1.  Gather and comprehend information from reading texts, handouts, and lecture notes. 
2.  Analyze the structure of a problem situation and (when possible) translate it into a variety of useful mathematical representations. 

Mathematical Reasoning

The following five numbered categories specify the mathematical reasoning abilities that are the targeted abilities for each student to acquire/develop by the end of the course. Beneath each ability category are general performance criteria indicating the type of content-specific performances that are necessary to demonstrate mastery of the related skills and knowledge. 

1. Mathematical Modeling 

• Express, in ordinary (natural) language, model specifications and relationships that are presented mathematically and/or visually using a graph, diagram, or geometric figure. 
• Recognize whether a mathematical model applies to a given situation, e.g., a linear function, a quadratic function, an exponential growth, a first-order kinetic process, etc.
• Develop a mathematical model from an ordinary language specification, including an appropriate visual representation, e.g., formula, equation, graph, diagram, geometric figure. 
• Recognize what assumptions underlie a particular mathematical model and how those assumptions can affect the validity of the model, e.g., the implications of neglecting aspects of a biological or  physical situation in developing a mathematical model of it. 
• Reason symbolically with parameters, diagrams, etc., in order to determine the influence of structural changes to a mathematical model. 

• Formulate a conjecture or draw conclusions from a given set of results or observations.
• Construct a valid argument to support or refute a conjecture or hypothesis. 
• Determine the validity of an argument or identify the flaw in an invalid argument.

• Recognize patterns, trends, or symmetries; continue a pattern.
• Identify relationships between alternate conceptions of mathematical ideas and processes, e.g., the relationship between the visual representation of changing slope and the rate of change of a (biological or physical) process. 

• Use intelligent guessing and conjecture to narrow the solution space and to inform a choice of solution strategy. 
• Reduce a problem to a simpler case, solve this case first, and then try to generalize. 
• Determine when a certain procedure is appropriate for solving a problem, e.g., computing an average, slope, or area. 

• Determine when estimation techniques are appropriate and determine the degree of accuracy in an estimate. 

Recognize the reasonableness of a result through the use of an approximation or an appropriate validity check, e.g., correct order of magnitude, correct units, appropriate sign for a physical quantity such as time or distance.