A Pathway to Introductory Statistics

Jay Lehmann has taught at College of San Mateo for more than twenty years, where he has received the Shiny Apple Award for excellence in teaching. He has worked on a NSF-funded grant to study classroom assessment and has performed research on collaborative directed-discovery learning. Jay has served as the newsletter editor for CMC3 (California Mathematics Council, Community College) for twelve years. He has presented at more than seventy-five conferences, including AMATYC, ICTCM, and T3, where he has discussed curve fitting and sung his "Number Guy" song. Jay plays in a rock band called The Procrastinistas, who play at various clubs in the San Francisco Bay Area, where Jay, his wife Keri, and son Dylan reside. He plays a number of instruments including bass, guitar, piano, violin, and baritone. In addition to his elementary, intermediate, and combined algebra textbooks, Jay is currently writing a heist novel for high school students, which he hopes will be published before Dylan outgrows it. Dylan, a devoted drummer and artist, drafted many of the cartoons that are included in Jay's textbooks. In the words of the author: Before writing my algebra series, it was painfully apparent that my students couldn't relate to the applications in the course. I was plagued with the question, "What is this good for?" To try to bridge that gap, I wrote some labs, which facilitated my students in collecting data, finding models via curve fitting, and using the models to make estimates and predictions. My students really loved working with the current, compelling, and authentic data and experiencing how mathematics truly is useful. My students' response was so strong that I decided to write an algebra series. Little did I know that to realize this goal, I would need to embark on a 15-year challenging journey, but the rewards of hearing such excitement from students and faculty across the country has made it all worthwhile! I'm proud to have played even a small role in raising peoples' respect and enthusiasm for mathematics. I have tried to honor my inspiration: by working with authentic data, students can experience the power of mathematics. A random-sample study at my college suggests that I am achieving this goal. The study concludes that students who used my series were more likely to feel that mathematics would be useful in their lives (P-value 0.0061) as well as their careers (P-value 0.024). The series is excellent preparation for subsequent courses; in particular, because of the curve fitting and emphasis on interpreting the contextual meaning of parameters, it is an ideal primer for statistics. In addition to curve fitting, my approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, and of course, a large bank of skill problems. The curve-fitting applications serve as a portal for students to see the usefulness of mathematics so that they become fully engaged in the class. Once involved, they are more receptive to all aspects of the course.

