Pedagogical Content Knowledge

Co-Designing for Statewide Alignment of a Vision for High-Quality Mathematics Instruction (Collaborative Research: Wilson)

This project will develop a process for creating a shared, state-wide vision of high-quality mathematics instruction. It will also develop and study the resources to implement that vision at the state, district, and school levels. In addition, the project will investigate a collaborative process of designing and implementing high-quality mathematics instruction at a state level.

Award Number: 
2100903
Funding Period: 
Thu, 07/15/2021 to Mon, 06/30/2025
Full Description: 

Mathematics teaching and learning is influenced by policy and practice at the state, district, and school levels. To support large-scale change, it is important for high-quality mathematics instruction to be aligned and cohesive across each level of the education system. This can be supported through regional partnerships among state, district, and school-based leaders, mathematics teachers, education researchers, and mathematicians. Such partnerships create instructional tools and resources to document the vision for instruction. For example, teams can work together to create instructional frameworks for each grade band that describe standards, mathematics teaching, and units for teaching. This project will develop a process for creating a shared, state-wide vision of high-quality mathematics instruction. It will also develop and study the resources to implement that vision at the state, district, and school levels. In addition, the project will investigate a collaborative process of designing and implementing high-quality mathematics instruction at a state level.

This project will develop a shared vision of high-quality mathematics instruction intended to improve systemic coherence during the implementation of education innovations. The project uses a research-practice partnership with a design-based implementation research design. To examine and support implementation of the vision, partners will continue a process of developing instructional frameworks, research and practice briefs, as well as additional resources as needed by stakeholders in the system. Engaging partners at all levels of the system is a central component of developing the shared vision of instruction. This project includes three major research questions. First, what are visions of high-quality mathematics instruction held by educators at different levels of a state educational system? Second, in what ways do educators' visions of high-quality mathematics instruction mediate their use of implementation resources in practice? Finally, in what ways do educators’ visions of high-quality mathematics instruction mediate their participation in the co-design of implementation resources? An activity theory framework is used to understand the interactions between partners at different levels in the system and the creation of artifacts during the design process. The research methods for the study are situated in design-based research to capture the conjectures, instructional resources, design processes, and outcomes of the process. The project will use case studies of partner districts, data gathering from interactions with partners, artifacts of the design process, and other documentation to understand how the vision is created and enacted in different settings and to develop an empirically supported design framework and methodology for implementing STEM innovations at scale that centralizes a shared instructional vision.

Co-Designing for Statewide Alignment of a Vision for High-Quality Mathematics Instruction (Collaborative Research: Mawhinney)

This project will develop a process for creating a shared, state-wide vision of high-quality mathematics instruction. It will also develop and study the resources to implement that vision at the state, district, and school levels. In addition, the project will investigate a collaborative process of designing and implementing high-quality mathematics instruction at a state level.

Lead Organization(s): 
Award Number: 
2100833
Funding Period: 
Thu, 07/15/2021 to Mon, 06/30/2025
Full Description: 

Mathematics teaching and learning is influenced by policy and practice at the state, district, and school levels. To support large-scale change, it is important for high-quality mathematics instruction to be aligned and cohesive across each level of the education system. This can be supported through regional partnerships among state, district, and school-based leaders, mathematics teachers, education researchers, and mathematicians. Such partnerships create instructional tools and resources to document the vision for instruction. For example, teams can work together to create instructional frameworks for each grade band that describe standards, mathematics teaching, and units for teaching. This project will develop a process for creating a shared, state-wide vision of high-quality mathematics instruction. It will also develop and study the resources to implement that vision at the state, district, and school levels. In addition, the project will investigate a collaborative process of designing and implementing high-quality mathematics instruction at a state level.

This project will develop a shared vision of high-quality mathematics instruction intended to improve systemic coherence during the implementation of education innovations. The project uses a research-practice partnership with a design-based implementation research design. To examine and support implementation of the vision, partners will continue a process of developing instructional frameworks, research and practice briefs, as well as additional resources as needed by stakeholders in the system. Engaging partners at all levels of the system is a central component of developing the shared vision of instruction. This project includes three major research questions. First, what are visions of high-quality mathematics instruction held by educators at different levels of a state educational system? Second, in what ways do educators' visions of high-quality mathematics instruction mediate their use of implementation resources in practice? Finally, in what ways do educators’ visions of high-quality mathematics instruction mediate their participation in the co-design of implementation resources? An activity theory framework is used to understand the interactions between partners at different levels in the system and the creation of artifacts during the design process. The research methods for the study are situated in design-based research to capture the conjectures, instructional resources, design processes, and outcomes of the process. The project will use case studies of partner districts, data gathering from interactions with partners, artifacts of the design process, and other documentation to understand how the vision is created and enacted in different settings and to develop an empirically supported design framework and methodology for implementing STEM innovations at scale that centralizes a shared instructional vision.

