The complexity of knowledge construction in a classroom setting

Tommy Dreyfus (1) , Chris Rasmussen (2) , Naneh Apkarian (2) , Michal Tabach (1)

1 TAU - Tel Aviv University
2 SDSU - San Diego State University

We study a class of mathematics education MA students in an introductory course on Chaos and Fractals, as they grapple with the Sierpinksi triangle, and in particular with the apparent paradox that its area equals 0, while its perimeter is infinitely long. For this purpose, we network an approach for investigating the construction of knowledge in small groups with one for examining how ideas and ways of reasoning function-as-if-shared in a classroom. Our results show complexities: (i) small group work and whole class discussions mutually influence each other; (ii) ideas may function-as-if-shared in the whole class even if the majority of students have not previously constructed them in their groups; (iii) knowledge constructed in the small groups may or may not later function-as-if-shared in the whole class.

Mots clés: Teachers' and students' practices at university level; teaching and learning of analysis and calculus; knowledge construction in classrooms; paradoxes

Domaines: Education; Histoire et perspectives sur les mathématiques [math.HO]

Tommy Dreyfus, Chris Rasmussen, Naneh Apkarian, Michal Tabach. The complexity of knowledge construction in a classroom setting. INDRUM 2018, INDRUM Network, University of Agder, Apr 2018, Kristiansand, Norway. ⟨hal-01849971⟩