Course Syllabus
Math 3116 (CRN 932)
Modeling in Algebra for Teachers
This course meets on Mondays, Wednesdays & Fridays
in Room 209 from 1:00 - 1:50
Click here for the List of Assignments
Syllabus: | Description
| Content
& Objectives | Required
Materials | Policies,
etc.| Helpful Links |
Prerequisites
for Math 3116 Six hours of college-level mathematics
(including Elementary Statistics) and at least junior standing.
It is strongly suggested that students have completed the course
MATH 3100 - Number Systems.
Description This
course designed for elementary and middle grades pre-service teachers
focuses on variables, expressions, equations, inequalities, systems
of equations, matrices, and linear, non-linear, and inverse functions.
Emphasis is on problem solving, active learning, appropriate communication,
substantive connections, technology utilization, and multiple
representations of algebraic structures. This course may not be
used to fulfill the academic concentration requirement for mathematics
or secondary mathematics education students.
Course Content
and Objectives Students in
Math 3116 will have the opportunity to...
Patterns
- Model and solve contextualized
problems using various representations, such as graphs, tables,
and equations
- Recognize, investigate, analyze,
extend, and generalize numeric patterns
- Formulate a rule for a pattern
- Understand the concept of variable
- Evaluate expressions and solve
equations (single and multi-variable)
- Explore the concept of linear
combinations
- Explore problems associated
with converging and diverging sequences and series, including
arithmetic, geometric, recursive, infinite, and the Fibonacci
sequence
- Investigate patterns related
to Pascal's Triangle
- Consider patterns and relationships
associated with square and triangular numbers
Functions
and Equations
- Represent the concept of function
verbally, numerically, symbolically, and graphically
- Apply algebraic ideas such as
the Pythagorean Theorem and trigonometry to geometric problems
- Understand linear function concepts,
such as slope and intercepts
- Formulate the equation of a
line in various forms
- Study quadratic functions and
parabolic graphs
- Investigate tangent lines and
their equations
- Solve a system of equations
- Solve problems associated with
linear inequalities
- Generalize the effects of a
graph as the coefficients of its equation are modified
- Find the roots of a function
algebraically and graphically
- Determine the minimum and maximum
values of nonlinear functions
- Explore converging and diverging
end behavior of a function
- Solve equations graphically
by considering intersecting functions
- Solve equations numerically
and symbolically
- Translate verbal expressions
into algebraic expressions/sentences and vice versa
Graphing
- Investigate quadratic functions
and properties of parabolas
- Analyze the slopes of parallel
and perpendicular lines
- Solve for an equation graphically
- Find the equation of a circle
centered at the origin or entered at the coordinate (h,k)
- Transform a graph by modifying
its equation
- Use and apply the distance formula
Required
Textbooks and Resources
Texts
Title: Navigating through Algebra PreKindergarten-2 Grades (with CD-ROM)
Publisher: NCTM (National Council of Teachers of Mathematics)
ISBN Number: 0-87353-499-9
Title: Navigating through Algebra Grades 3-5 (with CD-ROM)
Publisher: NCTM (National Council of Teachers of Mathematics)
ISBN Number: 0-87353-500-6
Title: Navigating through Algebra Grades 6-8 (with CD-ROM)
Publisher: NCTM (National Council of Teachers of Mathematics)
ISBN Number: 0-87353-501-4
Title: Principles and Standards for School Mathematics (with CD-ROM)
Authors: National Council of Teachers of Mathematics
Publisher: NCTM
You may purchase the book or use the online version at http://www.nctm.org
Software
Geometers' Sketchpad Student Edition which may be purchased for $39.95 at
http://www.keymath.com/STORE/software/gsp.html. GSP is also available in all
of the computer labs on the North Georgia Campus
You need to have access to Microsoft Excel - or a spreadsheet package that will
graph data and calculate regression equations.
Other
Materials
You will need
to purchase a pad of square-grid graph paper.If you have a graphing
calculator, please bring it to class when requested. If you are
considering purchasing a graphing calculator, I suggest a TI-83.
