Tentative Syllabus Math 3064

Course:

Math 3064

4 credits

Number Concepts for Middle School Teachers
Fall 2010

Department:

Mathematics and Computer Science

 

Program(s):

Elementary Education Major, B.S. (Teacher Licensure)

Meeting:

9:00-9:50 AM MWF

HS 231

Extras:

 

 

Instructor:

Dr. Glen Richgels

HS 360

Office: 218-755-2824

Email: grichgels@bemidjistate.edu

www: http://faculty.bemidjistate.edu/grichgels/

Office Hours:

  7-  8 M-F

11-12 M-F

 

Course Description:

3064 Number Concepts for Middle School Teachers (4 credits)

This course helps meet the new BOT rule with respect to number sense. Provides a background in special number concepts that are pertinent to middle school mathematics. Topics include elementary algebra, properties of integers, prime and composite numbers, divisors, GCDs, LCMs, the number of divisors, the sum of divisors, the Euclidean Algorithm, famous unsolved problems, finite mathematical systems, modular arithmetic and congruences, and sequences. Emphasis given to problem solving techniques as they relate to number concepts and algebraic representation.

Prerequisite:

MATH 1011 or consent of instructor.

 

Professional Education Mission Statement

Bemidji State University prepares teachers through inquisitive, involved, reflective practice. The framework outlining our program sets a standard that is rigorous, exemplary and innovative. The curricular structure is research based and organized around the Standards of Effective Practice. Graduates are proficient, collaborative, technologically literate and environmentally aware teachers, who work effectively in various settings with diverse learners.

Text:

 

Recommended:           

Mathematics for Elementary Teachers a Contempory Approach,
Musser, Burger & Peterson

Technology:

 

A calculator

 

Attendance by all students is expected for all classes.

 

Homework:  Homework assignments will be made in class.  You should come prepared to discuss the various reading assignments and compare and contrast them with what you have observed in schools.

Class participation and quizzes:  Class participation is expected and in order to participate you need to be present. 

Exams: Exams will be approximately tri-weekly. There will be a final exam.

Evaluation:There will be 3-5 tests given throughout the quarter.  Quizzes may be given frequently and may be unannounced.  The content for the quizzes and tests will be based on assignments, classroom discussion and lecture, and textbook material.

Grades: Grades will be based on the homework, quizzes, tests, and final exam.

Homework, Quizzes   -  one-sixth                 

            Tests                           - one-half                    

            Final                            - one-third                  

The following grading scale will be used to determine grades:

            A         90% - 100%

            B         80% -   89%

            C         70% -   79%

            D         60% -   69%

 

A grade of C or better indicates that the student has successfully met the competencies measured in this class through discussion, homework, and projects.

Incomplete: An incomplete (I) grade will only be given in documented emergency situations. BSU policies will be followed.

 

Students are expected to practice the highest standards of ethics, honesty, and integrity in all of their academic work.  Any form of academic dishonesty (e.g. plagiarism, cheating, misrepresentation) may result in disciplinary action.  Possible disciplinary actions include failure for part or all of the course, as well as suspension from the University.

 

NOTE: Upon request, this document and others distributed in this course can be made available in alternate formats.  If you have a documented disability and need accommodations for this course please contact the instructor,  the Disability Services Office in 202 Sanford Hall, Bemidji State University or Kathi Hagen in the Office for Students with Disabilities at 755-3883 for assistance.. Any other questions about this course should be directed to the instructor.

 

Change in Course Syllabus: The Instructor reserves the right to change this syllabus as this course proceeds if the need arises. Should a change be required the class will be notified.

