North Georgia College & State University

Department of Mathematics and Computer Science

Course Syllabus

Fall 2009

 

 

General Information

 

Course Number:             MAED 4201

Course Title:                   Mathematics Education Seminar

Credit Hours:                  3 semester hours

Class Times:                   MWF  1:25 – 2:20 p.m.

Withdrawal Deadline:      Tuesday, October 13

Instructor:

Dr. Dianna J. Spence

Newton Oakes Center 213

E-Mail: djspence@ngcsu.edu  

Phone:  (706) 864-1808

 

Office Hours:

MWF   9:00 – 11:00 a.m. 

 

 

Text/Materials:               Materials provided by the instructor as needed; TI-83/84 calculator and PC/Internet access are required.

 

Policies and Expectations

 

Academic Integrity:

                        All work submitted for credit 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 to NGCSU’s Undergraduate Bulletin for additional details.

 

Withdrawals:   You may withdraw with a grade of “W” any time on or before the withdrawal deadline.

 

Attendance:    Attendance is required.  Any student accruing absences for more than 14% of the scheduled class meetings (6 absences) will be dropped with a WF.   

Excused absences:

For an absence to be excused, you must provide documentation of a valid extenuating circumstance (e.g., illness, death in the family, traffic accident, etc.) If this documentation is not provided, the absence is considered unexcused.  Whether or not an absence is excused will govern how missed assignments are handled, as outlined below in “Missed Work”. 

Tardiness and/or early departures:

Students are expected to arrive on time and stay until class is dismissed.

If you miss part of a class, you will be charged with a partial absence.  Each 5 minutes of class time is worth approximately 10% of your attendance for the day.

Missed work:  Missed work will be handled as noted in the following grid, depending on whether the work was missed due to excused or unexcused absence.  Note that all in-class activities, if missed, may not be made up under any circumstances.  Excused absences only allow for more lenient grading of missed work. 

 

Type of work

Unexcused Absence

Excused Absence

Participation/class work

Grade of zero is assigned

Missed grade is not counted in average

Homework due

See late work policy below

Full credit if submitted by next class; otherwise see late work policy below.

 

Late work:       Homework and assignments completed outside of class are due at the beginning of class on the designated due date unless otherwise specified. Assignments turned in late will be penalized 25% per day (see table below). In-class assignments are not accepted late.

 

Time of submission

Highest possible score

By beginning of class on due date

100%

By 11:00 p.m. on due date

90%

By 11:00 p.m. one day late

75%

By 11:00 p.m. two days late

50%

By 11:00 p.m. three days late

25%

More than three days late

Assignment not accepted; grade is zero.

 

Evaluation and Grading:

                        Student performance will be evaluated through class participation, in-class activities, and a course portfolio.  The course portfolio includes multiple entries in seven content areas.  The portfolio is considered a gateway assessment:  To pass the course, minimal performance on all components and an overall score of C or better on the course portfolio is required. The student’s overall grade will be computed as follows.

                        Attendance/Participation                        10%

                        Assignments/Activities                           20%

                        Course Portfolio                                    70%

 

                        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

 

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.

 

Course Content and Resources

Description:    This capstone course focuses on assisting pre-service secondary mathematics teachers to make insightful connections between advanced mathematics courses and the high school mathematics they will be teaching while contributing to their mathematical understanding and pedagogical skills.

 

Course Content:        

  • Instructional design, strategies, methods, materials, and activities appropriate for teaching mathematics in grades 7-12
  • Mathematics manipulatives and instructional technology for developing middle grades and secondary mathematics concepts
  • Formative and summative assessment techniques for mathematics instruction in grades 7-12
  • Application of knowledge gained from observing and assisting a cooperating teacher in a public school setting
  • Reflection on mathematics teaching practices

 

Course Objectives:    

Students will be able to:

