using activity- and web-based materials in post-calculus probability and statistics courses allan...
TRANSCRIPT
![Page 1: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/1.jpg)
Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses
Allan Rossman (and Beth Chance)
Cal Poly – San Luis Obispo
![Page 2: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/2.jpg)
Goals
To generate productive thought and discussion about appropriate
Goals Content Pedagogy
of an introductory statistics course for mathematically inclined students
![Page 3: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/3.jpg)
Goals (cont.)
To introduce you to curricular materials that aim to help prepare you to:
Present a course that provides a more balanced introduction to statistics for mathematically inclined students
Infuse a post-calculus introductory statistics course with activities and data
Model recommended pedagogy and content for future teachers of statistics
![Page 4: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/4.jpg)
Format
Activity sessions will consist of working through activities/investigations
Please be willing to play the role of student Investigations chosen from throughout course to
illustrate guiding principles More “lecture” than with my students Implementation suggestions offered along the way
![Page 5: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/5.jpg)
Features of Statistics Education Reform Active Learning Conceptual Understanding Genuine Data Use of Technology Communication Skills Interpretation in Context Authentic Assessment
![Page 6: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/6.jpg)
Products of Statistics Education Reform Textbooks Activity Books Lab Manuals Books of Data Sources Books of Case Studies On-line Books Journals
Dynamic Software Java Applets Web Sites Project Templates Assessment
Instruments Workshops
![Page 7: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/7.jpg)
What’s the Problem?
Vast majority of reform efforts have been directed at the “Stat 101” service course
Rarely reaches Mathematics or Statistics majors Option A: Take Stat 101 Option B: Standard Prob and Math/Stat sequence
![Page 8: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/8.jpg)
What’s the Problem?
Option A Does not challenge students mathematically Rarely counts toward major
Option B Does not give balanced view of discipline Fails to recruit all who might be interested Leaves prospective K-12 teachers ill-prepared to
teach statistics, implement reform methods Does not even prepare assistants for Stat 101!
![Page 9: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/9.jpg)
Is This Problem Important?
“The question of what to do about the standard two-course upperclass sequence in probability and statistics for mathematics majors is the most important unresolved issue in undergraduate statistics education.”
- David Moore
![Page 10: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/10.jpg)
Is This Problem Important?
“The standard curriculum for mathematics majors allows little time for statistics until, at best, an upper division elective. At that point, students often find themselves thrust into a calculus-based mathematical statistics course, and they miss many basic statistical ideas and techniques that are at the heart of high school statistics courses.”
- CBMS MET report (ch. 5)
![Page 11: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/11.jpg)
Is This Problem Important?
“In most teacher preparation programs appropriate background in statistics and probability will not be provided by simply requiring a standard probability-statistics course for mathematics majors. It is essential to carefully consider the important goals of statistical education in designing courses that reflect new conceptions of the subject.”
- CBMS MET report (ch. 5)
![Page 12: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/12.jpg)
My Project (with Beth Chance)To develop and provide a:
Data-Oriented, Active Learning, Post-Calculus Introduction to Statistical Concepts, Applications, Theory
Supported by the NSF DUE/CCLI #9950476, 0321973
![Page 13: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/13.jpg)
Principle 1
Motivate with real studies, genuine data Statistics as a science Wide variety of contexts Some data collected on students themselves
![Page 14: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/14.jpg)
Principle 2
Emphasize connections among study design, inference technique, scope of conclusions Issues arise in chapter 1, recur often Observational study vs. controlled experiment Randomization of subjects vs. random sampling Inference technique follows from randomization in
data collection process
![Page 15: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/15.jpg)
Principle 3
Conduct simulations often Problem-solving tool and pedagogical device Address fundamental question: “How often would
this happen in the long run?” Hands-on simulations usually precede
technological simulations Java applets Small-scale Minitab programming (macros)
![Page 16: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/16.jpg)
Principle 4
Use variety of computational tools For analyzing data, exploring statistical concepts Assume that students have frequent access to
computing Not necessarily every class meeting in computer lab
Choose right tool for task at hand Analyzing data: statistics package (e.g., Minitab) Exploring concepts: Java applets (interactivity,
visualization) Immediate feedback from calculations: spreadsheet
(Excel)
![Page 17: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/17.jpg)
Principle 5
Investigate mathematical underpinnings Primary distinction from “Stat 101” course Some use of calculus but not much Will assume familiarity with mathematical ideas
such as function Example: study principle of least squares in
univariate and bivariate settings Often occurs as follow-up homework exercises
![Page 18: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/18.jpg)
Principle 6
Introduce probability “just in time” Not the goal Studied as needed to address statistical issues Often introduced through simulation Examples
Hypergeometric distribution: Fisher’s exact test for 2x2 table
Binomial distribution: Sampling from random process Continuous probability models as approximations
![Page 19: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/19.jpg)
Principle 7
Foster active explorations Students learn through constructing own
knowledge, developing own understanding Need direction, guidance to do that
![Page 20: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/20.jpg)
Principle 8
Experience entire statistical process over and over Data collection Graphical and numerical displays Investigate sampling/randomization distribution Apply inference procedure Communicate findings in context Repeat in new setting
Repeat in new setting Repeat in new setting…
![Page 21: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/21.jpg)
Content- Chapter 1
Comparisons and conclusions Categorical variables Two-way tables Relative risk, odds ratio Variability, confounding, experimental design,
randomization, probability, significance Fisher’s exact test
![Page 22: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/22.jpg)
Content- Chapter 2
Comparisons with quantitative variables Visual displays Numerical summaries Randomization distribution
Significance, p-value, …
![Page 23: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/23.jpg)
Content- Chapter 3
Sampling from populations and processes Bias, precision Random sampling Sampling variability, distributions Bernoulli process and binomial model
Binomial approximation to hypergeometric Significance, confidence, types of errors
![Page 24: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/24.jpg)
Content- Chapter 4
Models and sampling distributions Probability models, including normal Approximate sampling distribution for sample
proportion Normal approximation to binomial
Sampling distribution of sample mean t-procedures
Bootstrapping
![Page 25: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/25.jpg)
Content- Chapter 5
Comparing two populations Categorical variables
Two-sample z-test Approximation to randomization distribution Odds ratio
Quantitative variables Two-sample t-test Approximation to randomization distribution
![Page 26: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/26.jpg)
Content- Chapter 6
Association and relationships Chi-square tests Analysis of variance Simple linear regression
![Page 27: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/27.jpg)
Why this sequence?
Spiral through entire process over and over Start with comparisons
More scientifically interesting Observation vs. experiment early
Start with categorical variables Easy, natural to work with Lead to mathematically interesting analyses
Change one thing at a time
![Page 28: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/28.jpg)
Course Materials- Structure
Investigations Can be adapted for variety of teaching styles
Exposition Study conclusions, discussion, summaries
Technology explorations Detours for terminology, probability Practice problems
Help students to assess their understanding Expand their knowledge
![Page 29: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/29.jpg)
Course Materials- Status
Preliminary version to be published by Duxbury in August Hot-off-the-press version in your binders Companion website: www.rossmanchance.com/iscam/
Next year: polishing, refining, developing resource materials Homework problems/solutions, teachers’ guide,
powerpoint, practice problem solutions to appear on web Include more worked out examples
Please share your suggestions
![Page 30: Using Activity- and Web-Based Materials in Post-Calculus Probability and Statistics Courses Allan Rossman (and Beth Chance) Cal Poly – San Luis Obispo](https://reader036.vdocuments.net/reader036/viewer/2022062408/56649e9f5503460f94ba17ed/html5/thumbnails/30.jpg)
Questions?