Project-Based Instruction in Mathematics for the Liberal Arts

*New!! * This
PBL site has
now been translated into Romanian.
Click to access
the Romanian version.

* NOTICE:*
Although I have retired from the University, I intend to support this
problem-based learning site for use by those interested in materials posted on
it. In the near future, I may have to move the site to a new server.
If you wish to be notified of the new address (when and if the site moves),
please send me ( mulmer@uscupstate.edu
) your email address. I will not use it for any purpose other
than the one intended. I never share user addresses with anyone else
without permission. -- MBU

QuickLinks to Projects: Preliminaries | Linear | Stat/Prob | Non-Linear | Exponential | Logistic

Current Assessment Data on the Course

Data on Subsequent Performance in statistics

The purpose of this web site is to provide projects and resources for instructors and students who wish to teach and learn college mathematics or post-algebra high school mathematics via project-based instruction. Check the site often for additions and improvements.

Project-Based Instruction in Mathematics for the Liberal Arts (PBI-MLA) was developed at the University of South Carolina Spartanburg (now known as University of South Carolina Upstate). In six years, it developed a 30% higher success rate than traditional textbook-driven sections of College Mathematics.

We hope to provide support for others who wish to attempt this innovative and very practical form of instruction. If you have comments or suggestions, please contact Dr. M.B. Ulmer at mulmer@uscupstate.edu or at USC Upstate, 800 University Way, Spartanburg, SC 29303. Phone (864)503-5224, and leave a message. (Since I've retired, I'm probably not there! :) )

This site receives many hits from outside the USA. (Click the graph icon at
the bottom of this page for the latest count.) **If you are interested in
attending a university in the heart of the region of highest per capita
international investment in the USA**,
click
this link.

About the program

- An article describing the program – procedures & success
- Description of the associated booklet
- Philosophy and requirements
- Credits – Who’s been doing this?

Examples of course organization materials

- A class-tested syllabus
- Table of Contents of the booklet
- Student understanding contract
- Mid-term portfolio checklist
- Final portfolio checklist
- Absence forms
- Student opinion survey form
- Cooperative learning activity report form
- Sample Test 1
- Sample Test 2

A class-tested selection of activities and associated day-by-day procedures

Projects, activities and handouts in .PDF format (If you do not have a reader for PDF files, you may get Adobe Acrobat Reader free of charge by clicking this link.) [Projects and activities are placed in the categories below for purposes of organization. Placement of a project in, e.g., the Linear Function category means it addresses linear functions. It may also address other listed concepts, e.g. exponential functions and probability. Notations in brackets indicate sections in the course booklet pertaining to that activity. The notation "s/c" indicates that the activity is self contained and needs no concurrent assignment from the booklet.]

- First Word Processing Session (Word, first day activity) [s/c]
- Understanding and Interpreting Quantity (Quick group icebreaker)[s/c]
- Writing assignments for portfolio (Optional, but informative)[s/c]
- Word Processor Practice and Math Review (Good second day activity)[Section 1]
- The Runner (A suitable assignment for in-class self assessment with this Rubric)[s/c]
- Picking Pizzas (A good activity for introducing non-linear thinking)[s/c]
- A Morning’s Commute (An exercise in being precise)[s/c]
- Plotting Points, Interpreting Data (Exercise in contextual thinking)[s/c] See also Version 2 and Auto Theft Version.
- Introduction to the spreadsheet Excel[s/c]
- Rising and Falling Prices [s/c, may use Excel]
- Choosing Job Offers (A comparison of linear and exponential growth)[s/c, Excel] See also Version 2.
- Graphing Paired Data with Excel[s/c]
- Graphing Several Sets of Pairs on the Same Axes[s/c]

Linear functions

- Linear Modeling, Part I (A review of the point-slope form)[2.1-2.3]See also Version 2 and updated Version 3.
- Functions from Data on the TI 83/4
- Is the Globe Warming? activity
- Least Squares Line (An intro to linear regression in context)[2.3-2.5] If you'd rather use Excel on this activity, check out Linear Regression Using Excel[s/c] Also see New Microwave Activity.
- Predicting Concentration (A short revisit to linear regression. Prerequisite: Least Squares Line activity. Can be enhanced with an associated writing assignment.) [2.3-2.5]
- Per Capita Income Group Activity (Making projections)[2.3-2.5]
- Predicting the VD Rate (Linear modeling with a bit of probability)[2.3-2.5, Section 3]See also Version 2.
- Linear Modeling, Part II (A consideration of nonlinearity)[Section 2] If Version 2 of Linear Modeling, Part I was chosen, choose Version 2 for this one, too.
- Learning Progress (An exercise in selecting independent and dependent variables)[Section 2]

Statistics and probability

- Stat Functions of the TI-82/83 (An out-of-class individual activity)A rubric for this activity[s/c]
- Fractured Spaghetti and Other Probability Topics (Probability and linear inequalities)[Sections 3 and 4]

Non-linear functions

- Cutting a Sandwich with a Cleaver (Linear, exponential, power and quadratic modeling)[5.1]
- Golf Ball Toss (A quick whole-class quadratic activity)[s/c, 5.1 may be referenced] Also see Version with Data.
- Puff the Cubic Function (Intro data transformation activity)[5.4]
- Medicine Drop (A use of quadratic functions)[5.2-5.3]
- A Function for the Vet (More advanced data transformation activity) [5.2]
- A Quadratic Model of Per Capita Income (Another look at an earlier problem)[5.3]
- Prosperity and the Family Farm (Trying to model with cubics and quartics)[5.4]
- CleanUp (Data transformations, rational functions and asymptotes)[5.5-5.6]
- Age of Menarche (Advanced data transformation and exponential modeling. Suitable for a term project.)[Ch 5]
- Infant Mortality Rates Revisited (Simple exponential modeling)[6.1] See also Version 2.

Managing money with the exponential function

- Interested in Credit Cards? (An introduction to the exponential in context)[6.1-6.2]
- More About Loans with the TI-82/83 (The annuity, exponential thinking) [6.4,6.5]
- Solving for the Interest Rate (Technology where it's needed)[6.5]
- The Magic of Compound Interest (Exponential thinking. Don't skip this!)[6.4]
- Really, Now! Applying Your Interest (Possible end-of-term project) [6.4]

The logistic function – constrained growth and decay

- CleanUp-83 (A fresh look at an earlier problem)[Section 7]
- Rise and Fall of Infectious Syphilis (Piece-wise defined functions)[Section 7]

Note to the Instructor: The above projects and activities have been designed and selected with attention to the underlying functions which describe relationships between variables addressed by the activities. It is not recommended that time be spent in this course on description of general data sets. If care is not taken to select data sets whose analysis produces discovery of target course concepts, valuable instructional time may be lost. It is with this admonition that we link to the following very inclusive sources of data sets:

- Math Forum Data Collections
- The Data and Story Library (This is one of many good links from Math Forum.)

Want to know more about Problem Based Learning? Check these:

- Univ of Delaware and their extensive list of Other PBL Sites
- http://www.startlocal.com.au/articles/educational_problem_learning.html (Thanks to J.P. for this suggestion.)

Last Update: 9 Dec 2011