International Portal of Teacher Education

Source: Journal of Mathematics Teacher Education, Volume 17, p. 245–270 (2014)
(Reviewed by the Portal Team)

Building on research on teacher noticing, this study focused on examining how mathematics teacher educators (MTEs) can support the development of prospective teachers (PSTs’) noticing key aspects of mathematics teaching and learning through a carefully constructed video analysis activity.

Methods
Throughout the semester, PSTs from four mathematics methods classes (each at a different university) engaged in four or five video analyses of excerpts of mathematics lessons. Prospective teachers’ used four lenses to analyze the videos. Each lens focused on one of the four facets of a mathematics lesson: teaching, learning, task, or power and participation. All four lenses included an explicit focus on students’ resources (e.g., mathematical, cultural, community, family, linguistic, student interests, and peers).
Mathematics teacher educators prepared PSTs for the video analysis by assigning a reading that provided appropriate background for the focus of the activity (e.g., for the mathematics content or for foci on the lenses) and/or by engaging PSTs in a mathematics problem that they would later see students solving in the video.
All PSTs in the methods courses were undergraduates working on certification to teach within K-8 grades.
The authors collected data for all instructor and PST activities related to the video analysis activities: PSTs’ small group and whole class discussions after watching each video, as well as instructors’ planning materials and reflective journals.

The authors explored PSTs’ noticing of equitable instructional practices and children’s MMKB over the course of the mathematics methods semester. To support PSTs’ learning in this regard, the authors decomposed and approximated practice by designing the video analysis activity. Consistent with their work across the larger TEACH MATH project, the authors endeavored to respect PSTs as developing professionals with prior experiences and knowledge that informed what they noticed.
The findings showed that prospective teachers evidenced noticing of mathematics teaching and learning as early as the mathematics methods course. The authors also found that the prompts and structure of the activity supported prospective teachers by increasing their depth of noticing and their foci in noticing, moving from attending primarily to teacher moves (and merely describing what they saw) to becoming aware of significant interactions (and interpreting effects of these interactions on learning).

The findings suggest that the repeated use of the lenses focused PSTs’ attention on key aspects of teaching and learning mathematics, allowing them to consider the impact of teachers’ and students’ decisions and actions, and in some instances begin to make connections between teacher moves and students’ mathematical thinking, students’ participation, and students’ resources. The authors also found that PSTs tended to hold a teacher-centric perspective when demonstrating lower levels of noticing: noticing at Level 2 they attended predominately to teaching. In regard to student resources, PSTs tended to attend only to students’ home languages at Level 2 and evidenced noticing of other resources (e.g., family, community, and mathematics knowledge) as they began to analyze intentions and impacts of teaching and learning (Level 3). This may be attributed at least in part to the fact that two of the three videos discussed in this article come from bilingual classrooms and afforded the opportunity to focus on language.

In regard to participation, PSTs tended to limit attention to students being involved or engaged in a lesson at Level 2 and evidenced noticing of the importance of authority, status, and competence at Level 3. The findings indicated that PSTs can learn to notice across multiple foci as early as during the methods course. The authors thus see that focusing on equitable instructional practices does not overcomplicate or overwhelm PSTs’ learning. Furthermore, they found that when provided support for noticing in these areas, PSTs can begin to notice a range of student resources and to analyze how and why these resources enhance learning. Furthermore, they can notice how students participate and are provided opportunities to demonstrate authority and competence in learning.
With the authors' deliberate efforts to focus attention on equitable instructional practice through repeated enactments of noticing, PSTs demonstrated that they can develop awareness for multiple aspects of teaching and learning and notice at deeper levels; however, their prompts and video choices, along with opportunities to repeat the activity, seemed critical components of inducing and developing this noticing.

As PSTs interacted in small groups and then in the whole class, the authors found that they built on each other’s ideas, perspectives, and observations such that higher levels of noticing were attained. Moreover, the authors recognize that the activity as they constructed it provides specific affordances and constraints in regard to what is observable in the videos and how PSTs respond to the video through consideration of the prompts we provide. The authors also endeavor to understand PSTs’ past experiences that led them to perspectives that evidenced fragmented awareness toward children and their home languages, so that they can disrupt these views. The authors found that the views expressed in group discussions at the beginning of the semester were not static; PSTs engaged with each other and their instructor to consider the interaction among teaching, students’ perspectives, and students’ MMKB. This finding suggests that PSTs need multiple opportunities to expose and identify their fragmented awareness and to develop more informed and considered perspectives. Discussion with peers as well as input from instructors can help PSTs move toward a greater understanding of the resources available to and used by students.
This study provides some understandings of PSTs’ learning through a particular form of approximation and decomposition of practice by developing PSTs’ noticing through video analysis.