Download A Course Syllabus - University of Central Missouri

A Course Syllabus
for
Math 4851
Probability and Statistics for Middle / High School Mathematics
(Three semester hours credit)
in the
Department of Mathematics and Computer Science
of the
COLLEGE OF SCIENCE AND TECHNOLOGY
Catalog description:
A course focusing on the concepts and methods of teaching probability and statistics in the
middle and high school mathematics program. Not available for graduate credit for
MS, Mathematics. Prerequisites: Math 4821 and Math 4822 or Math 1151.
UNIVERSITY OF CENTRAL MISSOURI
Warrensburg, Missouri
2008-2009
I.
Purpose of the Course
This three-hour course provides instruction on the content and methods of
teaching probability and statistics in secondary school mathematics. In recent
years there has been an increasing emphasis on the relevance of probability and
statistics for the middle grade and high school mathematics curriculum. Various
organizations, such as the National Council of Teachers of Mathematics, the
Mathematical Association of America, and the Missouri Mathematics Association
for the Advancement of Teacher Training, have recommended that probability and
statistics be given increased attention at both the middle and high school levels.
Preservice teachers will need adequate preparation to teach these topics to their
students. This course is designed to provide a background in the content of
probability and statistics for future middle grade and secondary mathematics
teachers. The course will use materials and activities suitable for the 6-12 level
and will attempt to help the pre-service teachers develop a rich understanding that
will enhance later teaching experiences. Specifically, the course is designed to:
A.
Provide a background in the content of probability and statistics for middle grade
and high school mathematics teachers.
B.
Provide students with opportunities to apply the basic concepts and techniques of
probability and statistics in a variety of problems and settings.
C.
Develop models of teaching which focus on the appropriate mathematical content,
relevant learning theories, and alternative teaching strategies for probability and
statistics.
II. Objectives and Desired Student Competencies
Upon completion of this course, the student should be able to:
A.
B.
C.
D.
E.
F.
G.
H.
I.
Collect, organize, and represent data using a variety of models and procedures.
Determine measures of central tendency, interpret their meaning, and select
appropriate measures for a given set of data.
Find standard deviation and apply it to normal distributions/area under the curve.
Describe and interpret randomness.
Use the basic rules of probability, simulations, and counting techniques to solve
various probability problems.
Determine theoretical probability where appropriate.
Describe relationships between sets of data using basic correlation and regression
terminology and procedures.
Use inferential statistics to test hypotheses relative to a single mean and the
difference between two means.
Compare and contrast theoretical and empirical probability and use a variety of
J.
K.
L.
M.
models and techniques to perform simulations.
Utilize an understanding of random variables and probability distributions to
model various problems and applications.
Describe sources of real data and other resources that would be useful in teaching
probability and statistics to middle grade and high school mathematics students.
Use a variety of computer software programs to represent data in tables and
graphs, to compute various statistical measures and tests, and to perform
probability simulations.
Use a graphing calculator to represent data in tables and graphs and to compute
various statistical measures.
III. Course Content Outline
Text: Elementary Statistics, A Step by Step Approach, 5th Edition, by A. Bluman,
McGraw-Hill Publisher, July 2004.
A variety of other resources will be used including:
Discrete Mathematics Across the Curriculum, NCTM 1991 Yearbook
Dealing with Data and Chance, NCTM
Data Analysis and Statistics. NCTM
Exploring Probability Quantitative Literacy Series. Dale Seymore
Exploring Data. Quantitative Literacy Series. Dale Seymore
Texts from NSF -funded new curricula for middle/high school
Thinking and Reasoning with Data and Chance. NCTM Yearbook.
A.
Introduction to Probability and Statistics
1. Theoretical and empirical probability
2. Simulation -using experiments and software
3. Fundamental elements in statistics
4. Uses and misuses of statistics
B.
Descriptive Statistics
1. Organizing and representing data- histograms, frequency polygons, stem and
leaf, box plots, scatter plots
2. Measures of central tendency: mean, median, mode,
3. Measures of dispersion: range, variance, standard deviation, percentiles,
standard scores
4. Correlation, regression, and curve fitting
C.
Probability and Probability models
1. Basics of probability-experiment, outcome, sample space, event, and
probability of an event.
2. Counting techniques-permutations, combinations
3. Rules of Probability - mutually exclusive events, conditional probability,
independent events, Bayes= theorem
4.
5.
Representations for probability experiments- tree diagrams, contingency
tables
Probability distributions- binomial, normal, normal approximations to
binomial.
D.
Probability Distributions Introduction to:
1. Discrete random variables and probability distribution functions
2. Continuous random variables and probability density functions
3. Binomial distribution, normal distribution, and normal approximation to
binomial distribution, chi square distribution
E.
Statistical Inference
1. Sampling and sampling distributions-random sampling, Central Limit
theorem
2. Introduction to estimation-estimating a population mean, confidence
intervals
3. Introduction to hypothesis testing
F.
Probability and Statistics in the 6-12 Mathematics Curriculum
1. Rationale for including probability and statistics
2. Objectives for the study of probability and statistics at grades 6-12
3. Role in curriculum reform effort-curricula from NSF funded materials for 612
IV. Grading and Evaluation
Student evaluation uses a criterion-referenced model of group and individual
assignments, regular examinations, and a final examination. The evaluation may
also include special projects, student presentations, or a portfolio of student work.
The grading scale will be:
100 - 90 % A
89 - 80% B
79 - 70% C
69 - 60 % D
below 60% F
A student enrolling in the course for graduate credit will be expected to complete
a project or a paper. The project would be a unit of study for use in his/her
classroom incorporating at least 3 different teaching strategies and include
complete lesson plans for at least one week with the unit assessments. A paper
would be a 5 - 6 page analysis of the probability and statistics strand in one of the
National Science Foundation endorsed curricula: SIMMS, CorePlus,
Mathematics: Modeling our World, or IMP (Integrated Mathematics Project).
TEACHER EDUCATION
1. Conceptual Framework information
Belief Statement
The Central educator is a competent, caring, reflective practitioner committed to the premise that
all can learn.
Mission
As a cornerstone of the institution for over 130 years, the University of Central Missouri's
Teacher Education Program develops teachers and other school professionals who are well
grounded in theory, display competence in content knowledge and instructional strategies, and
possess the dispositions to ensure success for all learners. The Teacher Education Program
prepares individuals as professional educators for an ever-changing, culturally diverse
population. Faculty and candidates provide support and service to schools in meeting their
present and future challenges by developing communities that learn through research and
scholarly activities. Educator preparation is a campus-wide responsibility, a commitment that
reflects the honor and worth of serving a vital profession.
2. Course Objectives - In your Course Objectives section, please include the MoSTEP and/or
content area standards and student outcomes that are covered in the course. This can be
accomplished by listing the objectives in your own words and citing the relevant standard, or by
including the entire standard as a course objective. For example:
Upon completion of the course, the student will be able to (a) describe four major philosophical
models of human behavior, (b) use a variety of strategies to record and graphically display
classroom behavior and social skills, (c) conduct a functional behavioral assessment, and (d)
select appropriate interventions to improve active engagement in learning, prosocial behavior,
and self-efficacy. (MoSTEP 1.2.6) or
MoSTEP 1.2.6 The preservice teacher uses an understanding of individual and group motivation
and behavior to create a learning environment that encourages positive social interaction, active
engagement in learning, and self-motivation.