MATH 112 Mathematics for Elementary Teachers I:
It is important to ask yourself What do I want my students to learn,
and why? It may also be helpful to your students to know what
skills, strategies and information you expect them to master. Below
is my list of outcomes for MATH112. (Of course, the ultimate goal of
this course is to train you to teach mathematics. The list
below is the result of breaking that goal into parts, and should be
read in that context.)
To prepare for teaching mathematics, Mathematics for Elementary Teachers I students will:
- Understand the number system and the concept of place values.
- Analyze the structures and properties of the base ten and other numeral systems, including numeration systems of ancient cultures.
- Recognize decimal expansions.
- Use scientific notation in an appropriate context.
- Analyze procedures (e.g., rounding, regrouping) for estimation.
- Determine whether estimates are reasonable.
- Identify subsets of real numbers and their characteristics.
- Understand integers, fractions, decimals, percents, and mixed numbers.
- Understand the meaning and models of integers, fractions, decimals, percents, and mixed numbers and apply them to the solution of word problems.
- Analyze and convert among representations of numbers (e.g., graphic, numerical, symbolic, verbal).
- Use number lines.
- Compare, sort, order, and round numbers.
- Recognize equivalent representations of numbers (e.g., fractions, decimals, percents).
- Understand and apply principles of number theory.
- Identify prime and composite numbers and their characteristics.
- Find and use the prime factorization of a number.
- Demonstrate knowledge of the divisibility rules and why they work.
- Find the least common multiple (LCM) and the greatest common factor (GCF) of a set of numbers.
- Use the LCM and GCF to solve problems.
- Understand operations of numbers.
- Understand the meaning and models of operations on real and rational numbers.
- Analyze and justify standard and nonstandard computational algorithms and mental math techniques (e.g., by application of the arithmetic properties, such as commutativity, associativity and distributivity).
- Evaluate the validity of nonstandard or unfamiliar computational strategies.
- Recognize and analyze various representations (e.g., graphic, pictorial, verbal) of number operations.
- Recognize relationships among operations (e.g., addition and subtraction, addition and multiplication, multiplication and exponentiation).
- Identify and apply the arithmetic properties and the transitive properties of equality and inequality.
- Apply the order of operations.
- Apply the laws of exponents.
- Demonstrate fluency in arithmetic computation, including operations with fractions.
- Interpret the concept of absolute value.
- Apply appropriate strategies (e.g., proportional thinking, ratios) to estimate quantities in diverse contexts.
- Solve problems using arithmetic operations with various representations of numbers.