Hala Ghousseini | University of Wisconsin-Madison (original) (raw)

Papers by Hala Ghousseini

Research in mathematics education, 2023

International Group for the Psychology of Mathematics Education, Oct 1, 2017

In this paper, we integrate a set of theoretical considerations that together serve as a model fo... more In this paper, we integrate a set of theoretical considerations that together serve as a model for investigating how high-leverage practices could be generative of teacher learning. We use the context of rehearsals to investigate how the use of a specified question sequence aimed at eliciting student mathematical thinking can afford opportunities for novices and instructors to consider goals of ambitious mathematics teaching. In our results, we provide thematic categories for the problems that arose as novices used the sequence of questions, and demonstrate how they afforded the teacher educator opportunities to connect novices' work to goals of ambitious mathematics teaching. In particular, we highlight how these opportunities arose in the midst of modifying to the question sequence and investigating the consequences of its enactment.

L ike the other contributors to this volume, we are interested in classroom talk and the role it ... more L ike the other contributors to this volume, we are interested in classroom talk and the role it plays in the learning of those who are talking. The "classroom" in our case is a professional education setting. The teachers in this classroom are teacher educators and the learners are novice teachers. We are interested in designing learning environments for novice teachers with attention to the ways in which they are entitled, expected, and obligated to act in and toward the work of teaching. We seek to position them as sense-makers in dialogue about the challenges of ambitious mathematics teaching, so they can come to know their practice in a way that enables them to construct meaning, make inferences, and solve problems. What we want these novices to be able to do, in turn, is to position their students in elementary school classrooms as mathematical sense-makers. Our focus on sense-making by both teachers and their students has been influenced by Greeno's integration of cognitive and interactive perspectives on learning, in which he identifies approaches to teaching that are intended to achieve students' commitment to learning goals and their sustained, persistent participation (2007, table 1, p. 37). Greeno's work correlates on both levels with the principles of Accountable Talk articulated by Michaels, O'Connor, and Resnick (2008). Linking these conceptual frames, we might say that participating in accountable talk helps learners to develop what Greeno (2007) calls intellective character and Gordon (2007) calls intellective competence. These theories, linking positioning in a social world with individual identity, suggest ways in which people can learn to make connections between who they are and what they are able to do (Holland, Lachicotte, Skinner, & Cain, 1998). Developing intellective character means developing both conceptual and interpersonal components of the learner's identity. Conceptually, it involves learning to be accountable to ways of knowing in a subject domain. Personally, it concerns both individual and social achievements, namely, learning to become accountable to a community of learners, or in Gordon's terms, becoming "compassionate and thinking interdependent members of humane human communities" (as cited in Greeno, 2007, p. 42). Much of Lampert's past work centered on designing relationships in the elementary school classroom community so that all students could develop intellective character, that

The Journal of the Learning Sciences, Jun 16, 2015

Recently, attention has focused on identifying core instructional practices that could leverage n... more Recently, attention has focused on identifying core instructional practices that could leverage novice teachers’ development of professional knowledge and skill. To help novices learn to implement these practices, there is also increasing interest in developing enactment tools that could translate abstract conceptual tasks into more concrete steps. Less attention, however, has been paid to understanding how novices might learn to use these tools adaptively in the context of practice. We address this issue by integrating a set of theoretical considerations that together serve as a model for investigating how novices could learn within a community of practice to use a specified elicitation sequence adaptively, guided by more experienced members in that community. In our results, we provide thematic categories for the problems that arose as novices used the sequence of questions and demonstrate how these problems afforded the teacher educator opportunities to connect novices’ work to a set of professional commitments that could guide their adaptive practice. In particular, we highlight how these opportunities arose in the midst of modifying the question sequence and investigating the consequences of its enactment. Although our analysis focuses on a particular question sequence, we see our results as relevant to the development of other forms of enactment tools for use in adaptive practice across a range of professional domains.

