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COURSE NUMBER: MATH 282
COURSE TITLE: Mathematical Reasoning for Teaching
NAME OF INSTRUCTOR: Dr Wendy Stienstra
CREDIT WEIGHT AND WEEKLY TIME DISTRIBUTION: credits 3 (hrs lect 3 - hrs sem 0 - hrs lab 0)
COURSE DESCRIPTION: This course explores the mathematical reasoning embedded in concepts encountered in the upper elementary and junior high curriculum. The course emphasizes conceptual understanding, reasoning, explaining why algorithms work, and problem solving. The content follows sequentially from Math 281. Topics include proportional reasoning, number theory, algebraic reasoning and aspects of geometry and probability.

Same as EDUC 582.
REQUIRED TEXTS: Beckmann, S. (2014). Mathematics For Elementary Teachers (4th ed.). Boston: Pearson Addison-Wesley. (package includes textbook and activities manual)
MARK DISTRIBUTION IN PERCENT:
Homework/Participation 25%
Midterm 25%
Project 20%
Final Exam 30%
100%
COURSE OBJECTIVES: In order to develop a deeper understanding of the mathematics necessary for both prospective and inservice
elementary and junior high teachers, the course emphasizes the need for explaining why the mathematics works, rather than simply memorizing procedures

Working with the concepts of proportional reasoning, number theory, algebraic reasoning and aspects
of probability and statistics students will:
  • make sense of and reason about the mathematics they will teach;
  • develop flexible mathematical reasoning;
  • develop a repertoire of problem solving skills;
  • develop the ability to use mental math to follow mathematical explanations;
  • develop the ability to communicate mathematical ideas clearly and logically during classroom discussions;
  • know how mathematics is used and applied in the classroom.
COURSE OUTLINE:
  • Intro to class
  • Review of Basic Concepts – Multiplication; Division; Fractions
  • Defining Ratio and Proportional Relationships
  • Solving Proportions by Reasoning
  • Unit Rates and Ratio Values
  • Proportional vs Inversely Proportional Relationships
  • Percent Increase and Decrease
  • Examples of Proportionality – Similarity and Scaling
  • Number Theory: Factors & Multiples; Even and Odd
  • Divisibility Tests; Prime Numbers
  • Greatest Common Factor; Least Common Multiple
  • Rational and Irrational Numbers
  • Number Systems; Review
  • Numerical Expressions
  • Expressions with Variables
  • Equations; Solving Equations
  • Solving Word Problems
  • Sequences
  • Functions
  • Linear Functions
  • Statistics Using Samples
  • The Centre of Data
  • Pull it All Together - Review


Required texts, assignments, and grade distributions may vary from one offering of this course to the next. Please consult the course instructor for up to date details.

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