MATH 114: Mathematics for Elementary Teachers III
Outcomes, Fall 2012
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 MATH114. (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 with that in mind.)
Students will be able to
apply mathematical knowledge and reasoning to communicate mathematics concepts
as a result of:
Additional topics explored this semester:
- Understanding algebra as generalized arithmetic:
- Recognizing and applying the concepts of variable, function equality, and
equation to express relationships algebraically.
- Manipulating simple algebraic expressions and solving linear equations and
- Justifying algebraic manipulations by application of the properties of
equality, the order of operations, the number properties, and the order
- Using algebra to solve word problems involving fractions, ratios, proportions,
- Identifying variables and deriving algebraic expressions that represent
- Understanding the concept of function:
- Understanding the definition of function and the various representations of
functions (e.g., statements, input/output machines, tables, graphs, mapping
- Recognizing and extending patterns using a variety of representations (e.g.
verbal, numeric, pictorial, algebraic).
- Identifying and analyzing direct and inverse relationships in tables, graphs,
algebraic expressions and real-world situations.
- Using qualitative graphs to represent functional relationships in the real
- Translating among different representations (e.g., tables, graphs, algebraic
expressions, verbal descriptions) of function relationships.
- Understanding linear functions and linear equations:
- Recognizing the formula and graph of a linear function.
- Distinguishing between linear and nonlinear functions.
- Finding a linear equation that represents a graph.
- Analyzing the relationships among proportions, constant rates, and linear
- Interpreting the meaning of slope and the intercepts of a linear equation that
models a real-world situation.
- Selecting the linear equation that best models a real-world situation.
Students will be able to apply mathematical knowledge and reasoning to communicate mathematics concepts as a result of:
- Understanding non-linear functions
- Representing functions in multiple ways: graph, function rule, table, and words
- Recognizing characteristics of functions in different representations
- Given one representation of functions, generating other representations of functions
- Using mathematical models
- Recognizing patterns and functions in everyday life
- Recognizing the power of algebraic reasoning in everyday life
- Recognizing the power and limitations of mathematical models.
- Developing mathematical ways of thinking and habits of mind
- Persevering in making sense and solving complex problems
- Constructing and analyzing mathematical arguments
- Consider precision and estimation
- Looking for patterns, common structure, and repeated reasoning in mathematics.