Download Syllabus - College of Education

COLLEGE OF EDUCATION
DEPARTMENTAL COURSE SYLLABUS
The College of Education CAREs
The College of Education is dedicated to the ideals of Collaboration, Academic Excellence, Research, and
Ethics/Diversity. These are key tenets in the Conceptual Framework of the College of Education. Competence
in these ideals will provide candidates in educator preparation programs with skills, knowledge, and
dispositions to be successful in the schools of today and tomorrow. For more information on the Conceptual
Framework, visit: www.coedu.usf.edu/main/qualityassurance/ncate_visit_info_materials.html
1.
Course Prefix and Number: MAE 6137
2.
Course Title
Probability and Statistics for Middle Grades Teachers
3.
Regular Instructor(s)
Dr. Richard A. Austin
Dr. Helen Gerretson
Dr. Gladis Kersaint
Dr. Denisse R. Thompson
adjuncts credentialed by program faculty (Several faculty at Manatee Community
College have completed the Ph.D. in mathematics education at USF and will likely help
with the teaching of this course.)
4.
Course Prerequisites (if any)
Admission into the MAT in Middle Grades Mathematics or CI
5.
Course Description
This course examines in depth topics from probability and statistics appropriate for
middle grades mathematics teachers, including historical connections. Topics studied
include data collection and display, measures of central tendency and variability, use of
tree diagrams to find probabilities, independent and dependent events, combinations and
permutations, and sampling procedures. Teachers experience instructional approaches
appropriate for use in middle grades classrooms. This course is required in the MAT in
Middle Grades Mathematics. Prerequisite: Admission to the MAT program in middle
grades mathematics or CI.
6.
Course Objectives
Upon completion of this course, students will demonstrate the following:
1.
The ability to define probability and statistics;
2.
The ability to display data using a variety of graphical displays (bar, line, picture,
circle, scatterplot, box and whisker, stem and leaf);
Probability and Statistics
3.
4.
5.
6.
7.
8.
9.
The ability to identify measures of central tendency and situations in which they
are appropriate;
The ability to identify measures of variability and use such measures to interpret
results;
The ability to find probabilities of independent and dependent events and to use
tree diagrams to find probabilities;
The ability to find combinations or permutations as appropriate for the situation;
The ability to design an experiment or simulation, collect data, and interpret the
results;
The ability to discuss different sampling procedures, including the use of random
samples;
Knowledge of major historical developments in statistics and probability.
7.
Content Outline
Week 1. Displaying data: discrete and continuous data
(bar graphs vs. histograms, picture, circle, line graphs, stem and leaf plots)
Historical connections with statistics
Week 2. Measures of central tendency
Situations in which different measures are most appropriate
Week 3. Measures of variability
Box and whisker diagrams
Using central tendency, variability, and graphs to interpret results
Week 4. Definitions of probability
Historical connections to probability
Using tree diagrams to find probabilities
Week 5. Independent and dependent events
Week 6. Solving problems with probability
Week 7. MIDTERM
Week 8. Permutations and combinations
Week 9. Counting problems
Week 10. Designing experiments – sampling issues
Week 11. Random samples
Week 12. Hypothesis testing
Week 13. Further work with hypothesis testing
Week 14. Computer simulations
Week 15. Computer simulations
8.
Evaluation of Student Outcomes

Exams or tests will evaluate students' content knowledge on the major content topics
in the course. Students will have to pass the final, comprehensive exam in order to
pass the course. (CF #2)

Problem sets will evaluate students' ability to explore open and extended problems.
(CF #2)
Probability and Statistics
9.

Historical paper will give students an opportunity to explore the historical
background of a topic from statistics and/or probability. (CF #2 and #4)

External project will have students engage in a statistics or probability project of the
instructor's design or of their own approved design. (CF #2, #4 and #6)

A journal will provide on-going evaluation of students' facility with the content of the
course and emphasize the importance of writing throughout the curriculum. (CF #4)
Grading Criteria
Exams or Tests or Quizzes
Problem Sets and Journal
Historical Paper
External Project
50-55% of Grade
15-20% of Grade
10-15% of Grade
15-20% of Grade
The university's plus/minus system of grading will be used.
USF Policy on Religious Observances
"No student shall be compelled to attend class or sit for an examination at a day or time
prohibited by his or her religious belief. In accordance with the University policy on
observance of religious holy days, students are expected to notify their instructors if they
intend to be absent for a class or announced examination prior to the scheduled meeting."
10.
Required Textbooks
Sample text: The following units from the Connected Mathematics Project are possible
texts.
Data About Us
How Likely Is It?
What Do You Expect?
Clever Counting
(Glenda Lappan, James T. Fey, William M. Fitzgerald, Susan N. Friel, and Elizabeth
Difanis Phillips. Menlo Park, CA: Dale Seymour Publications, 1998.)
A packet of supplemental readings related to statistics and probability activities and/or
historical aspects of statistics and probability will also be used. Sample readings might
include the following:
Zawojewski, Judith S. and J. Michael Shaughnessy. "Mean and Median: Are They Really
So Easy?" Mathematics Teaching in the Middle School, 5 (March 2000): 436-440.
Norton, Robert M. "Determining Probabilities by Examining Underlying Structure."
Mathematics Teaching in the Middle School, 7 (October 2001): 78-82.
Probability and Statistics
Note: The actual text and readings will be selected at the time the course is offered in
order to permit the most current materials to be used. The above samples reflect the
nature of the materials intended for use to help teachers address the content of this course.
11(a) ADA Statement: Students with disabilities are responsible for registering with the
Office of Student Disabilities Services in order to receive special accommodations and
services. Please notify the instructor during the first week of classes if a reasonable
accommodation for a disability is needed for this course. A letter from the USF
Disability Services Office must accompany this request.
11(b). USF Policy on Religious Observances:
Students who anticipate the necessity of being absent from class due to the observation of
a major religious observance must provide notice of the date(s) to the instructor, in
writing, by the second class meeting.
Probability and Statistics
COLLEGE OF EDUCATION
DEPARTMENTAL COURSE SYLLABUS
Graduate Level Course
ATTACHMENT I
Please respond to each of the following questions and complete the attached Matrix:
1.
Rationale for Setting Goals and Objectives: What sources of information (e.g.,
research, best practices) support the formulation and selection of course goals and
objectives?
The aim of the course is to provide middle grades mathematics teachers with a solid
background related to the statistics and probability content they would be expected to
teach. The course will not only focus on providing a solid foundation in statistics and
probability but will approach that content from pedagogical perspectives that are
appropriate for use in a middle grades classroom. In this way, teachers experience
learning mathematics through the types of approaches they are expected to use when they
teach.
2.
What aspects of the COE conceptual framework is/are specifically addressed in this
course?


