%0 Book Section %1 Krummheuer99 %A Krummheuer, Götz %B Selected Papers from the Annual Conference of Didactics of Mathematics 1997 %D 1999 %E Fresenborg, Elmar C. %E Maier, Hermann %E Reiss, Kristina %E Toerner, Guenter %E Weigand, Hans G. %I Osnabrueck %K argumentation ijceell06 mathematics mythesis narrative sociocognitive vds-arg %P 127--135 %T Narrative Elements of Children's Agrumentations in Primary Mathematics Classrooms %U http://www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/cerme1-proceedings.html

@incollection{Krummheuer99, added-at = {2006-06-05T02:55:19.000+0200}, author = {Krummheuer, Götz}, biburl = {https://www.bibsonomy.org/bibtex/242ae64bfa703001a7329442fc4f5dd6c/yish}, booktitle = {Selected Papers from the Annual Conference of Didactics of Mathematics 1997}, citeulike-article-id = {391940}, comment = {in the classroom "argumentation dissolves in narrative representation" classroom learning is predominantly based on participation in narrativly structures argumentative activities. --- Following Bruner, identifies the charectaristics of narrative as: 1. sequenciality 2. factual indiference between the real and the imaginary 3. unique ways of managing departures from the canonical 4. dramatic quality --- meaning is implicit, and invisible to the listener who does not share the storyteller's interpretation --- argues that in order to successfully harness classroom argumentation as powerful catalysts of learning, we need to acknowledge their narrative nature, and understand its potentials and drawbacks. Krummheur stresses the distinction between narrative in its literary sense, which has little relevance to our discussion, and narrative as a form of everyday discussion. Narrative discourse in the mathematics classroom is rational, in the sense that it contains facts and arguments. However, these are typically implicit and, as we claimed above, conveyed through analogy or metaphor. This realization is important when analyzing students’ expressions and attempting to assert what knowledge they hold. On the other hand Krummheur issues a caveat: students who fail to infer the implied general statements will be at loss, left behind with a story that makes no sense. It is therefore crucial to encourage students to externalize the reasoning behind their story and express the general rules they identify. This observation is in line with Vygotsky’s approach, as noted by many studies (Collins, Brown \& Holum, 1991; Kaptelinin, 1995; Martí, 1996; Daniels, 2004), which emphasizes the construction of individual and collective knowledge through the processes of internalizing actions into thoughts and externalizing thoughts into actions. What has not perhaps been stressed enough is the role of externalization from the individual perspective. The process of transforming a vague web of ideas into a coherent and consistent narrative forces us to structure our thoughts. In the words attributed to Robert Cecil Day Lewis: First, I do not sit down at my desk to put into verse something that is already clear in my mind. If it were clear in my mind, I should have no incentive or need to write about it. We do not write in order to be understood; we write in order to understand.}, editor = {Fresenborg, Elmar C. and Maier, Hermann and Reiss, Kristina and Toerner, Guenter and Weigand, Hans G.}, interhash = {2efc417d60ae0af3b3f311e40fba80c4}, intrahash = {42ae64bfa703001a7329442fc4f5dd6c}, keywords = {argumentation ijceell06 mathematics mythesis narrative sociocognitive vds-arg}, pages = {127--135}, priority = {4}, publisher = {Osnabrueck}, timestamp = {2008-04-27T15:58:19.000+0200}, title = {Narrative Elements of Children's Agrumentations in Primary Mathematics Classrooms}, url = {http://www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/cerme1-proceedings.html}, year = 1999 }