Co-Designing for Statewide Alignment of a Vision for High-Quality Mathematics Instruction (Collaborative Research: Schwartz)

This project will develop a process for creating a shared, state-wide vision of high-quality mathematics instruction. It will also develop and study the resources to implement that vision at the state, district, and school levels. In addition, the project will investigate a collaborative process of designing and implementing high-quality mathematics instruction at a state level.

Lead Organization(s): 
Award Number: 
2100895
Funding Period: 
Thu, 07/15/2021 to Mon, 06/30/2025
Full Description: 

Mathematics teaching and learning is influenced by policy and practice at the state, district, and school levels. To support large-scale change, it is important for high-quality mathematics instruction to be aligned and cohesive across each level of the education system. This can be supported through regional partnerships among state, district, and school-based leaders, mathematics teachers, education researchers, and mathematicians. Such partnerships create instructional tools and resources to document the vision for instruction. For example, teams can work together to create instructional frameworks for each grade band that describe standards, mathematics teaching, and units for teaching. This project will develop a process for creating a shared, state-wide vision of high-quality mathematics instruction. It will also develop and study the resources to implement that vision at the state, district, and school levels. In addition, the project will investigate a collaborative process of designing and implementing high-quality mathematics instruction at a state level.

This project will develop a shared vision of high-quality mathematics instruction intended to improve systemic coherence during the implementation of education innovations. The project uses a research-practice partnership with a design-based implementation research design. To examine and support implementation of the vision, partners will continue a process of developing instructional frameworks, research and practice briefs, as well as additional resources as needed by stakeholders in the system. Engaging partners at all levels of the system is a central component of developing the shared vision of instruction. This project includes three major research questions. First, what are visions of high-quality mathematics instruction held by educators at different levels of a state educational system? Second, in what ways do educators' visions of high-quality mathematics instruction mediate their use of implementation resources in practice? Finally, in what ways do educators’ visions of high-quality mathematics instruction mediate their participation in the co-design of implementation resources? An activity theory framework is used to understand the interactions between partners at different levels in the system and the creation of artifacts during the design process. The research methods for the study are situated in design-based research to capture the conjectures, instructional resources, design processes, and outcomes of the process. The project will use case studies of partner districts, data gathering from interactions with partners, artifacts of the design process, and other documentation to understand how the vision is created and enacted in different settings and to develop an empirically supported design framework and methodology for implementing STEM innovations at scale that centralizes a shared instructional vision.

Co-Designing for Statewide Alignment of a Vision for High-Quality Mathematics Instruction (Collaborative Research: McCulloch)

This project will develop a process for creating a shared, state-wide vision of high-quality mathematics instruction. It will also develop and study the resources to implement that vision at the state, district, and school levels. In addition, the project will investigate a collaborative process of designing and implementing high-quality mathematics instruction at a state level.

Award Number: 
2100947
Funding Period: 
Thu, 07/15/2021 to Mon, 06/30/2025
Full Description: 

Mathematics teaching and learning is influenced by policy and practice at the state, district, and school levels. To support large-scale change, it is important for high-quality mathematics instruction to be aligned and cohesive across each level of the education system. This can be supported through regional partnerships among state, district, and school-based leaders, mathematics teachers, education researchers, and mathematicians. Such partnerships create instructional tools and resources to document the vision for instruction. For example, teams can work together to create instructional frameworks for each grade band that describe standards, mathematics teaching, and units for teaching. This project will develop a process for creating a shared, state-wide vision of high-quality mathematics instruction. It will also develop and study the resources to implement that vision at the state, district, and school levels. In addition, the project will investigate a collaborative process of designing and implementing high-quality mathematics instruction at a state level.