Annals of Surgery, May 1, 2018

for the Wisconsin Surgical Coaching Program Objective: We sought to develop and evaluate a video-... more for the Wisconsin Surgical Coaching Program Objective: We sought to develop and evaluate a video-based coaching program for board-eligible/certified surgeons. Summary Background Data: Multiple disciplines utilize coaching for continuous professional development; however, coaching is not routinely employed for practicing surgeons. Methods: Peer-nominated surgeons were trained as coaches then paired with participant surgeons. After setting goals, each coaching pair reviewed videorecorded operations performed by the participating surgeon. Coaching sessions were audio-recorded, transcribed, and coded to identify topics discussed. The effectiveness with which our coaches were able to utilize the core principles and activities of coaching was evaluated using 3 different approaches: self-evaluation; evaluation by the participants; and assessment by the study team. Surveys of participating surgeons and coach-targeted interviews provided general feedback on the program. All measures utilized a 5-point Likert scale format ranging from 1 (low) to 5 (high). Results: Coach-participant surgeon pairs targeted technical, cognitive, and interpersonal aspects of performance. Other topics included managing intraoperative stress. Mean objective ratings of coach effectiveness was 3.1 AE 0.7, ranging from 2.0 to 5.0 on specific activities of coaching. Subjective ratings by coaches and participants were consistently higher. Coaches reported that the training provided effectively prepared them to facilitate coaching sessions. Participants were similarly positive about interactions with their coaches. Identified barriers were related to audio-video technology and scheduling of sessions. Overall, participants were satisfied with their experience (mean 4.4 AE 0.7) and found the coaching program valuable (mean 4.7 AE 0.7). Conclusions: This is the first report of cross-institutional surgical coaching for the continuous professional development of practicing surgeons, demonstrating perceived value among participants, as well as logistical challenges for implementing this evidence-based program. Future research is necessary to evaluate the impact of coaching on practice change and patient outcomes.

JAMA Surgery, Apr 19, 2017

IMPORTANCE Peer surgical coaching is a promising approach for continuing professional development... more IMPORTANCE Peer surgical coaching is a promising approach for continuing professional development. However, scant guidance is available for surgeons seeking to develop peer-coaching skills. Executive coaching research suggests that effective coaches first establish a positive relationship with their coachees by aligning role and process expectations, establishing rapport, and cultivating mutual trust. OBJECTIVE To identify the strategies used by peer surgical coaches to develop effective peer-coaching relationships with their coachees. DESIGN, SETTING, AND PARTICIPANTS Drawing on executive coaching literature, a 3-part framework was developed to examine the strategies peer surgical coaches (n = 8) used to initially cultivate a relationship with their coachees (n = 11). Eleven introductory 1-hour meetings between coaching pairs participating in a statewide surgical coaching program were audiorecorded, transcribed, and coded on the basis of 3 relationship-building components. Once coded, thematic analysis was used to organize coded strategies into thematic categories and subcategories.

Journal of The American College of Surgeons, Oct 1, 2016

JAMA Surgery, Jun 1, 2020

ImportanceSurgical coaching continues to gain momentum as an innovative method for continuous pro... more ImportanceSurgical coaching continues to gain momentum as an innovative method for continuous professional development. A tool to measure the performance of a surgical coach is needed to provide formative feedback to coaches for continued skill development and to assess the fidelity of a coaching intervention for future research and dissemination.ObjectiveTo evaluate the validity of the Wisconsin Surgical Coaching Rubric (WiSCoR), a novel tool to assess the performance of a peer surgical coach.Design, Setting, and ParticipantsSurgical coaching sessions from November 2014 through February 2018 conducted by 2 statewide peer surgical coaching programs were audio recorded and transcribed. Twelve raters used WiSCoR to rate the performance of the surgical coach for each session. The study included peer surgical coaches in the Wisconsin Surgical Coaching Program (n = 8) and the Michigan Bariatric Surgery Collaborative coaching program (n = 15). The data were analyzed in 2019.Interventions or ExposuresUse of WiSCoR to rate peer surgical coaching sessions.Main Outcomes and MeasuresThere were 282 WiSCoR ratings from the 106 coaching sessions included in the study. WiSCoR was evaluated using a framework, including inter-rater reliability assessed with Gwet weighted agreement coefficent. Descriptive statistics of WiSCoR were calculated.ResultsEight coaches (35%) and 11 coachees (29%) were from the Wisconsin Surgical Program and 15 coaches (65%) and 27 coachees (71%) were from the Michigan Bariatric Surgery Collaborative. The validity of WiSCoR is supported by high interrater reliability (Gwet weighted agreement coefficient, 0.87) as well as a weakly positive correlation of WiSCoR to coachee ratings of coaches (r = 0.22; P = .04), rigorous content development, consistent rater training, and the association of WiSCoR with coach and coaching program development. The mean (SD) overall coach performance rating using WiSCoR was 3.23 (0.82; range, 1-5).Conclusions and RelevanceWiSCoR is a reliable measure that can assess the performance of a surgical coach, inform fidelity to coaching principles, and provide formative feedback to surgical coaches. While coachee ratings may reflect coachee satisfaction, they are not able to determine the quality of a coach.

