NSF TxMSMP Spring 2002
Quantitative Reasoning
MTE 564 - Quantitative Reasoning
Course Instructors:
Dr. Kimberly Childs, childs@math.sfasu.edu
Dr. Jasper Adams, adams@math.sfasu.edu
Course Facilitators/Mentors:
Dr. Lesa Beverly, lbeverly@math.uttyl.edu
Ms. Jennie Freeman, jfree@lufkinisd.org
Ms. Mary Ann Williford, mawilliford@hotmail.com
Office:
NM 304, (936) 468-3805
Ms. Linda Boozer, Dept Secretary
boozer@math.sfasu.edu
Textbooks: Van DeWalle, John A. (2001). Elementary and Middle School
Mathematics: Teaching Developmentally. New York, N.Y.:
Addison Wesley Longman.
Long, Calvin T. & DeTemple, Duane W. (2000). Mathematical
Reasoning for Elementary Teachers. New York, N.Y.: Addison
Wesley Longman.
Bassarear, Tom (2001). Mathematics for Elementary Teachers (with
Explorations manual). Boston, MA.: Houghton Mifflin.
Course Description: Elementary concepts of patterns, number theory, and properties
of the natural numbers, integers, rational, and real number systems with an emphasis on
problem solving and critical thinking.
Course Goals and Objectives: The goal of Quantitative Reasoning is to investigate
mathematics content and pedagogy necessary for teaching mathematics in grades 4-8 in
such a way as to engage students in mathematical thinking and discourse which allows
for construction of concepts, algorithms, and problem solving. Course content, goals, and
objectives are consistent with the NCTM Principles and Standards for School
Mathematics, the SBEC Standards, and with the Texas Essential Knowledge and Skills.
Specific goals and objectives include:
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To become a more efficient problem solver
To learn concepts underlying algorithmic procedures
To become a better communicator of knowledge and experiences by regularly
justifying ideas verbally, concretely, and in writing.
To develop appropriate language and notation over time
To learn to value mathematics and to teach mathematics using multiple methods
of presentation and assessment.
NSF TxMSMP Spring 2002
Quantitative Reasoning
Course Evaluation
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Reflective Journal (10%)
At the end of each class cycle send an electronic journal entry to your mentor
reacting to the class activities and summarizing the readings including :
o The major things you learned
o How the learning relates to SBEC and NCTM Standards, and TEKS
o Questions you have
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Assigned Work (30%)
This includes maintaining a notebook of all class activities along with your
participation in on-line discussions, chat, homework problems, take-home
tests/projects, and reading quizzes.
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Presentations (10%)
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Lesson Sequence (20%)
Design a sequence of lesson plans for a grade level and content area you are
teaching. On a cover sheet describe your rationale for selecting the content area
and how it relates to course objectives, SBEC and NCTM Standards, and TEKS.
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Final Exam (30%)
The final exam will be based on course readings, activities and notes you have
taken during the semester. It will measure how well you have met course
objectives.
Course Syllabus
Class: January 18 - 19
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Exploring Patterns
o Develop Understanding in Mathematics
o Introduce Polya’s Problem Solving Process: Understanding the Problem,
Devise a Plan, Carry Out Plan, Look Back
o Explore Basic Problem Solving Strategies
o Explore Patterns in Language, Figures, Numbers, and Geometry; Sequences,
including Arithmetic and Geometric
o Develop A Model for Mathematical Reasoning
o Describe Patterns using Multiple Formats: Recursive and Closed Form Rules
NSF TxMSMP Spring 2002
Quantitative Reasoning
Class: February 8 - 9
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Number Theory/ Mental Math
o Explore Primes and Composites using Geometry Connections
o Generate Prime Numbers using the Sieve of Eratosthenes
o Explore Basic Divisibility Properties of Sums and Products
o Explore Applications of the Fundamental Theorem of Arithmetic
o Define the GCD and LCM
o Explore Algorithms for Finding the GCD and LCM
o Explore Applications of the GCD and LCM
o Explore Estimation and Mental Arithmetic Techniques
Class: March 1 - 2
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Integers/ Fractions
o Model Integer Operations Using a Variety of Methods
o Develop Fraction Models
o Develop Fraction Number Sense and Equivalent Forms
o Investigate Extensions of Whole Number Operations and Their Properties:
Additive Inverse; Closed, Commutative, Associative, DistributiveMultiplication Over Addition, Identities, Additive Inverse, Multiplication By
Zero to Integers and Fractions
o Explore Absolute Value
o Explore Connections Between Fractions, Rational Numbers, Decimals, and
Percents and Application to Real-world Problems
Class: April 5 - 6
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Proportional Thinking
o Develop Decimal and Percent Number Sense and Connect to Real-world
applications
o Make Appropriate Connections to Probability
o Develop and Justify Methods for Solving Using Proportions
o Make Appropriate Connections to Algebra
o Investigate Practical Uses for Fractions
o Explore Proportional Thinking as a Habit of Mind