Boom's Taxonomy Interpreted for Mathematics

By: Lindsey Shorser

Bloom's Taxonomy is an educational tool developed by Benjamin S. Bloom (1913-1999) that ranks the relative cognitive complexity of various educational objectives. This taxonomy is often used as an aid when creating test questions and assignments. Below is an interpretation of Bloom's Taxonomy in the context of mathematical understanding with examples drawn from introductory-level, single-variable calculus.

Level of Understanding Description Key Terms Sample Question
Knowledge Questions involve stating definitions, theorems, steps to a given method and other features of the course notes. List, define, describe, show, name, what, when, etc. What are the conditions of the Mean Value Theorem.
Comprehension "Use the definition to identify...", "Which of the following satisfies the conditions of...", "Use a specified method to..." Summarize, compare and contrast, estimate, discuss, etc. Find the slope of the tangent line to the following function at a given point.
Application Questions use more than one definition, theorem, and/or algorithm. Apply, calculate, complete, show, solve, modify, etc. Find the derivative of the following implicitly defined function. (This question might also involve logarithmic differentiation.)
Analysis Questions require the student to identify the appropriate theorem and use it to arrive at the given conclusion or classification. Alternatively, these questions can provide a scenario and ask the student to generate a certain type of conclusion. Separate, arrange, classify, explain, etc. Let f(x) be a fourth-degree polynomial. How many roots can f(x) have? Explain.
Synthesis Questions are similar to Analysis questions, but the conclusion to be reached by the student is an algorithm for solving the given question. This also includes questions which ask the student to develop their own classification system. Integrate, modify, substitute, design, create, What if..., formulate, generalize, prepare, etc. Optimize the given quantity after generating the function that represents the given quantity.
Evaluation Questions are similar to Synthesis questions, except the student is required to make judgements about which information should be used. Assess, rank, test, explain, discriminate, support, etc. Related rate word problem where students decide which formulae are to be used and which of the given numbers are constants or instantaneous values.

For a general description of Bloom's Taxonomy, see: University of Victoria - Counselling Services