 

Course Outline:

Discrete mathematics topics

 

 

(a) application of discrete models to problem situations using appropriate representations, including sequences, finite graphs and trees, matrices, and arrays;

 

(b) application of systematic counting techniques in problem situations to include determining the existence of a solution, the number of possible solutions, and the optimal solution;

 

(c) application of discrete mathematics strategies including pattern searching; organization of information; sorting; case-by-case analysis; iteration and recursion; and mathematical induction to investigate, solve, and extend problems; and

 

(d) exploration, development, analysis, and comparison of algorithms designed to accomplish a task or solve a problem;

Number Sense topics

 

 

(a) understand number systems; their properties; and relations, including whole numbers, integers, rational numbers, real numbers, and complex numbers;

 

(b) possess an intuitive sense of numbers including a sense of magnitude, mental mathematics, estimation, place value, and a sense of reasonableness of results;

 

(c) possess a sense for operations, application of properties of operations, and the estimation of results;

 

(d) be able to translate among equivalent forms of numbers to facilitate problem solving; and

 

(e) be able to estimate quantities and evaluate the reasonableness of estimates;

 
  • the foundations for algebraic ideas in the elementary mathematics classroom
  • Understand connections between graphic, algebraic, and numeric representations
  • Prime and composite numbers
  • GCDÕs and LCMÕs
  • Euclidean algorithm
  • problem solving and mathematical modeling to understand and make decisions about real world problems
  • Discern structure, pattern, organization, and alternative ways of thinking mathematically
  • Mathematical Induction and proof concepts
  • Modular arithmetic and congruences

 

 

 

 

Instructional Strategies used by instructor in course:

 

PolyaÕs problem solving steps

1.     Understand the problem

    1. Devise a plan
    2. Carry out the plan
    3. Reflect

 

Lesson Sequencing

            Intuitions Þ Concrete ó Semi-Concrete ó Abstract

 

GlenÕs Teaching/Learning Principles

1.     Teach the way students learn

2.     Use group work, heterogenous, 3-4, change monthly

3.     Communication student ó student

4.     Communication teacher ó student

5.     Multiple solution paths

6.     Use contextual settings / problem solving

7.     Assessment

a.     Grading

b.     To inform instruction

 

Updated by Glen Richgels

March 2, 2010

 

TENTATIVE Daily Course Outline

Day 1

Fractions in bases 4, 5, and 6.  Do they terminate or repeat?  How to convert fractions to decimals in other bases.

Day 2

Fraction circles - Lesson # 1, 2, 4, 6, 9, 12, 15, & 20.

Day 3

More fraction circles

Day 4

Repeating to terminating decimals

Day 5

Fraction circles and repeating to terminating decimals Decimal operations

Day 6

1) first three digits of phone # times 80 || 2) add 1 || 3) multiply by 250 || 4) add the last four digits of your phone # || 5) add the last four digits of your phone # - AGAIN || 6) subtract 250 || 7) Divide by 2.  Do you recognize the answer?  Why does this work??

Day 7

Number Puzzles and properties

Day 8

Magic Squares

Day 9

Positive and negative numbers

Day 10

Sierpinski triangle -- dimension problem

Day 11

Patterns in Pascal's triangle

Day 12

Review for Test 1

Day 13

Test 1

Day 14

Rotations and flips of a triangle

Day 15

Rotations and flips of a triangle (continued)

Day 16

Scientific notation & division algorithm

Day 17

Divisibility tests

Day 18

Divisibility tests from the perspective of Blocks, Flats, Longs, and Units

Day 19

Divisibility tests from the perspective of Blocks, Flats, Longs, and Units

Day 20

Divisibility tests from the perspective of Blocks, Flats, Longs, and Units

Day 21

Review closure, associative, zero, inverses (+ and x), commutative, distributive.

Day 22

Division algorithm

Day 23

Prime numbers - sieve of Erastosthenes

Day 24

Prime numbers - sieve of Erastosthenes

Day 25

Remainder of One

Day 26

GCD's

Day 27

LCM's -- the locker problem

Day 28

Wrap-up GCD's & LCM's -- reading formal mathematics

Day 29

Wrap-up LCM -- Krazy method VS book method for three numbers

Day 30

Cayley tables revisited -- Closure, Associative, Commutative, Identity, Inverses, and Distributive properties.

