Building a model for characterizing critical events: Noticing classroom situations using multiple dimensions

Sigal H. Rotem, Michal Ayalon

Research output: Contribution to journalArticlepeer-review


Anyone involved in mathematics education will at some point encounter a classroom situation in which a student's statement provides an opportunity for the teacher to enhance students’ mathematical understanding. This paper aims to characterize such classroom situations, known as critical events, as noticed by pre-service mathematics teachers during classroom observations and teaching. Analysis of 80 critical events reported by 20 pre-service mathematics teachers during a field-based teaching preparation program yielded a model that enables teacher-educators and researchers to characterize critical events while reflecting on the wide variations within these events. The model comprises three axes: the participants in the event, the focus of the event, and the dimensions in learning and teaching mathematics (i.e., cognitive, affective and social). The paper discusses the theoretical and empirical construction of the model and demonstrates its potential contribution using examples taken from our research.

Original languageEnglish
Article number100947
JournalJournal of Mathematical Behavior
StatePublished - Jun 2022

Bibliographical note

Funding Information:
The project is generously supported by the Trump (Israel) Foundation (Grant # 213 ) and the University of Haifa . We thank Prof. Roza Leikin for her help in monitoring the project. The first author, Sigal-Hava Rotem, is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship.

Publisher Copyright:
© 2022 Elsevier Inc.


  • Critical events
  • Field-based teacher preparation program
  • Secondary school mathematics
  • Teacher noticing

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics


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