Student trajectories in high school mathematics: Issues of choice, support, and identity‐making

Connecting the dots: toward a networked framework to conceptualizing identity in mathematics education

“…The challenge will most probably be to harness identity work intentionally to what schools are for, and to bring educational change that allows all to attain mathematically. Educational systems where identities are, more often than not, institutionally assigned (see Boaler 2005;Boaler et al 2000;Mason and McFeetors 2007;Oakes 1990), and contexts where identities are socioculturally disseminated (see Epstein et al 2010) need to provide better support to learners by recognizing their developing identities as simultaneously multi-dimensional. Seriously, and carefully, attending to learners' four-part identity network can rigorously demonstrate how identity work forms and informs learners' future trajectories as learners of mathematics.…”

“…The four-part model suggested in this paper informs the use of multiple-method research designs that can be conducive to an investigation of ipse mathematics identity. In addition to use of drawings to elicit learners' beliefs and experiences (see Towers et al 2018), such research designs and methodologies can include both focus group and oneon-one interviews (see Fellus 2018); conversation over video-recorded classroom situations where students watch video clips of their own or others' classroom interactions and provide interpretations of what they see while at the same time also engaging in identity work (see Mason and McFeetors 2007); elicitation of past experiences through the use of what McAdams (1995) calls life chapters where participants organize their past experiences with mathematics in the form of book chapters and provide interpretations of the relationship between past events, present actions, and future plans (see Fellus 2018); invitation to assign humanlike characteristics to mathematics in order to elicit learners' relationships with mathematics, as Zazkis (2015) did in asking his prospective mathematics teachers to describe their relationship with mathematics as if it were a human being; use of metaphors in thinking about mathematics as Markovits and Forgasz (2017) did, asking young children to think about animal metaphors to express their thoughts about mathematics; harnessing the method of duoethnography, which builds on a collective sense making over mathematics-related issue through interaction among two (thus duo) or more participants as Zazkis and Koichu (2015) did in their conversation on understanding the infinitude of primes; capturing visual representations through photographs and videos-also known as photovoice-of thoughts about mathematics to allow for students' voices to be heard as they express ideas in and about mathematics thus developing their mathematics authorial identity (see Harkness and Stallworth 2013); and writing short mathematics-related poems that are instrumental for their structural and expressive simplicity as Haltiwanger and Simpson (2013) illustrate through examples of students' cinquains (five-line poems) on mathematical concepts. (Ivanič 2006) Stories that "are reifying, endorsable, and significant" (Sfard and Prusak 2005, p. 16) Andersson et al Bishop 2012Boaler 2005Boaler et al 2000Damarin 2000Heyd-Metzuyanim 2013Hogan 2008Mason and McFeetors 2007Oakes 1990Sfard and Prusak 2005Wood 2013 Stating positions, ideas, and beliefs (Ivanič 1998) Appropriation of content knowledge, words, and ideas…”

“…Here, too, how students are identified as mathematically competent or incompetent by self and others has been shown to be a determining aspect in one's identity as a learner of mathematics. Mason and McFeetors (2007) interviewed 400 Grade-10 students over a full school year. They demonstrate through students' "narration about goals, actions, and decision making" (p. 294) how identity is strongly associated with students' course selection among four available levels of mathematics courses in Grade 10 (Honours, Pre-Calculus, Applied, or Consumer) and how the way students identify themselves as learners of mathematics informs their ongoing decision making.…”

“…For example, being identified as smart in mathematics nullified the option of seeking help-students simply decided not to ask for help when they needed it because they feared that if they did, they would no longer be identified as smart in mathematics. Mason and McFeetors (2007) explain, "asking for help was a difficult identity matter for these students: They were in the academic mathematics courses precisely because they were smart kids, and (as they had experienced personally throughout their junior high years) smart kids do not need to ask for help" (p. 309).…”

From Data Through Coding Toward Categorizing: Negotiating Data Analysis in Constructivist Grounded Theory

“…The researcher's sensitivities-what the researcher attends to because of her/his experiences of conducting research, scholarship in the field, and interests-are explored and employed as a starting place in data analysis. My sensitizing concepts developed out of two related research projects (Mason & McFeetors, 2007;McFeetors, 2006), and include: intentions, voice, identity, and relationships with sources of knowledge.…”