MTH 115W - Mathematics for Elementary Teachers I

1. Develop problem-solving skills.
   1. Give a general definition of problem solving in mathematics and distinguish between exercises and problems.
   2. Explain, illustrate and use Polya's 4-step problem solving process:
      1. understand the problem;
      2. devise a plan;
      3. carry out the plan;
      4. look back.
   3. Explain, illustrate, and apply strategies that include but are not limited to:
      1. guess and test;
      2. use a variable;
      3. draw a picture;
      4. look for a pattern;
      5. make a list;
      6. solve a simpler problem.
2. Use technology appropriately to do mathematics.
   1. Use and review software packages established for use in the elementary classroom for mathematics. 
3. Demonstrate understanding of whole numbers.
   1. Define a set by using:
      1. the roster or list method.
      2. set builder notation
   2. Use the concept of matching sets to formalize the meaning of whole numbers.
   3. Describe and compare the concepts of cardinal, ordinal, and identification numbers.
   4. Describe the difference between a whole number, the name of a whole number, and the numeral of the whole number.
   5. Describe the relations of less than and greater than for whole numbers using sets.
4. Demonstrate computational skill.
   1. Add, subtract, multiply and divide whole numbers.
   2. Add, subtract, multiply, and divide fractions.
   3. Add, subtract, multiply, and divide decimals.
   4. Add, subtract, multiply, and divide with percents.
   5. Add, subtract, multiply, and divide real numbers.
   6. Set-up and simplify ratios and rates.
   7. Solve proportions.
   8. Carry out fraction, decimal, and percent conversions.
   9. Solve percent equations.
   10. Simplify numerical expressions using the order of operations.
   11. Add, subtract, multiply, and divide integers.Add, subtract, multiply, and divide real numbers.
5. Demonstrate understanding of mathematical ideas or operations with concrete models.
   1. Represent addition, subtraction, multiplication, and division of whole numbers (fractions, and decimals) using a set model and a measurement model.
   2. Give examples of real world addition, subtraction, multiplication and division problems involving set and measurement models.
   3. Explain and illustrate the comparison model of subtraction.
   4. Represent fractions, decimals, and percents using area models, measurements models, set models, and towers of bars.
   5. Represent integers with the chip (or charged ion) model.
   6. Use manipulative to illustrate basic arithmetic operations.
6. Demonstrate understanding of computational algorithms.
   1. Explain, illustrate and use a)intermediate algorithm, b) standard algorithm, c) the lattice method for addition and multiplication.
   2. Explain, illustrate and use long division algorithms that lead to the standard division algorithm (scaffolding, intermediate).
   3. Find the GCF and LCM of a given pair of numbers using a) the set intersection method, (factor list method), b) the prime factorization method and c) the Euclidean Algorithm.
7. Demonstrate ability to make estimations.
   1. Use, identify, and apply various mental computation and estimation strategies including:
      1. rounding strategy
      2. compatible numbers strategy
      3. using properties
      4. equal additions method
8. Demonstrate understanding of thinking strategies associated with numeracy.
   1. Explain, illustrate, and use the following thinking strategies for learning basic addition facts:
      1. commutativity
      2. adding zero
      3. counting on by 1 and 2
      4. combinations to 10
      5. doubles
      6. adding 10
      7. associativity
   2. Explain, illustrate, and use the following thinking strategies for learning basic multiplication facts:
      1. commutativity
      2. multiplication by 0
      3. multiplication by 1
      4. multiplication by 2
      5. multiplication by 5
      6. multiplication by 9
      7. associativity
      8. distributivity
9. Demonstrate understanding of number theory.
   1. Define, compare, and contrast the following terms: prime, composite, divides, factor (divisor), factor trees, multiple, is divisible by, common factor (divisor), common multiple, greatest common factor (GCF), least common multiple (LCM).
   2. Use the sieve of Eratosthenes to find prime numbers.
   3. State and apply the fundamental theorem of arithmetic.
   4. State and apply tests for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, 12.
   5. Find the prime factorization of a given composite number.
   6. Use the exponents in the prime factorization of a number to count its factors.
   7. Relate the GCF and LCM of any two numbers to the product of the numbers.
   8. State and use the Prime Number Test.
10. Communicate effectively about mathematics.
    1. Perform writing tasks to promote learning.