### MATH 114: Mathematics for Elementary Teachers III Outcomes, Fall 2012

Syllabus | Schedule | Student Outcomes
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:

• 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 inequalities.
• Justifying algebraic manipulations by application of the properties of equality, the order of operations, the number properties, and the order properties.
• Using algebra to solve word problems involving fractions, ratios, proportions, and percents.
• Identifying variables and deriving algebraic expressions that represent real-world situations.
• 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 diagrams, formulas).
• 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 world.
• 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 functions.
• 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.
Additional topics explored this semester:
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.