Past INRUG Meetings

• reproducibility (rmarkdown)
• visualization (ggplot2 and shiny)
• data cleaning and wrangling (tidyr and dplyr)

A Few Remarks for Today

• we'll talk about teaching statistics (theory), not data science
• national recommendations for statistics pedagogy call for a tool such as R
• theory can't be compromised for neat tricks in R

Recent Efforts

• make R more accessible for intro stats courses
• include visualization and simulation to complement an intro stats course
• incorporate aspects of Data Science in an intro stats course

My Training

• applied mathematician and probabilist, but not a really a statistician…
• enthusiastic user of R for ~1-2 years

Courses I Teach

• calculus sequence, differential equations, …, linear algebra, and statistics
  • MATH 121: introductory statistics
  • MATH 321: calculus-based introductory statistics
  • MATH 421/422: proof-based probability and statistics

Why I'm Partial to Using Mathematical/Statistical Software

• computational thinking and literacy
• provides a mechanism for inquiry via exploration, experimentation, and discovery
• move beyond the (often tedious) formulas and grapple with the more interesting questions
• appreciate the increasing role that computation plays in mathematics
  • software is no replacement for understanding the underlying concepts for the calculations

• Project NExT workshop on Teaching Intro Stats (Aug. 2014)
  • Carolyn Cuff (Westminster)
• MAA-StatEd (since Aug. 2014)
• Isolated Statisticians Network (since Aug. 2014)
• Inland Northwest R Users Group (since Aug. 2014)
• Minicourse at JMM on Project MOSAIC (Jan. 2015)
  • Nick Horton (Amherst) and Randy Pruim (Calvin)
• USCOTS at Penn. St. University (May 2015)
• Workshop at USCOTS on Data Science in R Studio (May 2015)
  • Nick Horton (Amherst) and Daniel Kaplan (Macalester)

Upcoming

• MAA MathFest (Aug. 2015)
• Joint Statistical Meeting in Seattle, WA (Aug. 2015)

GAISE Recommendations:

1. emphasize statistical literacy and develop statistical thinking
2. use real data
3. use technology for developing concepts and analyzing data
   • "to the maximum extent feasible, calculations and graphics should be automated."
4. stress conceptual understanding, rather than mere knowledge of procedures

\(\star\) read more at http://www.amstat.org/education/gaise/

ASA Curriculum Guidelines:

1. increased importance of data science
2. real applications
3. more diverse models and approaches
4. ability to communicate

\(\star\) read more at http://www.amstat.org/education/curriculumguidelines.cfm

Some sort of software is necessary, but which and how?

• instructor demonstrations vs. hands-on experience?
• possible software: R Studio, Minitab, SPSS, SAS/JMP, Deducer/RCmdr, StatCrunch, etc.
• online applets: StatKey, Rossman-Chance, etc.

R is…

• "R is a free software environment for statistical computing and graphics.
  It compiles and runs on a wide variety of UNIX platforms, Windows and MacOS"
  • The R Project Organization
• "R is a data analysis software; R is a programming language; R is an
  environment for statistical analysis; R is open-source; R is a community"
  • http://www.inside-r.org
• "R is extremely powerful"
  • Revolution Analytics

• free and open source
  • SAS, SPSS, Maple, Mathematica, MATLAB, etc. are expensive
  • valuable and employable skill (accessible after graduation)
• R is growing (rapidly in popularity)
  • http://blog.revolutionanalytics.com/popularity/
• students won't outgrow it (it will grow with them)
• instructional data is pre-loaded
• R provides a gentle introduction to coding, computation, and \(\LaTeX\)
• reproducible rather than point, drag, click, copy/paste, cross-your-fingers, …
• high-quality graphics
• clear and intuitive workflow

R is used in some fashion for ~75% of my lectures

• planned demonstrations (static and/or interactive)
• simulations and graphics on the fly
• post notes online in HTML format