Educational Researcher, Nov 10, 2021

Recent innovations in professional development are rife with a wide array of efforts focused on t... more Recent innovations in professional development are rife with a wide array of efforts focused on teacher collaboration. In this essay, we address some of the unexamined assumptions about the nature and significance of interactions in teacher professional collaboration, drawing on the concept of the “fourth wall” from theater and film studies. The fourth wall is a term used to describe the invisible wall that separates actors from their audience. We use this metaphor to interrogate the function of the fourth wall in professional learning and argue that it reflects a culture of professional learning that, despite innovations that tout teacher collaboration, upholds isolation in teaching and teacher learning and deep embedded norms of noninterference in one another’s practice. We also attend to the possibilities for supporting teacher learning that breaching the fourth wall affords when shared enactments of practice are used as a context for teachers’ sensemaking and collaboration.

Mathematics Teachers at Work, 2011

Mathematics Teacher: Learning and Teaching PK-12

Three deliberate teaching practices can help students strengthen multiple connections to a unifyi... more Three deliberate teaching practices can help students strengthen multiple connections to a unifying concept.

Cognition and Instruction, 2022

Abstract Researcher-practitioner collaborations often stop short of engaging researchers and teac... more Abstract Researcher-practitioner collaborations often stop short of engaging researchers and teachers in collectively negotiating the moment-to-moment improvizational decision-making of instructional practice when students are present. We consider the potential for learning at one boundary that often exists between researchers and practitioners as they collaborate on instructional practice: the boundary between performing-teaching and observing-teaching. We draw on performance studies to conceptualize this boundary as a fourth wall. Our analysis examines researcher-practitioner collaboration across four sites in which participants were learning together about the complex work of facilitating student discussion. We analyze how one boundary crossing routine provided opportunities for researchers and practitioners to interact at the boundary of the fourth wall during enactment of discussion-based instruction with students. To analyze episodes of this routine, we draw on conceptualizations of potential learning mechanisms of boundary crossing in research-practice partnerships. Our findings identify and describe the mechanisms for researcher/practitioner learning that arose when our participants crossed the boundary of the fourth wall: perspective taking, boundary spanning, and recognition of shared problem spaces. We argue that these learning mechanisms create potential for researchers and practitioners to wrestle with and learn about the challenges and opportunities within facilitation of student discussions.

Language is a vital component in mathematics classrooms and researchers have thoroughly examined ... more Language is a vital component in mathematics classrooms and researchers have thoroughly examined how language functions in instruction. However, less is known about how teachers think about language enacted in their own classrooms. In this report, we describe how a teacher, Olivia, explicitly attended to language, particularly with emergent bilinguals. We describe affordances and tensions as she thought through language in the context of a professional development and in video- stimulated recall interviews.

Teaching and Teacher Education, 2019

h i g h l i g h t s Two sites with differing organizational structures draw on a common decomposi... more h i g h l i g h t s Two sites with differing organizational structures draw on a common decomposition. A decomposition is not prescriptive, it is a framework for conversation. Understanding how decompositions are taken up requires examining in the moment work.

Cognition and Instruction, 2017

ABSTRACT This study addresses how rehearsals of teaching could support teachers in developing mat... more ABSTRACT This study addresses how rehearsals of teaching could support teachers in developing mathematical knowledge for teaching (MKT). The analysis of 30 rehearsals, from elementary methods courses in 3 teacher education programs, attends to what novice teachers and teacher educators did in rehearsal that enlisted MKT. The findings elaborate the tasks that enlisted MKT in practice and the work of the teacher educator in supporting novice teachers' learning of MKT inside the interactive work of teaching.

Journal of the American College of Surgeons, 2016

Teaching Children Mathematics, 2017

Teachers can use these instructional strategies during the launching phase of a lesson to prepare... more Teachers can use these instructional strategies during the launching phase of a lesson to prepare students for productive math talk in their small groups.

