RTTP SocSec Sample Syllabus

Based on emich.edu Math 110: Mathematical Reasoning

Prof. Andrew M. Ross

Winter Semester 2011

This is a sample syllabus for a course that includes the Reacting to the Past (RTTP) game Ways and Means 1935. It is essentially the same syllabus that one of the game authors uses in his Math 110 class at Eastern Michigan University. Math 110 is our general-education math requirement in quantitative reasoning (QR) or quantitative literacy (QL). This class is not typically taken by students who major in the sciences, engineering, mathematics, or some technology fields (STEM). Business majors do typically take this course.

Official Course Catalog Entry

An introduction to quantitative reasoning, with the aim of developing the capacity to comprehend and analyze the quantitative information that is prevalent in modern society. Topics include mathematical modeling, basic probability and statistics, and practical applications.

Prerequisites for this class

Placement or at least C in Math 098 (a developmental algebra course, gives no college credit, not College Algebra), or at least D- in any of

Math 104: Algebra II (not developmental; gives college credit but is not College Algebra)
Math 105: College Algebra
Math 107: Trigonometry

The specific skills you will need from prerequisite courses are:

Basic percents: such as
- 1.2 is what percent of 4.9?
- If the budget is now 10.1 when it was 10.3, what is the percent change?
- If something cost 5.7 and it increased 6.1 percent, what does it cost now?
Scientific notation: ability to convert 4e8 to 400,000,000 for example.
Direct Proportionas: ability to set up and solve.

This class as a Prequisite for others

Math 110 is one of the math courses that fulfills the General Education requirement for mathematical reasoning, in many cases. It also fulfills prerequisites for courses in Chem, CompSci, Econ, Business, and Psych, among others.

Class Meetings

75 minutes per class meeting, twice a week (typically Mon/Wed or Tue/Thu).
3 credit hours.

Class meetings will be mostly interactive lectures, with some time to work on problems in class, and some time to go over problems from the homework. Some class sessions will meet in a computer lab or use a cartful of laptops. Exams will also be held during class meetings.

I expect that you will work on Math 110 for 6 to 10 hours per week outside of class.

Instructor information

Professor Andrew Ross
Office: Pray-Harrold building, room 515z
andrew.ross@emich.edu
http://people.emich.edu/aross15/
(734) 487-1064, but I strongly prefer e-mail instead of phone contact.

Required materials

"Quantitative Reasoning in Mathematics" Course Pack by Ahlbrandt, Calin, Curran, Gardiner, and Ross. There's no ISBN. I strongly recommend you not buy a copy more than 1 year old
Scientific Calculator. Bring it to class each day. A good example is the TI-30X-IIS calculator ($15-$20). It does not have to be a graphing calculator, but the TI-83plus graphing calculator is recommended. Cell-phone calculators are not allowed on quizzes or tests.
Microsoft Excel, or other spreadsheet software such as MS Works or Gnumeric or OpenOffice.org Calc or Google Docs.

Optional Materials

Graphing Calculator Manual for TI-83plus and TI-86 (ISBN: 0534-379001)
In past years, we have used other textbooks for this course; some people may like to read them in addition to our current textbook. They are:
- "Using and Understanding Mathematics: A Quantitative Reasoning Approach" by Bennett and Briggs (any edition),
- "For All Practical Purposes: Mathematical literacy in today's world" (any edition), and
- "Quantitative Reasoning: Tools for Today's Informed Citizen" by Sevilla and Somers
You may also enjoy "How to Lie with Statistics", by Darrell Huff, "200% of Nothing" by A.K. Dewdney, and "Proofiness" by Charles Seife.

Course Goals

Upon completing the course, students should be able to:

Carry out the steps of a mathematical modeling process.
Apply a variety of mathematical models to problem situations.
Analyze data using descriptive statistics.
Calculate and interpret discrete probabilities.
Use the normal distribution.
Apply statistical criteria such as significance tests, correlation and confidence intervals.
Explain the meaning of statistical criteria such as significance tests, correlation and confidence intervals.
Present a written or oral report outlining a problem situation, a proposed mathematical model, and a solution, together with a discussion of both the assumptions upon which the model is based and the limitations of the model.
Analyze data using a spreadsheet program.
Use a spreadsheet program to produce tables and graphs, and include them in a written report.

Math 110 qualifies as a Quantitative Reasoning course for almost everyone. The QR outcomes defined by the General Education program (up to 2011) are:

Identify an appropriate model.
Identify and discuss assumptions.
Collect or generate appropriate data.
Analyze a situation using arithmetic, geometric, algebraic, and probabilistic or statistical methods.
Estimate answers.
Propose and evaluate solutions.
Predict outcomes in other situations based on what they have learned from their analysis.
Understand and communicate quantitative relationships using symbols, equations, graphs, and tables.
Share their findings in oral and written reports using appropriate mathematical language.
Write summaries to explain how they reached their conclusions.
Draw inferences from a model.
Discuss the limitations of the model.

General Education

This course will provide students with ways to approach the quantitative information that they are certain to encounter in later coursework at Eastern Michigan University, throughout their careers, and in daily life. The emphasis is on learning methods for comprehending, analyzing and using quantitative information and on techniques for using data to inform decisions about real world events and problems. For these reasons, MATH 110 will satisfy the Quantitative Reasoning requirement in the general education program, Education for Participation in the Global Community.

Course Topics

Here are the topics in the order we cover them, with the relevant chapter/section numbers in our book.

