Prefix, Number, and Name of Course:
MAT 581 Math for Teachers: Probability and Statistics
Credit Hours: 3
In-Class Instructional Hours: 3 Labs: 0 Field Work: 0
Catalog Description:
Prerequisite: Two semesters of calculus; MAT 325, MAT 311 or the equivalent
Probability, probability distributions, sampling, design of experiments, hypothesis testing, regression, analysis of variance, nonparametric statistics.
Reasons for Revision:
2. 2. To
provide a graduate level course that integrates graphing calculator technology
into the learning of Probability and Statistics.
3. 3. To
provide an advanced, in-depth study of the connections between school
mathematics and the areas of probability and statistics.
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Student Learning Outcomes:
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Course Content References: |
Asessment: |
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1. Students will create, calculate, interpret and use various types of graphs, measures of central tendency and standard deviation. |
I, III - VII |
1. Group work in class, individual homework assignments |
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2. Student will solve problems using the principles, properties and techniques of probability and probability distributions. |
I - VII |
2. Group work in class, individual homework assignments, exam |
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3. Students will use graphing calculators to gather actual data, run simulations, analyze and interpret data for a variety of real life problems. |
I - VII |
3. Group work in class, individual homework assignments, exam, individual project. |
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4. Students will apply a variety of regression techniques to create, interpret and apply mathematical models and will analyze the fit of the various models. |
III - VII |
4. Group work in class, individual homework assignments, exam, individual project. |
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5. Students will apply knowledge of experimental design and hypothesis testing and interpret the outcomes of a given statistical test. |
III -VII |
5. Group work in class, individual homework assignments, exam, group project. |
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6. Students will demonstrate the ability to appropriately apply nonparametric statistics. |
V, VII |
6. Group work in class, individual homework assignments, exam |
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7. Students will demonstrate the ability to make and use connections between school mathematics and the areas of probability and statistics. |
I - VII |
7. Group work in class, individual homework assignments, exam, individual and group projects. |
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Course Content:
I. Data Organization, Measures of Central Tendency and Standard Deviation A. Mean, Median and Mode B. Range, Variance and Standard Deviation C. Scatterplots, Histograms, Box and Whisker Plots
II. Counting Methods and Probability A. Permutations B. Combinations C. Partitions D. Principles of Probability E. Expectation F. Simulations G. Geometric Probability
III. Probability Distributions A. Normal Distribution B. Sampling Distributions C. Binomial Distribution D. Geometric Distribution E. t Distribution F. F Distribution G. Chi Square Distribution
IV. Regression and Correlation A. Linear Regression B. Multiple Regression C. Nonlinear Regression D. Assessing the fit of the model
V. Confidence Intervals and Hypothesis Testing A. Mean B. Proportion C. Variance and Standard Deviation D. Goodness of Fit E. Independence F. Regression G. Tests for Normality H. Design of Experiments
VI. Analysis of Variance A. One way ANOVA B. Two way ANOVA
VII. Nonparametric Statistics A. Signed B. Sign-Rank C. Ranked Sum D. Kruskal-Wallis E. Rank Correlation
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Resources:
Classic Scholarship in the field:
Gnanadesikan, R. (1997). Methods for Statistical Data Analysis of Multivariate Observations, 2nd Edition. New York: John Wiley and Sons.
Theory and Application of the Linear Model. New York: John Wiley and Sons.
Greenwood, P. E. & Nikulin, M. S. (1996). A Guide to Chi-Squared Testing. New York: John Wiley and Sons.
Keppel, G. & Zedeck, S. (1989). Data Analysis for Research Designs. New York: W. H. Freeman and Company.
2nd Edition. Pacific Grove, CA: Duxbury.
Welsh, A. H. (1996). Aspects of Statistical Inference. New York: John Wiley and Sons.
Current Scholarship in the field:
Bright, G. W., Brewer, W., McClain, K. & Mooney E.S. (2003). Navigating through Data Analysis in Grades 6 - 8. Reston, VA: National Council of Teachers of Mathematics.
Conover,
W. J. (1999). Practical Nonparametric Statistics,
3rd Edition. New York: John Wiley and Sons.
Evans, M. J. and Rosenthal, J. S. (2004). Probability and Statistics: The Science of Uncertainty. New York: W. H. Freeman and Company.
, J.J. (2004). Introduction to Modern Nonparametric Statistics. Pacific Grove, CA: Duxbury.
, R. O. (2000). Design of Experiments - Statistical Principles of Research Design and Analysis, 2nd edition. Pacific Grove, CA: Duxbury.
Multivariate Statistical Methods, 4th Edition. Pacific Grove, CA: Duxbury.
Ramsey, F. & Schafer, D. W. (2002). The Statistical Sleuth: A Course in Methods of Data Analysis, 2nd edition. Pacific Grove, CA: Duxbury.
Rossman, A. J., Chance, B. L. & Von Oeshen J. B. (2001). Workshop Statistics: Discovery with Data and the Graphing Calculator, 2nd edition. Emeryville, CA: Key College Publishing.
Spurrier, J. D. (2000). The Practice of Statistics - Putting the Pieces Together. Pacific Grove, CA: Duxbury.
Yates, D. S., Moore, D. S. & Starnes, D. S. (2003). The Practice of Statistics, 2nd edition. New York: W. H. Freeman and Company.
Periodicals:
Teaching Mathematics in the Middle School
The American Statistician
The Annals of Statistics
The Mathematics Teacher
Electronic Resources:
A. C. Nielson Company Public Access Database, found at http://tv.yahoo.com/nielsen/
American Statistical Association's Statistics In Sports, found at http://www.amstat.org/sections/sis/sports.html
Committee on the Undergraduate Program in Mathematics, Mathematics and the Mathematical Sciences in 2010: What Should Students Know?, found at http://www.maa.org/news/cupm_front.pdf
Committee on the Undergraduate Program in
Mathematics, Undergraduate Programs and Courses
in the Mathematical Sciences: CUPM
Curriculum Guide 2004, found at
http://www.maa.org/cupm/curr_guide.html
Directory of links to data sources, found at http://www.statistics.com/
National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, found at http://standards.nctm.org/
Statistical Resources on the Web, found at http://www.lib.umich.edu/govdocs/stats.html
U.S. Department of Labor Bureau of Labor Statistics, found at http://www.bls.gov/data/home.htm