Pedagogical Content Knowledge

Science Communities of Practice Partnership

This project will study implementation of an effective professional learning model for elementary science teachers that includes teacher leaders, administrators and university educators in a system perspective for improving science instruction in ways that make it sustainable.

Award Number: 
1813012
Funding Period: 
Wed, 08/01/2018 to Sun, 07/31/2022
Full Description: 

This project will study implementation of an effective professional learning model for elementary science teachers that includes teacher leaders, administrators and university educators in a system perspective for improving science instruction in ways that make it sustainable. The working model involves reciprocal communities of practice, which are groups of teachers, leaders and administrators that focus on practical tasks and how to achieve them across these stakeholder perspectives. The project will provide evidence about the specific components of the professional development model that support sustainable improvement in science teaching, will test the ways that teacher ownership and organizational conditions mediate instructional change, and will develop four tools for facilitating the teacher learning and the accompanying capacity building. In this way, the project will produce practical knowledge and tools necessary for other school districts nationwide to create professional learning that is tailored to their contexts and therefore sustainable.

This study posits that communication among district teachers, teacher leaders, and administrators, and a sense of ownership for improved instruction among teachers can support sustainable change. As such, it tests a model that fosters communication and ownership through three reciprocal communities of practice--one about district leadership including one teacher per school, coaches and university faculty; another about lesson study including teachers, coaches and faculty; and a third about instructional innovation including teachers and administrators, facilitated by coaches. The research design seeks to inform what the communities of practice add to the effects in a quasi-experimental study involving 72 third to fifth grade teachers and 6500 students in four urban school districts. Mixed methodologies will be used to examine shifts in science teaching over three years, testing the professional development model and the mediating roles of reform ownership and organizational conditions.

Determining Teachers' Baseline Practice and Alignment Prior to a Systemic Curriculum Change

In this study, researchers will collaborate with Baltimore City Public Schools to collect and document teacher classroom practices prior to the implementation of an extended professional development model that targets pedagogical skills associated with the NGSS. The broad objective of the project is to characterize the benefits and limitations of utilizing controlled practice-teaching as a key component of teacher professional development for integrating NGSS aligned practices in middle school science classrooms.

Partner Organization(s): 
Award Number: 
1822029
Funding Period: 
Sun, 04/01/2018 to Sun, 03/31/2019
Full Description: 

The goal of this research is to document current teaching practices prior to the systemic integration of the Next Generation Science Standards (NGSS) in Baltimore City Public schools. In this study, UMBC will collaborate with Baltimore City Public Schools (City Schools) to collect and document teacher classroom practices prior to the implementation of an extended professional development model that targets pedagogical skills associated with the Next Generation Science Standards. The broad objective of the project is to characterize the benefits and limitations of utilizing controlled practice-teaching as a key component of teacher professional development for integrating NGSS aligned practices in middle school science classrooms. Success will be measured by changes in teacher attitudes, enhancement of teacher pedagogical skills and student learning gains. Sixty teachers, and over 4,500 students in Baltimore City will be directly impacted through the professional development and curriculum enactment efforts proposed. As a full partner in the project, the City Schools' leadership will also learn what works, for whom, and under what conditions in schools that are representative of their diverse district. Lessons learned have the potential to inform the implementation of other new reform initiatives within City Schools and beyond. Findings from the proposed research have the potential to advance our understanding of innovative professional development strategies and their impact on classroom practices and student learning.

This project focuses on a national need of models for high quality professional development that directly tie specific strategies to classroom-based instructional changes and student learning outcomes. One particular shift in classroom practice that is fundamental for the classroom implementation of NGSS is scientific discourse and argumentation. One particular strategy that has shown promise for supporting teachers' use of strategies supporting argumentation is the use of controlled practice teaching. The proposed study explicitly attempts to determine the impact of the controlled practice-teaching using a quasi-experimental design. The research plan involves middle science teachers being assigned to one of two experimental conditions (PD including or excluding a controlled practice-teaching component) and then to investigate potential differences among the two treatments and control conditions related to changes in attitudes toward NGSS, classroom practices and impact on student learning. The researcher hypothesizes that the inclusion of control-practice teaching that is imbedded in a sustained professional development program will promote the development of teacher pedagogical skills aligned with NGSS more effectively than sustained professional development that does not include a control-practice component.

