MT 118 - Mathematics for Elementary Education Teachers I

Taken from: The Mathematical Education of Teachers from Conference Board of Mathematical Sciences in conjunction with the American Mathematical Society and the Mathematical Association of America.

• demonstrate an understanding of models and interpretations of operations with whole numbers:
  • demonstrate a large repertoire of interpretations of addition, subtraction, multiplication and division, and of ways they can be applied; and
  • demonstrate understanding of relationships among operations.
• demonstrate a strong sense of place value in the base-10 number system:
  • show understanding of how place value permits efficient representation of number;
  • demonstrate recognition of the value of each place as ten times larger than the value of the next place to the right and the implications of this for ordering numbers and for estimation and approximation;
  • demonstrate how the operations of addition, multiplication, and exponentiation are used in representing numbers; and
  • demonstrate the relative magnitude of numbers.
• demonstrate an understanding of multi-digit calculations, including standard algorithms, “mental math,” and nonstandard methods commonly created by students:
  • demonstrate how the base-10 structure of number is used in multi-digit computations.
  • demonstrate how decimal notation allows for approximation by “round numbers” (multiples of powers of 10).
  • demonstrate an understanding of the properties of commutativity, associativity, and distributivity as useful tools for organizing thinking about computation.
  • demonstrate flexibility in mental computation and estimation
• demonstrate an understanding of the concepts of integer and rational number and extend the operations to these larger domains:
  • demonstrate an understanding of what integers are and the meaning of sign and magnitude;
  • demonstrate an understanding of what rational numbers are, how fractions and decimals relate, different representations of rationals, and a sense of their relative size;
  • demonstrate knowledge of interpretations and for the arithmetic operations in the extended domains;
  • demonstrate understanding of the relationship between fractions and the operations of multiplication and division;
  • demonstrate an understanding of how whole number arithmetic extends to integers and rational numbers;
  • demonstrate an understanding of how any number represented by a finite or repeating decimal is rational, and conversely; and
  • demonstrate an understanding of how and why whole number decimal arithmetic extends to finite decimals and, in particular, how place value extends to decimal fractions.
• demonstrate an ability to generalize arithmetic and quantitative reasoning:
  • demonstrate an ability to use a variety of representations, including conventional algebraic notation, to articulate and justify generalizations;
  • demonstrate an understanding of algebraic expressions as shorthand for describing calculation; and to demonstrate an understanding of algebraic identities as statements of equivalence of expressions; and
  • demonstrate an ability to solve word problems via algebraic manipulation.
• demonstrate the ability to use manipulatives to understand the meaning of numbers and arithmetic operations throughout the course.

Technology Objectives:

• demonstrate the ability to use the arithmetic operations on the scientific calculator to solve algebraic and real world algebraic problems;
• demonstrate an understanding of the keys:
  
  √n ,x²,y^x,π,±,%, (  ) 2^nd inv key; and
   
• demonstrate an understanding of order of operations on the scientific calculator.

 

Prerequisites: MT 007 or MT 013 or appropriate college equivalent and/or appropriate mathematics level code.*
F/S (C, N, S)

*Level code is determined by Mathematics Department placement test and/or successful completion of math courses.