Florida’s revised mathematics standards emphasize teaching and learning the most important K-12 mathematics concepts in depth at each grade level. After adoption of the new math standards, the Florida Center for Research in Science, Technology, Engineering and Mathematics (FCR-STEM) at Florida State University convened a group of Florida math teachers, district math supervisors, and math education faculty to rate the cognitive demand of each benchmark. Meeting in teams for each body of knowledge, they reviewed and discussed each benchmark, then reached consensus on level of cognitive complexity using a classification system adapted from the “depth of knowledge” system developed by Dr. Norman Webb at the University of Wisconsin.

Cognitive complexity refers to the cognitive demand of tasks associated with the benchmark. The depth of knowledge levels (Webb, 1999) reflect the relative complexity of thinking that a given benchmark demands of students — what it requires the student to recall, understand, analyze, and do. Florida’s depth of knowledge rating system focuses on expectations of students at three levels:

Low Complexity
This category relies heavily on the recall and recognition of previously learned concepts and principles. Items typically specify what the student is to do, which is often to carry out some procedure that can be performed mechanically. It is not left to the student to come up with a low complexity original method or solution. Skills required to respond to low complexity items include

• solving a one-step problem; 
• computing a sum, difference, product, or quotient; 
• evaluating a variable expression, given specific values for the variables; 
• recognizing or constructing an equivalent representation; 
• recalling or recognizing a fact, term, or property; 
• retrieving information from a graph, table, or figure; 
• identifying appropriate units or tools for common measurements; or 
• performing a single-unit conversion.

Moderate Complexity
Items in the moderate complexity category involve more flexible thinking and choice among alternatives than low complexity items. They require a response that goes beyond the habitual, is not specified, and ordinarily has more than a single step. The student is expected to decide what to do—using informal methods of reasoning and problem-solving strategies—and to bring together skill and knowledge from various domains. Skills required to respond to moderate complexity items include

• solving a problem requiring multiple operations; 
• solving a problem involving spatial visualization and/or reasoning; 
• selecting and/or using different representations, depending on situation and purpose; 
• retrieving information from a graph, table, or figure and using it to solve a problem; 
• determining a reasonable estimate; 
• extending an algebraic or geometric pattern; 
• providing a justification for steps in a solution process; 
• comparing figures or statements; 
• representing a situation mathematically in more than one way; or 
• formulating a routine problem, given data and conditions.

High Complexity
High complexity items make heavy demands on student thinking. Students must engage in more abstract reasoning, planning, analysis, judgment, and creative thought. The high-complexity item requires that the student think in an abstract and sophisticated way. Skills required to respond correctly to high complexity items include

• performing a procedure having multiple steps and multiple decision points; 
•  solving a non-routine problem (as determined by grade-level appropriateness); 
•  solving a problem in more than one way; 
•  describing how different representations can be used for different purposes; 
•  generalizing an algebraic or geometric pattern; 
•  explaining and justifying a solution to a problem; 
•  describing, comparing, and contrasting solution methods; 
•  providing a mathematical justification; 
•  analyzing similarities and differences between procedures and concepts; 
•  formulating an original problem, given a situation; 
•  formulating a mathematical model for a complex situation; or 
•  analyzing or producing a deductive argument.

Webb, N.L., 1999, Alignment Between Standards and Assessment, University of Wisconsin Center for Educational Research.

Source: Cognitive Complexity Classification of FCAT SSS Test Items, July, 2006, Florida Department of Education.