Relating Bloom’s Taxonomy and the TIMSS Cognitive Domains from a Mathematical Perspective

Bloom’s Taxonomy and the Trends in International Mathematics and Science Study (TIMSS) cognitive domains are two of the most successful hierarchical models in classifying cognitive demands of educational objectives, assessments, and activities. The Bloom’s Taxonomy was named after Benjamin Bloom, the chair of the committee of educators who invented the taxonomy. The TIMSS cognitive domains, on the other hand, was the offshoot of a series of international assessments joined by more than 40 countries for the past 20 years.

Although Bloom’s taxonomy includes three domains namely cognitive, affective, and psychomotor, this discussion will only focus on the cognitive domain. The goal of this post is to relate Bloom’s Taxonomy’s cognitive domains to the TIMSS cognitive domains.

Blooms Taxonomy’s Cognitive Domains

Bloom’s levels of cognitive domains are as follows (Wikipedia).

1. Knowledge-remembering facts, terms, basic concepts, or answers without necessarily understanding what they mean

2. Comprehension – demonstrating understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating the main ideas.

3. Application – solving problems in new situations by applying acquired knowledge, facts, techniques and rules

4. Analysis- breaking information into component parts, determining how the parts relate to one another, identifying motives or causes, and making inferences and find evidence to support generalizations. Its characteristics include:

5. Synthesis – building a structure or pattern from diverse elements; it also refers to the act of putting parts together to form a whole

6. Evaluation – presenting and defending opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria.

A slight revision about the taxonomy was done in 2001. The nouns used to name the levels were changed to verbs, Evaluation and Synthesis were swapped, and Synthesis was renamed to Creating as shown in the figure below.

The TIMSS Cognitive Domains

Over the past two decades, the TIMSS cognitive domains have evolved and have been simplified into three levels: Knowing, Apply, and Reasoning. The definitions are as follows:

1. Knowing – knowing facts and procedures, recalling and understanding concepts

2. Applying – applying concepts to solve problems; applying mathematics in a range of context

3. Reasoning – solving novel problems, systematic thinking, inductive reasoning

These domains have sublevels (See (Grønmo, Arora & Mullis, 2015) for details).

Relating Bloom’s Taxonomy and TIMSS Cognitive Domains

Bloom’s Remembering and Comprehension/Understanding levels of objectives clearly fall under the Knowing domain of TIMSS domains. This involves knowing facts and procedures like remembering a formula and understanding a certain procedure such as getting the root of a quadratic equation using the method of completing the square. The TIMSS Knowing domain involves familiarity with mathematical concepts (understanding) as well as procedural fluency.

I have placed Bloom’s Applying and Evaluating fall under the Applying cognitive domain. This is a bit tricky because Evaluating is one of the highest levels of the Bloom’s but note that the taxonomy was originally created for college students. Evaluating in college is a different level in elementary and high school. Evaluation in elementary and high school can range from thinking if a particular reasoning is correct or not or at the highest level evaluating someone’s solutions. In higher mathematics, of course, evaluating will be more complicated than analyzing since Evaluation will require analysis.

Blooms Taxonomy and TIMSS Cognitive Domain

I have placed Creating and Analyzing are under the Reasoning domain. According to both taxonomies, Analyzing is breaking information into parts. This is one of the skills that students should learn in order to solve problems.

Creating (originally Synthesis) is the highest form of reasoning since it includes creating something new or ideas that are new at least in the perspective of the students. This includes new ideas that cannot be reached by many students or at least some novel solutions to problems.

Bloom’s Taxonomy and the TIMSS Cognitive domains are hierarchical models that can be used to guide us in creating educational objectives, tasks, and assessment items. Let’s use them to improve our teaching and produce better learners.


Bloom’s taxonomy. (2017, June 8). In Wikipedia, The Free Encyclopedia. Retrieved
June 25, 2017 from

Clark, D. (n.d.). Bloom’s Taxonomy of Learning Domains. Retrieved June 25, 2017, from

Grønmo, L. S., Lindquist, M., Arora, A., & Mullis, I. V. (2015). TIMSS 2015 mathematics framework. TIMSS, 11-28.

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