MATH 7523 – Probability and Statistics for Inservice Teachers

Spring 2007

Dr. Janie Cates

jcates@westga.edu

 

Purpose: PSC Standards –2 ix, x, xi, 3, 4, 5, 6, 7, 8 v, viii, 9, 10, 11, 12, and 13

This course focuses on preparing P-5 mathematics specialist candidates to:

a)     Make decisions and predictions through collecting, representing, processing, summarizing, analyzing, and transforming data taken from real-world scenarios.

b)     Solve problems using multiple strategies, manipulatives, and technological tools; interpret solutions; and determine reasonableness of answers and efficiency of methods.

c)     Nurture collaboration, critical thinking, hands-on exploration, manipulative use, problem-based inquiry, technology utilization, and activity implementation addressing various learning styles and multiple intelligences.

d)     Select and use a variety of formative and summative assessment techniques to monitor student progress, gauge students’ mathematical understanding, and interpret school-based progress.

 

Learning Outcomes: PSC Standards – 2 ix, x, xi, 3, 4, 5, 6, 7, 8 viii, 9, 10, 11, 13

All students will learn to:

1)     Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

2)     Select and use appropriate statistical methods to analyze data.

3)     Develop and evaluate inferences and predictions that are based on data.

4)     Understand and apply basic concepts of probability.

5)     Demonstrate a deep understanding of how P-5 students learn mathematics and of the pedagogical content knowledge appropriate to P-5 mathematics teaching.

 

Course Objectives: PSC Standards – 2 ix, x, xi, 5, 7, 8 v, viii    

All students will be able to:

Content Objectives

1)     Identify, locate, and explore resources for real-world data.

2)     Formulate and solve problems that involve data collection and analysis.

3)     Design, conduct, and interpret surveys/experiments using appropriate sampling techniques.

4)     Select appropriate instructional technologies for gathering, describing, and analyzing data

5)     Recognize the appropriate or inappropriate use of statistics.

6)     Construct, read, and interpret displays of data such as scatter plots, box plots, line graphs, circle graphs, histograms, bar charts, stem and leaf plots, pictographs, and frequency distributions.

7)     Make predictions and draw conclusions based on data displays.

8)     Use appropriate tools to select, justify, calculate, and apply an appropriate measure of center (mean, median, and mode), dispersion (standard deviation, range and interquartile range), position (quartiles, percentiles, deciles and median), and regression equations (linear, quadratic, and logistic) to describe a set of data.

9)     Interpret correlation and use curve fitting to make predictions from data.

10)  Make inferences and evaluate arguments from data analysis.

11)  Determine probability of a given event (equally likely, least likely, most likely, likely, and not likely).

12)  Explore concepts of fairness, uncertainty, and chance.

13)  Identify possible outcomes of simple experiments and predict, describe, and calculate the probability of a given event expressed as a rational number from 0 through 1.

14)  Compute probabilities for simple compound events using such methods as organized lists, sample spaces, counting techniques (including Pascal’s triangle), tree diagrams, and area models.

15)  Calculate odds and relate them to probability.

16)  Explore the relationship between experimental and theoretical probability

17)  Model situations by devising and carrying out experiments or simulations (using manipulatives and technology) to determine probabilities.

18)  Apply probability in practical, real-life settings.

19)  Make predictions that are based on experimental or theoretical probabilities.

20)  Become aware of common misconceptions (percentile versus percentage) and errors in probability and statistics.

21)  Create and interpret discrete and normal probability distributions.

22)  Apply the concept of a random variable to generate and interpret probability distributions

23)  Select and utilize appropriate measurement units, techniques, and tools in collecting and analyzing data.

24)  Use the language of mathematics to formulate accurate, precise, and pedagogically appropriate definitions of terms related to data analysis and probability.

 

Pedagogy and Professional Development Objectives

1)     Select and use appropriate concrete materials and technological tools for learning mathematics

2)     Select, use, and determine the suitability of the wide variety of available mathematics curricula and teaching materials.

3)     Recognize the role of national, state, and local level mathematics standards and legislation in developing local curriculum and planning instruction that addresses the needs of diverse student populations.

4)     Demonstrate knowledge of different types of mathematical instructional strategies.

5)     Use multiple strategies to assess students’ mathematical knowledge.

6)     Identify professional mathematics organizations and describe their contributions to the teaching of mathematics and the professional development of teachers.

 

Evaluation Methods: PSC Standards – 2 ix, x, xi, 3, 4, 5, 6, 7, 8 v, viii, 9, 10, 11, 12, and 13

Student performance will be evaluated through the use of varied assessments including projects, in-class presentations, tests, reflective logs, peer and self-assessment, content and pedagogical proficiency demonstrations, and a teaching/instructional unit. The Instructional Unit is to serve as the culminating assessment and to address best practices for mathematics at the elementary level and PSC Standards 2 ix, x, xi, 4, 5, 6, 9, 10, 11, and 12 for the Early Childhood endorsement.

 

Assignments: All assignments, with the exception of the partner projects, are individual assignments and must be in a typed, double-spaced format with Times/Times New Roman font, size 12, and 1-inch margins unless otherwise indicated. Assignments are due at the BEGINNING OF CLASS on the designated date. Failure to meet deadlines and/or follow directions will result in a grade reduction of at least 10% per assignment. Technical/computer problems are not an acceptable excuse for a late assignment. Rubrics are provided for each assignment and must be turned in with the corresponding assignment. Assignments submitted without the rubric will counted as late submissions. If you are absent, it is your responsibility to get any missed work and turn in any assignments that are due. An absence DOES NOT change an assignment’s due date. Remember: Assignments are not negotiable, however, due dates are. Contact the instructor to make arrangements if necessary BEFORE the assignment is due.