Improving Multi-Dimensional Assessment and Instruction: Building and Sustaining Elementary Science Teachers' Capacity through Learning Communities (Collaborative Research: Lehman)

The main goal of this project is to better understand how to build and sustain the capacity of elementary science teachers in grades 3-5 to instruct and formatively assess students in ways that are aligned with contemporary science education frameworks and standards. To achieve this goal, the project will use classroom-based science assessment as a focus around which to build teacher capacity in science instruction and three-dimensional learning in science.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1813938
Funding Period: 
Sun, 07/01/2018 to Thu, 06/30/2022
Full Description: 

This is an Early-Stage Design and Development collaborative effort submitted to the assessment strand of the Discovery Research PreK-12 (DRK-12) Program. Its main goal is to better understand how to build and sustain the capacity of elementary science teachers in grades 3-5 to instruct and formatively assess students in ways that are aligned with contemporary science education frameworks and standards. To achieve this goal, the project will use classroom-based science assessment as a focus around which to build teacher capacity in science instruction and three-dimensional learning in science. The three dimensions will include disciplinary core ideas, science and engineering practices, and crosscutting concepts. These dimensions are described in the Framework for K-12 Science Education (National Research Council; NRC, 2012), and the Next Generation Science Standards (NGSS; NGSS Lead States, 2013). The project will work closely with teachers to co-develop usable assessments and rubrics and help them to learn about three-dimensional assessment and instruction. Also, the project will work with teachers to test the developed assessments in diverse settings, and to create an active, online community of practice.

The two research questions will be: (1) How well do these assessments function with respect to aspects of validity for classroom use, particularly in terms of indicators of student proficiency, and tools to support teacher instructional practice?; and (2) In what ways do providing these assessment tasks and rubrics, and supporting teachers in their use, advance teachers' formative assessment practices to support multi-dimensional science instruction? The research and development components of this project will produce assessments and rubrics, which can directly impact students and teachers in the districts and states that have adopted the NGSS, as well as those that have embraced the vision of science teaching and learning embodied in the NRC Framework. The project will consist of five major tasks. First, the effort will iteratively develop assessments and rubrics for formative use, using an evidence-centered design approach. Second, it will collect data from evidence-based revision and redesign of the assessments from teachers piloting the assessments and rubrics, project cognitive laboratory studies with students, and an external review of the assessments design products. Third, it will study teachers' classroom use of assessments to understand and document how they blend assessment and instruction. The project will use pre/post questionnaires, video recordings, observation field notes, and pre/post interviews. Fourth, the study will build the capacity of participating teachers. Teacher Collaborators (n=9) will engage in participatory design of the assessment tasks and act as technical assistants to the overall implementation process. Teacher Implementers (n=15) will use the assessments formatively as part of their instructional practice. Finally, the work will develop a community of learners through the development of a technical assistance infrastructure, and leveraging teacher expertise to formatively assess students' work, using the assessments designed to be diagnostic and instructionally informative. External reviewers and an advisory board will provide formative feedback on the project's processes and summative evaluation of the project's results. The main outcomes of this endeavor will be prototypes of elementary science multi-dimensional assessments and new knowledge for the field on the underlying theory for developing teachers' capacity for engaging in multi-dimensional science instruction, learning, and assessment.

Investigating Impact of Different Types of Professional Development on What Aspects Mathematics Teachers Take Up and Use in Their Classroom

This project will study the design and development of PD that supports teacher development and student learning, and provide accumulation of evidence to inform teacher educators, administrators, teachers, and policymakers of factors associated with successful PD experiences and variation across teachers and types of PDs.

Lead Organization(s): 
Award Number: 
1813439
Funding Period: 
Sun, 07/01/2018 to Wed, 06/30/2021
Full Description: 