1. Performing Operations and Evaluating Expressions

1.1 Variables, Constants, Plotting Points, and Inequalities

1.2 Expressions

1.3 Operations with Fractions and Proportions; Converting Units

1.4 Absolute Value and Adding Real Numbers

1.5 Change in a Quantity and Subtracting Real Numbers

1.6 Ratios, Percents, and Multiplying and Dividing Real Numbers

1.7 Exponents, Square Roots, Order of Operations, and Scientific Notation

Hands-On Projects: Stocks Project

2. Designing Observational Studies and Experiments

2.1 Simple Random Sampling

2.2 Systematic, Stratified, and Cluster Sampling

2.3 Observational Studies and Experiments

Hands-On Projects: Survey about Proportions Project; Online Report Project

3. Graphical and Tabular Displays of Data

3.1 Frequency Tables, Relative Frequency Tables, and Bar Graphs

3.2 Pie Charts and Two-Way Tables

3.3 Dotplots, Stemplots, and Time-Series Plots

3.4 Histograms

3.5 Misleading Graphical Displays of Data

Hands-On Projects: Student Loan Default Project

4. Summarizing Data Numerically

4.1 Measures of Center

4.2 Measures of Spread

4.3 Boxplots

Hands-On Projects: Comparison Shopping of Cars Project

5. Computing Probabilities

5.1 Meaning of Probability

5.2 Complement and Addition Rules

5.3 Conditional Probability and the Multiplication Rule for Independent Events

5.4 Finding Probabilities for a Normal Distribution

5.5 Finding Values of Variables for Normal Distributions

Hands-On Projects: Heights of Adults Project

6. Describing Associations of Two Variables Graphically

6.1 Scatterplots

6.2 Determining the Four Characteristics of an Association

6.3 Modeling Linear Associations

Hands-On Projects: Climate Change Project; Volume Project

Linear Graphing Project: Topic of Your Choice 421

7. Graphing Equations of Lines and Linear Models; Rate of Change

7.1 Graphing Equations of Lines and Linear Models

7.2 Rate of Change and Slope of a Line

7.3 Using Slope to Graph Equations of Lines and Linear Models

7.4 Functions

Hands-On Projects: Climate Change Project; Workout Project; Balloon Project

8. Solving Linear Equations and Inequalities to Make Predictions

8.1 Simplifying Expressions

8.2 Solving Linear Equations in One Variable

8.3 Solving Linear Equations to Make Predictions

8.4 Solving Formulas

8.5 Solving Linear Inequalities to Make Predictions

9. Finding Equations of Linear Models

9.1 Using Two Points to Find an Equation of a Line

9.2 Using Two Points to Find an Equation of a Linear Model

9.3 Linear Regression Model

Hands-On Projects: Climate Change Project; Golf Ball Project;

Rope Project; Shadow Project; Linear Project: Topic of Your Choice

10. Using Exponential Models to Make Predictions

10.1 Integer Exponents

10.2 R ational Exponents

10.3 G raphing Exponential Models

10.4 Using Two Points to Find an Equation of an Exponential Model

10.5 E xponential Regression Model

Hands-On Projects: Stringed Instrument Project; Cooling Water Project

Exponential Project: Topic of Your Choice

Appendices

A. Using A TI-84 Graphing Calculator A-1

A.1 Turning a Graphing Calculator On or Off

A.2 Making the Screen Lighter or Darker

A.3 Selecting Numbers Randomly

A.4 Entering Data for a Single Variable

A.5 Constructing a Frequency Histogram

A.6 Computing Median, Mean, Standard Deviation, and other Measures

A.7 Constructing a Boxplot

A.8 Computing Probabilities for a Normal Distribution

A.9 Finding a Value of a Variable for a Normal Distribution

A.10 Constructing a Time-Series Plot or Scatterplot

A.11 Constructing Two Scatterplots That Share the Same Axes

A.12 Computing Correlation Coefficients and Coefficients of Determination

A.13 Turning a Plotter On or Off

A.14 Entering an Equation

A.15 Graphing an Equation

A.16 Tracing a Curve without a Scatterplot

A.17 Zooming

A.18 Setting the Window Format

A.19 Graphing Equations with a Scatterplot

A.20 T racing a Curve with a Scatterplot

A.21 Constructing a Table

A.22 Constructing a Table for Two Equations

A.23 Using “Ask” in a Table

A.24 Finding the Intersection Point(s) of Two Curves

A.25 Turning an Equation On or Off

A.26 Finding a Regression Equation

A.27 Constructing a Residual Plot

A.28 Responding to Error Messages

B. Using Statcrunch

B.1 Selecting Numbers Randomly

B.2 Entering Data

B.3 Constructing Frequency and Relative Frequency Tables

B.4 Constructing Bar Graphs or Multiple Bar Graphs

B.5 Constructing Pie Charts

B.6 Constructing Two-Way Tables

B.7 Constructing Dotplots

B.8 Constructing Stemplots and Split Stems

B.9 Constructing Time-Series Plots

B.10 Constructing Histograms

B.11 Computing Medians, Means, Standard Deviations, and Other Measures

B.12 Constructing Boxplots

B.13 Computing Probabilities for a Normal Distribution

B.14 Finding Values of a Variable for a Normal Distribution

B.15 Constructing Scatterplots

B.16 Computing Linear Correlation Coefficients and Coefficients of Determination

B.17 Finding Linear Regression Equations

B.18 Constructing Residual Plots for Linear Regression Models

C. Standard Normal Distribution

Table C-1