3.
USF prepares professionals who know the content they teach. USF education
candidates demonstrate an understanding of his/her subject field, its linkage to
other disciplines, and applications to real world, integrated settings.
USF professionals are reflective and analytical problem-solvers. USF education
candidates engage in continuous professional improvement for self and school
through a commitment to life-long learning.
List the specific competencies addressed from the relevant national guidelines.
National Council of Teachers of Mathematics
1.5.5 "use both descriptive and inferential statistics to analyze data, make
predictions, and make decisions;"
1.5.6 "interpret probability in real-world situations, construct sample spaces,
model and compare experimental probabilities with mathematical
expectations, use probability to make predictions;"
1.5.11 "use mathematical modeling to solve real-world problems;"
1.5.12 "use counting to enumerate and order; use matrices, finite graphs, and
trees to model problem situations; describe basic algorithms for
accomplishing tasks;"
1.6
"Programs prepare prospective teachers who have a knowledge of
historical development in mathematics that includes the contributions of
underrepresented groups and diverse cultures."
Probability and Statistics
4.
Are there field-based experiences in this course? If so, please briefly indicate nature
and duration.
No.
5.
a.
Is technology used in this course?
Students will be expected to have access to a graphing calculator throughout the duration
of the course. Graphing calculators have built-in functions that will be useful in exploring
statistics and probability functions studied in the course.
b.
Are students required to access and demonstrate use of technology in
instruction or record keeping in this course?
No.
6.
How are issues of diversity addressed in this course? Indicate which aspect of the
course (e.g., instructional strategies and/or experiences) provides the candidate the
opportunity to acquire and/or apply knowledge, skills and/or dispositions necessary
to help all students learn. ("All students" includes students with various learning
styles, students with exceptionalities and different ethnic, racial, gender, language,
religious, socioeconomic, and regional/geographic origins and achievement levels.)
A variety of instructional methods are used in the course to accommodate learning
environments with diverse kinds of students.
Students will explore historical connections to probability and statistics, including the
contributions made by diverse peoples and cultures. Students will be expected to
complete a historical paper related to some statistics or probability topic.
7.
(For initial certification programs)
a.
List the specific competences addressed from the Florida Adopted Subject
Matter Content Standards or the Florida Adopted Subject Area Competencies.
Knowledge of mathematics as problem solving (1-4)
Knowledge of mathematics as communication (1)
Knowledge of mathematics as reasoning (1)
Knowledge of mathematical connections (3)
Knowledge of statistics (1-5)
Knowledge of probability (1-5)
Probability and Statistics
b.
Describe any component of the course designed to prepare teacher
candidates to help PK-12 students achieve the Sunshine State Standards.
The Sunshine State Standards are drawn from the national content recommendations
from the National Council of Teachers of Mathematics. This course will address aspects
from Strand E on Data Analysis and Probability.
Probability and Statistics
Course Objectives
Matrix
Evidence of
Achievement
Accomplished
Practices
1.0 The ability to define probability and
statistics.
Exams
Journals
#8 Knowledge of
subject matter
2.0 The ability to display data using a
variety of graphical displays (bar, line,
picture, circle, scatterplot, box and
whisker, stem and leaf).
Exams
Problem sets
Project
#8 Knowledge of
subject matter
3.0 The ability to identify measures of
central tendency and situations in
which they are appropriate.
Exams
Problem sets
Journals
#8 Knowledge of
subject matter
4.0 The ability to identify measures of
variability and use such measures to
interpret results.
Exams
Problem sets
#8 Knowledge of
subject matter
5.0 The ability to find probabilities of
independent and dependent events and
to use tree diagrams to find
probabilities.
Exams
Problem sets
#8 Knowledge of
subject matter
6.0 The ability to find combinations or
permutations as appropriate for the
situation.
Exams
Problem sets
Journals
#8 Knowledge of
subject matter
7.0 The ability to design an experiment or
simulation, collect data, and interpret
the results.
Problem sets
Project
#8 Knowledge of
subject matter
8.0 The ability to discuss different
sampling procedures, including the use
of random samples.
Problem sets
Project
#8 Knowledge of
subject matter
9.0 Knowledge of major historical
developments in statistics and
probability.
Historical paper
#8 Knowledge of
subject matter
Probability and Statistics