Professional development is a critical way in which teachers who are currently in classrooms learn about changes in mathematics teaching and learning and improve their practice. Little is known about what types of professional development (PD) support teachers' improved practice and student learning. However, federal, state, and local governments spend resources on helping teachers improve their teaching practice and students' learning. PD programs vary in their intent and can fall on a continuum from highly adaptive, with great latitude in the implementation, to highly specified, with little ability to adapt the program during implementation. The project will study the design and development of PD that supports teacher development and student learning, and provide accumulation of evidence to inform teacher educators, administrators, teachers, and policymakers of factors associated with successful PD experiences and variation across teachers and types of PDs. The impact study will expand on the evidence of promise from four 2015 National Science Foundation (NSF)-funded projects - two adaptive, two specified - to provide evidence of the impact of the projects on teachers' instructional practice over time. Although the four projects are different in terms of structure and design elements, they all share the goal to support challenging mathematics content, practice standards, and differentiation techniques to support culturally and linguistically diverse, underrepresented populations. Understanding the nature of the professional development including structure and design elements, and unpacking what teachers take up and use in their instructional practice potentially has widespread use to support student learning in diverse contexts, especially those serving disadvantaged and underrepresented student populations.

This study will examine teachers' uptake of mathematics content, pedagogy and materials from different types of professional development in order to understand and unpack the factors that are associated with what teachers take up and use two-three years beyond their original PD experience: Two specified 1) An Efficacy Study of the Learning and Teaching Geometry PD Materials: Examining Impact and Context-Based Adaptations (Jennifer Jacobs, Karen Koellner & Nanette Seago), 2) Visual Access to Mathematics: Professional Development for Teachers of English Learners (Mark Driscoll, Johanna Nikula, & Pamela Buffington), two adaptive: 3) Refining a Model with Tools to Develop Math PD Leaders: An Implementation Study (Hilda Borko & Janet Carlson), 4), TRUmath and Lesson Study: Supporting Fundamental and Sustainable Improvement in High School Mathematics Teaching (Suzanne Donovan, Phil Tucher, & Catherine Lewis). The project will utilize a multi-case method which centers on a common focus of what content, pedagogy and materials teachers take up from PD experiences. Using a specified sampling procedure, the project will select 8 teachers from each of the four PD projects to serve as case study teachers. Subsequently, the project will conduct a cross case analysis focusing on variation among and between teachers and different types of PD. The research questions that guide the project's impact study are: RQ1: What is the nature of what teachers take up and use after participating in professional development workshops? RQ2: What factors influence what teachers take up and use and in what ways? RQ3: How does a professional development's position on the specified-adaptive continuum affect what teachers take up and use?

Developing and Validating Assessments to Measure and Build Elementary Teachers' Content Knowledge for Teaching about Matter and Its Interactions within Teacher Education Settings (Collaborative Research: Hanuscin)

The fundamental purpose of this project is to examine and gather initial validity evidence for assessments designed to measure and build kindergarten-fifth grade science teachers' content knowledge for teaching (CKT) about matter and its interactions in teacher education settings.

Partner Organization(s): 
Award Number: 
1814275
Funding Period: 
Sun, 07/01/2018 to Thu, 06/30/2022
Full Description: 

This is an Early-Stage Design and Development collaborative effort submitted to the assessment strand of the Discovery Research PreK-12 (DRK-12) Program. Its fundamental purpose is to examine and gather initial validity evidence for assessments designed to measure and build kindergarten-fifth grade science teachers' content knowledge for teaching (CKT) about matter and its interactions in teacher education settings. The selection of this topic will facilitate the development of a proof-of-concept to determine if and how CKT assessments can be developed and used to measure and build elementary teachers' CKT. Also, it will facilitate rapid and targeted refinement of an evidence-centered design process that could be applied to other science topics. Plans are to integrate CKT assessments and related resources into teacher education courses to support the ability of teachers to apply their content knowledge to the work of teaching and learning science. The project will combine efforts from prior projects and engage in foundational research to examine the nature of teachers' CKT and to build theories and hypotheses about the productive use and design of CKT assessment materials to support formative and summative uses. Likewise, the project will create a set of descriptive cases highlighting the use of these tools. Understanding how CKT science assessments can be leveraged as summative tools to evaluate current efforts, and as formative tools to build elementary teachers' specialized, practice-based knowledge will be the central foci of this effort.