  • demonstrate understanding of the properties of the natural, integer, rational, real, and complex number systems;
  • understand the ways that basic ideas of number theory and algebraic structures underlie rules for operations on expressions, equations, and inequalities;
  • demonstrate understanding and skill in using algebraic reasoning to model and solve problems from number theory, geometry, discrete mathematics, and statistics that reflect real-world situations;
  • demonstrate explicitly how the number and algebraic operations of secondary school can be explained by more general principles;
  • trace the development of key number and algebraic ideas from early secondary school through contemporary applications;
  • demonstrate mastery of core concepts and principles of Euclidean geometry in the plane and space and applications such as tiling, fractals, computer graphics, robotics, and visualization;
  • understand the nature of axiomatic reasoning and the role that it has played in the development of mathematics and facility with proof;
  • demonstrate facility with a variety of methods and associated concepts and representations, including transformations, coordinates, and vectors;
  • understand trigonometry from a geometric perspective;
  • apply the major concepts of abstract algebra to justify algebraic operations and formally analyze algebraic structures;
  • examine trigonometric and closely related geometry ideas including the laws of sines and cosines, identities, the Pythagorean Theorem, similarity, and the interplay of exploration and proof;
  • revisit elementary functions of high school mathematics from an advanced standpoint;
  • examine conceptual difficulties in learning mathematics concepts;
  • identify functions associated with relationships such as f(xy) = f(x) + f(y) or f’(x) = kf(x) or f(x+k) = f(x);
  • recognize patterns in modeled data, equations, and formulas associated with each important class of functions and the way that parameters in these representations determine particular cases;
  • translate information from one representation (tables, graphs, or formulas) to another;
  • use functions to solve problems in calculus, linear algebra, geometry, statistics, trigonometry, and discrete mathematics;
  • explore data using a variety of standard techniques for organizing and displaying data in order to detect patterns and departures from patterns;
  • identify misuses of statistics and invalid conclusions from probability;
  • draw conclusions involving uncertainty by using hands-on and computer-based simulation for estimating probabilities and gathering data to make inferences and conclusions;
  • use appropriate methods such as random sampling or random assignment of treatments to estimate population characteristics, test conjectured relationships among variables, and analyze data;
  • determine and interpret confidence intervals;
  • anticipate patterns using theory and simulations to study probability distributions and apply them as models of real phenomena;
  • use probability models to draw conclusions from data and measure the uncertainty of those conclusions;
  • understand basic concepts of probability such as conditional probability and independence, and develop skill in calculating probabilities associated with those concepts;
  • apply discrete structures (sets, logic, relations, and functions) and their applications in the design of data structures and programming;
  • demonstrate knowledge of basic elements of discrete mathematics such as graph theory, recurrence relations, finite difference approaches, linear programming, and combinatorics;
  • apply the fundamental ideas of discrete mathematics in the formulation and solution of problems arising from real-world situations;
  • design and analyze algorithms, including the use of recursion and combinatorics;
  • utilize varied informal and formal assessment techniques for evaluating students’ mathematical understanding;
  • make and investigate mathematical conjectures;
  • use representations to model and interpret physical, social, and mathematical phenomena;
  • build new mathematical knowledge through problem solving;
  • monitor and reflect on the process of mathematical problem solving;
  • use graphing calculators, computer algebra systems, spreadsheets, and programming to explore mathematical ideas and to solve problems related to discrete structures and algorithms, calculus, geometry, probability, statistics, number, and algebra;
  • apply appropriate techniques, tools, and formulas to determine measurements and their application in a variety of contexts; and
  • complete error analysis through determining the reliability of the numbers obtained from measurement.

 

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 methods that are determined by the instructor. These methods may include, but are not limited to lecture; problem-solving sessions with informal assessment by the student or instructor; discussion; projects; computer, calculator, or web-based explorations; and student presentations.  Students will be encouraged to assess and monitor their own problem-solving process to determine when an error has been made or a new strategy should be used.

 

Bibliography and Supplementary Reading:

 

·                                                                                 Principles and Standards for School Mathematics (NCTM, 2000)

·                                                                                 NCTM Navigations Series

o                                                                                            Navigating through Algebra in Grades 9–12

o                                                                                            Navigating through Algebra in Grades 6–8

o                                                                                            Navigating through Geometry in Grades 9–12

o                                                                                            Navigating through Geometry in Grades 6–8

o                                                                                            Navigating through Data Analysis in Grades 6–8

o                                                                                            Navigating through Data Analysis in Grades 9–12

o                                                                                            Navigating through Mathematical Connections in Grades 9-12

o                                                                                            Navigating through Measurement in Grades 9–12

o                                                                                            Navigating through Measurement in Grades 6–8

o                                                                                            Navigating through Number and Operations in Grades 9-12

o                                                                                            Navigating through Number and Operations in Grades 6-8

o                                                                                            Navigating through Probability in Grades 9–12

o                                                                                            Navigating through Probability in Grades 6–8

·                                                                                                         Empowering the Beginning Teacher of Mathematics: High School (NCTM, 2004)

·                                                                                                         Empowering the Beginning Teacher of Mathematics: Middle School (NCTM, 2004)

·                                                                                                         Mathematics Assessment Sampler 9-12 (NCTM, 2005)

·                                                                                                         Mathematics Assessment Sampler 6-8 (NCTM, 2005)

·                                                                                 Assessment Standards for School Mathematics (NCTM, 1995)

·                                                                                 Professional Standards for Teaching Mathematics (NCTM, 1991)

·                                                                                 Mathematics Assessment: A Practical Handbook, 9-12 (NCTM, 1999)

·                                                                                 Mathematics Teacher (NCTM)

·                                                                                 Mathematics Teaching in the Middle School (NCTM)

·                                                                                 Addenda Series Grades 9-12 (NCTM)

·                                                                                 Addenda Series Grades 5-8 (NCTM)

·         The Standards: What Teachers Should Know and Be Able to Do, National Board for Professional Teaching Standards (2002)

·         Knowing and Learning Mathematics for Teaching, National Research Council, National Academy Press, 2001

 

 

World Wide Web Resources:

·         National Library of Virtual Manipulatives – http://nlvm.usu.edu/en/nav/index.html  

·         Project Interactivate – www.shodor.org/interactivate

·         Wolfram MathWorld – http://mathworld.wolfram.com

·         National Council of Teachers of Mathematics – www.nctm.org

·         SOS Mathematics – www.sosmath.com

·         Transformations – www.utc.edu/~cpmawata

·         Math Archives – http://archives.math.utk.edu

·         Math Forum Internet Library – http://mathforum.org/library/            

·         Georgia Council of Teachers of Mathematics (GCTM) – www.gctm.org

·         Georgia Performance Standards – http://www.georgiastandards.org/

·         Texas Instruments – http://www.education.ti.com

·         Key Curriculum Press – www.keypress.com

 

 

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

 

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 will need accommodations in this class, reasonable prior notice needs to be given to the instructor and the Office of Student Disability Resources.  If you believe you have a disability requiring an accommodation, please contact the Office of Student Disability Resources at 867-2782 or visit 122 Barnes Hall.