Pedagogical Content Knowledge

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.

Science and Engineering Education for Infrastructure Transformation

This project focuses on the research and develop an engineering education technology and pedagogy that will support project-based learning of science, engineering, and computation concepts and skills underlying the strategically important "smart" and "green" aspects of the infrastructure. The project will develop transformative technologies and curriculum materials to turn the campus of a high school or a geographical information system such as Google Maps into an engineering laboratory with virtually unlimited opportunities for learning and exploration.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1721054
Funding Period: 
Sun, 10/01/2017 to Thu, 09/30/2021
Full Description: 

The Concord Consortium in collaboration with Purdue University will research and develop an engineering education technology and pedagogy that will support project-based learning of science, engineering, and computation concepts and skills underlying the strategically important "smart" and "green" aspects of the infrastructure. This project will develop transformative technologies and curriculum materials to turn the campus of a high school or a geographical information system such as Google Maps into an engineering laboratory with virtually unlimited opportunities for learning and exploration. The project will deliver two innovations: 1) The Smart High School is an engineering platform for designing Internet of Things systems for managing the resources, space, and processes of a school based on real-time analysis of data collected by various sensors deployed by students on campus; and 2) the Virtual Solar World is a computational modeling platform for students to design, deploy, and connect virtual solar power solutions for their homes, schools, and regions. Six standards-aligned curriculum units based on these technologies will be developed to guide student learning and support educational research. Approximately 2,000 students from rural, suburban, and urban high schools in Indiana, Massachusetts, New Hampshire, and Ohio will participate in this research. project products and findings through the Internet, conferences, publications, and partner networks.

The research is designed to identify technology-enhanced instructional strategies that can simultaneously foster the growth of skills and self-efficacy in scientific reasoning, design thinking, and computational thinking, all of which are needed to build the future infrastructure. The focus on infrastructure transformation is aligned with NSF's vision of smart and connected communities. Although this project will use the context of smart and green infrastructure to engage students to solve real-world problems, the skills of scientific reasoning, design thinking, and computational thinking that they will acquire through meeting the challenges of this project can be transferrable to other topics and fields. Using a design-based research approach, a rich set of formative and summative data will be collected from these students for probing into three research questions: 1) To what extent does the integrated learning model help students develop and connect scientific reasoning, design thinking, and computational thinking skills?; 2) To what extent is students' interest in cognate careers affected by the authenticity of engineering design challenges?; and 3) How do the variations in the solutions to overcome the cognitive and practical difficulties of real-world problems impact learning outcomes and career interest? The data sources include pre/post-tests, process data, self-reports, observations, surveys, interviews, and participant information.

Culturally Responsive Indigenous Science: Connecting Land, Language, and Culture

This Culturally Responsive Indigenous Science project seeks to advance this knowledge base through research and by catalyzing new approaches to Indigenous science, technology, engineering, and mathematics (ISTEM) learning. Using an ISTEM focused model, the project will develop, test, and implement a culturally responsive land-based curriculum that integrates Western science, multimodal technologies and digital tools, and Native American tribal knowledge, cultures and languages to investigate and address local environmental science and sustainability concerns.

Lead Organization(s): 
Award Number: 
1720931
Funding Period: 
Fri, 09/01/2017 to Tue, 08/31/2021
Full Description: 

The intersection between Indigenous and Western science continues to be of great importance to K-12 science education, particularly with regards to broadening participation in STEM. With over five hundred federally recognized Native American tribes in the United States, there is much to learn and understand. This Culturally Responsive Indigenous Science project seeks to advance this knowledge base through research and by catalyzing new approaches to Indigenous science, technology, engineering, and mathematics (ISTEM) learning. Using an ISTEM focused model, the project will develop, test, and implement a culturally responsive land-based curriculum that integrates Western science, multimodal technologies and digital tools, and Native American tribal knowledge, cultures and languages to investigate and address local environmental science and sustainability concerns. While Indigenous STEM teaching and learning as constructs have existed for many years, the rigorous research design and extensive integration of multimodal technologies as platforms for scientific inquiry, data management, knowledge dissemination and curation are innovative and timely. Few, if any, Design and Development projects in the current DRK-12 portfolio explore similar work. Therefore, the broader impacts of this project are poised to not only contribute to the DRK-12 portfolio but also advance knowledge in Indigenous STEM education and science education, more broadly.