Day 31

Conclude Cayley tables -- Magic Math:

1) first three digits of phone # times 80 || 2) add 1 || 3) multiply by 250 || 4) add the last four digits of your phone # || 5) add the last four digits of your phone # - AGAIN || 6) subtract 250 || 7) Divide by 2.  Do you recognize the answer?  Why does this work??

Day 32

Mathematical Induction and introduce Magic Squares

Day 33

Magic squares - conjectures and proof.  Aside: letter of application germane to the position.

Day 34

Counting -- Combinations and permutations using intuition

Day 35

Combinations and permutations -- using the formula

Day 36

Counting -- permutations, paths, combinations, codes, ...

Day 37

 

Day 38

 

Day 39

 

 

 

 

 

 

 

 

Four four's activity

 

Building algebraic ideas with pattern blocks

 

 TomÕs Book

 

 

 

Final Exam – 2 Hours Comprehensive

 

Board of Teaching Standards

 

8710.3320 MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS.

Department of Mathematics and Computer Science

 

EVIDENCE OF LEARNING & ASSESSMENT OPPORTUNITIES

8710.3320 MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS

Course ID

Number

Activity or unit

Assessment

C.A teacher with a middle level endorsement for teaching mathematics in grades 5 through 8 must demonstrate knowledge of fundamental concepts of mathematics and the connections among them. The teacher must know and apply:

 

 

 

(2)  concepts of discrete mathematics:

 

 

 

(a) application of discrete models to problem situations using appropriate representations, including sequences, finite graphs and trees, matrices, and arrays;

M3064

Tournament matrix; Euler circuits/Hamilton circuits;

 

(b) application of systematic counting techniques in problem situations to include determining the existence of a solution, the number of possible solutions, and the optimal solution;

M3064

Sales routes; fib seq, lucas seq, golden ratio; sprouts; discrete yearbook

 

(c) application of discrete mathematics strategies including pattern searching; organization of information; sorting; case-by-case analysis; iteration and recursion; and mathematical induction to investigate, solve, and extend problems; and

M3064

Sorting algorithms; tower of Hanoi;

 

(d)  exploration, development, analysis, and comparison of algorithms designed to accomplish a task or solve a problem;

M3064

Greedy algorithm; Nearest Neighbor

 

(3)  concepts of number sense:

 

 

 

(a)  understand number systems; their properties; and relations, including whole numbers, integers, rational numbers, real numbers, and complex numbers;

M3064

Reals, modular, dihedral group; complex numbers (# and operations 9-12)

 

(b)  possess an intuitive sense of numbers including a sense of magnitude, mental mathematics, estimation, place value, and a sense of reasonableness of results;

M3064

Craigs stories (number magnitude); scientific notation

 

(c)  possess a sense for operations, application of properties of operations, and the estimation of results;

M3064

Other base arithmetic from m1011

 

(d)  be able to translate among equivalent forms of numbers to facilitate problem solving; and

M3064

Fractions, decimals, percents

 

(e)  be able to estimate quantities and evaluate the reasonableness of estimates;

M3064

Items and estimate magnitudes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Professional Education Mission Statement

Bemidji State University prepares teachers through inquisitive, involved, reflective practice. The framework outlining our program sets a standard that is rigorous, exemplary and innovative. The curricular structure is research based and organized around the Standards of Effective Practice. Graduates are proficient, collaborative, technologically literate and environmentally aware teachers, who work effectively in various settings with diverse learners.

 

The middle level teachers from BSU that take the campus M3064 class will increase their content knowledge and understanding of how students learn as they experience studying fundamental operations, discrete mathematics, and number sense. M3064 is a mixture of challenging students in the understanding of number sense, discrete  mathematics and experiencing activity based pedagogy. This translates into a more positive attitude toward mathematics for themselves that hopefully they will take with them into their teaching.

 

The best practices of activity oriented learning is demonstrated in class from day one. In addition group work and collaborative learning are encouraged and used almost daily. These best practices are discussed at the beginning of the course and pointed out and discussed throughout the semester.