22M:006 Mathematics for Elementary School Teachers
Syllabus
Possible catalog course description:
22M:006 Mathematics for Elementary Teachers
Description: The natural number system via finite set, number line, manipulative and other
mathematical and elementary school models. Place value systems. The arithmetic operations in
context, multiple algorithmic approaches and the mathematical and pedagogical relations
between the algorithms. Conceptual and contextual development of the integers, rational and
irrational numbers. Extensions of the arithmetic operations and multiple representations.
Prerequisites: 22M:001 or equivalent or consent of instructor.
The goal of this course is to ensure that students in it work on developing a deep understanding
of the mathematics of number systems, place value, arithmetic operations in a variety of
algorithms, and the mathematical and pedagogical relations between these algorithms. Designed
with prospective elementary school teachers in mind, wherever possible the mathematics will
focus on mathematics underlying elementary school contexts and applied settings.
The class will meet twice per week in lecture format, and twice per week in discussion section
format. It is a three credit-hour course.
Text (preliminary):
Mathematics For Elementary Teachers: A
Contemporary Approach, Sixth Edition
Gary L. Musser, Oregon State University
William F. Burger
Blake E. Peterson, Brigham Young University
ISBN: 0-471-16425-9
©2003
We will use portions of chapter 1-9 of the text. We may also use additional sources for course
work.
Additional resources:
1. Adding It Up: Helping Children Learn Mathematics National Research Council
http://www.nap.edu/books/0309069955/html/
2. The Mathematical Education of Teachers The Conference Board of Mathematical Sciences
http://www.cbmsweb.org/MET_Document/index.htm
3. Principles and Standards for School Mathematics
National Council of Teachers of Mathematics
http://standards.nctm.org/
4. Knowing and Teaching Elementary Mathematics by Liping Ma;
Lawrence Erlbaum Assoc; (May 1999)
02/17/2016
1/26/2003 New El Ed Math course Preliminary Syllabus
Notes by Walter Seaman
1
Grading:
Graded homework and/or in-class assignments, projects, activities
25%
Mid-term tests or quizzes- up to 3 tests/assessments planned
25%
Discussion section grade-participation and graded work
25%
Final Exam
25%
Concise outline of syllabus:
Weeks 1-2: Introductions, pattern recognition, place value, models of natural numbers N.
Text chapters 1, 2
Weeks 3-7: Conceptual and multiple algorithmic study of arithmetic operations in N
Text chapters 3, 4
Weeks 8-12: Conceptual models of the positive rational numbers and extensions of arithmetic
operations, decimals, irrationals, percents and proportions
Text chapters 6, 7 and 8
Weeks 13-14: Conceptual models and extensions of arithmetic operations to integers Z
Text chapter 8
Week 15: Prime numbers, LCM, GCD, applications
Text chapter 5
Week #1
Introduction to goals and methods of course, expectations for student work and assessments
Problem solving and patterns recognition. Text chapter 1.
Week #2
Continuation-numerical patterns. Natural/whole numbers as counting numbers, place value systems. Text chapters 1
and 2.
Week #3
Place value systems continued. Conceptual and contextual models of addition. Multiple algorithms and their
mathematical and pedagogical relations-extensions to other bases. Text chapters 3, 4 and additional materials.
Week #4
Conceptual and contextual models of subtraction in natural numbers Multiple algorithms and their mathematical and
pedagogical relations-extensions to other bases. Text chapters 3, 4 and additional materials
Week #5
Review and assessment on patterns, place value, natural numbers, conceptual models and
multiple algorithmic approaches to addition and subtraction
Conceptual and contextual models of multiplication in natural numbers. Multiple algorithms and their mathematical
and pedagogical relations-extensions to other bases. Text Chapters 3, 4 and additional materials.
Week #6
Completion of multiplication algorithms and related questions.
02/17/2016
1/26/2003 New El Ed Math course Preliminary Syllabus
Notes by Walter Seaman
2
Conceptual and contextual models of division in natural numbers. The division algorithm, multiple algorithms and
their mathematical and pedagogical relations-extensions to other bases. Text Chapters 3, 4 and additional materials.
Week #7
Completion of natural number division algorithms and related questions. Summary and review of various arithmetic
operations and algorithm techniques, their uses and relations. Text Chapters 3, 4 and additional materials.
Week #8
Review and assessment on conceptual models and multiple arithmetic algorithms for
natural numbers
Conceptual and contextual development of fractions (positive rational numbers). Extensions of the arithmetic
operations and algorithms to fractions and multiple representations. Orderings and comparisons. Text Chapter 6.
Week #9
Extensions of the arithmetic operations and algorithms to rationals and multiple representations.
Decimals as place values systems, orderings and comparisons. Text Chapters 6 and 7.
Week #10
Decimals, percents and proportions, the finite decimal number system. Text Chapter 7.
Week #11
Completion of rationals, decimals, irrationals, percents and proportions. Applications to probability/statistics types
of problems. Text Chapter 7.
Week #12
Review and assessment on rational numbers, decimals and comparisons, arithmetic
operations and algorithms
Completion of decimals, percents and proportions. Applications to probability/statistics types of problems.
Text Chapters 7.
Week #13
Conceptual and contextual development of integers. Extensions of the arithmetic operations and algorithms to
integers. Text chapter 8
Week #14
Extensions of the arithmetic operations and algorithms to integers. Text Chapters 5, 4
Week #15
Prime numbers, prime factorization, GCD, LCM and applications.
Additional topics may include multiple methods of estimation and mental math. Text chapter 5.
02/17/2016
1/26/2003 New El Ed Math course Preliminary Syllabus
Notes by Walter Seaman
3