SYLLABUS FOR MATH Q114 Quantitative Reasoning , Spring 2005
Part I: Quantitative Reasoning in the Social Sciences
Using real data from our social environment, we begin our search for patterns in quantitative information. Starting with a small data set collected on the class, we explore how to use mathematical and technological tools to organize, visualize, and analyze single-variable data. We learn how quantitative arguments can be used and abused when describing patterns in data. Using a much larger data set (a random sample of current data about 1000 families extracted from the Current Population Survey of the U.S. Census), we experiment with using lines to describe possible relationships between two variables such as income and education.
Date Topic and Class Work
January 24 Introduction to Course and Class Web Page [1]
What is quantitative reasoning? How can numbers, data, graphs and charts be used to convince others in an argument? We will give an overview of the course material and discuss how this will be a very different kind of math class. Also: a review of percentages and a brief introduction to the internet using the class web page. First assignment is distributed.
January 26 Numerical You: Introduction to Data Collection [2]
Collect quantitative data about members of the class. Discuss properties and use of different types of variables. Explore issues of validity and accuracy of data. (Start Exploration 1.1)
January 28-31 What Is Average Anyway? [3, 4]
Talk about data (quantitative vs. qualitative), errors in data collection, and measurement. Use numerical descriptors to describe data. Analyze different kinds of averages. (Ch. 1, Sec. 1.1). Introduction to Excel. (Note: Add/Drop ends on Monday, January 31.)
February 2-7 Getting the Picture: Looking for Patterns in Single Variable Data [5, 6, 7]
Continue work with Excel to create visual displays of data. Describe the shape of the data using frequency and relative frequency histograms; discuss distribution of data. Discuss writing about data. Partners work together to analyze one variable about the class and compare their results to other data sets. (Ch. 1, Sec. 1.2).
February 9 Presentations about class data [8]
Class presentation of results from Exp. 1.1.
February 11-16 Surfing the Web; Functions of Change [9, 10, 11]
Learn how to get onto the Internet and search for information. Begin working on world wide web assignment. Introduction to functions. Representing functions with tables, graphs and symbols. Notions of independent and dependent variables, domain and range, functions as models. (Ch. 1, Sec. 1.3-1.6).
February 18 In-class computer gateway exam,
plus take-home exam on Chapters 1.1 and 1.2. [12]
February 23-25 Average Rates of Change & percentage change [13, 14]
Measuring average rate of change in single variables over time. Generate and compare rates of change. Other ways of measuring change, such as percentage change and absolute change. Putting a slant on data. (Ch. 2, Sec. 2.1-2.4, Exp. 2.1)
Note: No classes February 21, Presidents Day Holiday
February 28 – March 4 When Rates of Change are Constant [15, 16, 17]
A first look at linear functions. (Ch.2, Sec. 2.5-2.6).
March 7 - 11 The Straight Talk about Lines [18, 19, 20]
Small group exploration of properties of y = b+mx.
Linear models. (Ch. 2., Sec. 2.8; Exp. 2.2A).
Note: No classes, March 14- 18, Spring Break
March 21- 23 Group Presentations from Exploration 2.1 [21, 22]
March 25-30 Looking for Links: Are Education & Income Related? [23, 24, 25]
Who collects data about what? Discuss federal data collection and the U.S. Census and Current Population Survey. Exploration of possible linear relationships between two variables such as education and income using the U.S. Census data set of 1000 families. Discuss correlation vs. causation. Groups work together to generate, compare linear models, and present results to class. (Extended Exploration: Looking for Links)
April 1 MIDTERM EXAM [26]
Part II: Quantitative Reasoning in the Physical and Life Sciences
Using examples rooted in astronomy, physics, and the life sciences, we extend our search for underlying mathematical patterns to the physical universe. We start by learning how exponential notation is useful in describing the vast scale of the universe. By measuring the growth of E. coli bacteria under differing conditions, we can learn how to construct mathematical descriptions for exponential growth (or decay).
Note: Thursday, April 7 is the Pass/Fail and Withdrawal deadline.
April 4 – 8 Deep Space and Time [27, 28, 29]
An interactive website
"Powers of Ten", leads off the conversation about the relative size
of things in the universe. Small groups graph size vs. age of various objects
in the universe using scientific notation, estimating skills, and unit
conversions. Discuss general properties of exponents, unit conversions, orders
of magnitude (Ch. 4, Sec. 4.1-4.4).
April 11- 20 Star Powers [30, 31, 32, 33]
Laws of exponents are extended to fractional powers. Estimate terms with real exponents. Orders of magnitude and logarithmic scales (Ch. 4, Sec. 4.5, 4.6; Exploration 4.1).
Note: No classes April 18, Patriots Day Holiday
April 22 – May 9 Growth and Decay [34 – 41]
The growth of E. coli bacteria. Examples of exponential growth and decay. Fitting exponential models to data. Half-life and doubling time; Rule of 70. Comparison of linear and exponential models. (Ch. 5; Exp. 5.1)
May 11 Review for final exam [42]
Portfolios and end-of-semester reflections due on last day.
Classes end: Wednesday, May 11
Study Period: Thursday, May 12 - Sunday, May 15
Final Exam Period: Monday to Friday, May 16 - 20