Department of Mathematics and Computer Science Official Syllabus

 

Title: Foundations of Numbers and Operations, Mathematics 2008

3 hours – Summer 2008

 

Instructor: Margaret Poitevint (mpoitevint@ngcsu.edu)
Newton-Oakes Center 227
(706) 867 - 2722
 http://radar.ngcsu.edu/~mpoitevint/index.htm

Office Hours: See website or my office door.

Prerequisite:  Six hours of college level mathematics with a grade of C or above and admittance to the teacher education program. A student will not be allowed credit for MATH 2008 after completing MATH 3100 with a grade of “C” or better. 

 

Catalog Description:  This course will emphasize the understanding and use of the major concepts of number and operations. Topics include problem-solving strategies; inductive and deductive reasoning; numeration systems and place value; operations and algorithms; identity elements and inverse operations; rational and irrational numbers; integers and number theory; special sets of numbers; exponents and decimals; ratios, percents, and proportional reasoning. 

 

Course Objectives:  After completion of the course the student will be able to:

  • apply a variety of problem-solving strategies such as guess and check, make a table, make an organized list, identify a pattern, solve a simpler problem, and build a model;
  • apply inductive and deductive reasoning to determine the validity of a statement;
  • represent and explore place value using manipulatives such as base ten blocks;
  • model arithmetic operations (+, -, *, ÷) in the base ten numeration system using manipulatives such as base ten blocks;
  • apply mental math and estimation strategies for whole-number operations ;
  • perform operations (+, -, *, ÷) involving positive and negative integers using algorithms and manipulatives such as Two-color Counters;
  • investigate divisibility using manipulatives and divisibility rules;
  • determine whether or not numbers are prime or composite using manipulatives such as Cuisenaire Rods and factor trees;
  • determine GCF and LCM using algorithms and manipulatives such as Cuisenaire Rods and Multi-link Cubes;
  • describe and solve real-world problems involving GCF and LCM;
  • model the concepts of ratio and proportion using manipulatives such as Cuisenaire Rods;
  • perform operations (+, -, *, ÷) involving rational numbers using algorithms and manipulatives such as Pattern Blocks and Cuisenaire Rods;
  • describe and solve real-world problems involving operations on rational numbers;
  • determine if a given number is rational or irrational;
  • illustrate the concept of decimals and percent using grid paper and manipulatives such as Base Ten Blocks;
  • model arithmetic operations (+, -, *, ÷) involving decimals using manipulatives such as base ten blocks;
  • apply the properties of exponents to simplify expressions;
  • represent values and arithmetic operations in alternate bases;
  • explore, compare, and contrast ancient numeration systems; and
  • access mathematics resources on the Internet using search engines and URLs. 

 

 

Methods of Instruction:  The methods of instruction are determined by the instructor; however, the instructor is expected to use a variety of methods.  These methods may include, but are not limited to lecture; problem-solving sessions with informal assessment by the student or instructor; discussion; group projects; timely feedback from test, quiz, or project results (formative assessment); question and answer; computer or calculator-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.

 

Metacognitive Model and 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

 

 

Evaluation Methods: Student performance will be evaluated through the use of varied formative assessment tools such as projects, in-class presentations, peer and self-assessment, reflective logs, written tests, and/or short quizzes. Summative assessment will be in the form of a final examination.  Special projects and daily grades may be used at the discretion of the instructor.

Grading: Student grades are reported to the registrar based on a rounded final average as follows:

  A 90-100                Participation:        15%                               
  B 80-89                  Major Tests:          54%  (27% each)            
  C 70-79                  Final exam:            31%                               
  D 60-69                                                                                     
  F Below 60

There will be two major tests and one grade composed of projects and class participation, including pop quizzes.  If students are text-messaging (or other distracting behavior), in each instance 5 points will be deducted from the participation grade. The final will be comprehensive.  All tests must be taken with pencil - no erasable pens.  If a test is turned in that has been taken with a pen, 10 points will be deducted from the grade.  There will be no make-up tests.  A test missed with an excuse approved by the instructor will be replaced with the grade made on the final.  Mathematics is a discipline and students are expected to work hard, keep up with homework, get help if needed, etc.  In short, students are responsible for their own learning.  I will do everything I can to help you succeed in this endeavor.  An absence does not excuse a student from having assignments in on the date due.  Points will be deducted for late assignments.  "Late" means any time after the beginning of the class on the day the assignment is due.   Due to FERPA regulations, grades cannot be e-mailed to students so please don't ask.