Percents pre-test
Ch 1.1: Fish in the Lake: accuracy and precision
Ch 8.1: Intro to Spreadsheets: text/number/formula, cell references, formatting
Ch 1.2: Big Numbers (Scientific Notation), analytic estimation
Ch 1.3: Compared to What? Putting numbers in context
Ch 8.2: Intro to Spreadsheets: Simple and Compound interest
Ch 2.1: Direct Proportions
Ch 2.2: Inverse Proportions
Ch 2.3: Advanced Percents:
- Spreadsheet formulas and formatting
- percentage points
- comparisons other than increase/decrease, like "Your proposal costs 90% more than mine"
Ch 2.5: Inflation and Consumer Price Index (CPI)
- using CPI to convert from one year to another
- computing inflation as a percent from CPI
- "nominal" vs "real" percent changes
- "in constant dollars"
Ch 3.1-3.3: Linear models review
Ch 3.4: Piecewise Linear models:
- Economies of Scale/Bulk Discounts
- Diseconomies of Scale/Increasing Marginal Costs
- Progressive/Flat/Regressive taxes
- use of =max() and =min() in spreadsheets
Ch 3.5: linear regression on spreadsheets
Ch 4: Exponential models, mainly compound interest (I actually skip this, preferring to do them year-by-year on a spreadsheet)
Ch 5.1: Sampling, Random Sampling, Bias
Ch 5.2: Probability
- Axioms (called "basic rules")
- Empirical probability
- Expected Frequency
- specifically skipped: combinatorics, binomials, etc.
Ch 5.3: Expected Value and insurance
Ch 6.1: histograms
Ch 6.2: Mean and Median
Social Security Game
- a week of preparation: worksheets from the gamebook, game instructions, etc.
- a week of role playing
Ch 3.5: correlation vs. causation
Ch 5.4: Gambler's Fallacy, classical vs. frequentist vs. Bayesian
Ch 7: confidence intervals, statistical significance vs. practical significance

Grading Policies

Your grade will be computed from a weighted average, with the following components:

50%: Homework, In-Class Work, Projects, and possible Quizzes
15%: each of 2 Midterm Exams
20%: Final Exam

Some homeworks and worksheets might be graded as credit/no credit instead of graded in detail. These homeworks might then be counted as only half of a graded-in-detail homework.

Final course grades will be assigned as follows: 90+ is an A, 85-90 is an A-, 80-85 is a B+, etc.

Note that there are about 17 homework assignments/worksheets, and homework all together is worth 50 percent of your grade. So, each assignment or worksheet is worth about 3 percent of your grade. Missing two can knock you from an A to an A-, or an A- to a B+, etc.

Or, put it this way: if you paid about $1000 to take this course, each homework is worth about $30. So not turning in a homework is like taking a $10 and a $20 out of your wallet and burning them--and that's just the immediate effect, not including doing worse on the tests, and increasing the chances you might have to take the whole course again.

Similarly, we have about 28 class meetings this semester. So, you are paying about $36 per class meeting--miss one, and you might as well burn two $20 bills.

Attendance

I take attendance every day. Research shows that taking attendance improves student success, so that is why I do it. There will be material presented in class that is not in the textbook, yet will be required on the exams. Similarly, there are things in the textbook that are might not be covered in class, but are still required on the homework and exams. If you must miss a class, arrange to get a copy of the notes from someone, and arrange for someone to ask your questions for you.

My lectures and discussions mostly use the chalkboard. I do not usually have PowerPoint-like presentations, and thus cannot hand out copies of slides.

Homework

Sometimes we may have work that is assigned but not collected. Even if homework or worksheets are not collected, you are responsible for learning it--it could be on the tests!

Project

Our project this semester will be a role-playing game where we pretend that it is 1935 and we are members of the US House of Representatives. You will stand up and make short speeches to persuade your fellow Representatives to vote for what you want included (or not included) in the new Social Security law, using cost estimates that you derive as your main line of reasoning. This will occupy a week of class about 2 weeks before the last day of class.

Exams

The final will be comprehensive, with a special emphasis on any material not covered by the midterm exam(s).

You might be assigned seats while exams are in progress. No extra time will be given for late arrivals to exams. During the exam, all electronic equipment other than your calculator should be put away. Remember, calculators embedded in cell phones are not allowed.

Do not purchase any airline tickets to depart before the final exam. Be sure to allow enough time to get to the airport, etc. You will not be allowed to "take the exam early because you have already purchased a non-refundable airline ticket". See above for the final exam schedules.

Overall Grades

No scores will be dropped, unless a valid medical excuse with evidence is given (subject to the school's H1N1 Flu policy). In the unfortunate event of a medical need, the instructor will decide between a make-up being given or the grade being dropped, or any appropriate other options. Even if a grade is dropped, you are strongly encouraged to still complete the relevant assignments or exams and consult with me during office hours to ensure you know the material.

General Caveat

The instructor reserves the right to make changes to this syllabus throughout the semester. Notification will be given in class or by e-mail or both. If you miss class, it is your responsibility to find out about syllabus and schedule changes, especially the dates and times of exams.

Advice from Other Math 110 Students

In the last two semesters, I've asked my Math 110 students to give advice to you, future Math 110 students, based on their experiences in my course. Here are some of the highlights:

Study, prepare and take advantage of office hours if needed!
Come to class, take notes & use the opportunity to make the sheet for exams. Very helpful were the sheets we could use on exams.
Write all that you can on the note sheet you can use for the test because it's better to have more than you need instead of missing something :)
Be prepared to understand the math and its various applications.
You will be spending a lot of time on the computer, but the areas that you cover will really benefit you.
Read the book (at least some of it). The examples from the book are very helpful. Sometimes things are better explained in the book if you don't completely understand how to do something first.
Listen to what is talked about in class to help prepare for the exams.
Have a calculator & do the homework. Watch your calculations.
Make sure you always ask questions and go to office. It is what helped me get through this class. Professor Ross always helped when we asked.
Come to class, ask questions, see Dr. Ross in office hours he will help explain things.
Don't round up on the homework until you get to your final answer.