Over a three year period, hundreds of Native American students (grades 4-9) in tribal schools located in Oregon, Washington, and Idaho will engage in the project. Each year, approximately 60-80 students (grades 7-9), with some returning students, will also participate in enrichment activities and in years 1-3, in the residential summer experience at Washington State University. A qualitative, quasi-experimental design-based study will be conducted to address three salient research questions: (a) What are the impacts of culturally responsive and land education-based ISTEM curriculum and technology on Native American student engagement, efficacy and achievement in school? (b) What types of professional development activities foster teacher efficacy and improve teacher learning and teaching of ISTEM in classrooms? and (c) How can ISTEM foster greater family and community engagement in schools and in Tribal Communities? Data will be collected through interviews, surveys, and or questionnaires from participating students, teachers, and Tribal members. Consistent with Indigenous methodologies, focus group interviews (talking circles) will also be facilitated after ISTEM community expositions and engagement activities to capture community impacts. Formative and summative evaluations will be conducted by the Learning and Performance Research Center (LPRC) at Washington State University, an independent entity of the University with extensive expertise in project evaluation. A broad range of dissemination activities will be employed to achieve maximum impacts, including the use of the Plateau People's Web Portal, a digital tool designed to help Native communities to manage, circulate, and curate their digital materials using their own cultural protocols, language and social systems. This regional collaboration includes partnerships with the Confederated Tribes of Warm Springs (Oregon), Confederated Tribes of the Colville Reservation (Washington), and the Coeur D'Alene Tribe (Idaho).


Project Videos

2020 STEM for All Video Showcase

Title: Culturally Responsive Indigenous Science

Presenter(s): Paula Price, Carladean Caldera, Landon Charlo, Kellie Fry, Zoe Higheagle Strong, Sandra Larios, James Lasarte-Whistocken, Lotus Norton-Wisla, & T Watson


Youth Participatory Science to Address Urban Heavy Metal Contamination

This project is focused on the work and learning of teachers as they engage youth from underrepresented groups in studying chemistry as a subject relevant to heavy metal contamination in their neighborhoods. The project will position Chicago teachers and students as Change Makers who are capable of addressing the crises of inequity in science education and environmental contamination that matter deeply to them, while simultaneously advancing their own understanding and expertise.

Award Number: 
1720856
Funding Period: 
Mon, 05/15/2017 to Thu, 04/30/2020
Full Description: 

This project is focused on the work and learning of teachers as they engage youth from underrepresented groups in studying chemistry as a subject relevant to heavy metal contamination in their neighborhoods. The project is a collaboration of teachers in the Chicago Public Schools, science educators, chemists, and environmental scientists from the University of Illinois at Chicago, Northwestern University, Loyola University, and members of the Chicago Environmental Justice Network. The project is significant because it leverages existing partnerships and builds on pilot projects which will be informed by a corresponding cycle of research on teachers' learning and practice. The project will position Chicago teachers and students as Change Makers who are capable of addressing the crises of inequity in science education and environmental contamination that matter deeply to them, while simultaneously advancing their own understanding and expertise. The project will examine the malleable factors affecting the ability of teachers to engage underrepresented students in innovative urban citizen science projects with a focus on the synergistic learning that occurs as teachers, students, scientists, and community members work together on addressing complex socio-scientific issues.

The goal is to provide a network of intellectual and analytical support to high school chemistry teachers engaged in customizing curricula in response to urban environmental concerns. The project will use an annual summer institute where collaborators will develop curriculum and procedures for collecting soil and water samples. In the project, the teachers and students will work with university scientists to analyze these samples for heavy metals, and students will share their results in community settings. The study design will be multiple case and be used to study the content knowledge learned and mobilized by participating teachers as they develop these authentic projects. The project includes explicit focus on the professional development of high school science teachers while it also aims to create rich learning opportunities for underrepresented high school students in STEM fields. The contextualized science concepts within students' everyday experiences or socio-scientific issues will likely have a positive impact on student motivation and learning outcomes, but the experiences of urban students are less likely to be reflected by the curriculum, and the practices of effective secondary science teachers in these contexts are under-examined.

