May 20, 2016

Foundations at Georgetown College

Foundations and Core

Georgetown's "new gen ed" (since 2010):

  • Foundations (basic skills)
    • two-semester Foundations sequence in first year
    • basic proficiency in:
      • mathematics
      • composition
      • lifetime fitness
  • Core
    • Courses selected from four Areas of Inquiry
    • flagged courses for continued development of basic skills in mathematics and composition
    • flagged courses for cultural awareness

Foundations I (FDN 111)

  • Fall semester of first year
  • mostly uniform across all sections
  • unifying theme:
    • "Revolution and Renaissance" (2010-2015)
    • "What is it to be Human?" (2016 - ?)
  • chronological approach
  • primary texts (some art/music as well)
  • stress on development of basic skills within given content

Basic Skills

  • Primary Skills ("Read-Write-Argue" Trinity)
    • Analytical Reading
    • Argumentation
    • Composition
  • Meta-Skills
    • Engagement
    • Self-Assessment

The three primary skills have (inter-woven) components that are explicitly addressed in most sections of the course.

Reading

  • Read for Structure
  • Read to Interpret
  • Read in Context
  • Read in a Spirit of Critical Engagement

Reading for Structure

The structure of a thing is

  • the kind of thing that it is (e.g., drama, novel, short-story, poem, etc.), and
  • a statement of:
    • its parts
    • how these parts are related to one another

Structure guides interpretation.

Outlining: a typical exercise in reading for structure.

Reading to Interpret

  • macro level – overall theme
  • micro levels – paragraph, sentence, phrase, words
  • typical exercises:
    • sentence paraphrase
    • summarize paragraph in sentence
    • analyse similes (often involves structural analysis)

Simile and Structure

[From the Iliad:]

Achilles wasted no time. Leaving his spear Propped against a tamarisk And holding only his sword, he leaped from the bank He struck over and over …

Fish fleeing from a dolphin’s huge maw

Hide by the hundreds in the harbor’s crannies

But the dolphin devours whatever it catches.

Likewise the Trojans beneath the riverbanks.

Simile as Isomorphism

Tenor (literal) Vehicle (symbolic)
Achilles Dolphin
Trojans Fish
Sword Huge maw
Riverbank Crannies of the harbor


The map is structure-preserving:

  • dolphin pursues the fish; Achilles pursues the Trojans
  • dolphin destroys with mouth, Achilles destroys with sword
  • etc.

Read in Context

Consider

  • the time period, cultural setting
  • situation and purposes of the author
  • intended audience

Read with Critical Engagement

  • Do I really believe this claim?
  • Who else makes a similar point?
  • What would the author have said if … ?

Often explicitly treated. In class, instructor might ask: "What's a good critical engagement question about this passage?"

Argue

Sub-skills are:

  • Describing arguments (identifying premises, conclusion)
    • Often combined with structural reading.
  • Evaluating arguments
  • Constructing one's own arguments
    • Often done in interpretation. FDN 111 mantra: "Back up your interpretation with specific citations from the text!"

Write

  • Two major (4-5 page) thesis-driven essays, prepared for by near-daily small assignments.
  • Process-writing is taught:
    • free-writing
    • writing down reasons to believe/disbelieve a claim
    • outlining
    • draft and draft conference
    • peer review, etc.

Foundations II (FND 112)

  • Spring of the first year
  • topic varies from section to section
  • "modestly interdisciplinary"
  • emphasis is on continued skills development in the context of the primary discipline

FDN 112/ MAT 111: Elementary Statistics

FDN 112

  • fulfills quantitative proficiency requirement (QPR)
  • quantitative "flag" for those who have already fulfilled (QPR)
  • mostly traditional content

FDN 112

  • descriptive statistics
  • early into to chi-square inference (association)
  • simple linear regression (almost no inference)
  • confounding variables
  • Interlude: basic predictive statistics with trees (classification, regression)
  • design of studies
  • whirlwind probability (including probability in simple random sampling)
  • confidence intervals for the "Basic Five"" parameters
  • hypothesis tests for the same
  • chi-square Goodness of Fit (as time permits)

FDN 112

Non-traditional aspects:

  • predictive statistics
  • simulation-based inference taught as much as possible (apps employed heavily)
  • but no bootstrap (yet)
  • taught with R, in the R Studio IDE (server)
  • integrates FDN skills approach/terminology

The RStudio Environment

Skills Integration

"Elementary statistics isn't really a course in mathematics.

It's a course about judgement."

—Daniel Kaplan, Macalester College

Skills Integration

We read, argue and write about data.

(Typically in the form of an R data data frame!)

Understanding of data is driven by employing the Read skill in each of its four aspects:

  • reading for structure
  • reading to interpret
  • reading in context
  • reading to engage

"Watch your process: be aware of when you are applying each sub-skill."

Reading

Reading for Structure

R reads for structure, with the str() function:

str(iris)
## 'data.frame':    150 obs. of  5 variables:
##  $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
##  $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
##  $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
##  $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
##  $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

Structure of Variables:

with(iris, str(Species))
##  Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

In the IDE

Read to Interpret

Tell the story of the data as it stands? (Numerical and graphical summaries.)

"Structure guides interpretation." Appropriate tools chosen by mean of variable analysis:

  • Given a Research Question, identify all variables in the data frame that pertain to it.
  • Identify the type of each variable (numerical, factor).
  • If appropriate, identify explanatory/response variables.

Read in Context

help(iris)

Read for Critical Engagement

  • Are there any unusual observations? What should I do about them?
  • I see a pattern in the sample, but is it also present in the population, or could it just be due to chance variation in the process by which I got the data?
  • Are there confounding variables? How could I correct for them?
  • Could there have been a different/better way to measure this variable?
  • Data-snooping/mining?

Argumentation

Arguments: Description/Evaluation

Favor Oppose
No 375 199
Yes 243 59


Comment: "Folks who don't own a gun are more likely to oppose capital punishment than those who do own a gun, because 199 non-owners oppose capital punishment whereas only 59 gun-owners do."

Arguments: Construction

  • Small-scale:
    • explain why a given random variable can/cannot be modeled with a binomial distribution
    • explain why a given variable is a confounding factor in an observational study
    • back up a statement of relationship with specific relevant features of a table/graph
  • Larger-scale:
    • Inferential procedures
    • Building and testing predictive models
    • Reasoning about causation

Writing

Writing (Major)

Two Data Analysis Reports:

  • (individual) Wage-discrimination study from CPS data. Is there good evidence for wage discrimination based on sex, or could the wage-gap be ascribed to one or more confounding factors?
  • (group) Predictive modeling project: Mushrooms or Diabetes.

Process:

  • draft
  • draft conference
  • final version (w/oral presentation, for group project)

Rubrics-based grading.

Writing (Technique)

  • Daily R Markdown documents, electronically collected
  • Small-scale skills development addressed in the Dailies
  • Reports are R Markdown, knit to pdf
  • R graphics via custom-written GUI (R Studio Addin)
  • Student-oriented R-package for predictive modeling with trees

Final Thoughts

Next Time Around …

  • Should have added an "informal analysis" stage to the first Data Analysis Report
  • Nice to have more Addins to address:
    • construction of numerical tables
    • data-manipulation
    • selection/implementation of inferential techniques
  • Maybe drop trees in favor of multiple regression (with emphasis on application to correcting for confounding factors)

Resources