MATH taxonomy

Posted by @natasabrouwer on April 16, 2022, 2:19 p.m.


The MATH taxonomy by Smith, et. al. (1996) defines the difficulty level of mathematics assignments. This taxonomy has three levels: A (Reproduction); B (Connection) and C (Reasoning). These levels are further broken down into different sub levels as shown in Table.

Table: MATH Taxonomy by Smith, et. al., (1996).

Level A: Reproduction

Level B: Connection

Level C: Reasoning

A1: Factual knowledge

A2: Comprehension

A3: Routine use of

B1: Information

B2: Application in new

C1: Justifying and

C2: Implications,
      conjectures and

C3: Evaluation

  • Level A includes remembering facts, formulas and recognize situations and routinely calculations and applying given algorithms.
  • Level B continues with the classification of a mathematical object, interpreting a situation or response and the ability to design a plan or select characteristics to work out an assignment.
  • Level C involves reasoning, justify, disprove, argue and prove, expressing presumptions and implications, compare situations, recognize or discover patterns, and constructing of an example or an extension of a concept. 


Smith, G., Wood, L., Coupland, M., Stephenson, B., Crawford, K., Ball, G. (1996): Constructing mathematical examinations to assess a range of knowledge and skills, International Journal of Mathematical Education in Science and Technology, 27:1, 65-77.

Smith, G., Wood, L. (2000) Assessment of learning in university mathematics, International Journal of Mathematical Education in Science and Technology, 31 (1), 125-132.

Original author: Natasa Brouwer
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