The following article is in press and will be available soon:

Morales-Doyle, D., Childress-Price, T., & Chappell, M. (in press). Chemicals are contaminants too: Teaching appreciation and critique of science in the era of NGSS. Science Education. https://doi.org/10.1002/sce.21546

Learning in Places: Field Based Science in Early Childhood Education

This project aims to develop an innovative field-based science learning approach that will support the capacity of culturally diverse students in Grades K-3 to engage in complex ecological reasoning and related problem solving. To provide rich learning environments, outdoor learning gardens will be created in which students, teachers, garden educators, and families participate in activities that facilitate the investigation of tangible ecological challenges such as water capture and food security.

Lead Organization(s): 
Award Number: 
1720578
Funding Period: 
Sat, 07/01/2017 to Wed, 06/30/2021
Full Description: 

Recent evidence suggests that reasoning and making decisions about ecological systems is a cultural activity that impacts participation in the core scientific practices of observation, evidence use, and claims making. This project aims to develop an innovative field-based science learning approach that will support the capacity of culturally diverse students in Grades K-3 to engage in complex ecological reasoning and related problem solving. To provide rich learning environments, outdoor learning gardens will be created in which students, teachers, garden educators, and families participate in activities that facilitate the investigation of tangible ecological challenges such as water capture and food security.

Using design-based research, the project team will collaborate with teachers, parents of participating students, and community garden educators to collectively design and develop four key components: 1) field-based curricular units for K-3 classrooms; 2) a model of family and community engagement that strengthens cultural relevance and equity in field-based science learning; 3) a pilot program of teacher professional development that informs future scaling efforts; and 4) research that unpacks student learning and teacher instructional practices that support children?s complex ecological reasoning and the cultural contexts of such knowledge. Data sources will include video, interviews, surveys, and student-created artifacts. A mixed-methods approach will be used to produce research findings at multiple levels including: student learning about complex ecological phenomena and field-based practices; classroom-level learning and high-leverage teaching practices in model units at each grade level; impacts of co-design on professional learning and practice; and family and community organizations learning and engagement in field-based science education. The project will be carried out by a research-practice-community partnership in Seattle, Washington that includes learning scientists (University of Washington), K-3 teachers and school administrators (Seattle Public Schools), garden educators (Seattle Tilth), and parents of participating students. In total, eight schools, 32 teachers, 800 students, and 32 families are expected to participate.

Investigating Productive Use of High-Leverage Student Mathematical Thinking (Collaborative Research: Peterson)

This project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. The study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks.

Lead Organization(s): 
Award Number: 
1720410
Funding Period: 
Sat, 07/01/2017 to Mon, 05/31/2021
Full Description: 

The project will examine how secondary mathematics teachers respond to and use students' thinking during whole class discussion. An ongoing challenge for teachers is making the best use of students' emerging mathematical ideas during whole class discussion. Teachers need to draw on the ideas students have developed in order to create opportunities for learning about significant mathematical concepts. This study will create tasks specifically designed to generate opportunities for teachers to build on students' thinking and then use classroom observation and analysis of classroom video to develop tools to support teachers in leading whole class discussion.

The project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. This study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks. The project engages teacher-researchers in exploring the building practice. The teacher-researchers will use the project-designed tasks in their classrooms and then engage in a cycle of analysis of their own teaching with the research team. Data collection and analysis will rely on video analysis of classrooms, teachers' reflections on task enactment, and data collected during research team meetings convened with teacher-researchers to analyze practice.

CAREER: Investigating Changes in Students' Prior Mathematical Reasoning: An Exploration of Backward Transfer Effects in School Algebra

This project explores "backward transfer", or the ways in which new learning impacts previously-established ways of reasoning. The PI will observe and evaluate algebra I students as they learn quadratic functions and examine how different kinds of instruction about the new concept of quadratic functions helps or hinders students' prior mathematical knowledge of the previous concept of linear functions.

