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 Expressions1.1 Variables, Constants, Plotting Points, and Inequalities1.2 Expressions1.3 Operations with Fractions and Proportions; Converting Units1.4 Absolute Value and Adding Real Numbers1.5 Change in a Quantity and Subtracting Real Numbers1.6 Ratios, Percents, and Multiplying and Dividing Real Numbers1.7 Exponents, Square Roots, Order of Operations, and Scientific NotationHands-On Projects: Stocks Project2. Designing Observational Studies and Experiments2.1 Simple Random Sampling2.2 Systematic, Stratified, and Cluster Sampling2.3 Observational Studies and ExperimentsHands-On Projects: Survey about Proportions Project; Online Report Project3. Graphical and Tabular Displays of Data 3.1 Frequency Tables, Relative Frequency Tables, and Bar Graphs3.2 Pie Charts and Two-Way Tables3.3 Dotplots, Stemplots, and Time-Series Plots3.4 Histograms3.5 Misleading Graphical Displays of DataHands-On Projects: Student Loan Default Project4. Summarizing Data Numerically4.1 Measures of Center4.2 Measures of Spread4.3 BoxplotsHands-On Projects: Comparison Shopping of Cars Project5. Computing Probabilities5.1 Meaning of Probability5.2 Complement and Addition Rules5.3 Conditional Probability and the Multiplication Rule for Independent Events5.4 Finding Probabilities for a Normal Distribution5.5 Finding Values of Variables for Normal DistributionsHands-On Projects: Heights of Adults Project6. Describing Associations of Two Variables Graphically6.1 Scatterplots6.2 Determining the Four Characteristics of an Association6.3 Modeling Linear AssociationsHands-On Projects: Climate Change Project; Volume ProjectLinear Graphing Project: Topic of Your Choice 4217. Graphing Equations of Lines and Linear Models; Rate of Change7.1 Graphing Equations of Lines and Linear Models7.2 Rate of Change and Slope of a Line7.3 Using Slope to Graph Equations of Lines and Linear Models7.4 FunctionsHands-On Projects: Climate Change Project; Workout Project; Balloon Project8. Solving Linear Equations and Inequalities to Make Predictions 8.1 Simplifying Expressions8.2 Solving Linear Equations in One Variable8.3 Solving Linear Equations to Make Predictions8.4 Solving Formulas8.5 Solving Linear Inequalities to Make Predictions9. Finding Equations of Linear Models 9.1 Using Two Points to Find an Equation of a Line9.2 Using Two Points to Find an Equation of a Linear Model9.3 Linear Regression ModelHands-On Projects: Climate Change Project; Golf Ball Project;Rope Project; Shadow Project; Linear Project: Topic of Your Choice10. Using Exponential Models to Make Predictions 10.1 Integer Exponents10.2 R ational Exponents10.3 G raphing Exponential Models10.4 Using Two Points to Find an Equation of an Exponential Model10.5 E xponential Regression ModelHands-On Projects: Stringed Instrument Project; Cooling Water ProjectExponential Project: Topic of Your ChoiceAppendicesA. Using A TI-84 Graphing Calculator A-1A.1 Turning a Graphing Calculator On or OffA.2 Making the Screen Lighter or DarkerA.3 Selecting Numbers RandomlyA.4 Entering Data for a Single VariableA.5 Constructing a Frequency HistogramA.6 Computing Median, Mean, Standard Deviation, and other MeasuresA.7 Constructing a BoxplotA.8 Computing Probabilities for a Normal DistributionA.9 Finding a Value of a Variable for a Normal DistributionA.10 Constructing a Time-Series Plot or ScatterplotA.11 Constructing Two Scatterplots That Share the Same AxesA.12 Computing Correlation Coefficients and Coefficients of DeterminationA.13 Turning a Plotter On or OffA.14 Entering an EquationA.15 Graphing an EquationA.16 Tracing a Curve without a ScatterplotA.17 ZoomingA.18 Setting the Window FormatA.19 Graphing Equations with a ScatterplotA.20 T racing a Curve with a ScatterplotA.21 Constructing a TableA.22 Constructing a Table for Two EquationsA.23 Using “Ask” in a TableA.24 Finding the Intersection Point(s) of Two CurvesA.25 Turning an Equation On or OffA.26 Finding a Regression EquationA.27 Constructing a Residual PlotA.28 Responding to Error MessagesB. Using StatcrunchB.1 Selecting Numbers RandomlyB.2 Entering DataB.3 Constructing Frequency and Relative Frequency TablesB.4 Constructing Bar Graphs or Multiple Bar GraphsB.5 Constructing Pie ChartsB.6 Constructing Two-Way TablesB.7 Constructing DotplotsB.8 Constructing Stemplots and Split StemsB.9 Constructing Time-Series PlotsB.10 Constructing HistogramsB.11 Computing Medians, Means, Standard Deviations, and Other MeasuresB.12 Constructing BoxplotsB.13 Computing Probabilities for a Normal DistributionB.14 Finding Values of a Variable for a Normal DistributionB.15 Constructing ScatterplotsB.16 Computing Linear Correlation Coefficients and Coefficients of DeterminationB.17 Finding Linear Regression EquationsB.18 Constructing Residual Plots for Linear Regression ModelsC. Standard Normal DistributionTable C-1