Examples of Notes and R Code

• permutation hypothesis tests
• continuous RVs
• simple linear regression

Examples of shiny Applications

• confidence intervals
• Type I and II errors

In-depth exploration of a concept

• groups are often asked to play the role of a consulting company
  • inspired by Gavin Larose (Univ. of Michigan)
• use R outside of class; wrestle with R on their own
• made R relevant and important
• formed collaborative groups (and aided rapport)
• students are given the .Rmd file to edit
  • they begin to take pride in producing high-quality documents

Examples

• Descriptive Statistics
• Airline Overbooking
• Planning a Picnic

In-class labs are held in College 243

• focused on discovery and inquiry
  • rather than learn concepts and R at the same time
• collaborative teams encouraged
• use R while exploring material from a different perspective
• bimodal response from students (useful vs. waste of time)

Example

• drug efficacy via sleep dataset

With provided code, students create plots similar to these:

Next time, I'll have students explore with mplot instead.

A predominant philosophy: Less Volume, More Creativity

• xpnorm, xqnorm, xpt, xqt, favstats, tally, do, etc. are functions built in the mosaic package
• mplot, mScatter, mWrangle, mBar, etc. are functions that utilize the manipulate package

Freely available books:

• A Compendium of Commands to Teach Statistics with R
• Start Teaching Statistics Using R
• Start R in Calculus

Other instructional material:

• under development by Horton, Kaplan, and Pruim, e.g., activity/key and activity/key

• less number of R commands, but each with more flexibility and power
• provide enough commands so that students can do something, but not so many that it is overwhelming
• avoid programming aspects (if, for, etc.)
• give students the bare minimum and make them "beg" for more

A Quote to Live By

• "if R is the hardest thing in the course, then the R is too hard and your questions are too easy"
  • R. Pruim (2015)

mplot

• powerful way to both do data exploration as well as learn ggplot2

require(mosaic)
require(manipulate)
mplot(ToothGrowth)

mosaic and manipulate

xqnorm(0.975,5,7)
manipulate(xqnorm(alpha,verbose=FALSE),alpha = slider(0.001,0.999,step=0.001))

mWrangle

• several Data Science courses are popping up around the country and spend ~1/3 to ~1/2 of the time on data wrangling
• how to easily include it in an introductory course?
  • maybe mWrangle (currently in development) or http://rstudio.calvin.edu:3838/rpruim/dataOps/

require(DCF)
require(DCFinteractive)
require(mosaicData)
mWrangle(KidsFeet)

Selling R To Students

• R can be tough to sell (it's free, remember?)
• the exposure to R seems conducive to learning and to have a positive impact on retention
  • but it may not help a student immediately, e.g., on the next exam
• some students have really invested themselves in learning R

Lab Space

• the mathematics department has no lab space; A&S has limited lab space
  • a 10 person seat license for Mathematica
• R Studio on a server, using personal machines, and SageMathCloud are each options

R Changes Things

MATH 321 with R (i.e., students using R) is fundamentally different than without R

How much math? How much data? How much R?

• the "correct" balance changes from MATH 121 to MATH 321 to MATH 421

Keep Learning R

• based off of GAISE recommendations (and others), software is necessary
  • R is one viable (and good) option
• more deeply connects students to important concepts
• provides a computational tool for exploration
• fundamentally changed my course organization and structure
  • ease of creating lecture notes and interactive demonstrations

Possible Directions

• interactive webpages
• partially flipped classroom
  • expose students to software before coming to class
• more writing projects and less exams
• randomized notes, examples, HWs, textbooks, etc.

SoTL Questions Regarding R

• how best to deliver the material to students?
  • labs, demonstrations, and/or group projects?
  • potential for pseudo-flipped classroom
• how does using R impact learning?
• how does using R impact attitude/interest?
• how should testing be done?
  • with or without R?
• this is a math class about the study of data
  • does incorporating data help or hurt the learning of the material?
  • showing neat tricks in R is not a replacement for learning the (mathematical) content

How Well Would R Work in a Calculus Course?