Research in mathematics education, 2023

International Group for the Psychology of Mathematics Education, Oct 1, 2017

In this paper, we integrate a set of theoretical considerations that together serve as a model fo... more In this paper, we integrate a set of theoretical considerations that together serve as a model for investigating how high-leverage practices could be generative of teacher learning. We use the context of rehearsals to investigate how the use of a specified question sequence aimed at eliciting student mathematical thinking can afford opportunities for novices and instructors to consider goals of ambitious mathematics teaching. In our results, we provide thematic categories for the problems that arose as novices used the sequence of questions, and demonstrate how they afforded the teacher educator opportunities to connect novices' work to goals of ambitious mathematics teaching. In particular, we highlight how these opportunities arose in the midst of modifying to the question sequence and investigating the consequences of its enactment.

L ike the other contributors to this volume, we are interested in classroom talk and the role it ... more L ike the other contributors to this volume, we are interested in classroom talk and the role it plays in the learning of those who are talking. The "classroom" in our case is a professional education setting. The teachers in this classroom are teacher educators and the learners are novice teachers. We are interested in designing learning environments for novice teachers with attention to the ways in which they are entitled, expected, and obligated to act in and toward the work of teaching. We seek to position them as sense-makers in dialogue about the challenges of ambitious mathematics teaching, so they can come to know their practice in a way that enables them to construct meaning, make inferences, and solve problems. What we want these novices to be able to do, in turn, is to position their students in elementary school classrooms as mathematical sense-makers. Our focus on sense-making by both teachers and their students has been influenced by Greeno's integration of cognitive and interactive perspectives on learning, in which he identifies approaches to teaching that are intended to achieve students' commitment to learning goals and their sustained, persistent participation (2007, table 1, p. 37). Greeno's work correlates on both levels with the principles of Accountable Talk articulated by Michaels, O'Connor, and Resnick (2008). Linking these conceptual frames, we might say that participating in accountable talk helps learners to develop what Greeno (2007) calls intellective character and Gordon (2007) calls intellective competence. These theories, linking positioning in a social world with individual identity, suggest ways in which people can learn to make connections between who they are and what they are able to do (Holland, Lachicotte, Skinner, & Cain, 1998). Developing intellective character means developing both conceptual and interpersonal components of the learner's identity. Conceptually, it involves learning to be accountable to ways of knowing in a subject domain. Personally, it concerns both individual and social achievements, namely, learning to become accountable to a community of learners, or in Gordon's terms, becoming "compassionate and thinking interdependent members of humane human communities" (as cited in Greeno, 2007, p. 42). Much of Lampert's past work centered on designing relationships in the elementary school classroom community so that all students could develop intellective character, that

The Journal of the Learning Sciences, Jun 16, 2015

Recently, attention has focused on identifying core instructional practices that could leverage n... more Recently, attention has focused on identifying core instructional practices that could leverage novice teachers’ development of professional knowledge and skill. To help novices learn to implement these practices, there is also increasing interest in developing enactment tools that could translate abstract conceptual tasks into more concrete steps. Less attention, however, has been paid to understanding how novices might learn to use these tools adaptively in the context of practice. We address this issue by integrating a set of theoretical considerations that together serve as a model for investigating how novices could learn within a community of practice to use a specified elicitation sequence adaptively, guided by more experienced members in that community. In our results, we provide thematic categories for the problems that arose as novices used the sequence of questions and demonstrate how these problems afforded the teacher educator opportunities to connect novices’ work to a set of professional commitments that could guide their adaptive practice. In particular, we highlight how these opportunities arose in the midst of modifying the question sequence and investigating the consequences of its enactment. Although our analysis focuses on a particular question sequence, we see our results as relevant to the development of other forms of enactment tools for use in adaptive practice across a range of professional domains.

