Catalog Description: This course involves a careful examination of mathematical ideas behind the mathematics taught in grades K-6, and their history and applications to daily life.  It is intended primarily for future elementary school teachers to provide them with a better understanding of the mathematics they will teach.  The course will also be of value for any student who wants a better understanding of these ideas.  The course will focus on understanding and exploring the mathematics through problem solving, projects, group explorations, use of manipulatives, and some use of technology.  MA 203 concentrates on problem solving, whole number arithmetic and theory, discrete math (set theory and number theory), integers, fractions, decimals, and algebraic concepts. MA 203 does not count towards the mathematics major or minor requirements.

Course Goals:  The course will give students

• an active understanding of problem-posing and problem-solving in mathematics, including a familiarity with problem-solving heuristics;
• experience with the use of manipulatives, calculators and computer software, small-group discovery, and other current techniques for teaching and learning mathematics;
• the opportunity to examine and construct for themselves the mathematical concepts underlying the methods of arithmetic computation;
• experience developing algebraic models of mathematical situations;
• experience with a variety of applications of elementary mathematics;
• a deeper understanding of fractions and decimals;
• confidence in their abilities to solve mathematical problems, and to determine whether a proposed solution to a problem is valid or invalid;
• an appreciation of the historical development of mathematics.

Course Objectives:  Students will be able to

• demonstrate proficiency in the major concepts, procedures, and reasoning processes involved with pre-number concepts and whole numbers, including using multiple ways to explore and present number concepts
• apply the four basic operations fluently and flexibly to solve problems and develop computational algorithms
• demonstrate proficiency with the major concepts, procedures and reasoning processes of the natural numbers, including divisibility, primes and composites, and greatest common divisors and least common multiples
• demonstrate proficiency in the major concepts, procedures, and reasoning processes to represent mathematical situations and relationships using algebraic symbols, patterns, relations, and functions
• demonstrate proficiency with the concepts, procedures, and reasoning processes of  integers, fractions and decimals.

Class Schedule:  Edison 117 (TC C1), Monday, Thursday 2:30 - 03:45 p.m.

Instructor:  B. Gold, Howard Hall 247, 732-571-4451, bgold@monmouth.edu

Office Hours:  Monday 11:30 - 12:30, Wednesday 4:30 - 5:30, Thursday 1 - 2, Friday 2:15 - 3:15, or by appointment or chance.

Required Texts:  Sybilla Beckmann, Mathematics for Elementary Teachers with Activity Manual, 3^rd edition.

Course Requirements:  Daily homework assignments, classroom participation, reflective journal, major project,  three in-class examinations.

Methods of Evaluation and Grading Policy:  In-class group work 20%, homework 20%, project 15%, examinations 30%, reflective mathematical journal 15%.

On a scale of 0 to 100, grades of:

     A and A- will be assigned to scores of 90 and above

     B+, B and B- will be assigned to scores between 80 and 89

     C+, C and C- will be assigned to scores between 65 and 79

     D+, D and D- will be assigned to scores between 50 and 65

     F will be assigned to scores below 50.

If you are have to miss an examination, you must let me know prior to the exam or you receive an automatic 0.  You must make arrangements with me prior to the next class about when you will take a make-up exam.

Attendance Requirement:  As in-class group work is a large component of the grade, attendance in mandatory.  All unexcused absences will result in reduction in grade, and excused absences (for illness, family emergency, or participation in official college activities) must be promptly made up with additional work assigned by the instructor in consultation with the student.  If a student expects to miss more than 3 classes during the semester, she or he is advised to take the course during a different semester.

Last date to Withdraw with automatic assignment of “W” grade:   November 9, 2010.

Statement on Academic Honesty:  You are welcome to consult other students in the class on homework via the eC@mpus discussions only.  Students are not otherwise to work together on homework.  If you consult with a tutor in the Mathematics Learning Center, you are to state that at the beginning of the solution to the problem  Unless it becomes excessive, there will be no reduction in credit for getting such assistance.

Examination Rules:  No student is permitted to have at his or her desk any books or papers that are not given out by the instructor.  Possession of such material will be regarded as evidence of intent to use the information dishonestly.  No communication between students during the examination is permitted.  If there are questions, or if there is a need for additional material, the instructor should be asked.  Details of calculations should be written on the pages of the exam.  The following pledge must be signed and submitted with the examination:

“I, ____________________________, certify that I have read the above rules for examinations, and that I have abided by them. By signing, I affirm that I have neither given nor received aid during this examination, and I understand that violation of this affirmation may result in suspension or expulsion from Monmouth University.”

Statement on Special Accommodations:  Students with disabilities who need special accommodations for this class are encouraged to meet with me or the appropriate disability service provider on campus as soon as possible.  In order to receive accommodations, students must be registered with the appropriate disability service provider on campus as set forth in the student handbook and must follow the University procedure for self-disclosure, which is stated in the University Guide to Services and Accommodations for Students with Disabilities.  Students will not be afforded any special accommodations for academic work completed prior to the disclosure of the disability, nor will they be afforded any special accommodations prior to the completion of the documentation process with the appropriate disability office.

Reflective mathematical journals should document your mathematical development through the course, your questions and concerns, your inspirations and ideas.  If you couldn’t do a problem, this is where to share what you tried.  If something happened in class that you felt was important, write it here.  There should be at least one journal entry of at least 100 words per week.  These must be submitted via e-campus’s Dropbox feature by class time on Thursdays.

Be sure to bring your Activity Manual to every class:  we will do activities from it every day.  You may work with other students on homework assignments but you MUST say who you worked with:  otherwise, if two students’ papers are similar, both will receive a 0.  Working with another student is different from copying another student's work.  When you each write the problem up separately, it should be in your own words!

There will be one major project.  This will involve choosing an article from the journal Teaching Children Mathematics, summarizing and critiquing it, and then developing an elementary-school class activity, including appropriate manipulatives and presentation aids based on the article.  These will be presented on the last day of class and during our final examination period.  Detailed expectations for the project will be handed out later in the semester.

Tentative schedule:

1.1  homework:

1. Use bundling to represent, in base 6, the following number of toothpicks:

a.       15_ten           b. 35_ten             c. 43_ten

2. What number, in base 6, comes after:

a.       32_six           b. 35_six             c. 155_six

3. What number, in base 6, comes before:

a.       32_six           b. 30_six             c. 500_six

3.3 additional homework:  Do the following addition and subtraction problems in base 6.   Do not convert to base 10.

   34         215      412                             54         215      400

+ 23     + 454   + 244                           - 23      - 154    - 241

4.6 additional homework:  Do the following multiplication problems in base 6.   Do not convert to base 10.  Do each twice:  once using the standard algorithm and a second time using lattices.

   34                                25       

× 23                             × 54