This project will develop a shared vision of high-quality mathematics instruction intended to improve systemic coherence during the implementation of education innovations. The project uses a research-practice partnership with a design-based implementation research design. To examine and support implementation of the vision, partners will continue a process of developing instructional frameworks, research and practice briefs, as well as additional resources as needed by stakeholders in the system. Engaging partners at all levels of the system is a central component of developing the shared vision of instruction. This project includes three major research questions. First, what are visions of high-quality mathematics instruction held by educators at different levels of a state educational system? Second, in what ways do educators' visions of high-quality mathematics instruction mediate their use of implementation resources in practice? Finally, in what ways do educators’ visions of high-quality mathematics instruction mediate their participation in the co-design of implementation resources? An activity theory framework is used to understand the interactions between partners at different levels in the system and the creation of artifacts during the design process. The research methods for the study are situated in design-based research to capture the conjectures, instructional resources, design processes, and outcomes of the process. The project will use case studies of partner districts, data gathering from interactions with partners, artifacts of the design process, and other documentation to understand how the vision is created and enacted in different settings and to develop an empirically supported design framework and methodology for implementing STEM innovations at scale that centralizes a shared instructional vision.

Building Insights through Observation: Researching Arts-based Methods for Teaching and Learning with Data

This project will use visualizations from an easily accessible tool from NOAA, Science On a Sphere, to help students develop critical thinking skills and practices required to effectively make meaning from authentic scientific data. The project will use arts-based pedagogies for observing, analyzing, and critiquing visual features of data visualizations to build an understanding of what the data reveal. The project will work with middle school science teachers to develop tools for STEM educators to use these data visualizations effectively.

Lead Organization(s): 
Award Number: 
2101310
Funding Period: 
Thu, 07/01/2021 to Mon, 06/30/2025
Full Description: 

Innovations in data collection, infrastructure, and visualization play an important role in modern society. Large, complex datasets are accessible to and shared widely with the public. However, students need to learn how to interpret and reason about visualizations of scientific data. This project will use visualizations from an easily accessible tool from NOAA, Science On a Sphere, to help students develop critical thinking skills and practices required to effectively make meaning from authentic scientific data. The project will use arts-based pedagogies for observing, analyzing, and critiquing visual features of data visualizations to build an understanding of what the data reveal. The project will work with middle school science teachers to develop tools for STEM educators to use these data visualizations effectively. This project focuses on visual thinking skills that have been found to apply in both science and art: describing, wondering, recognizing uncertainty, and interpreting with evidence.

The project will conduct foundational research to understand the ways in which arts-based instructional methods and geospatial data visualization can be successfully applied by science teachers. The research will examine: (1) the ways in which arts-based instructional methods can be successfully applied by STEM teachers; (2) critical elements in the process of learning and applying these techniques to influence teachers’ content, pedagogical, and technological knowledge; and (3) for which transferable data literacy skills these approaches show most promise with children. This project will use a design-based research framework to develop data literacy teaching approaches in partnership with middle school teachers. The research process will include data about teachers’ development and students’ learning about data literacy. Data to be collected include qualitative and quantitative information from teachers and students.

Reducing Racially Biased Beliefs by Fostering a Complex Understanding of Human Genetics Research in High School Biology Students (Collaborative Research: Donovan)

The project will refine a genetics education curriculum, called Humane Genome Literacy (HGL), in order to reduce belief in genetic essentialism. This research will provide curriculum writers and educators with knowledge about how to design a humane genetics education to maximize reductions in students’ genetic essentialist beliefs. The research findings will demonstrate how to support teachers who wish to reduce beliefs in genetic essentialism by teaching students about the complexity of human genetics research using the HGL learning materials.

Lead Organization(s): 
Award Number: 
2100864
Funding Period: 
Wed, 09/01/2021 to Sun, 08/31/2025
Full Description: 

Genetic essentialism is the belief that people of the same race share genes that make them physically, cognitively, and behaviorally uniform, and thus different from other races. The project will refine a genetics education curriculum, called Humane Genome Literacy (HGL), in order to reduce belief in genetic essentialism. This research will provide curriculum writers and educators with knowledge about how to design a humane genetics education to maximize reductions in students’ genetic essentialist beliefs and minimize the threat of backfiring (unintentionally increasing belief in essentialism). The research findings will demonstrate how to support teachers who wish to reduce beliefs in genetic essentialism by teaching students about the complexity of human genetics research using the HGL learning materials.  Project research findings, learning materials, and professional development institutes will be made available to educators and researchers across the country who desire to teach genetics to reduce racial prejudice.

