Improvement Without Change in Meta-rules

The Challenge of De-Ritualization

Abstrakti

 In this study, we explore the changes in mathematical participation of a student who underwent a one-on-one tutoring intervention, led by the first author, aimed at disrupting her ritual participation in the algebraic discourse. The student, Fani (pseudonym), was a 7th grader going on to 8th grade, who was on the verge of being transferred to a lower track in mathematics. Our intervention aimed to de-ritualize her discourse, that is, to assist her in becoming more agentive and to produce narratives about mathematical objects rather than follow procedures. To assess the effectiveness of the intervention, we compared the pre- and post-intervention interviews with Fani using the dimensions of ritual and explorative participation, including agentivity, syntactic/objectified mediation, bondedness and focus on procedure or on result. Our analysis shows that Fani’s enactment of algebraic tasks remained predominantly ritual both before and after the intervention. Nevertheless, the number of correct responses increased. Examining the interaction in the interview revealed that the instructor’s prompts, although designed to encourage justification and substantiation, mostly failed to produce de-ritualization due to different meta-rules followed by Fani than the canonical ones.