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Modeling in Algebra for Teachers

Course Time/Location: Mondays & Wednesdays 3:00 pm – 4:25 pm, NOC 207 (3 semester hours)

Required Materials:
• Activity packet will be prepared for student purchase.
• A TI-83 or TI-84 graphing calculator is required.

Description: This course is designed for K-8 pre-service teachers and 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.

Prerequisite: Grade of C or above in MATH 2008

Purpose: 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

Instructional Methods: This course will develop a mathematical and pedagogical knowledge base that fosters the development of the pre-service 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 national standards such as the NCTM Principles and Standards (2000) and the MAA’s Mathematical Education of Teachers Document Draft (2000);
diverse learning styles; and multicultural components.

Course Content:
•  Variables and expressions (15%)
•  Equations and inequalities (20%)
•  Introduction to functions (15%)
•  Linear functions (15%)
•  Non-linear functions (15%)
•  Inverses and inverse functions (5%)
•  Systems of equations (5%)
•  Matrices (5%)
•  Rates of Change (5%)

Course Objectives: Students will be able to:
• Determine, extend, and generalize numerical and algebraic patterns and sequences,
• Construct graphical representations of algebraic patterns,
• Identify subsets of numbers and their relationship to each other
• Understand the special properties of zero and one,
• Recognize and use the commutative, associative, distributive , multiplicative identity, and multiplicative inverse properties,
• Use order of operations,
• Perform operations on and with integers,
• Translate verbal expressions into algebraic expressions/sentences and vice versa,
Represent real -world situations algebraically,
• Discuss and recognize the truth of algebraic sentences,
• Evaluate expressions, including those with absolute value,
• Add and subtract algebraic expressions,
• Understand properties of exponents , including zero, rational, negative, and scientific notation,
• Multiply algebraic expressions concretely and abstractly,
• Discover and recognize polynomials and the special products,
• Recognize patterns and special products in polynomials,
Factor polynomials concretely and abstractly,
• Apply algebraic operations to real-world problems,
• Apply the concept of proportional reasoning,
• Solve real-world problems using proportions,
Simplify algebraic rational expressions,
• Recognize and use Properties of Equality to solve equations in one variable,
• Apply properties of equality to solve for a given variable in a formula,
• Solve for a variable in terms of other variables,
• Identify and apply formulas for distance , Pythagorean Theorem, area, circumference, perimeter, interest, and slope,
• Represent and compare solutions of equations and inequalities on number lines,
• Use language and symbols of inequalities,
• Use properties of equality to solve and understand the behavior of special case equations such as absolute value and radical,
• Represent one- and two-variable data graphically using number lines, lists, tables, and scatter plots,
• Determine if data sets are functions,
• Represent discrete and continuous functions numerically, using mappings, symbolically, and graphically,
• Identify domain, range, intercepts, and zeros of functions,
• Determine the composition of two functions ,
• Apply the definition of slope,
• Determine average and instantaneous rates of change for constant , linear, and non-linear functions,
• Determine whether functions are increasing or decreasing,
• Determine the equation of a line using slope-intercept and point-slope formulas,
• Determine the equation of vertical, horizontal, parallel, and perpendicular lines,
• Graph absolute value, greatest integer, and piecewise-defined linear functions and inequalities using transformations,
• Fit lines to data using visual estimation and linear regression on the calculator,
• Solve quadratic equations and inequalities graphically and numerically,
• Solve quadratic equations and inequalities by factoring, completing the square, and the quadratic formula,
• Investigate the behavior of nonlinear functions including max/min, increasing/decreasing, and even and odd symmetry,
• Identify polynomial functions by type (constant, linear, quadratic, cubic, quartic, etc.),
• Determine the end behavior and roots of polynomial functions,
• Apply the Fundamental Theorem of Algebra,
• Determine the inverse of a function numerically, graphically, and symbolically,
• Represent situations using matrices,
• Apply matrix operations to simplify matrix expressions,
• Apply the methods of substitution, elimination, graphing, and matrices to solve systems of equations,
• Solve systems of inequalities by graphing,
• Select appropriate instructional technologies for gathering, describing, and analyzing data and making predictions,
• Develop a repertoire of mathematical representations to model and interpret physical, social, and mathematical phenomena,
• Explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or
representations,
• Formulate, represent, abstract, and generalize in situations within and outside mathematics,
• Apply a wide variety of strategies to solve problems and adapt the strategies to new situations, and
• Monitor and reflect on their mathematical thinking in solving problems

Technology: Using technology as a tool for learning and doing mathematics and for accessing instructional materials via the Internet is an important component of this course. A graphing calculator is mandatory with any version of the TI-83 and TI-84 models strongly suggested. Other technology will be used including 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 TI-InterActive! Students are expected to have an e-mail address either on or off campus.

