MATH 230 - Data Analysis and Probability for the Middle Level Teacher

Department Syllabus

Description

Designed for middle level (4-8) teaching candidates as an introduction to probability and statistics. Course will cover the following topics at an appropriate level: descriptive statistics, counting and basic probability, concept of random sampling, random variables and probability distributions, and statistical inference involving confidence intervals and hypothesis testing. (3 credits)

For the Legacy General Education curriculum, this course may be taken for general education credit (G2).

For the Gateway General Education curriculum, the course may be taken to earn the Quantitative Literacy (QL) label.

 

Prerequisites

MATH 104 (C or better) or department permission.

Course Objectives

At the conclusion of this course the successful student will be able to:

  • Explain information presented in different mathematical representations (i.e. diagrams, statistical graphs, equations, and words).
  • Convert data and geometric measurements into a variety of mathematical forms (e.g. appropriate statistical graphs, and geometric drawings).
  • Make appropriate and consistent conclusions about a variety of statistical displays, including determining limitations which occur with estimation and modeling.
  • Make appropriate and consistent conclusions about a variety of statistical displays, including determining limitations which occur with estimation and modeling.
  • Use quantitative evidence to critique data displays and geometric representations, as appropriate to justify and support conclusions in context of the mathematical application being addressed.
  • Apply basic concepts of probability including counting principles, random variables and probability distributions.
  • Apply the Data Analysis and Probability Standards from the NCTM Principles and Standards for School Mathematics and the Pennsylvania Academic Standards for Teaching Mathematics.
  • Connect the content of statistics and probability to appropriate pedagogy for Middle Level teaching.
  • Use appropriate technology (graphing calculators and computers) to problem solve and facilitate a clear application of their understanding of the key concepts of statistics and probability in the classroom.
  • To provide enough statistical training so that students can read research articles, communicate with statisticians, and interpret computer outputs involving means, standard errors, significance levels, confidence limits and other fundamental measures.

  

Assessment

Assessment of student achievement of the course objectives will vary from one instructor to another. Typical assessment will be made through work in class, homework, and examinations.

 

Use of Technology

Technology use will vary by professor.

Topics

  1. Introduction
    1. Nature of Statistics
      1. Role of Data
      2. Role of Probability
    2. Nature of Data
  2. Descriptive Statistics (Univariate & Bivariate)
    1. Data Displays
      1. Categorical Data – Bar Graphs, Circle Graphs, Pie Graphs
      2. Quantitative Data – Histograms, Stem-and-Leaf, Dot-plots, Scatter-plots
    2. Numerical Summary Statistics
      1. Measures of Center/Location – Mode, Median, Mean
      2. Measures of Spread/Variation – Range, Variance, Standard Deviation
      3. Measures of Position – Z-Score, Empirical Rule, 5- number Summary, Box-plots
      4. Measures of Association Between 2 Quantitative Data Variables – Correlation, Best Fit Line
  3. Basic Probability
    1. Random phenomena and random experiments
      1. sample spaces and events
      2. combining events
      3. mutually exclusive events
    2. Definitions of Probability
      1. relative frequency probability
      2. equally likely outcomes probability
    3. Fundamental Properties of Probability
      1. additive property (mutually exclusive and non-mutually exclusive events)
      2. complement
      3. multiplicative property
        1. tree diagrams
        2. conditional probability
      4. independent events
    4. Counting – Multiplication Rule
  4. Random Variables And Probability Distributions
    1. Random Variables
    2. Mean And Standard Deviation Of Random Variables
    3. Special Random Variables
      1. Binomial Experiment, Binomial Random Variable, Binomial Distribution
      2. Normal Random Variable, Normal Distribution
    4. Random Sampling and Sampling Distributions
      1. Data Collection
      2. Distribution Of Sample Means
        1. Central Limit Theorem
        2. t-Distribution
      3. Distribution Of Sample Proportions
  5. Statistical Inference (Single Parameter) – Decisions Based Upon Data
    1. Estimating With Confidence
      1. Nature of Point Estimation
      2. Nature of Confidence Intervals
        1. Confidence Intervals For Proportions, Sample Size
        2. Confidence Intervals For Means, Sample Size
      3. Testing Hypotheses
        1. Nature of Hypothesis Testing
          1. Hypotheses, Type 1 Error, Type 2 Error
          2. Summarize the Evidence
          3. Assess the Evidence (P-Value)
          4. Reach Conclusion
        2. Testing About Proportions
        3. Testing About Means
  6. Synthesis of Statistical Ideas and Pedagogy {through-out the course}

 

Suggested Textbook

 

Data and Probability Connections:  Mathematics for Middle School Teachers

by Debra and Michael Perkowski, (2007) Pearson Prentice Hall. ISBN 0-13-144922-2.