Annals of Surgery, May 1, 2018

for the Wisconsin Surgical Coaching Program Objective: We sought to develop and evaluate a video-... more for the Wisconsin Surgical Coaching Program Objective: We sought to develop and evaluate a video-based coaching program for board-eligible/certified surgeons. Summary Background Data: Multiple disciplines utilize coaching for continuous professional development; however, coaching is not routinely employed for practicing surgeons. Methods: Peer-nominated surgeons were trained as coaches then paired with participant surgeons. After setting goals, each coaching pair reviewed videorecorded operations performed by the participating surgeon. Coaching sessions were audio-recorded, transcribed, and coded to identify topics discussed. The effectiveness with which our coaches were able to utilize the core principles and activities of coaching was evaluated using 3 different approaches: self-evaluation; evaluation by the participants; and assessment by the study team. Surveys of participating surgeons and coach-targeted interviews provided general feedback on the program. All measures utilized a 5-point Likert scale format ranging from 1 (low) to 5 (high). Results: Coach-participant surgeon pairs targeted technical, cognitive, and interpersonal aspects of performance. Other topics included managing intraoperative stress. Mean objective ratings of coach effectiveness was 3.1 AE 0.7, ranging from 2.0 to 5.0 on specific activities of coaching. Subjective ratings by coaches and participants were consistently higher. Coaches reported that the training provided effectively prepared them to facilitate coaching sessions. Participants were similarly positive about interactions with their coaches. Identified barriers were related to audio-video technology and scheduling of sessions. Overall, participants were satisfied with their experience (mean 4.4 AE 0.7) and found the coaching program valuable (mean 4.7 AE 0.7). Conclusions: This is the first report of cross-institutional surgical coaching for the continuous professional development of practicing surgeons, demonstrating perceived value among participants, as well as logistical challenges for implementing this evidence-based program. Future research is necessary to evaluate the impact of coaching on practice change and patient outcomes.

JAMA Surgery, Apr 19, 2017

IMPORTANCE Peer surgical coaching is a promising approach for continuing professional development... more IMPORTANCE Peer surgical coaching is a promising approach for continuing professional development. However, scant guidance is available for surgeons seeking to develop peer-coaching skills. Executive coaching research suggests that effective coaches first establish a positive relationship with their coachees by aligning role and process expectations, establishing rapport, and cultivating mutual trust. OBJECTIVE To identify the strategies used by peer surgical coaches to develop effective peer-coaching relationships with their coachees. DESIGN, SETTING, AND PARTICIPANTS Drawing on executive coaching literature, a 3-part framework was developed to examine the strategies peer surgical coaches (n = 8) used to initially cultivate a relationship with their coachees (n = 11). Eleven introductory 1-hour meetings between coaching pairs participating in a statewide surgical coaching program were audiorecorded, transcribed, and coded on the basis of 3 relationship-building components. Once coded, thematic analysis was used to organize coded strategies into thematic categories and subcategories.

Journal of The American College of Surgeons, Oct 1, 2016

JAMA Surgery, Jun 1, 2020

ImportanceSurgical coaching continues to gain momentum as an innovative method for continuous pro... more ImportanceSurgical coaching continues to gain momentum as an innovative method for continuous professional development. A tool to measure the performance of a surgical coach is needed to provide formative feedback to coaches for continued skill development and to assess the fidelity of a coaching intervention for future research and dissemination.ObjectiveTo evaluate the validity of the Wisconsin Surgical Coaching Rubric (WiSCoR), a novel tool to assess the performance of a peer surgical coach.Design, Setting, and ParticipantsSurgical coaching sessions from November 2014 through February 2018 conducted by 2 statewide peer surgical coaching programs were audio recorded and transcribed. Twelve raters used WiSCoR to rate the performance of the surgical coach for each session. The study included peer surgical coaches in the Wisconsin Surgical Coaching Program (n = 8) and the Michigan Bariatric Surgery Collaborative coaching program (n = 15). The data were analyzed in 2019.Interventions or ExposuresUse of WiSCoR to rate peer surgical coaching sessions.Main Outcomes and MeasuresThere were 282 WiSCoR ratings from the 106 coaching sessions included in the study. WiSCoR was evaluated using a framework, including inter-rater reliability assessed with Gwet weighted agreement coefficent. Descriptive statistics of WiSCoR were calculated.ResultsEight coaches (35%) and 11 coachees (29%) were from the Wisconsin Surgical Program and 15 coaches (65%) and 27 coachees (71%) were from the Michigan Bariatric Surgery Collaborative. The validity of WiSCoR is supported by high interrater reliability (Gwet weighted agreement coefficient, 0.87) as well as a weakly positive correlation of WiSCoR to coachee ratings of coaches (r = 0.22; P = .04), rigorous content development, consistent rater training, and the association of WiSCoR with coach and coaching program development. The mean (SD) overall coach performance rating using WiSCoR was 3.23 (0.82; range, 1-5).Conclusions and RelevanceWiSCoR is a reliable measure that can assess the performance of a surgical coach, inform fidelity to coaching principles, and provide formative feedback to surgical coaches. While coachee ratings may reflect coachee satisfaction, they are not able to determine the quality of a coach.

