Teacher Content Knowledge

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.

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).

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

Algebra Project Mathematics Content and Pedagogy Initiative

This project will scale up, implement, and assess the efficacy of interventions in K-12 mathematics education based on the well-established Algebra Project (AP) pedagogical framework, which seeks to improve performance and participation in mathematics of students in distressed school districts, particularly low-income students from underserved populations.

Award Number: 
1621416
Funding Period: 
Thu, 09/15/2016 to Mon, 08/31/2020
Full Description: 

Algebra continues to serve as a gatekeeper and potential barrier for high school students. The Algebra Project Mathematics Content and Pedagogy Initiative (APMCPI) will scale up, implement and assess the efficacy of interventions in K-12 mathematics education based on the well-established Algebra Project (AP) pedagogical framework. The APMCPI project team is comprised of four HBCUs (Virginia State University, Dillard University, Xavier University, Lincoln University), the Southern Initiative Algebra Project (SIAP), and four school districts that are closely aligned with partner universities. The purpose of the Algebra Project is to improve performance and participation in mathematics by members of students in distressed school districts, particularly those with a large population of low-income students from underserved populations including African American and Hispanics. The project will provide professional development and implement the Algebra Project in four districts and study the impact on student learning. The research results will inform the nation's learning how to improve mathematics achievement for all children, particularly those in distressed inner-city school districts.

The study builds on a prior pilot project with a 74% increase in students who passed the state exam. In the early stages of this project, teachers in four districts closely associated with the four universities will receive Algebra Project professional development in Summer Teacher Institutes with ongoing support during the academic year, including a community development plan. The professional development is designed to help teachers combine mathematical problem solving with context-rich lessons, which both strengthen and integrate teachers' understanding of key concepts in mathematics so that they better engage their students. The project also will focus on helping teachers establish a framework for mathematically substantive, conceptually-rich and experientially-grounded conversations with students. The first year of the study will begin a longitudinal quasi-experimental, explanatory, mixed-method design. Over the course of the project, researchers will follow cohorts who are in grade-levels 5 through 12 in Year 1 to allow analyses across crucial transition periods - grades 5 to 6; grades 8 to 9; and grades 12 to college/workforce. Student and teacher data will be collected in September of Project Year 1, and in May of each project year, providing five data points for each student and teacher participant. Student data will include student attitude, belief, anxiety, and relationship to mathematics and science, in addition to student learning outcome measures. Teacher data will include content knowledge, attitudes and beliefs, and practices. Qualitative data will provide information on the implementation in both the experimental and control conditions. Analysis will include hierarchical linear modeling and multivariate analysis of covariance.

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.

Strengthening Mathematics Intervention: Identifying and Addressing Challenges to Improve Instruction for Struggling Learners

This project's first goal is to study the national landscape of mathematics intervention classes, which are additional classes provided to struggling students, including learners with and without identified disabilities. We administered a survey to a nationally representative sample of 2,024 urban and suburban public schools with grades 6-8 to find out how these classes are being implemented and the types of challenges faced.

Award Number: 
1621294
Funding Period: 
Thu, 09/15/2016 to Mon, 08/31/2020
Full Description: 

Across the nation, schools face a pressing need to improve instruction for middle grades students who are not reaching proficiency on standardized assessments. One approach is to schedule additional mathematics classes to provide struggling learners with more time for instruction and support. For our study, we defined mathematics interventional classes as classes taken by struggling students during the regular school day in addition to their general education mathematics classes. These classes are for students who have difficulties learning mathematics, including learners who do not have identified disabilities and those with Individualized Education Programs (IEPs). 

While recommendations for intervention practices are present in the research literature, little is known about how schools are actually implementing intervention classes, including how often the classes meet, the number of students enrolled, who teaches them and the content focus. To address this gap in the knowledge base, we conducted an observational study and a national survey of current practices and challenges in mathematics intervention classes. The survey was administered to a nationally representative sample of 2,024 urban or suburban public schools with grades 6-8.  Approximately, 43% of schools (876 schools) responded; the findings revealed widespread implementation of mathematics intervention classes and variations in class structures and practices. 

The final aspect of the project involves the design of professional development for mathematics intervention teachers based on the needs identified in the earlier phases of the project. We are developing and testing a blended professional development course to help teachers build the knowledge and practices needed to provide high-quality, targeted instruction to struggling learners in mathematics intervention classes.

Related Resource:

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.

Building a Next Generation Diagnostic Assessment and Reporting System within a Learning Trajectory-Based Mathematics Learning Map for Grades 6-8

This project will build on prior funding to design a next generation diagnostic assessment using learning progressions and other learning sciences research to support middle grades mathematics teaching and learning. The project will contribute to the nationally supported move to create, use, and apply research based open educational resources at scale.

Award Number: 
1621254
Funding Period: 
Thu, 09/15/2016 to Sat, 08/31/2019
Full Description: 

This project seeks to design a next generation diagnostic assessment using learning progressions and other research (in the learning sciences) to support middle grades mathematics teaching and learning. It will focus on nine large content ideas, and associated Common Core State Standards for Mathematics. The PIs will track students over time, and work within school districts to ensure feasibility and use of the assessment system.

The research will build on prior funding by multiple funding agencies and address four major goals. The partnership seeks to address these goals: 1) revising and strengthening the diagnostic assessments in mathematics by adding new item types and dynamic tools for data gathering 2) studying alternative ways to use measurement models to assess student mathematical progress over time using the concept of learning trajectories, 3) investigating how to assist students and teachers to effectively interpret reports on math progress, both at the individual and the class level, and 4) engineering and studying instructional strategies based on student results and interpretations, as they are implemented within competency-based and personalized learning classrooms. The learning map, assessment system, and analytics are open source and can be used by other research and implementation teams. The project will exhibit broad impact due to the number of states, school districts and varied kinds of schools seeking this kind of resource as a means to improve instruction. Finally, the research project contributes to the nationally supported move to create, use, and apply research based open educational resources at scale.

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