Evaluation Methods: Student performance will be evaluated through the use of tests, a variety of in-class activities (including mathematical activities, discussions, and presentations), home work problems, and a final exam.
The standard grading scale (A = 90-100, B = 80-89, C = 70-79, D = 60-69, F = 0-59) will be used based on the following
percentages:

50% Exam average (3 exams will be given in addition to the final exam)
15% In-class activities and participation
15% Home work
20% Final Exam

Make-Up Work: If an assignment is take home, it will not be accepted after the due date. It is the student’s responsibility to check with the professor to determine if a take home assignment was given during an absence. If a student is absent on the day that an assignment is due, it is the student’s responsibility to make sure that the assignment is given to the professor by the due date. Make-up tests and assignments will not be allowed. If a student misses a test and has a valid, properly-documented reason, the final exam grade may count in place of that test score. There will be absolutely no make-ups allowed for the final exam, which will be given Wednesday April 22, 2009, from 3:30-5:30 pm.

Attendance Policy: Attendance each day in class is mandatory. If a student misses 5 or more class meetings without valid, extreme circumstances documented, he or she may be withdrawn from the class and assigned a grade of WF. If you must miss class for any reason, please notify me before the absence. If an emergency arises, please notify me as quickly as is reasonably possible. Tardiness is not acceptable. Students who show up to class several minutes late or leave early may be marked absent for the period.

Class evaluations: Class evaluations at NGCSU are now conducted on-line through Banner. Evaluation of the class is considered a component of the course and students will not be permitted to access their course grade until the evaluation has been completed. The evaluations will be accessible beginning one week prior to Final Exam week. Specific instructions will be made available when the surveys are activated.

Instructional Materials:
• Data Collection Activities for the Middle Grades with the TI-73, CBL, and CBR (Texas Instruments, 1998)
• Mathematics Activities for Teaching (Wheeler & Barnard, Kendall/Hunt Publishing Co, 2002)
• Hands-On Algebra! (Frances M. Thompson, The Center for Applied Research in Education, 2002)
• Math and Science in Motion: Activities for Middle School (Texas Instruments, 2000)
• Addenda Series Grades 5-8, Patterns and Functions (NCTM, 1991)

Library Resources:
• Mathematics Teaching in the Middle School (NCTM, February 1997)
• Discovering Algebra: An Investigative Approach (Murdock, Kamischke, & Kamischke, Key Curriculum Press, 2000)
• Addenda Series Grades 9-12, Algebra in a Technological World (NCTM, 1995)
• Addenda Series Grades 9-12, A Core Curriculum (NCTM, 1992)
• Women, Minorities and Persons with Disabilities in Science and Engineering: 1996 (National Science Foundation, 1997)
• High School Math Project, PBS Mathline, Focus on Algebra
• Hands-on Math! (Thompson, Center for Applied Research in Education, 1994)
• A Problem-Solving Approach to Mathematics for Elementary School Teachers (Billstein, Libeskind, & Lott, Addison-Wesley,
1997)
• Women And Science Celebrating Achievements Charting Challenges (National Science Foundation, 1997)
• Professional Standards for Teaching Mathematics (NCTM, 1991)
• Assessment Standards for School Mathematics (NCTM, 1995)
• Principles and Standards (NCTM, 2000)
• Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989)

General Expectations: The student is expected to abide by the university’s attendance policy and integrity code. Other general expectations may be given by the instructor.

Disabilities and Accommodations: North Georgia College and State University is committed to equal access to its programs,
services and activities for people with disabilities. If you believe that you have a disability requiring an accommodation,
reasonable prior notice needs to be given to the instructor and the Office of Student Disability Resources.

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