2020 Day 5: 29th May Presentation

Rough Concept Inventories

A. Mani
Homi Bhabha Centre for Science Education, TIFR, Mumbai, India

Concept inventories are MCQ-based instruments designed to test the understanding of concepts (and possibly the reasons for failure to understand) by learners. Often, they are deemed to be rather incompatible with student centered modes of learning and evaluation. Some inventories require students to provide justifications for their answer and thereby significantly boost the quality of assessment offered. In this research the problem of adapting the subject/concept specific instruments to make room for diverse response patterns (including vague ones) is explored in some detail by the present author. It is shown that high granular operator partial algebras invented by
her [1] with additional temporal and key operators are well suited for representing them. Rough concept inventories, proposed in the research, can handle vague subjective responses, improved standardization and the basic apparatus for the formal study of consequence in the contexts.

A weak summary of the proposed methodology is as follows:

  1. select a number of key concepts in a subject or topic;
  2. situate them relative to the concepts and granular concepts described in the model (or alternatively situate the concepts relative to a concept map in terms was constructed from and is a
    part of, and basic well-understood concepts);
  3. formulate multiple choice questions that aim to test key aspects of applications of the chosen concepts;
  4. each question is required to have at least one correct answer and a number of distractors based on alternative conceptions;
  5. require explanation from students for their choice;
  6. evaluate explanations relative to model in terms of concept approximations (or alternatively evaluate explanations relative to concepts that are definitely and possibly understood).


  1. Mani, A.: Dialectical Rough Sets, Parthood and Figures of Opposition-I. Transactions on Rough
    Sets XXI(LNCS 10810) (2018) 96_141