Attendance: Attendance is required.  Any student who is absent more than 14% of the scheduled class meetings may be dropped with a WF.  Excused absences will count toward the 14%; the word excused only indicates that make-up work is allowed.  Repeated tardiness is not allowed and the instructor may record two tardies as an absence.

E-mail:  There are times that I may have the need to communicate with the entire class by e-mail. When I do this I will use the e-mail address on the summary class list available to me on Banner. For most of you this means that the e-mail will go to your NGCSU e-mail. Preferring another e-mail address does not relieve you of the responsibility of any information on your NGCSU e-mail. You will either need to check it daily or have it forwarded to your preferred e-mail account. The same is true for when you leave campus. Not having e-mail at home does not relieve you of the responsibility to check your NGCSU e-mail. You will need to make arrangements through another source to keep abreast of information generated in your NGCSU account.

 

Course Content:

 

1.  Number Sense

2.  History of Numeration

3.  Number Theory

4.  Concepts of Operations

5.  Problem Solving

 

 

 

Knowledge Base: 

 

1.  Required Texts:  At the level of

  • Bennett and Nelson, Mathematics for Elementary Teachers: A Conceptual Approach, Seventh Edition, McGraw Hill, 2007
  • Bennett, Burton, and Nelson, Mathematics for Elementary Teachers: An Activity Approach, Seventh Edition, McGraw Hill, 2007

 

2.  Required Activity Text:  Dolan, Williamson, and Muri, Mathematics Activities for Elementary School Teachers: A Problem Solving Approach, Sixth Edition, Pearson Addison Wesley, 2004

 

3.  Library Resources:

·         Women and Science Celebrating Achievements Charting Challenges (National Science Foundation, 1997)

·         Teaching Children Mathematics (NCTM), Mathematics Teaching in the Middle School (NCTM)

·         Curriculum and Evaluation Standards for School Mathematics (NCTM)

·         Professional Standards for Teaching Mathematics (NCTM)

·         Assessment Standards for School Mathematics (NCTM)

·         Standards 2000 (Draft) (NCTM)

·         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)

·         Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity (Janet Trentacosta & J. Kenney, Eds., NCTM, 1997)

·         Discovering Mathematics on the TI-73: Activities for Grades 5 and 6 (Texas Instruments)

·         Math and Science in Motion: Activities for Middle School (Texas Instruments, 1997)

·         Women, Minorities and Persons with Disabilities in Science and Engineering: 1996 (National Science Foundation, 1997)

·         She Does Math! (Marla Parker, Ed., The Mathematical Association of America, 1995)

 

 

4.  Web-Based Resources:

  

·         Project Interactivate - http://www.shodor.org/interactivate/

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

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

·         The Math Forum - http://mathforum.org/

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

·         Math Cove - http://oneweb.utc.edu/~Christopher-Mawata/

·         Intermath - http://intermath.coe.uga.edu/

·         Fun Brain - http://www.funbrain.com/

·         Education Place Brain Teasers - http://www.eduplace.com/math/brain/index.html

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

·         Key Curriculum Press - http://www.keypress.com/

·         National Council of Teachers of Mathematics - http://www.nctm.org

·         Georgia Performance Standards for Mathematics - http://www.georgiastandards.org/math.aspx

·         SOS Mathematics - http://www.sosmath.com/

·         Helping Your Child Learn Math (for parents) - http://www.ed.gov/pubs/parents/Math/index.html

·         Math Nerds - http://www.mathnerds.com/mathnerds/

·         Association for Women in Mathematics - http://www.awm-math.org

 

 

5.       Technology Resources:  

  

·         Calculators such as the TI-15 and TI-73

·         Data collection devices such as the Calculator-Based Ranger (CBR) and the Calculator-Based Laboratory (CBL)

 

 

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.

Academic Integrity:  "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.  For additional information, refer to the Academic Integrity Policy.

 

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. 

 

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.  In this case, contact Elizabeth McIntosh, Coordinator, Student Disability Resources at 122 Barnes Hall, 867-2782, emcintosh@ngcsu.edu.

 

(October 2007)