Download Statistics and Statistical Modeling in The First

Statistics and Statistical Modeling in The
First Two Years of College Math
A. John Bailer
[email protected]
Outline
In my remarks, I will consider the general question of
when statistics and statistical modeling encountered in
the curriculum
• Why is this important?
• Past patterns
• Present (& evolving) practice
• Future opportunities
Context of remarks
My remarks apply to the statistics and statistical
modeling background of needed by both STEM majors
and to non-STEM majors.
My remarks extend beyond the ‘uses of math in physical
sciences’ category of this panel
Importance of statistics and stat modeling? [Gen. Ed.]
Quantitative Literacy / Data analytic skills are a critical
component of a general education (AAC&U LEAP core
competency – https://www.aacu.org/leap)
• “competency and comfort working with numerical
data”
• “ability to reason and solve quantitative problems
from a wide array of authentic contexts and everyday
life situations”
• “understand and can create sophisticated arguments
supported by quantitative evidence … clearly
communicate those arguments”
Importance of statistics and stat modeling? [Engineering]
ABET criteria for bioengineering (and others)
curriculum:
an understanding of biology and physiology
capability to apply advanced mathematics (including
differential equations and statistics) …
For manufacturing engineering:
(d) manufacturing systems design: ability to analyze,
synthesize, and control manufacturing operations
using statistical methods
Why is this important? [data rich world]
Data collected on all phases of life and decisions based
on models derived from these data (e.g., health
decisions from risk models, recommender systems).
Data in context matters (who was studied? Is this
relevant for me?)
Skepticism of what is reported is healthy (was a
predictive model validated?)
Why is this important?
Skills for extracting information and insight from data
are in demand
indeed.com search (02oct14)
‘statistician’ –1632 jobs
‘statistical analyst’ –13647 jobs
‘statistical programmer’ –2402 jobs
‘data scientist’ –11791 jobs
‘marketing research analyst’ – 6700 – many positions
require ‘proven data gathering and analytical skills’
Past Patterns
Early 80’s …
Statistics intro course began to change …
less procedural and more conceptual
Intro. to Practice of Statistics (Moore & McCabe)
included sections that addressed:
• describing data
• collecting data
• drawing conclusions from data
Regression for describing relationship between 2 vars
(not much in ways of explicit modeling)
Past Patterns
Early 80’s …
Statistics and Mathematics majors positioned to not
encounter any data analysis until their 3rd year of study.
First,
Calc I, Calc II, Calc III, Linear Algebra, Probability
Then,
Math Stat (estimation, testing, etc.)
Finally,
Regression [first time power of data analysis
modeling realized]
Present (& evolving) practice
Modify curriculum so that stat and math majors
(already true for STEM majors) see data analysis
concepts early (only one calc prereq; see before
probability)
Modify curriculum so that stat and math majors can
take an early intro to modeling (only one STA prereq vs.
the previous courses with 3 calc + linear algebra +
probability + intro stat prereqs).
Present (& evolving) practice
Expansion of stat ed efforts
• Journal of Stat Ed – First volume – 1993 http://www.amstat.org/publications/jse/
• ICOTS – 1982 (every 4 years)
• USCOTS – 2005 (every 2 years) + eCOTS
• GAISE – 2005 (college version) -
http://www.amstat.org/education/gaise/GaiseCollege_Full.pdf
• ASA guidelines for undergraduate stat curriculum
(2000 and 2014 revision in progress)
Present (& evolving) practice
New introductory curriculum – reflecting key GAISE
ideas (e.g. emphasize stat literacy, use real data, stress
concepts rather than procedures, active learning, use
tech, assess)
• Introductory statistics using randomization and
bootstrapping principles –
• Statistics: Unlocking the Power of Data
(www.lock5stat.com)
• Workshop Statistics (http://www.rossmanchance.com/ws/)
• Introduction to Statistical Investigations
(http://www.math.hope.edu/isi/)
Present (& evolving) practice
New accessible modeling books –
• Stat2 http://www.amazon.com/STAT2-Book-Companion-Premium-Access/dp/1464148260
designed to help students build on their statistical knowledge in order to
analyze rich datasets using statistical models. The book develops a systematic
approach to using different models and includes exercises to allow students to
practice working with real data alongside output from statistical software.
Future opportunities
Greater number of students with AP statistics credit
entering college (169K in 2013, 98K scored 3+; 185K in
2014)
College board lists AP stat exam as “can lead to a future
in…” 106 Career Areas and 32 College Majors
Common Core statistics and probability – includes
“interpret linear models”
(http://www.corestandards.org/Math/Content/HSS/introduction/)
MS and HS students will be doing simulations in classes
Future opportunities
How will we change the statistics curriculum in
response to more students entering college with AP Stat
credit and with years of exposure to statistics and
probability concepts in the common core?
One possible answer: the current ‘stat 2’ class (intro to
stat models) will become the future ‘stat 1’ class.
Thank you