To prepare for the research, the project will revise and augment the project’s existing HGL curriculum and professional development institutes.  In year one, the project will develop new versions of the HGL interventions. Using these materials, the project will train teachers to implement new versions of the HGL interventions in their classrooms. Researchers will video and audio record a sample of teachers and students as they learn. These data will be analyzed qualitatively to: (1) examine how the conceptual change of genetic essentialism was promoted or impeded by interactions between teachers, students, and the materials; and (2) identify and corroborate general factors undergirding the backfiring effect.  Knowledge constructed through these studies will be used to revise the HGL interventions and PDIs.  In year three, using the revised versions of the HGL intervention, the project will conduct a cluster randomized trial (CRT). The CRT will compare the HGL interventions to a well-defined “business as usual” genetics curriculum, using a statistically powerful and geographically diverse sample (N = 135 teachers, N = 16,200 students, from 33 states). Using data from the CRT, the project will identify classrooms where the interventions reduced essentialism, had no effect on it, and where it backfired. Then, the project will use stimulated recall methods to interview the teachers and students in those classrooms to make sense of factors that contributed to these outcomes. The project will use this information to develop the final version of the HGL interventions and PDI materials. By the end of year four, the project will have trained an additional 90-100 teachers to use HGL interventions, reaching an additional 10,800-12,000 students, in at least 33 different states.

Reducing Racially Biased Beliefs by Fostering a Complex Understanding of Human Genetics Research in High School Biology Students (Collaborative Research: Duncan)

The project will refine a genetics education curriculum, called Humane Genome Literacy (HGL), in order to reduce belief in genetic essentialism. This research will provide curriculum writers and educators with knowledge about how to design a humane genetics education to maximize reductions in students’ genetic essentialist beliefs. The research findings will demonstrate how to support teachers who wish to reduce beliefs in genetic essentialism by teaching students about the complexity of human genetics research using the HGL learning materials.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
2100876
Funding Period: 
Wed, 09/01/2021 to Sun, 08/31/2025
Full Description: 

Genetic essentialism is the belief that people of the same race share genes that make them physically, cognitively, and behaviorally uniform, and thus different from other races. The project will refine a genetics education curriculum, called Humane Genome Literacy (HGL), in order to reduce belief in genetic essentialism. This research will provide curriculum writers and educators with knowledge about how to design a humane genetics education to maximize reductions in students’ genetic essentialist beliefs and minimize the threat of backfiring (unintentionally increasing belief in essentialism). The research findings will demonstrate how to support teachers who wish to reduce beliefs in genetic essentialism by teaching students about the complexity of human genetics research using the HGL learning materials.  Project research findings, learning materials, and professional development institutes will be made available to educators and researchers across the country who desire to teach genetics to reduce racial prejudice.

To prepare for the research, the project will revise and augment the project’s existing HGL curriculum and professional development institutes.  In year one, the project will develop new versions of the HGL interventions. Using these materials, the project will train teachers to implement new versions of the HGL interventions in their classrooms. Researchers will video and audio record a sample of teachers and students as they learn. These data will be analyzed qualitatively to: (1) examine how the conceptual change of genetic essentialism was promoted or impeded by interactions between teachers, students, and the materials; and (2) identify and corroborate general factors undergirding the backfiring effect.  Knowledge constructed through these studies will be used to revise the HGL interventions and PDIs.  In year three, using the revised versions of the HGL intervention, the project will conduct a cluster randomized trial (CRT). The CRT will compare the HGL interventions to a well-defined “business as usual” genetics curriculum, using a statistically powerful and geographically diverse sample (N = 135 teachers, N = 16,200 students, from 33 states). Using data from the CRT, the project will identify classrooms where the interventions reduced essentialism, had no effect on it, and where it backfired. Then, the project will use stimulated recall methods to interview the teachers and students in those classrooms to make sense of factors that contributed to these outcomes. The project will use this information to develop the final version of the HGL interventions and PDI materials. By the end of year four, the project will have trained an additional 90-100 teachers to use HGL interventions, reaching an additional 10,800-12,000 students, in at least 33 different states.

