Department of Mathematics and Computer Science
Course Syllabus
Course
Number: MATH 6140
Course
Title: Probability and Statistics for Teachers
Class Times:
Instructor: Dr.
Dianna Spence
Office:
E-Mail: djspence@ngcsu.edu
Phone: (706) 864-1808
Office
Hours:
Text/Materials: MATH 6140 Resource Pack (purchase from
instructor)
Policies and Expectations
Evaluation
and Grading:
Student performance will be evaluated through
the use of class activities and assignments, homework, in-class presentations
and teaching demonstrations, a teaching portfolio, and a final exam. The final grade will be computed as follows.
Attendance
and Participation 10%
Daily Assignments 15%
Daily Quizzes 15%
Lesson Plan and
Presentation 20%
Probability Assignment
Portfolio 20%
Final Exam 20%
Letter grades are
assigned according to the following scale:
A 90 – 100%
B 80 – 89%
C 70 – 79%
D 60 – 69%
F 59% and below
Attendance: Attendance
is expected at all class sessions.
Students are expected to arrive on time and stay until class is
dismissed. Missing any part of class
will impair your ability to complete assignments satisfactorily and thereby
puts you at risk of failing the course.
You
are responsible for all material covered, all announcements made, and all
assignments given, whether or not you are present. Keeping up with these
items is your responsibility.
Missed work: Due to the intensive and fast-paced
nature of this class, daily quizzes and assignments are not accepted late and
may not be made up if they are missed. Daily assignments are due when
announced; assignments not submitted when collected will receive a grade of
zero. The lowest quiz score and the lowest daily assignment score will be
dropped to accommodate any extenuating circumstances that require you to miss
daily work. Project extensions and
rescheduling of exams are rare, but will be handled at the instructor’s
discretion in cases of extreme need.
Academic Integrity:
All work submitted is expected to be
your own. Students are expected to adhere to the Academic Integrity Policy for
the University: "On my honor, I
will not lie, cheat, steal, plagiarize, evade the
truth or tolerate those who do." Violations of the Academic
Integrity Policy will be reported to the Academic Integrity Council in an
incident report. Please refer the to NGCSU’s
Undergraduate Bulletin for additional details.
Academic
Disabilities:
General Course Information
Description: This
course is designed for elementary and middle grades pre-service and in-service
teachers and focuses on making decisions and predictions in the context of
solving real-world problems through the process of collecting, representing,
processing, summarizing, analyzing, and transforming data. Also included are a
portfolio project and a teaching demonstration component. This course may
not be used to fulfill the academic concentration requirement for graduate
secondary mathematics education students.
Prerequisites: Six hours of
college-level mathematics
Course Content and Resources
Purpose: As
one of four courses specifically developed for middle grades teachers who do
not have adequate college course preparation for teaching mathematics, this
course supports the philosophy that today’s mathematics teachers must be able
to nurture collaboration, critical thinking, hands-on exploration, appropriate
use of manipulatives, problem-based inquiry, incorporation of multiple forms of
technology, and activities that acknowledge multiple intelligences and learning
styles. The focus of this course is on providing rich opportunities to
synthesize and enact key concepts of probability and statistics. Exploring new
ideas; solving problems using multiple strategies, manipulatives, graphing
calculators, software, and other available technologies; and interpreting
solutions, reasonableness of answers, and efficiency of various methods form
the foundation for increasing the practicing teacher’s ability to bring
students of diverse backgrounds to high levels of achievement.