Educational Researcher, Nov 10, 2021

Recent innovations in professional development are rife with a wide array of efforts focused on t... more Recent innovations in professional development are rife with a wide array of efforts focused on teacher collaboration. In this essay, we address some of the unexamined assumptions about the nature and significance of interactions in teacher professional collaboration, drawing on the concept of the “fourth wall” from theater and film studies. The fourth wall is a term used to describe the invisible wall that separates actors from their audience. We use this metaphor to interrogate the function of the fourth wall in professional learning and argue that it reflects a culture of professional learning that, despite innovations that tout teacher collaboration, upholds isolation in teaching and teacher learning and deep embedded norms of noninterference in one another’s practice. We also attend to the possibilities for supporting teacher learning that breaching the fourth wall affords when shared enactments of practice are used as a context for teachers’ sensemaking and collaboration.

Mathematics Teachers at Work, 2011

Mathematics Teacher: Learning and Teaching PK-12

Three deliberate teaching practices can help students strengthen multiple connections to a unifyi... more Three deliberate teaching practices can help students strengthen multiple connections to a unifying concept.

Cognition and Instruction, 2022

Abstract Researcher-practitioner collaborations often stop short of engaging researchers and teac... more Abstract Researcher-practitioner collaborations often stop short of engaging researchers and teachers in collectively negotiating the moment-to-moment improvizational decision-making of instructional practice when students are present. We consider the potential for learning at one boundary that often exists between researchers and practitioners as they collaborate on instructional practice: the boundary between performing-teaching and observing-teaching. We draw on performance studies to conceptualize this boundary as a fourth wall. Our analysis examines researcher-practitioner collaboration across four sites in which participants were learning together about the complex work of facilitating student discussion. We analyze how one boundary crossing routine provided opportunities for researchers and practitioners to interact at the boundary of the fourth wall during enactment of discussion-based instruction with students. To analyze episodes of this routine, we draw on conceptualizations of potential learning mechanisms of boundary crossing in research-practice partnerships. Our findings identify and describe the mechanisms for researcher/practitioner learning that arose when our participants crossed the boundary of the fourth wall: perspective taking, boundary spanning, and recognition of shared problem spaces. We argue that these learning mechanisms create potential for researchers and practitioners to wrestle with and learn about the challenges and opportunities within facilitation of student discussions.

Language is a vital component in mathematics classrooms and researchers have thoroughly examined ... more Language is a vital component in mathematics classrooms and researchers have thoroughly examined how language functions in instruction. However, less is known about how teachers think about language enacted in their own classrooms. In this report, we describe how a teacher, Olivia, explicitly attended to language, particularly with emergent bilinguals. We describe affordances and tensions as she thought through language in the context of a professional development and in video- stimulated recall interviews.

Teaching and Teacher Education, 2019

h i g h l i g h t s Two sites with differing organizational structures draw on a common decomposi... more h i g h l i g h t s Two sites with differing organizational structures draw on a common decomposition. A decomposition is not prescriptive, it is a framework for conversation. Understanding how decompositions are taken up requires examining in the moment work.

Cognition and Instruction, 2017

ABSTRACT This study addresses how rehearsals of teaching could support teachers in developing mat... more ABSTRACT This study addresses how rehearsals of teaching could support teachers in developing mathematical knowledge for teaching (MKT). The analysis of 30 rehearsals, from elementary methods courses in 3 teacher education programs, attends to what novice teachers and teacher educators did in rehearsal that enlisted MKT. The findings elaborate the tasks that enlisted MKT in practice and the work of the teacher educator in supporting novice teachers' learning of MKT inside the interactive work of teaching.

Journal of the American College of Surgeons, 2016

Teaching Children Mathematics, 2017

Teachers can use these instructional strategies during the launching phase of a lesson to prepare... more Teachers can use these instructional strategies during the launching phase of a lesson to prepare students for productive math talk in their small groups.