Reducing Racially Biased Beliefs by Fostering a Complex Understanding of Human Genetics Research in High School Biology Students (Collaborative Research: Wedow)

The project will refine a genetics education curriculum, called Humane Genome Literacy (HGL), in order to reduce belief in genetic essentialism. This research will provide curriculum writers and educators with knowledge about how to design a humane genetics education to maximize reductions in students’ genetic essentialist beliefs. The research findings will demonstrate how to support teachers who wish to reduce beliefs in genetic essentialism by teaching students about the complexity of human genetics research using the HGL learning materials.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
2100959
Funding Period: 
Wed, 09/01/2021 to Sun, 08/31/2025
Full Description: 

Genetic essentialism is the belief that people of the same race share genes that make them physically, cognitively, and behaviorally uniform, and thus different from other races. The project will refine a genetics education curriculum, called Humane Genome Literacy (HGL), in order to reduce belief in genetic essentialism. This research will provide curriculum writers and educators with knowledge about how to design a humane genetics education to maximize reductions in students’ genetic essentialist beliefs and minimize the threat of backfiring (unintentionally increasing belief in essentialism). The research findings will demonstrate how to support teachers who wish to reduce beliefs in genetic essentialism by teaching students about the complexity of human genetics research using the HGL learning materials.  Project research findings, learning materials, and professional development institutes will be made available to educators and researchers across the country who desire to teach genetics to reduce racial prejudice.

To prepare for the research, the project will revise and augment the project’s existing HGL curriculum and professional development institutes.  In year one, the project will develop new versions of the HGL interventions. Using these materials, the project will train teachers to implement new versions of the HGL interventions in their classrooms. Researchers will video and audio record a sample of teachers and students as they learn. These data will be analyzed qualitatively to: (1) examine how the conceptual change of genetic essentialism was promoted or impeded by interactions between teachers, students, and the materials; and (2) identify and corroborate general factors undergirding the backfiring effect.  Knowledge constructed through these studies will be used to revise the HGL interventions and PDIs.  In year three, using the revised versions of the HGL intervention, the project will conduct a cluster randomized trial (CRT). The CRT will compare the HGL interventions to a well-defined “business as usual” genetics curriculum, using a statistically powerful and geographically diverse sample (N = 135 teachers, N = 16,200 students, from 33 states). Using data from the CRT, the project will identify classrooms where the interventions reduced essentialism, had no effect on it, and where it backfired. Then, the project will use stimulated recall methods to interview the teachers and students in those classrooms to make sense of factors that contributed to these outcomes. The project will use this information to develop the final version of the HGL interventions and PDI materials. By the end of year four, the project will have trained an additional 90-100 teachers to use HGL interventions, reaching an additional 10,800-12,000 students, in at least 33 different states.

Developing the Pedagogical Skills and Science Expertise of Teachers in Underserved Rural Settings

The project will develop and research an innovative model for rural science teacher professional development via technology-mediated lesson study (TMLS). This approach supports translating professional learning into classroom practice by developing a technology-based, social support system among rural teachers.

Lead Organization(s): 
Award Number: 
2101383
Funding Period: 
Wed, 09/01/2021 to Sun, 08/31/2025
Full Description: 

Rural science teachers are often isolated and have few opportunities for meaningful collaboration with fellow teachers, an important source of professional learning. The project will develop and research an innovative model for rural science teacher professional development via technology-mediated lesson study (TMLS). This approach supports translating professional learning into classroom practice by developing a technology-based, social support system among rural teachers. The project will host summer workshops for high school biology and chemistry teachers from four rural Utah regions to learn about 3D science teaching. (3D science teaching incorporates core ideas science disciplines, science research practices, and concepts cutting across disciplines to help students meet performance expectations by engaging with authentic science phenomena.) In the workshops, participants will collaborate with the project team and teachers of the same subject from the same region of the state to co-design 3D science lessons that align with state and national education standards. Building on relationships developed during the workshops, the regional teacher teams will engage in a novel form of professional learning: technology-mediated lesson study. (Lesson study is an instructional inquiry model where teachers work face-to-face in small collaborative groups to craft, deliver, observe, and refine teaching practice.) This project will develop capacity for science teaching for 88 rural science teachers in four regions of the state, who will reach approximately 10,000 rural Utah students each year. Many of the students are members of the sovereign Ute, Paiute, Goshute, Navajo (Diné), and Shoshone Nations. The science lesson plans participants design will be made available to all Utah teachers, and shared with a national audience through a website that shares peer-reviewed science lesson plans. Project research and resources will be further disseminated through conference presentations and publications in peer-reviewed and practitioner journals.