Course
Content:
¨
Experimental and
theoretical probability (20%)
¨
Simulations (15%)
¨
Random variable
(5%)
¨
Discrete
probability distributions (5%)
¨
Inferences, data
displays, data interpretation, and predictions (20%)
¨
Sampling and
experiment design (10%)
¨
Data
transformations and measures of central tendency, position, variability,
correlation (20%)
¨
Applications of
Probabilistic and Statistical Models (5%)
Course
Objectives:
Students
will be able to:
1)
use experimental
or theoretical probability to represent and solve problems involving
uncertainty,
2)
select
appropriate counting techniques and calculate possible outcomes,
3)
model situations
by devising and carrying out experiments or simulations to determine
probabilities,
4)
model situations
by constructing a sample space to determine probabilities,
5)
compare experimental
results with mathematical expectations,
6)
make predictions
that are based on experimental or theoretical probabilities,
7)
conduct a
compound experiment and analyze the results,
8)
apply
probabilistic models to real-life situations,
9)
explore the
concepts of chance,
10)
calculate odds
and relate them to probability,
11)
create and
interpret discrete probability distributions,
12)
apply the concept
of a random variable to generate and interpret probability distributions,
13)
explore and use a
variety of data collection methods,
14)
formulate and
solve problems that involve collecting and analyzing data,
15)
construct and
interpret data displays such as scatter plots, box and whisker plots, circle
graphs, histograms, bar graphs, stem and leaf plots, line plots, line graphs,
pictographs, and frequency distributions that summarize real-world data,
16)
make inferences
and convincing arguments from data analysis,
17)
evaluate
arguments that are based on data analysis,
18)
use curve fitting
to predict from data,
19)
select and apply
measures of central tendency, position, variability, and correlation,
20)
determine
appropriate sampling techniques,
21)
design, conduct,
and interpret surveys/experiments related to real-world problems and
communicate the outcomes,
22)
make predictions
and draw conclusions based on data displays,
23)
select
appropriate instructional technologies for gathering, describing, and analyzing
data and making predictions,
24)
hypothesize
outcomes of experiments,
25)
recognize the
appropriate or inappropriate use of statistics,
26)
identify, locate,
and explore resources for real-world data,
27)
use statistics to
persuade an audience,
28)
demonstrate the
use of a variety of instructional strategies and methods for teaching
mathematics in grades 7-12,
29)
demonstrate
flexibility in adapting instruction necessitated by students’ performance,
special needs, and learning styles,
30)
complete an
individual special project related to the application of modeling techniques,
and
31)
conduct
an in-class lesson addressing one topic from the course or an advanced topic
directly related to the special project.
Instructional Methods:
This course will develop a
mathematical and pedagogical knowledge base that fosters the development of the
practicing teacher as a facilitator, decision maker, and leader through the use
of a variety of:
·
instructional
strategies and methods including lecture, guided discussion, modeling,
simulations, cooperative and collaborative learning groups, student
presentations, and hands-on activities that actively engage students in the learning
process; and
·
instructional
materials, assessment techniques, and scoring rubrics that reflect the spirit
of the NCTM Principles and Standards
(2000) and the National Board for Professional Teaching
Standards (1998); diverse learning
styles; multiple intelligences; and multicultural components
Using technology as a tool for learning and doing
mathematics and for accessing statistical data and instructional materials via the
Internet is an important component of this course. Suggested tools include
graphing calculators such as the TI-73 and TI-83 Plus; data collection devices
such as the Calculator-Based Ranger (CBR) with a built-in motion detector and
the Calculator-Based Laboratory (CBL) with temperature probes, pressure probes,
and microphones; and software such as Fathom and TI-InterActive!
§
Data in Depth – Exploring Mathematics with Fathom (Key Curriculum Press, 2000)
§
Workshop Statistics Series (Key Curriculum Press, 1995)
§
Probability
Activities for Problem Solving and Skills Reinforcement, R. Lovell, Key Curriculum Press, 1993
§
Quantitative
Literacy Series (Landwehr,
Watkins, Gnanadesikan, Newman, Obremski,
Scheaffer, and Swift, Dale Seymour Publications,
1986)
§
Teaching Children
Mathematics (NCTM)
§
Mathematics Teaching in the Middle School (NCTM)
§
Principles and Standards for School Mathematics (NCTM, 2000)
§
Professional Standards for Teaching Mathematics (NCTM, 1991)
§
Assessment Standards for School Mathematics (NCTM, 1995)
§
Addenda Series Grades K-6 (NCTM)
§
Addenda Series Grades 5-8 (NCTM)
§
Addenda Series Grades 9-12 (NCTM)
§
Data Collection Activities for the Middle Grades with
the TI-73, CBL and CBR (Texas
Instruments, 1998)
§
Women, Minorities and Persons with Disabilities in
Science and Engineering: 1996 (National Science Foundation,
1997)
§
Women And Science Celebrating Achievements Charting
Challenges (National Science
Foundation, 1997)
§
Mathematics
Activities for Teaching, Wheeler and
Barnard, Kendall-Hunt Publishers, 2000
World Wide Web Resources:
Metacognitive Model & Teacher Education Program Competencies:
The NGCSU Graduate Mathematics Education Program prepares teachers to
assume within the school community the roles of Decision-Maker, Facilitator,
and Leader as identified in the metacognitive model. Twelve Teacher Education Program competencies
reflecting the model are aligned to a specific role. Overlap into more than one role and
mathematics course may occur. Current
research and professional standards identify these competencies as important
for effective teaching (NBPTS and ASCD Framework).
|
Decision-Maker |
Facilitator |
Leader |
|
Assessment |
Individual Differences |
Ethical Perspectives |
|
Planning |
Subject Matter Knowledge |
Reflection/Metacognition |
|
Problem Solver |
Communication |
Professional Leadership |
|
Methods, Materials, Resources |
Classroom Management |
Research & Evaluation |