HOW DOES M 326K ADDRESS SBEC STANDARD I: NUMBER CONCEPTS?

This standard is the main focus of M 326K. The exact content of the course will vary somewhat from semester to semester, but will be drawn mainly from the following items in SBEC Standard I: Number Concepts.

"The beginning teacher of mathematics is able to:

(1.1s) compare and contrast numeration systems;
(1.2s) analyze, explain, and model the structure of numeration systems and, in particular, the role of place values and zero in the base ten system;
(1.3s) demonstrate a sense of quantity and number for whole numbers, integers, rational numbers, and real numbers;
(1.4s) analyze, explain, and model the four basic operations with whole numbers, integers, and rational numbers;
(1.5s) recognize, model , and describe different ways to interpret the four basic operations involving whole numbers, integers, and rational numbers;
(1.6s) analyze and describe relationships among number properties, operations, and algorithms involving the fours basic operations with whole and rational numbers;
(1.7s) … demonstrate, explain, and model how some situations that have no solutions in the whole, integer, or rational number systems have solutions in the real number system;
(1.8s) analyze error patterns that often occur when students use algorithms to perform operations;
(1.9s) recognize and analyze appropriate nontraditional algorithms for the four basic operations with whole numbers;
(1.10s) describe ideas from number theory (e.g., prime numbers, composite numbers, greatest common factors) as they apply to whole numbers, integers, and rational numbers and use these ideas in problem situations; …
(1.12s) apply place values and other number properties to develop techniques of mental mathematics and computational estimation. …
(1.14s) demonstrate a sense of equivalency among different representations of rational numbers;
(1.15s) select appropriate representations of real numbers (e.g., fractions, decimals, percents, roots, exponents, scientific notation) for particular situations and justify that selection;
(1.16s) analyze, explain, and model the four basic operations involving integers and real numbers;
(1.17s) analyze and describe relationships between number properties, operations, and algorithms for the four basic operations involving integers, rational numbers, and real numbers;
(1.18s) work with complex numbers and demonstrate, explain, and model how some situations that have no solution in the integer, rational, or real number systems have solutions in the complex number system;
(1.19s) explain and justify the traditional algorithms for the four basic operations with integers, rational numbers, and real numbers and analyze common error patterns that may occur in their application;
(1.21s) extend and generalize the operations on rationals and integers to include exponents, their operations, their properties, and their applications to the real numbers. …
(1.24s) describe and analyze properties of subsets of the real numbers (e.g., rational, irrational, algebraic, transcendental) and the complex numbers (e.g., real numbers, imaginary numbers);
(1.25s) select appropriate representations of complex numbers (e.g., vector, ordered pair, polar, exponential) for particular situations and justify that selection;
(1.26s) describe real and complex number operations and their interrelationships using geometric and symbolic representations;
(1.27s) apply properties of the real and complex numbers to explain and justify algebraic algorithms;
(1.28s) investigate and apply fundamental number theory concepts and principles (e.g., divisibility, Euclidean algorithm, … the fundamental theorem of arithmetic) in a variety of situations. " (pp. 1 - 5)