Lead Organization(s): 
Award Number: 
1651571
Funding Period: 
Sat, 07/01/2017 to Thu, 06/30/2022
Full Description: 

As students learn new mathematical concepts, teachers need to ensure that prior knowledge and prior ways understanding are not negatively affected. This award explores "backward transfer", or the ways in which new learning impacts previously-established ways of reasoning. The PI will observe and evaluate students in four Algebra I classrooms as they learn quadratic functions. The PI will examine how different kinds of instruction about the new concept of quadratic functions helps or hinders students' prior mathematical knowledge of the previous concept of linear functions. More generally, this award will contribute to the field of mathematics education by expanding the application of knowledge transfer, moving it from only a forward focused direction to include, also, a backward focused direction. An advisory board of scholars with expertise in mathematics education, assessment, social interactions, quantitative reasoning and measurement will support the project. The research will occur in diverse classrooms and result in presentations at the annual conferences of national organizations, peer-reviewed publications, as well as a website for teachers which will explain both the theoretical model and the findings from the project. An undergraduate university course and professional development workshops using video data from the project are also being developed for pre-service and in-service teachers. Ultimately, the research findings will generate new knowledge and offer guidance to elementary school teachers as they prepare their students for algebra.

The research involves three phases. The first phase includes observations and recordings of four Algebra I classrooms and will test students' understanding of linear functions before and after the lessons on quadratic functions. This phase will also include interviews with students to better understand their reasoning about linear function problems. The class sessions will be coded for the kind of reasoning that they promote. The second phase of the project will involve four cycles of design research to create quadratic and linear function activities that can be used as instructional interventions. In conjunction with this phase, pre-service teachers will observe teaching sessions through a course that will be offered concurrently with the design research. The final phase of the project will involve pilot-applied research which will test the effects of the instructional activities on students' linear function reasoning in classroom settings. This phase will include treatment and control groups and further test the hypotheses and instructional products developed in the first two phases.

Analysis of Effective Science Coaching: What, Why and How

This project will conduct an in-depth analysis of instructional coaching by analyzing archived video-recorded coaching sessions with middle and high school science teachers. The goal of the project is to analyzing the videos and previously collected quantitative outcome data to create descriptive profiles of instructional coaching and identify which key coaching elements lead to desired teacher and student outcomes.

Lead Organization(s): 
Award Number: 
1621308
Funding Period: 
Sat, 10/01/2016 to Mon, 09/30/2019
Full Description: 

This Exploratory project will conduct an in-depth analysis of instructional coaching by analyzing 520 hours of archived video-recorded coaching sessions with 75 middle and high school science teachers in grades 6-12 collected in a U.S. Department of Education IES-funded coaching research study. The goal of the project is to "unpack" the coaching intervention by analyzing the videos and previously collected quantitative outcome data to (a) create descriptive profiles of instructional coaching and (b) identify which key coaching elements ("active ingredients") lead to desired teacher and student outcomes.

Following a design-based research approach, relying on iterative feedback and using data saturation process to analyze data, the project will translate theorized, conceptual characteristics of coaching into empirical models to guide future coaching research and practical guidance through identification of critical elements needed for coaching to work.

Sensing Science through Modeling: Developing Kindergarten Students' Understanding of Matter and Its Changes

This project will develop a technology-supported, physical science curriculum that will facilitate kindergarten students' conceptual understanding of matter and how matter changes. The results of this investigation will contribute important data on the evolving structure and content of children's physical science models as well as demonstrate children's understanding of matter and its changes.

Lead Organization(s): 
Award Number: 
1621299
Funding Period: 
Sat, 10/01/2016 to Wed, 09/30/2020
Full Description: 

Despite recent research demonstrating the capacity of young children to engage deeply with science concepts and practices, challenging science curriculum is often lacking in the early grades. This project addresses this gap by developing a technology-supported, physical science curriculum that will facilitate kindergarten students' conceptual understanding of matter and how matter changes. To accomplish these goals, the curriculum will include opportunities for students to participate in model-based inquiry in conjunction with the use of digital probeware and simulations that enable students to observe dynamic visualizations and make sense of the phenomena. To support the capacity of kindergarten teachers, a continuous model of teacher development will be implemented.

