Opening mathematics texts: resisting the seduction

Abstract

This analysis of the writing in a grade 7 mathematics textbook distinguishes between closed texts and open texts, which acknowledge multiple possibilities. I use tools that have recently been applied in mathematics contexts, focussing on grammatical features that include personal pronouns, modality, and types of imperatives, as well as on accompanying structural elements such as photographs and the number of possibilities presented. I extend this discussion to show how even texts that appear open can seduce readers into feeling dialogue while actually leading them down a narrow path. This phenomenon points to the normalizing power of curriculum. For this analysis and reflection, I draw on mathematics textbook material that I wrote. As a way of modelling an alternative to normalization, I identify myself as a self-critical author and thus invite readers to be critical of their reading and writing of mathematics texts.

Teaching math in real time

“…Lately, I feel that perhaps the experiences I have for my students are too far removed from the experiences they have had and will have (Yackel & Cobb, 1996 ). This leads to me feeling the “seduction” of a canonical curriculum, as might be present in a textbook (Wagner, 2012 ), and a compulsion to deliver such a curriculum at least in part. To that end, I steer the course in the direction of probability theory, not losing sight of having this emerge from social networks.…”

Primary students’ participation in school based mathematical reasoning practices: Coordinating reciprocal teaching and systemic functional linguistics to support reasoning in the Swedish context

“…In contrast, SFL contributes towards visualizing the students' linguistic choices in a specific situation and context of culture during the classroom intervention. In earlier studies, SFL has been used for studying written and spoken language use in mathematics classrooms (see, for example, Herbel-Eisenmann, 2007;Wagner, 2012). This conceptual framework is used not only as an analysis tool but also as a tool to develop the design of the activities in the intervention.…”

“…Relationships can be revealed by examining the 'voice' of the text through identifying the use of imperatives, personal pronouns and modal verbs (Herbel-Eisenmann, 2007), and this approach is also adopted in this study. Imperatives command readers or listeners to do something, such as 'write', whereas personal pronouns, such as 'I' and 'you', identify the participants exemplifying their personal engagement (Morgan, 1998;Wagner, 2012), and finally, modal verbs indicate the level of certainty, for example, 'shall' and 'can'. The third metafunction, the textual metafunction is constituted by the mode which involves what role language plays involving different representations such as symbols, words and illustrations and how they work together to create cohesiveness when expressing meaning (Halliday & Hasan, 1985).…”

Supporting mathematical reasoning through reading and writing in mathematics : making the implicit explicit

“…First, it allows for analysing the impact of the cultural and situational aspects on the mathematical meaning making, and second, it allows theory to be used as a tool for developing strategies to improve students' reasoning and reading competence. In previous mathematics education research, this approach has been a helpful tool for studying spoken and written texts in mathematics classrooms (Atweh, Bleicher & Cooper 1998;Bergwall, 2016;Herbel-Eisenmann, 2007;Morgan, 1998Morgan, , 2006Temple & Doerr, 2012;Wagner, 2012). In line with this, two directions in mathematics education apply SFL (Schleppegrell, 2010).…”

“…Within the latter theoretical framework, SFL, language is viewed as a system of meaning which can be analysed at the clause level to understand how contexts, such as classrooms, are reflected in participants' linguistic choices. SFL has previously been put forward as a suitable tool when studying spoken or written texts in mathematics classrooms (Herbel-Eisenmann, 2007;Morgan 2006;Wagner, 2012), but reading has not been an explicit focus, with the exception of Bergwall's (2016) study of TIMSS tasks.…”