 

1.        Presentations – Select 2 activities to present to the class – one on Probability and one on     Data Analysis. You will have 15-20 minutes for your presentation.

Sources of Problems and Activities – Data Analysis, Probability, and Statistics

• NCTM Illuminations - http://illuminations.nctm.org/
• NCTM E-Examples - http://standards.nctm.org/document/eexamples/index.htm

• Intermath – http://www.intermath-uga.gatech.edu/
• TEAMS Mathematics Resources - http://teams.lacoe.edu/documentation/places/math/probability.html
• Ask Dr. Math - http://mathforum.org/library/drmath/sets/high_probability.html
• Guessing Correlations - http://www.stat.uiuc.edu/~stat100/java/GCApplet/GCAppletFrame.html
• K-12 Statistics - http://www.mste.uiuc.edu/stat/stat.html
• Regression Applet - http://www.stat.sc.edu/~west/javahtml/Regression.html
• JAVA Applets - http://www.stat.duke.edu/sites/java.html
• Marilyn is Wrong - http://www.wiskit.com/marilyn.html
• Math Tools for Data Analysis - http://mathforum.org/mathtools/cell.html?tp=9.16&id=440&new_tp=9.15
• Permutations and Combinations - http://forum.swarthmore.edu/dr.math/faq/faq.comb.perm.html
• Probability and Statistics - http://forum.swarthmore.edu/probstat/probstat.html
• Exploring Data - http://forum.swarthmore.edu/workshops/usi/dataproject/index.html
• Java Demonstrations for Probability and Statistics - http://www.math.csusb.edu/faculty/stanton/m262/probstat.html
• Take a Chance! - Probability and Statistics for Elementary Teachers - http://www.richmond.edu/~pstohrhu/syllabi/probstat/

 

Sources of Problems and Activities - Probability

• Math Tools - http://mathforum.org/mathtools/cell.html?tp=9.1&id=440&new_tp=9.16
• The Probability Web - http://www.mathcs.carleton.edu/probweb/probweb.html
• Probability Puzzles - http://einstein.et.tudelft.nl/~arlet/puzzles/probability.html
• Conditional Probability and Probability of Simultaneous Events - http://www.shodor.org/interactivate/lessons/pm4.html
• Adventures in Maths - http://www.cut-the-knot.com/probability.html
• AIDS Testing and Probability - http://www.imsa.edu/edu/math/journal/volume3/webver/aidstest.html
• Let’s Make a Deal - http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html
• Monty Hall Simulation - http://cuwu.editthispage.com/stories/storyReader$144
• Let’s Make a Puzzler – Monty Hall Puzzler Proof – www.cartalk.cars.com/About/Monty/
• Rock, Paper, Scissors - http://www.col-ed.org/cur/math/math15.txt
• Introduction to Probability - http://forum.swarthmore.edu/dr.math/faq/faq.prob.intro.html
• Probability by Surprise - http://www-stat.stanford.edu/%7Esusan/surprise/

 

Sources of Problems and Activities – Statistics

·      Berrie’s Statistics Page - http://huizen.dds.nl/~berrie/ (QuickTime movies and java applets)

• Workshop Statistics: Discovery with Data and the Graphing Calculator - http://www.keycollege.com/workshopstatistics/vonoehse/guide.html
• Web Resources for Teaching Statistics - http://it.stlawu.edu/~rlock/tise98/

 

2.        Partner Project – Create a vertical progression for your grade level’s (K-2, 3-5 or 6-8)

           Mathematics GPS Probability and Data Analysis Strand. How do these align with NCTM’s            goals for grades K-2, 3-5, and 6-8?

 

3.        Glossary – Develop a glossary throughout the course. Words can be found in the      margins of      your text. You may also add your own words. Each word should be on a separate page. For    each word, complete a Frayer model – see sample. (Examples should include picture      representations if appropriate.)

 

4.        Field Assignments – You will have 3 field assignments to complete outside of class. More details to follow.

 

5.        Journal Entries – You will have 8 Probability/Data Analysis journal “prompts” to respond           to in your reflective journal. Begin each entry on a new page.

 

6.       Probability & Statistics Unit – Develop a 5-10 day teaching unit addressing one or more   data analysis and probability concepts or objectives.

 

           The teaching unit must include the following:

1.    Historical perspectives, including contributions of underrepresented groups and diverse cultures.

2.    Strategies addressing diversity (gender, ethnicity, learning styles, etc.) to support full participation by all students.

3.    Appropriate use of technology, print and electronic resources, and manipulative and visual materials.

4.    Interdisciplinary activities and problem solving.

5.    Effective uses of student groupings such as peer teaching and collaborative grouping.

6.    Varied instructional strategies based on current research and local, state, and national standards.

7.    Formative and summative assessments to determine student achievement.

 

The unit must follow the following format:

Title Page

Table of Contents

Unit Overview

Grade Level

Description of Topic and Historical Perspectives

Prerequisite Knowledge

NCTM Standards Addressed

GPS Objectives Addressed

Daily Lesson Plans

Alternative Assessments (at least 3)

Parent Letter

Unit lesson plans must include the following information:

Lesson Title

NCTM Standards and GPS Objectives

Student Performance Objectives

Materials

Key Vocabulary

Activity Description

Assessment Method

7.        Tests – There will be two tests this semester covering the topics discussed in class.

 

Grading

 

Final grades will be distributed according to the following scale:

A	=	540 < x < 600
B	=	480 < x < 540
C	=	420 < x < 480
F	=	x < 420

 

Class Outline (Tentative)