Throughout development, the project team will collaborate with kindergarten teachers and more than 300 demographically diverse students across eight classrooms in Massachusetts and Indiana. A design based research approach will be used to iteratively design and revise learning activities, technological tools, and assessments that meet the needs and abilities of kindergarten students and teachers. The project team will: 1) work with kindergarten teachers to modify an existing Grade 2 curricular unit for use with their students; 2) design a parallel curricular unit incorporating technology; 3) evaluate both units for feasibility and maturation effects; and 4) iteratively revise and pilot an integrated unit and assess kindergarten student conceptual understanding of matter and its changes. The results of this investigation will contribute important data on the evolving structure and content of children's physical science models as well as demonstrate children's understanding of matter and its changes.

Proportions Playground: A Dynamic World to Support Teachers' Proportional Reasoning

This project focuses on the creation of the initial functionality for a dynamic microworld, Proportions Playground, designed to support teachers in developing a coherent understanding of proportional reasoning. The Proportions Playground project seeks to both develop a unique pilot software application for the iPad and explore how it supports teachers in developing a coherent, robust definition of proportions.

Award Number: 
1621290
Funding Period: 
Thu, 09/01/2016 to Thu, 02/28/2019
Full Description: 

Proportions are a critical topic in mathematics that is simultaneously complicated and over-simplified in typical instruction. Current research undertaken by the research team suggests that the over-simplification is related to limitations in teachers' understandings of proportional relationships. Presenting proportions in a dynamic environment offers teachers the opportunity to create key developmental understandings related to this area of mathematics. This project focuses on the creation of the initial functionality for a dynamic microworld, Proportions Playground, designed to support teachers in developing a coherent understanding of proportional reasoning. Proportions Playground is conceptualized as a tool for supporting the development of coherent understandings by allowing teachers to interact in concrete ways with otherwise abstract ideas and by allowing teachers easy access to dynamic objects and other representations. It is meant to address the significant limitations for reasoning about the relationships between measurable aspects of two objects as well as in manipulating those relationships. Building from work currently underway, Proportions Playground will explore key areas in which there are opportunities for engaging teachers in the development of a coherent and robust understanding of proportional reasoning that extends beyond the typical "3 given, 1 unknown" proportion problem. This approach attempts to engage teachers in an array of dynamic, visually-rich sets of tasks designed to challenge teachers' preconceptions of proportions and to strengthen their connections between proportions and related areas of mathematics. This project is funded by the Discovery Research PreK-12 (DRK-12) and EHR Core Research (ECR) Programs. the DRK-12 program supports research and development on STEM education innovations and approaches to teaching, learning, and assessment. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.

The Proportions Playground project seeks to both develop a unique pilot software application for the iPad and explore how it supports teachers in developing a coherent, robust definition of proportions. The software will be designed to support either numeric manipulation (e.g., graphing software) or geometric constructions (e.g., dynamic geometry software). Specifically, for this project the mathematics of interest will include the relationships between similarity and proportion and the nature of covariation. The research will focus on how teachers are developing a robust and coherent understanding of proportions and how the dynamic environment promotes such understandings. Working with six teacher advisors, the project will develop three task sets. Using teaching experiments and individual interviews, results will be used to refine the task sets. The revised task sets will be piloted with 40 teachers. Data will be collected on participants' thinking and any changes seen in the knowledge resources they are using. The researchers will be looking for factors that seem to impact teachers' thinking as well as evidence to support or deny the assertion that the Proportions Playground activities engage teachers in (a) different ways of reasoning about proportions and (b) support them in drawing from a wide array of resources so that coherence may be developed were the teachers to have a prolonged engagement with the tools. The project will rely on Epistemic Network Analysis to identify the connections between knowledge resources.

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