Source: The Teacher Educator, 56:4, 347-371
(Reviewed by the Portal Team)
The purpose of this paper is to present work and research related to pre-service teachers (PSTs) and professional teacher noticing.
More specifically, the work and research reported in this paper utilized a rubric to characterize the professional noticing skills, attending, interpreting, and deciding, PSTs recorded in a reflective journal after planning and implementing instruction for a small group of students over the course of an eight week after-school tutoring program.
This study was designed as an instructional intervention in an integrated mathematics content and methods course (with a concurrent field experience) with the goal of preparing PSTs for a future practice anchored in mathematics education reform efforts focused on student thinking (CCSSM, 2010; Kilpatrick et al., 2001; NCTM, 2000, 2014).
The purpose of the intervention was to engage PSTs in learning about and enacting professional teacher noticing (Jacobs et al., 2010) in the context of the well-defined mathematical content and associated student thinking about the meaning of addition and subtraction (Carpenter et al., 2014; CCSSM, 2010; Dougherty, 2014; NRC, 2009).
The study examined the following questions: When recording professional teacher noticing skills in a reflective journal –
1. Attending; What strategies do PSTs identify in elementary student solutions to addition and subtraction problems and what mathematical details do PSTs provide when identifying these strategies?
2. Interpreting; What evidence do PSTs use to interpret elementary student understanding of addition and subtraction?
3. Deciding; What evidence of elementary student understanding of addition and subtraction do PSTs use in deciding what to do next?
Context and participants
An elementary number and operations mathematics content course and concurrent mathematics methods course with a field experience (College of Education after-school tutoring program) provided the context for this study.
Taught jointly by faculty from the Department of Mathematics and the College of Education (author), the integrated courses drew on situated cognition learning theory (Brown et al., 1989; Greeno, 1997) to support PSTs in learning how to teach mathematics with a view toward student thinking.
Accordingly, PST learning was situated in the context of authentic activity, teaching mathematics in an after-school tutoring program.
Thus, PSTs learned how to utilize professional teacher noticing as a conceptual tool to develop a vision for their beginning practice.
Participants included 12 PSTs enrolled in the courses at a mid-sized private university in the Midwestern U.S.
At the time of the study, the participants, who were seeking a license to teach in grades one through eight and were one semester away from their student-teaching experience.
Data for this study included 16 journal entries PSTs completed over the course of eight weeks.
The content PSTs included in their response to each of the reflective journal questions served as the unit of analysis.
PST responses to journal questions differed in terms of word count with a mean word count of 634 words, a minimum word count of 175 words and a maximum word count of 1278 words.
Results and discussion
Characterizing PST attending skills
Results related to the first research question, which examined PST attending skills, are promising and provide important insights for teacher educators involved in the work of professional teacher noticing.
Overall, PSTs in this study were near proficient (score 3) in attending, consistently including significant mathematical details related to the meaning of addition or subtraction in their reflective journals to chronicle strategies students used to solve addition and subtraction problems.
Additional analysis of PST attending responses, however, revealed that PSTs received fewer (3), Proficient scores when attending to Derived Fact strategies as compared to Direct Modeling, Counting, and Recalled Fact strategies.
These results need to be interpreted with caution given that students select a solution strategy when solving addition or subtraction problems.
Nonetheless, the results may suggest that it was more difficult for PSTs to attend to the significant details involved in the Derived Facts strategy.
Results related to the first research question suggest that situating professional teacher noticing within the well-defined mathematics domain and associated student learning trajectory related to the meaning of addition and subtraction provided scaffolding that supported PSTs in learning how to attend to the strategies students use to solve addition and subtraction problems.
Situating professional teacher noticing within a well-defined content domain provides a viable avenue to support PSTs in simultaneously learning about mathematics content while developing attending skills
Characterizing PST interpreting and deciding skills
The second and third research questions in this study investigated the evidence PSTs used and the rationale they provided when interpreting student understanding of the meaning of addition or subtraction and deciding next steps.
Overall, the findings indicate that PSTs were developing (score 2) their interpreting and deciding skills.
In addition, results of quantitative analysis, which compared overall mean scores for attending, interpreting, and deciding, uncovered significant differences between each of the means.
These results reinforce the findings of several other studies (Castro Superfine et al., 2017; Fernandez et al., 2013; Ivars et al., 2019; Schack et al., 2013), which suggest that interpreting and deciding skills are more difficult for PSTs than attending skills.
In this study, which was situated in the domain of the meaning of addition and subtraction and associated student thinking, not only are attending and interpreting inextricably linked, but so too are the conceptual categories of problem types and taxonomy of strategies.
PST deciding skills
Overall, PST deciding responses were characterized as developing (score 2).
Thus, while PSTs made instructional decisions using evidence generally connected to student understanding of addition or subtraction, they included a rationale to explain their next steps.
In fact, additional analysis of PST deciding responses uncovered that half of all responses included a rationale to explain their decisions relative to:
(1) supporting student understanding of the meaning of addition and subtraction,
(2) providing students more practice with a particular problem type, and
(3) teaching students solution strategies to help them move along the trajectory of learning.
These findings are promising, and as consistent with Ivars et al. (2019), indicate that PSTs who use a student learning trajectory as a scaffolding mechanism to develop their deciding skills can choose appropriate next activities for their students.
Furthermore, these results highlight how PSTs were beginning to use their knowledge of the meaning of addition and subtraction and related student thinking in action to make appropriate instructional decisions for their students.
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