However, you are not required to have a graphing calculator for
this course.
Assignments Weekly assignments will be discussed in
class and posted on the course webpage. Below is an overview of
the projected types of assignments and corresponding points. This
is just an approximation. I firmly believe that students' interests,
questions, concerns, etc... should be a significant part of any
course planning. Thus, I reserve the right to make changes as
we go.
|
Type
of Assignment |
Brief Description |
Approximate
Number of Points |
|
Journal |
Weekly prompts will be posted |
10 pts each |
|
Mathematical Activities |
Weekly write-ups and/or presentations
of in-class activities |
10 pts each |
|
Problem Solving
(InterMath Website)
http://www.intermath-uga.gatech.edu
|
From a given list, you will select
and solve a set number of problems related to the weekly topic
and class activities. We will discuss these problems andyour
solutions in class. |
10 pts each |
|
Quizzes |
Periodic announced quizzes - approximately
6-8 quizzes this semester |
30 ~ 50 pts each |
|
Mid-term Exam |
To be discussed |
100 pts |
|
Final Exam |
Tuesday, May 6th, 5:00 - 7:00pm |
150 pts |
|
Miscellaneous Assignments |
readings, discussions, observations,
etc... |
~50 pts total |
Grades
Course Grade will
be assigned base on the percentage of total possible points a
student earns during the semester.
A =
90 % or higher
B =
80 - 89 %
C =
70 - 79%
D =
60 - 69%
F =
Below 60%
Time Outside
of Class
You can not expect to
accomplish what you should from this course without spending time
with the material outside of class. The usual expectation of 2
hours study outside of class for every hour in class is a minimum.
Please communicate with me as soon as possible if you are having
trouble managing time - I want to help you get the most out of
this course that you can.
Attendance Policy As
part of being a professional teacher, regular participation in
course activities and on-time completion of assignments is expected.
If you are ill, please call and leave me a message letting me
know that you will be missing class - prior to that class meeting.
If there is a date that you know you will be absent due to personal
reasons, please let me know that in advance. Not only is this
professional behavior, it also helps me help you. I will be able
to let you know in advance what you will be missing and I can
ask someone in the class to allow me to copy notes for you. Please
note that according to the policies of North Georgia College &
State University, students that miss more than 14% of the scheduled
classes may be dropped from the course (see p. 59 of the Undergraduate
Bulletin).
Academic Integrity The
integrity code will be upheld in this course. The NGCSU catalog
states:
North
Georgia College & State University is dedicated to providing
an educational climate characterized by integrity. Academic integrity,
in particular, must be the cornerstone of an institution of higher
learning and must pervade all segments of the NGCSU community.
Furthermore, academic integrity is the mutual responsibility of
the various constituencies (students, faculty, staff, and administration)
which comprise the university. The integrity code, "On my
honor, I will not lie, cheat, steal, plagiarize, evade the truth
or tolerate those who do," reflects NGCSU's commitment to
academic integrity.
Course
Purpose and Rationale
This course reflects
the recommendations of the MAA's Mathematical Education of Teachers
Document and the Georgia P-16 Council's Plan for Having a Qualified
Teacher in Every Public School Classroom by 2006. Both documents
support the philosophy that today's mathematics teachers must
possess an in-depth understanding of the mathematics they will
teach; be able to nurture collaboration, critical thinking, hands-on
exploration, and problem-based inquiry; facilitate the appropriate
use of manipulatives, multiple forms of technology, and activities
that acknowledge multiple intelligences and learning styles. The
intent and focus of this course is not an exhaustive exercise
in symbol manipulation. Opportunities for exploring new ideas;
solving problems using multiple strategies, manipulatives, graphing
calculators and other available technologies; and interpreting
solutions, reasonableness of answers, and efficiency of various
methods form the foundation for increasing the pre-service teacher's
ability to bring students of diverse backgrounds to high levels
of achievement.
Metacognitive Model & Teacher Education Program Competencies The
NGCSU 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 |