The main research questions will be: (1) What is the nature of elementary science teachers' CKT about matter and its interactions?; and (2) How can the development of prospective elementary teachers' CKT be supported within teacher education? To address the research questions, the study will employ a mixed-methods, design-based research approach to gather various sources of validity evidence to support the formative and summative use of the CKT instrument, instructional tasks, and supporting materials. The project will be organized around two main research and development strands. Strand One will build an empirically grounded understanding of the nature of elementary teachers' CKT. Strand Two will focus on developing and studying how CKT instructional tasks can be used formatively within teacher education settings to build elementary teachers' CKT. In addition, the project will refine a conceptual framework that identifies the science-specific teaching practices that comprise the work of teaching science. This will be used as well to assess the CKT that teachers leverage when recognizing, understanding, and responding to the content-intensive practices that they engage in as they teach science. To that end, the study will build on two existing frameworks from prior NSF-funded work. The first was originally developed to create CKT assessments for elementary and middle school teachers in English Language Arts and mathematics. The second focuses on the content challenges that novice elementary science teachers face. It is organized by the instructional tools and practices that elementary science teachers use, such as scientific models and explanations. These instructional practices cut across those addressed in the Next Generation Science Standards' (NGSS; Lead States, 2013) disciplinary strands. The main project's outcomes will be knowledge that builds and refines theories about the nature of elementary teachers' CKT, and how CKT elementary science assessment materials can be designed productively for formative and summative purposes. The project will also result in the development of a suite of valid and reliable assessments that afford interpretations on CKT matter proficiency and can be used to monitor elementary teachers learning. An external advisory board will provide formative and summative feedback on the project's activities and progress.

Developing and Validating Assessments to Measure and Build Elementary Teachers' Content Knowledge for Teaching about Matter and Its Interactions within Teacher Education Settings (Collaborative Research: Mikeska)

The fundamental purpose of this project is to examine and gather initial validity evidence for assessments designed to measure and build kindergarten-fifth grade science teachers' content knowledge for teaching (CKT) about matter and its interactions in teacher education settings.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1813254
Funding Period: 
Sun, 07/01/2018 to Thu, 06/30/2022
Full Description: 

This is an Early-Stage Design and Development collaborative effort submitted to the assessment strand of the Discovery Research PreK-12 (DRK-12) Program. Its fundamental purpose is to examine and gather initial validity evidence for assessments designed to measure and build kindergarten-fifth grade science teachers' content knowledge for teaching (CKT) about matter and its interactions in teacher education settings. The selection of this topic will facilitate the development of a proof-of-concept to determine if and how CKT assessments can be developed and used to measure and build elementary teachers' CKT. Also, it will facilitate rapid and targeted refinement of an evidence-centered design process that could be applied to other science topics. Plans are to integrate CKT assessments and related resources into teacher education courses to support the ability of teachers to apply their content knowledge to the work of teaching and learning science. The project will combine efforts from prior projects and engage in foundational research to examine the nature of teachers' CKT and to build theories and hypotheses about the productive use and design of CKT assessment materials to support formative and summative uses. Likewise, the project will create a set of descriptive cases highlighting the use of these tools. Understanding how CKT science assessments can be leveraged as summative tools to evaluate current efforts, and as formative tools to build elementary teachers' specialized, practice-based knowledge will be the central foci of this effort.

The main research questions will be: (1) What is the nature of elementary science teachers' CKT about matter and its interactions?; and (2) How can the development of prospective elementary teachers' CKT be supported within teacher education? To address the research questions, the study will employ a mixed-methods, design-based research approach to gather various sources of validity evidence to support the formative and summative use of the CKT instrument, instructional tasks, and supporting materials. The project will be organized around two main research and development strands. Strand One will build an empirically grounded understanding of the nature of elementary teachers' CKT. Strand Two will focus on developing and studying how CKT instructional tasks can be used formatively within teacher education settings to build elementary teachers' CKT. In addition, the project will refine a conceptual framework that identifies the science-specific teaching practices that comprise the work of teaching science. This will be used as well to assess the CKT that teachers leverage when recognizing, understanding, and responding to the content-intensive practices that they engage in as they teach science. To that end, the study will build on two existing frameworks from prior NSF-funded work. The first was originally developed to create CKT assessments for elementary and middle school teachers in English Language Arts and mathematics. The second focuses on the content challenges that novice elementary science teachers face. It is organized by the instructional tools and practices that elementary science teachers use, such as scientific models and explanations. These instructional practices cut across those addressed in the Next Generation Science Standards' (NGSS; Lead States, 2013) disciplinary strands. The main project's outcomes will be knowledge that builds and refines theories about the nature of elementary teachers' CKT, and how CKT elementary science assessment materials can be designed productively for formative and summative purposes. The project will also result in the development of a suite of valid and reliable assessments that afford interpretations on CKT matter proficiency and can be used to monitor elementary teachers learning. An external advisory board will provide formative and summative feedback on the project's activities and progress.

