Developing an Interview Module to Support Secondary PST's Noticing of Student Thinking

2016 ◽  
Vol 5 (1) ◽  
pp. 29-46 ◽  
Author(s):  
Kristin Lesseig ◽  
Stephanie Casey ◽  
Debra Monson ◽  
Erin E. Krupa ◽  
Maryann Huey

Effective mathematics teaching involves eliciting and interpreting student thinking, and then using students' current understandings as a basis for instruction. Research indicates these skills are not innate but can be acquired through structured experiences. In this article, we describe the development and implementation of an interview module aimed at supporting secondary preservice teachers' ability to elicit and use evidence of student thinking. Analysis of preservice teachers' noticing of student thinking across components of the interview module demonstrated positive benefits of the assignment. We share our design considerations and results, and offer potential adaptations to the module for other mathematics methods instructors interested in using the module to develop secondary preservice teachers' ability to notice student thinking.

2019 ◽  
Vol 2019 ◽  
pp. 1-20
Author(s):  
Mary Gichobi ◽  
Alejandro Andreotti

This study examined the extent to which preservice teachers (PSTs) develop their capacity to attend to children’s strategies and interpret and respond on the basis of children’s mathematical understanding in the context of two well-designed assignments: Inquiry into Student Thinking assignment and tutoring assignment. The two assignments were assigned after 6 and 10 weeks of instruction, respectively. The analysis revealed that PSTs attended to children’s strategies and interpreted children’s mathematical understanding but struggled with the component skill of responding to children’s mathematical understanding in the two assignments. Although the nature of tasks selected differed across the two assignments, generally PSTs focused on tasks that would develop children’s mathematical understanding. The findings have theoretical implications for a hypothesized trajectory of professional noticing of children’s mathematical understanding and the design of mathematics methods courses.


Author(s):  
Emily C. Bouck ◽  
Phil Sands ◽  
Holly Long ◽  
Aman Yadav

Increasingly in K–12 schools, students are gaining access to computational thinking (CT) and computer science (CS). This access, however, is not always extended to students with disabilities. One way to increase CT and CS (CT/CS) exposure for students with disabilities is through preparing special education teachers to do so. In this study, researchers explore exposing special education preservice teachers to the ideas of CT/CS in the context of a mathematics methods course for students with disabilities or those at risk of disability. Through analyzing lesson plans and reflections from 31 preservice special education teachers, the researchers learned that overall emerging promise exists with regard to the limited exposure of preservice special education teachers to CT/CS in mathematics. Specifically, preservice teachers demonstrated the ability to include CT/CS in math lesson plans and showed understanding of how CT/CS might enhance instruction with students with disabilities via reflections on these lessons. The researchers, however, also found a need for increased experiences and opportunities for preservice special education teachers with CT/CS to more positively impact access for students with disabilities.


2020 ◽  
Vol 122 (11) ◽  
pp. 1-40
Author(s):  
Britnie Delinger Kane

Background/Context The Core Practice movement continues to gain momentum in teacher education research. Yet critics highlight that equitable teaching cannot be reduced to a set of “core” practices, arguing that such a reduction risks representing teaching as technical work that will be neither culturally responsive nor sustaining. Instead, they argue that preservice teachers need opportunities to develop professional reasoning that takes the specific strengths and needs of students, communities, and subject matter into account. Purpose This analysis takes up the question of how and whether pedagogies of investigation and enactment can support preservice teachers’ development of the professional reasoning that equitable teaching requires. It conceptualizes two types of professional reasoning: interpretive, in which reasoners decide how to frame instructional problems and make subsequent efforts to solve them, and prescriptive, in which reasoners solve an instructional problem as given. Research Design This work is a qualitative, multiple case study, based on design research in which preservice teachers participated in three different cycles of investigation and enactment, which were designed around a teaching practice central to equitable teaching: making student thinking visible. Preservice teachers attended to students’ thinking in the context of the collaborative analysis of students’ writing and also through designed simulations of student-teacher writing conferences. Findings/Results Preservice teachers’ collaborative analysis of students’ writing supported prescriptive professional reasoning about disciplinary ideas in ELA and writing instruction (i.e., How do seventh graders use hyperbole? How is hyperbole related to the Six Traits of Writing?), while the simulation of a writing conference supported preservice teachers to reason interpretively about how to balance the need to support students’ affective commitment to writing with their desire to teach academic concepts about writing. Conclusions/Recommendations This analysis highlights an important heuristic for the design of pedagogies in teacher education: Teacher educators need to attend to preservice teachers’ opportunities for both interpretive and prescriptive reasoning. Both are essential for teachers, but only interpretive reasoning will support teachers to teach in ways that are both intellectually rigorous and equitable. The article further describes how and why a tempting assumption—that opportunities to role-play student-teacher interactions will support preservice teachers to reason interpretively, while non-interactive work will not—is incomplete and avoidable.


Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2842
Author(s):  
Ji-Eun Lee ◽  
Woong Lim

This study presents an analysis of 95 lesson play scripts—hypothetical dialogues between the teacher and a student—written by 32 preservice teachers (PSTs). Writing lesson scripts was part of the assessment design activities to elicit and respond to students’ thinking. The findings present the types and frequencies of teacher talks/moves in fraction-related tasks during a stage of lesson plays, such as launch, active elicitation, and closure. Our analysis indicates a wide range in the number of turns taken by the PSTs, while there is little correlation between the number of turns and effectiveness at eliciting and responding to student thinking. The study also confirmed that some unproductive talk moves were still present in the lesson play context, although the PSTs had plenty of time to craft a script. This study drew implications of PSTs’ prior perceptions, experiences, knowledge, and needs in mathematics teacher education regarding the ways to create learning opportunities for them to elicit and respond to student thinking.


2021 ◽  
Author(s):  
◽  
Raewyn Eden

<p>This study explores how participation in collaborative inquiry opens space for an expanded set of understandings and practices for mathematics teaching | learning. It examines the affordances of collaborative inquiry to promote, or constrain, teacher learning in the context of teachers’ day to day work.  Sociocultural perspectives underpin the study whereby professional learning is presumed to be situated in the social and cultural contexts of teachers’ work. A survey of the literature supports the assumption that persistent underachievement in mathematics for some groups of learners requires shifts in what teachers know and can do and reveals the importance of collaboration and inquiry for teacher learning.  The study involved a participatory, design-based approach underpinned by an authentic and appreciative inquiry stance. Design-based research was chosen for its proximity to practice and its focus on connections between the enactment of learning designs and outcomes of interest. The research was iterative and cyclical whereby the researcher worked with a group of four teachers in one New Zealand primary school to design, implement and refine an approach to teachers’ collaborative inquiry. A range of data were gathered during a 6-month collaboration, including from teacher interviews, classroom observations and three-weekly group meetings. The analysis took a pragmatic and multi-theoretical approach to examine what it meant to design and enact teachers’ collaborative inquiry. Cultural-historical activity theory (CHAT) was employed to capture the complexity of the teachers’ collaborative inquiry activity and to analyse and interpret the contradictions that arose.  A key finding was that a co-teaching inquiry approach fostered conditions that afforded teachers’ expanded access to and depth of engagement with new, and often dissonant, practice ideas. Through co-teaching, mathematics teaching | learning was restructured within three interconnected fields of practice: the teachers’ enacted practice, their talk about practice, and their noticing of student thinking within practice. The co-teaching inquiry activity was increasingly directed at a collective purpose; involved an interplay of risk and trust; supported shifts in teachers’ roles and responsibilities; and allowed teachers to constantly renegotiate the goals of their shared activity. The co-teaching arrangement disrupted practice whereby teachers’ actions served as minor interruptions to each other’s practice and thus became a resource for teacher learning. Opportunities to engage deeply with one another’s practice opened space for an expanded set of actions for each of the teachers in their own practice.  This thesis adds nuanced understandings of the interrelated roles of collaboration and inquiry in improving teaching. It contributes to the growing body of literature exploring co-teaching arrangements for teacher learning, in this case in the previously under-examined context of teachers’ collaborative inquiry for their ongoing professional learning. It offers insights into how co-teaching might support teachers to enact new and challenging pedagogies aimed at addressing the persistent and considerable challenges posed by an ethical imperative to promote mathematics learning for diverse (all) students. Participating in the co-construction of a design for their collaborative inquiry enabled teachers to restructure their work and expand the possibilities for their individual and collective practice. It allowed teachers to reconstruct their identities from the lone operator whose professional reputation needs protection from exposure of any weaknesses in their mathematics knowledge or practice, to a learner whose naïve questions and gaps in practice served as a resource for all in their learning.</p>


Author(s):  
Drew Polly

This chapter presents the theoretical background and overview of the design of an asynchronous online mathematics pedagogy course taken by graduate students who are seeking their initial teacher certification. The authors provide the theoretical underpinnings for the design of the course, and then using design-based research, describe the refinement of the course over three iterations of designing and implementing the course. Lastly, implications for the design and delivery of asynchronous online courses are discussed.


Author(s):  
Mary Grassetti ◽  
Silvy Brookby

The Standards for Mathematical Practice as delineated in the Common Core State Standards for Mathematics describe the processes, proficiencies, and habits of mind that students are expected to develop through their engagement with mathematics (Dacey & Polly, 2012). The purpose of this chapter is to discuss, anecdotally, how the iPad, a tablet computer designed by Apple ™, can be used to develop preservice teachers’ understanding and implementation of the Standards for Mathematical Practice, most specifically Mathematical Practice Standard 3: Construct viable arguments and critique the reasoning of others. Under examination are the authors’ experiences using the iPad as an observational tool during student teaching and as a teaching tool in their mathematics methods courses. The chapter concludes with suggestions for additional uses of the iPad to support preservice teachers as they work to develop their understanding of the Standards for Mathematical Practice.


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