The project will research how TMLS supports teachers in the process of translating professional learning into practice and investigate the impact of changing teachers’ social support network to include teachers of the same subject from other rural schools. The project will study the effects of co-design activities and TMLS cycles on teachers’ changing capacity, practice, and social support system using mixed-methods research. Changes in capacity and practice will be examined qualitatively through interviews, video observations of classroom teaching, and TMLS meetings. The effects of TMLS on teachers’ social support system will be analyzed quantitatively using social network analysis to identify individuals who act as information hubs for 3D science teaching. These teachers will be interviewed to better understand their social interactions. Using design-based implementation research, the project will iteratively improve the professional learning experience collaboratively with the science teacher leaders who participate in the project.

Teaching Amidst Uncertainty: Developing Mathematics Teachers' Groupwork Monitoring Practices

This study addresses two open questions in mathematics education and teacher learning research related to groupwork monitoring. Using contemporary information visualization techniques and open-source tools, alongside a video-based coaching activity, teachers will a) analyze classroom video records featuring group math discussions and b) uncover and investigate their specific interactions with student groups as well as their overall approach to this important phase of their lessons.

Lead Organization(s): 
Award Number: 
2100784
Funding Period: 
Sun, 08/01/2021 to Thu, 07/31/2025
Full Description: 

Decades of research shows that students learn best and instruction is more inclusive when students have opportunities to talk about mathematics. For this reason, many conceptually-oriented mathematics instructional approaches emphasize peer-to-peer discussion. Yet research diverges around questions of how teachers should manage such discussions, an instructional practice referred to as groupwork monitoring. There is contradictory guidance on issues of teacher involvement: should teachers stand back to support student autonomy or involve themselves frequently to support productive sensemaking? This study addresses two open questions in mathematics education and teacher learning research related to groupwork monitoring. The first question centers on groupwork monitoring itself: How can teachers foster productive mathematical talk among students? The second question touches on an underdeveloped topic in teacher education: in what ways can teacher preparation and professional development support teachers in learning effective group work monitoring. Many teacher education strategies–such as rehearsing routines or learning curriculum–aim for teachers to learn well-structured, predictable aspects of instruction, yet there are not clear approaches in helping teachers learn to support more interactive and emergent aspects of mathematics teaching. This Design and Development project addresses these challenges by studying experienced and accomplished secondary mathematics teachers’ learning about groupwork monitoring in a large urban school district. Using contemporary information visualization techniques and open-source tools, alongside a video-based coaching activity, teachers will a) analyze classroom video records featuring group math discussions and b) uncover and investigate their specific interactions with student groups as well as their overall approach to this important phase of their lessons. Through these tools, teachers will develop strategic and integrated understandings of effective groupwork monitoring strategies. As a result of this work, teachers and researchers will be able to better connect teachers’ monitoring choices to students’ peer-to-peer math talk.

To investigate how experienced secondary mathematics teachers learn about groupwork monitoring, the project will develop rich visualization tools to analyze classroom discussions, engage teachers in analytical activities, and study resultant teacher and student learning. In Phase 1, the project team will build on existing visualization tools to develop efficient processes for producing interactive visualizations of monitoring that provide new ways to link classroom video to teachers’ overall interactional patterns. In Phase 2, 12-16 experienced secondary mathematics teachers in six school-based teams will engage over a two-year period with teacher professional development designed to enhance their sensemaking about monitoring, both individually and in teams. The enhanced video feedback system will allow teachers to guide, document, and investigate their evolving sensemaking. In Phase 3, individual and team learning portraits of productive math talk will be developed from the rich corpus of classroom and teacher sensemaking data. At the same time, the corpus will be analyzed using quantitative methods to investigate the conditions under which different teacher monitoring moves support or impede students’ productive math talk. The primary research products will be: 1) novel, open-source tools that dynamically visualize teachers’ monitoring work over a lesson, coordinated with specific teacher-group interaction; 2) a framework for mathematics teachers’ monitoring; 3) a theory about teachers’ learning of responsive and situated practices, of which monitoring is an example; and 4) stronger empirical evidence to guide mathematics teachers’ monitoring practices.

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