Introduction
Welcome to MATH 190 Principles of Mathematics for Teachers. This course is designed to cover the following mathematical components as described in the calendar:
- Language and notation of mathematics.
- Problem solving.
- Whole number, fractional number, and rational number systems and their meanings.
- Mathematical ideas involved in numeration systems.
- Introduction to number theory.
- Elementary and middle school geometry: plane geometry, solid geometry, metric geometry, symmetry, similarity, and transformations.
- Introduction to probability and statistics.
- Overview of the historical development of these ideas, and their place in contemporary mathematics.
Learning Objectives
Mathematical Content
By the end of the course, students should be able to:
- Apply a variety of problem-solving strategies for mathematical problems.
- Describe and perform fundamental relations (greater than, less than, equal to) and operations (addition, subtraction, multiplication, division) on whole numbers, integers, and fractions.
- Write word problems on whole numbers, integers, and fractions and their operations, and solve those problems using multiple representations, standard algorithms, and nonstandard algorithms both in the discrete context and continuous context.
- Describe the structure of base counting systems, and represent numbers, count, and perform operations within this system.
- Justify and apply basic divisibility tests with an understanding of the role of prime numbers, composite numbers, greatest common divisors, and least common multiples.
- Draw, identify, and define a variety of common two- and three-dimensional objects, and identify and measure their attributes.
- Describe, classify, and identify symmetries, isometries, similarity, and congruency for 2D and 3D objects.
- Measure and estimate time, length, angles, perimeter, area, surface area, volume, weight, speed, and temperature in metric (SI) and nonstandard units, and convert from one unit to another.
- Derive and use standard measurement formulas by way of dissections as well as common misconceptions associated with standard formulas.
- Apply the Pythagorean Theorem and work through at least one proof of the theorem.
Mathematical Understanding
By the end of the course, students will have deepened their understanding of mathematics by:
- Participating in investigative experiences in mathematics.
- Developing multiple representations (physical, pictorial, and symbolic) for mathematical ideas.
- Explaining why mathematics makes sense by integrating the English language with conventional mathematical notation, mathematical definitions, and concrete representations.
- Writing and solving mathematical problems and exercises.
- Encountering the historical development of some of the mathematical ideas and their place in contemporary mathematics in order to gain the big picture behind elementary school mathematics.
- Addressing their fears and apprehensions towards mathematics.
- Gaining an appreciation of mathematics.
Course Design
Topics
The course consists of 12 topics spread over 13 weeks. Although Problem Solving is a topic on its own at the very beginning, it is also weaved into all of the other topics. Here is the list of the 12 topics:
- Introduction & Problem Solving
- Quantities
- Numeration Systems
- Whole Number Operations
- Number Theory
- Fractions: Meanings and Operations
- Ratios, Rates, Proportions, Percents
- Polygons
- Polyhedra
- Symmetry
- Similarity & Transformations
- 2D and 3D Measurements
Required Textbook
Reconceptualizing Mathematics: Combined Parts 1-3 (Arithmetic, Algebra, Geometry), Second Edition by Sowder, Sowder and Nickerson published by W.H. Freeman, ISBN: 978-1-4641-0335-3