles? Write them down here

Computing

• 16 / 19 Computing offers a framework for understanding statistical theory that is as legitimate as the theory based on probability rules and algebra.
  • but, earlier, 10 / 18 said “statistical concepts are intrinsically based in algebraic notation”
• 18 / 19 Proficiency in using computers to handle and manage data should be an important goal of a statistics course.
• Why aren’t you using preferred software?
  • 9 / 15 I haven’t had time to explore software / technology beyond what I’m currently using.
  • 4 / 15 Takes too much time for students to learn software / technology
  • Expense or Department or Access: at most 1 or 2 out of 15
• What do you use for software?
  • 9 / 14 Spreadsheets
  • 5 / 14 Graphing calculator
  • 4 / 14 Other
  • 3 / 14 Web apps
  • 2 / 14 R/RStudio
  • 1 / 14 Minitab/SPSS
  • 0 / 14 SAS/JMP
• What would you like to use for software?
  • 7 / 11 R/RStudio
  • 6 / 11 Spreadsheets
  • 4 / 11 SAS/JMP

Graphics

This was the strongest consensus …

Indicate the method of computing that you believe helps students learn introductory statistics best.

• 17 / 18 – Graphics routinely drawn using statistical software

Question: Do you teach them the algorithms and programming steps for producing graphics or just have them go at it with the appropriate software function?

Success

Out of 90 possible answers:

• 4 / 90 are very successful
• 36 / 90 are successful
• 51 / 90 are moderately successful
• 10 / 90 not successful

Grade: B- overall

Limits to change

• 10 / 15 Limited personal time
• 11 / 15 Student characteristics (e.g., ability, interest, etc.)
• Others (institutional constraints, transferability, no access to computing) got at most 3/15 each