Prospective elementary mathematics teachers’ noticing of childrens’ mathematics: a focus on extending moves

Abstract

Professional noticing of children's mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169-202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children's mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics teachers' (PTs') responses to a pedagogical activity designed to engage them in an approximation (Grossman et al. in Teach Coll Rec 111(9): 2055-2100 of professional noticing of children's mathematical thinking in the moment of teaching, with a focus on developing responses which extend the student's thinking. PTs were provided two different examples of student work and a series of questions designed to elicit information about their ability to professionally notice student work. We present data and analysis of 73 PTs' abilities to engage in the individual skills associated with noticing as well as their abilities to use the skills cohesively in concert. Our results demonstrate the type of representation used determined PTs' success in all three facets of noticing, with a particular effect on interpreting. Further, our focus on a specific type of response move, along with the introduction of a scaffold for that response move, made a difference in PTs' ability to successfully respond to student work when compared to a prior study with the same PTs (Tyminski et al. 2014). We unpack these results along with suggestions for pedagogical practice as well as directions for future research.

Prospective Primary Teachers’ Professional Noticing in Non-Formal Learning Environments: The Case of a Mathematics Fair

“…Firstly, we believe it is important for both initial and in-service teacher education programmes to address professional noticing more explicitly, along the lines of previous studies reporting successful attempts [17,20,25,27,28]. Since there was much less emphasis on mathematical related insights in each theme, we suggest that particular focus be placed on mathematics-specific noticing, such as pupil thinking, teaching strategies, concepts, and processes involved in tasks.…”

“…Video analysis of one's own teaching or the teaching of others appears to be the most prevalent approach, and can take place in different ways, such as analysis of lessons recorded for Lesson Study purposes [17], participation in video clubs [10,18], and analysis of full-length classroom videos [19] or of video vignettes [2,11,20]. Other activities include analysis of animations [21][22][23], technology-aided interventions [24], reflection on teaching rehearsals [25], examination of real pupils' written responses to mathematical tasks [26,27], or combinations of different mediums mentioned above [28]. Clearly, all these attempts are important in supporting participating pre-and in-service teachers in the development of their noticing skills, as they all report, to some extent, success in doing so.…”

Pre-service teachers’ professional noticing when viewing standard and holographic recordings of children’s mathematics

“…Although there is ample research that suggests more experienced teachers demonstrate more sophisticated professional noticing (Huang & Li, 2012;Jacobs et al, 2010;Yang et al, 2021b), Yang et al (2021b) note that "teaching experience indeed acts as a main-though not sufficient-factor in the development of noticing" (p. 37). Rather, it provides initial and necessary support for development of noticing, but targeted professional development experiences are needed for further growth (Jacobs et al, 2010;Tyminski et al, 2021). One approach to this is to engage teachers (novice or experienced) in various forms of decomposing practice.…”

“…For example, some scholars have engaged PSTs in using StudioCode to mark specific moments in standard videos of classroom instruction, and discuss these moments with peers or their course instructor Teuscher et al, 2017). Others have used specific resources such as frameworks for posing questions (Tyminski et al, 2021), scaffolds for specific types of noticing (Amador et al, 2016;van Es & Sherin, 2002), descriptions of forms of students' mathematical reasoning (Jacobs et al, 2010;Schack et al, 2013), and so forth. In most cases, the increased specificity in resources and prompts described above facilitated an increased specificity in how teachers describe students' reasoning of mathematics.…”

“…(Barnhart & van Es, 2015;Huang & Li, 2012). Teachers then begin to attend to students' procedural reasoning before eventually attending to and interpreting students' conceptual reasoning (Barnhart & van Es, 2015;Tyminski et al, 2021;van Es et al, 2017). Although experience in the classroom can and does facilitate growth in noticing, developing robust and sophisticated professional noticing typically requires professional development (Jacobs et al, 2010;Simpson & Haltiwanger, 2017;.…”