# Cognitive demands of a mathematical task

I'm looking for a theoretical framework to classify a task based on its cognitive demand.

I only have the Smith and Stein's (1998) proposal and PISA framework such as my principal references. In particular, the PISA categories which help us to classify items in standarized tests: Reproduction, Connection and Reflection.

Thank you in advance.

Smith, M. S., y Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344-350.

• Not giving this as an answer since I personally have always disliked it, but I feel obligated to mention Bloom's taxonomy (en.wikipedia.org/wiki/…) since it is a standard tool in my experience in American schools Dec 21 '17 at 15:22
• By the way, +1 I absolutely love this question. Dec 21 '17 at 15:23
• What is missing from Stein's work that you still need? Dec 24 '17 at 20:23
• Because it doesn't deep into what is behind of a mathematical task. I mean a mathematical task is complex and an specific framework should entail these aspects. Jan 3 '18 at 22:04

## 2 Answers

Extending the answer from Nate Bade: Within ECD (Evidence Centered Design), there are quite a few possible models for 'cognitive demand'. Probably the widest use within LSA (large scale assessment) such as PISA, but also for example Smarter Balanced or PARCC, models are based on Webb's concept of DOK (Depth of Knowledge).

General resources of Webb's concept can easily be found on the internet, so I won't even start listing resources. Specifically for Math, I find the conception of cognitive rigor by Kathrin Hess pretty enlightening.

That said, one can start discussing the relevance of these models. This is not a new question, but discussed (or at least commented...) on MESE:

Which mental model is most useful when thinking about math education: Webb's DoK, CCSM's Aspects of Rigor, or Bloom's Taxonomy? Are there others?

One theoretical framework for designing actives and assessments is ETS's Evidence Centered Design framework, although it requires long term analysis of a task or series of tasks in conjunction with other methods of measurement of ability. The basic idea is to use rigorous assignment/activity/test design process that allows more concrete conclusions to be drawn about the skills actually being tested. Item Response Theory is used to classify the difficulty and discrimination of actives.

That said I'm not sure if this is what you're looking for, it's more a design process framework than a framework for understand the cognitive components of a task.