Commognitive framework: thinking as communication and learning as participation in mathematical discourse¶

Theory · All theories
Evidence · 5 claims (5 for) · 1 study (1 review), q2 · 0 of 1 report an effect size · 5 claims rest on one study

Description¶

Commognition, named from the combination of communication and cognition, conceptualizes thinking as self-communication and learning mathematics as participation in a discourse. The paper explains that each discourse is distinguishable by four characteristics: "community's word use, visual mediators, (endorsed) narratives, and routines". It distinguishes object-level rules (narratives about regularities in object behavior) from meta-discursive rules, and object-level learning (endogenous expansion of the discourse) from meta-level learning (exogenous transition to a new discourse). The authors propose this framework as both a theoretical lens and pedagogical approach for studying proof teaching in lectures.

Design Implications¶

Context¶

Requirements¶

• Analytical focus on one or more of the four discourse characteristics (word use, visual mediators, narratives, routines) in lecture transcripts or discourse data

Constraints¶

• The paper applies the framework to lecture-type teaching in higher education mathematics, where communication is mostly one-way from lecturer to students

Target Learners¶

• university mathematics students

Target Learning Objectives¶

• participation in mathematical discourse
• understanding of proof and proving

Claims¶

• Commognitive analysis of lecturing offers micro-level insights into lecturer-student communication that non-commognitive approaches miss [+M]
• Review reports lecturers' discourses vary: distinct teaching styles and routine profiles despite superficially similar lectures [+M]
• Review reports lecturers' discourse contains endorsed and enacted meta-rules about doing mathematics that can model mathematical behavior [+M]
• Review reports students did not recognize the key points an exemplary lecturer presented in a proof [+M]
• Review reports TAs sharing the same agenda provided different meta-level learning opportunities through object-level adaptations [+M]

Related Theories¶

• Commognition
• Ritual versus exploration routines and the process of de-ritualization
• Socio-didactic-mathematical norms (SDMNs) as metadiscursive rules in pre-service teacher discourse

Examples¶

• Analyze lecturers' proof discourse for flexibility, bondedness, applicability, agentivity, objectification, and substantiability to study de-ritualization opportunities
• Six desirable characteristics of routine marking movement toward explorative participation

Key Sources¶

• Karavi, Mali, & Avraamidou. (2022). Commognition as an approach to studying proof teaching in university mathematics lectures. EURASIA Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/12173