Mathematics for Teachers

At the end of the course, the successful student should be able to:

• employ pattern recognition, Polya’s method and other critical thinking strategies to solve word problems
• understand and apply the concepts of set union, intersection and the Cartesian product
• use Venn diagrams to solve problems
• demonstrate addition, subtraction, multiplication and division of integers using a variety of appropriate models (e.g. sets, the real number line, tree diagrams, arrays)
• explain and apply the properties of the real numbers (e.g. commutative law, associative law, etc.)
• explain and apply the rules required to evaluate expressions involving integer exponents
• explain and use the Fundamental Theorem of Arithmetic and the Sieve of Eratosthenes
• demonstrate equivalence, addition, subtraction, multiplication, and division of fractions and decimals using a variety of appropriate models
• find and explain how to find greatest common factors and least common multiples
• convert and explain how to convert numbers from decimal to fractional or percentage form and vice versa
• solve problems involving applications of percent
• define and solve problems using commonly used terms of informal geometry:  collinear, parallel, perpendicular, skew, triangle, circle, polygon, parallelogram, trapezoid, rectangle, rhombus, square
• define and solve problems using terms used in the description of angles:  supplementary, complementary, adjacent, vertical, alternate, acute, obtuse
• explain and apply the basic properties of measurement to determine length, area and volume (i.e. the covering property, the congruence property, the additive property, the comparison property)
• convert between different units of measurement
• explain how geometric constructs separate the plane or space
• prove simple statements of geometry using deductive reasoning
• solve problems that require applying the concepts of symmetry, reflection and translation
• determine and explain how to determine if given triangles are similar, congruent or neither
• define terms and solve problems related to the geometry of triangles:  equilateral, isosceles, scalene, acute, obtuse

NOTE TO INSTRUCTORS:

While teaching Math 1191 the instructor’s objectives should be:

• to spark and nurture a positive attitude towards mathematics
• to help students to reach a level of mathematical competence which will allow them to function effectively as mathematics teachers in an elementary school setting
• to expose students to the beauty of mathematics, along with its fun and creative sides