Developing Teacher Noticing in Engineering in an Online Professional Development Program

This project will research how elementary (K-5) teachers in the Teacher Engineering Education Program (TEEP) program progress in one particular aspect of responsive teaching, noticing student thinking. Project research will also contribute to literature on how to support responsive teaching in web-based environments, expanding understanding of how design principles and features developed in in-person professional development settings can be implemented online.

Lead Organization(s): 
Award Number: 
1720334
Funding Period: 
Fri, 09/01/2017 to Mon, 08/31/2020
Full Description: 

The project will research how elementary (K-5) teachers in the Teacher Engineering Education Program (TEEP) program progress in one particular aspect of responsive teaching, noticing student thinking. TEEP includes four graduate-level courses that help them learn engineering content and pedagogical approaches. There has been little investigation of teacher professional development in engineering design. The work that has been done focuses on increasing teachers' content knowledge and familiarity in engineering. Most teacher professional development and research focus on teachers learning engineering content and process, with less attention on helping teachers develop new instructional practices necessary to help students navigate the complex, ill-defined problems in engineering. TEEP focuses on helping teachers develop practices of responsive teaching in engineering design, where teachers base their instructional moves on what they notice in their students are doing and saying. Project research will also contribute to literature on how to support responsive teaching in web-based environments, expanding understanding of how design principles and features developed in in-person professional development settings can be implemented online. The project will refine a program for engineering teachers nationwide, identify key features that are effective in developing teachers' practice, and create video resources for other professional development programs to use.

The project will address three research questions: (1) What do beginning engineering teachers notice in students' engineering design work? (2) What shifts occur in teachers' noticing over the course of a professional development program focused on responsive teaching and how do these shifts correlate with key features of the program? (3) What shifts occur in how teachers' talk about their goals for students' engineering and their instructional practice? The project will conduct independent analyses from two cohorts of teachers of three data streams: pre-post interviews about practice; teacher-captured classroom videos; video-stimulated interviews, and teachers' coursework. The analyses will then connect these analyses to address the research questions. Videocases of students' engineering will be disseminated for other teacher educators to use in supporting teacher noticing. The research outcomes of the research will not only advance our understandings of teacher learning, but will provide evidence that teachers can recognize, value, and leverage students' diverse resources for engineering. Research on the TEEP program will also provide much-needed empirical support on whether and how online programs can be effective for teachers' instructional practice.

A Partnership to Adapt, Implement and Study a Professional Learning Model and Build District Capacity to Improve Science Instruction and Student Understanding (Collaborative Research: Weiss)

This project will work in partnership with the Santa Clara Unified School District (SCUSD) to adapt a previously designed Professional Learning (PL) model based on the District's objectives and constraints to build the capacity of teacher leaders and a program coordinator to implement the adapted PL program. The project is examining the sustainability and scalability of a PL model that supports the development of teachers' pedagogical content knowledge and instructional practices.

Partner Organization(s): 
Award Number: 
1720894
Funding Period: 
Sun, 10/01/2017 to Thu, 09/30/2021
Full Description: 

The Lawrence Hall of Science (the Hall) and Stanford University teams have previously developed and tested the efficacy of a program of Professional Learning (PL) which is focused on improving teachers' ability to support students' ability to engage in scientific argumentation. Key components of the PL model include a week-long summer institute and follow-up sessions during the academic year that incorporate additional pedagogical input, video reflection, and planning time. In this project, the Hall and Stanford are working in partnership with the Santa Clara Unified School District (SCUSD) to adapt the PL model based on the District's objectives and constraints, to build the capacity of teacher leaders and a program coordinator to implement the adapted PL program. This will enable the District to continue to adapt and implement the program independently at the conclusion of the project. Concurrently, the project is studying the adaptability of the PL model and the effectiveness of its implementation, and is developing guidelines and tools for other districts to use in adapting and implementing the PL model in their local contexts. Thus, this project is contributing knowledge about how to build capacity in districts to lead professional learning in science that addresses the new teaching and learning standards and is responsive to the needs of their local context.

