Bloom's Taxonomy

Bloom’s taxonomy includes levels of learning for the cognitive domain, the affective domain, and the psychomotor domain.  The cognitive domain and affective domain are of particular use to two-year college mathematics faculty who consider these levels of learning in developing student learning outcomes.

Cognitive Domain

The cognitive domain of Bloom’s Taxonomy delineates six levels of intellectual abilities and skills that range from the simplest behavior of recall or recognition of specific facts at the lowest level to the most complex behavior of making judgments about the value of materials or ideas.  The descriptions of the six levels, the examples of learning outcome statements and the verbs for each level may be useful to faculty engaged in developing student learning outcomes for courses and programs in mathematics.

Category

Example and Key Words

Knowledge: Recall data or information.

Examples: Recite the definition of derivative. Quote formulas from memory. Know the rules for adding signed numbers.
Key Words: defines, describes, identifies, knows, labels, lists, matches, names, outlines, recalls, recognizes, reproduces, selects, states.

Comprehension: Understand the meaning, translation, interpolation, and interpretation of instructions and problems. State a problem in one's own words.

Examples: Rewrite the distributive principle. Explain in one’s own words the steps for taking the derivative of a quotient. Translate an equation into a computer spreadsheet.
Key Words: comprehends, converts, defends, distinguishes, estimates, explains, extends, generalizes, gives, infers, interprets, paraphrases, predicts, rewrites, summarizes, translates.

Application: Use a concept in a new situation or unprompted use of an abstraction. Applies what was learned in the classroom into novel situations in the work place.

Examples: Use the derivative to calculate marginal cost. Apply principles of statistics to evaluate the reliability of a written test.
Key Words: applies, changes, computes, constructs, demonstrates, discovers, manipulates, modifies, operates, predicts, prepares, produces, relates, shows, solves, uses.

Analysis: Separates material or concepts into component parts so that its organizational structure may be understood. Distinguishes between facts and inferences. 

Examples: Troubleshoot a piece of equipment by using logical deduction. Recognize logical fallacies in reasoning. Gather information for a project and select and apply the mathematics needed to carry out the project.
Key Words: analyzes, breaks down, compares, contrasts, diagrams, deconstructs, differentiates, discriminates, distinguishes, identifies, illustrates, infers, outlines, relates, selects, separates.

Synthesis: Builds a structure or pattern from diverse elements. Put parts together to form a whole, with emphasis on creating a new meaning or structure.

Examples: Integrate knowledge of electronics with mathematics to design and create an effective and efficient circuitry. Integrate training from several sources to solve a problem. Revise a process to improve the outcome.
Key Words: categorizes, combines, compiles, composes, creates, devises, designs, explains, generates, modifies, organizes, plans, rearranges, reconstructs, relates, reorganizes, revises, rewrites, summarizes, tells, writes.

Evaluation: Make judgments about the value of ideas or materials.

Examples: Select the most effective solution. Compare and contrast statistical tests used for data analysis based on a given set of circumstances.
Key Words: appraises, compares, concludes, contrasts, criticizes, critiques, defends, describes, discriminates, evaluates, explains, interprets, justifies, relates, summarizes, supports.

Affective Domain

The affective domain concerns the manner in which we process things emotionally, such as feelings, values, appreciation, enthusiasms, motivations, and attitudes. This domain has five major categories from the simplest behavior (being aware) to the most complex (behavior is controlled by an internal value system).

Category

Example and Key Words

Receiving Phenomena: Awareness, willingness to hear, selected attention.

Examples: Listen to teacher with respect. Listen for and remember assignments.
Key Words: asks, chooses, describes, follows, gives, holds, identifies, locates, names, points to, selects, sits, erects, replies, uses.

Responding to Phenomena: Active participation on the part of the learners. Attends and reacts to a particular phenomenon.  Learning outcomes may emphasize compliance in responding, willingness to respond, or satisfaction in responding (motivation). 

Examples:  Participate in class discussions.  Give a presentation. Question new ideals, concepts, models, etc. in order to fully understand them. Know the classroom rules and practices them.
Key Words: answers, assists, aids, complies, conforms, discusses, greets, helps, labels, performs, practices, presents, reads, recites, reports, selects, tells, writes.

Valuing: The worth or value a person attaches to a particular object, phenomenon, or behavior. This ranges from simple acceptance to the more complex state of commitment. Valuing is based on the internalization of a set of specified values, while clues to these values are expressed in the learner’s overt behavior and are often identifiable. 

Examples:  Demonstrate belief in the democratic process. Is sensitive towards individual and cultural differences (value diversity). Show the ability to solve problems. Propose a plan to social improvement and follows through with commitment. Inform teacher on matters that one feels strongly about.
Key Words: completes, demonstrates, differentiates, explains, follows, forms, initiates, invites, joins, justifies, proposes, reads, reports, selects, shares, studies, works.

Organization: Organizes values into priorities by contrasting different values, resolving conflicts between them, and creating an unique value system.  The emphasis is on comparing, relating, and synthesizing values. 

Examples:  Recognize the need for balance between freedom and responsible behavior. Accept responsibility for one’s behavior. Explain the role of systematic planning in solving problems. Accept professional ethical standards. Create a life plan in harmony with abilities, interests, and beliefs. Prioritizs time effectively to meet the needs of the organization, family, and self.
Key Words: adheres, alters, arranges, combines, compares, completes, defends, explains, formulates, generalizes, identifies, integrates, modifies, orders, organizes, prepares, relates, synthesizes.

Internalizing values (characterization): Has a value system that controls their behavior. The behavior is pervasive, consistent, predictable, and most importantly, characteristic of the learner. Instructional objectives are concerned with the student's general patterns of adjustment (personal, social, emotional).

Examples:  Show self-reliance when working independently. Cooperate in group activities (displays teamwork). Use an objective approach in problem solving.  Display a professional commitment to ethical practice on a daily basis. Revise judgments and changes behavior in light of new evidence. Value people for what they are, not how they look.
Key Words: acts, discriminates, displays, influences, listens, modifies, performs, practices, proposes, qualifies, questions, revises, serves, solves, verifies.

Psychomotor Domain

The psychomotor domain includes physical movement, coordination, and use of the motor-skill areas. These skills require practice to develop and are measured in terms of speed, precision, distance, procedures, or techniques in execution. Seven major categories list the simplest behavior to the most complex.

Category

Example and Key Words

Perception: The ability to use sensory cues to guide motor activity.  This ranges from sensory stimulation, through cue selection, to translation.

Examples:  Estimate measures of distance, mass, and volume. Detects non-verbal communication cues. Draw geometric figures in perspective. Estimate where a ball will land after it is thrown and then moving to the correct location to catch the ball.
Key Words: chooses, describes, detects, differentiates, distinguishes, identifies, isolates, relates, selects.

Set: Readiness to act. It includes mental, physical, and emotional sets. These three sets are dispositions that predetermine a person’s response to different situations (sometimes called mindsets).

Examples:  Know and acs upon a sequence of steps in a mathematical process.  Recognize one’s abilities and limitations. Show desire to learn a new process (motivation).
Key Words: begins, displays, explains, moves, proceeds, reacts, shows, states, volunteers.