Vicious Cycles of Identifying and Mathematizing: A Case Study of the Development of Mathematical Failure

Abstract

This study uses a new communicational lens that conceptualizes the activity of learning mathematics as interplay between mathematizing and identifying in order to study how the emotional, social, and cognitive aspects of learning mathematics interact with one another. The proposed framework is used to analyze the case of Idit, a girl who started out as a high achiever in 7th-grade math and ended up failing that same subject in 9th grade, complaining of severe “mathematics anxiety.” This article traces the narratives endorsed by Idit’s parents and teacher, which form the background for the development of her ritual participation in mathematical discourse. Next it attempts to link Idit’s ritual participation in a course I taught with her eventual failure in mathematics. The mechanism behind this failure is conceptualized as a vicious cycle that thrives on the basis of a ritualistic discourse motivated mainly by grades and other instrumental motives for learning mathematics. The analysis of this case gives rise to a model of how mathematical identities of failure may develop hand in hand with the failure to learn new mathematical skills.

Notes

¹ This definition is somewhat similar to Gee’s (2010) Discourse with a capital D.

² The movie can be found online at https://www.youtube.com/watch?v=qr7vCd0sgVE.

³ Indirect identifying is somewhat similar to positioning (Harré & van Langenhove, 1999), yet the connection between positioning and the construction of a certain identity narrative is not clear. Within the current framework, identifying (defined as the construction of identities) makes the connection between the action (identification) and the product (identity) more clear.

⁴ Hebrew: Ha’yiti Miztayenet (literally, “I was excellent (or I excelled) in math”). Excelling is used in the participle form, which here seems to be used as an adjective. This manner of usage most resembles how American students talk about being the top student in class.

⁵ Hebrew: To’il betuva (literally, “would be so kind as to”).

⁶ In the movie, the hero’s parents are portrayed as overtrusting of his excellent achievements and not aware of their boy’s deteriorating grades.

⁷ Hebrew: Makpidim (literally, “punctilious”). The Hebrew makpidim is probably less unpleasantly colored than strict, but this was the closest translation found.

⁸ Hebrew: Bakara (literally, “inspection or supervision”).

⁹ Orot is the name of Idit’s junior high school. All names are pseudonyms.

¹⁰ This routinized identification was even more pronounced during the ninth-grade interview, when Idit engaged with the same problem and identified herself as “not good with fractions” precisely at the same point, when I suggested that she should consider fractions as a solution. For an elaboration of this episode, see Heyd-Metzuyanim (2011).

¹¹ Because this excerpt is taken from a mathematical interview that was conducted at the end of the course, it makes sense to presume that the motive of being highly evaluated was prominent for Idit throughout the whole activity. Yet the change from explorative to ritual participation within this episode shows that despite an overall identifying motive that is inherent to such an evaluative situation, students can still participate in overlapping and differing motives within the same situation.

¹² The course terms 5 units, 4 units, and 3 units are shortenings of Units in Matriculation Exam. This is a very common way to refer to the different courses in mathematics at high school and has been part of the mathematical educational culture in Israel for several decades.

¹³ Idit was also presented with a geometrical proof task on which she performed satisfactorily. Note that geometrical proofs were studied in eighth and ninth grades and seemed to provide Idit with a fresh start independent of her former arithmetical gaps from elementary school.