The project is examining the sustainability and scalability of a PL model that supports the development of teachers' pedagogical content knowledge and instructional practices, with a particular focus on engaging students in argument from evidence. Results from the Hall and Stanford's previous research project indicate that the PL model is effective at significantly improving teachers' and students' classroom discourse practices. These findings suggest that a version of the model, adapted to the context and needs of a different school district, has the potential to improve the teaching of science to meet the demands of the current vision of science education. Using a Design-Based Implementation Research approach, this project is (i) working with SCUSD to adapt the PL model; (ii) preparing a district project coordinator and cadre of local teacher leaders (TLs) to implement and further adapt the model; and (iii) studying the adaptation and implementation of the model. The outcomes will be: a) a scalable PL model that can be continually adapted to the objectives and constraints of a district; b) a set of activities and resources for the district to prepare and support the science teacher leaders who will implement the adapted PL program internally with other teachers; and c) knowledge about the adaptations and resources needed for the PL model to be implemented independently by other school districts. The team also is researching the impact of the program on classroom practices and student learning.


Project Videos

2019 STEM for All Video Showcase

Title: Building District Leadership in Scientific Argumentation

Presenter(s): Coralie Delhaye, Emily Reigh, & Emily Weiss

2018 STEM for All Video Showcase


Mathematical Learning via Architectural Design and Modeling Using E-Rebuild

This project will explore the learning of mathematics through architectural tasks in an online simulation game, E-Rebuild. In the game-based architectural simulation, students will be able to complete tasks such as building and constructing structures while using mathematics and problem solving. The project will examine how to collect data about students' learning from data generated as they play the game, how students learn mathematics using the simulation, and how the simulation can be included in middle school mathematics learning.

Lead Organization(s): 
Award Number: 
1720533
Funding Period: 
Tue, 08/01/2017 to Sat, 07/31/2021
Full Description: 

This project will explore the learning of mathematics through architectural tasks in an online simulation game, E-Rebuild. There is a need to connect mathematics to real world contexts and problems. In the game-based architectural simulation, students will be able to complete tasks such as building and constructing structures while using mathematics and problem solving. The learning platform will be flexible so teachers can customize tasks for their students. The project will examine how to collect data about students' learning from data generated as they play the game. The project will explore how students learn mathematics using the simulation and how the simulation can be included in middle school mathematics learning.

The project includes two major research questions. First, how will the design of a scalable game-based, design-centered learning platform promote coordination and application of math representation for problem solving? Second, how and under what implementation circumstances will using a scalable architectural game-based learning platform improve students multi-stranded mathematical proficiency (i.e., understanding, problem solving and positive disposition)? A key feature of the project is stealth-assessment or data collected and logged as students use the architectural simulation activities that can be used to understand their mathematics learning. The project uses a design-based research approach to gather data from students and teachers that will inform the design of the learning environment. The qualitative and quantitative data will also be used to understand what students are learning as they play the game and how teachers are interacting with their students. The project will include a mixed methods study to compare classrooms using the architectural activities to classrooms that are using typical activities.

The Mathematical Knowledge for Teaching Measures: Refreshing the Item Pool

This project proposes an assessment study that focuses on improving existing measures of teachers' Mathematical Knowledge for Teaching (MKT). The research team will update existing measures, adding new items and aligning the instrument to new standards in school mathematics.

Lead Organization(s): 
Award Number: 
1620914
Funding Period: 
Thu, 12/01/2016 to Sat, 11/30/2019
Full Description: 

This project proposes an assessment study that focuses on improving existing measures of teachers' Mathematical Knowledge for Teaching (MKT). The research team will update existing measures, adding new items and aligning the instrument to new standards in school mathematics. In addition, the team will update the delivery system for the assessment to Qualtrics, a more flexible online system.

The research team will build an updated measure of teachers' Mathematical Knowledge for Teaching (MKT). Project researchers will conduct item writing camps, develop new items, cognitively pilot and revise items, and factor analyze items. The researchers will also determine item constructs and calibrate items (and constructs) through an innovative application of Item Response Theory (IRT) employing a variant of the standard 2-parameter IRT model. Finally, the team will oversee the transition of the Teacher Knowledge Assessment System to the Qualtrics data collection environment to allow for more flexible item specification.

Pages

Subscribe to Pedagogical Content Knowledge