Mathematics

Usable Measures of Teacher Understanding: Exploring Diagnostic Models and Topic Analysis as Tools for Assessing Proportional Reasoning for Teaching

This project seeks to measure the kinds of knowledge developed in professional development (PD) programs that have been shown to matter for teachers' classroom practices and their students' learning. The project aims to develop an assessment that identifies patterns in the teachers' learning in a way that helps drive subsequent PD.The overall goal of this project is to pursue a potentially transformative approach to the assessment of teacher proportional knowledge by developing a measure that is well aligned with the content and skills taught in various PD programs.

Award Number: 
1813760
Funding Period: 
Sat, 09/01/2018 to Wed, 08/31/2022
Full Description: 

One of the great challenges related to teachers and their knowledge is measuring their learning in ways that are both formative and meaningful in relation to their likely impact on students. This challenge persists despite efforts to define the knowledge teachers should have and despite previous innovative efforts to create good measures. This project tackles the challenge by specifically aiming to measure the kinds of knowledge developed in professional development (PD) programs that has been shown to matter for teachers' classroom practices and their students' learning. The project aims to develop an assessment that identifies patterns in the teachers' learning in a way that helps drive subsequent professional development.

The overall goal of this project is to pursue a potentially transformative approach to the assessment of teacher proportional knowledge by developing a measure that is well aligned with the content and skills taught in various PD programs. This instrument will be based on a new approach that builds on emerging psychometric models. Specifically, diagnostic classification models (DCMs) will be utilized to diagnose teachers' learning during a PD program as well as employed to identify the progression in teachers' learning.  Statistical topic models (STMs) will be used to look for patterns of understanding that emerge from open-ended responses and provide natural-language insight into teachers' reasoning. A final version of the assessment will be constructed for a national sample based on the results from the predictive validity stage, and this version will be tested with teachers who participate in various types of PD programs targeting proportional reasoning. This project has broad implications for the creation of assessments and for teacher education. It will provide insights about whether there is a clear learning progression for teachers. While much work has been done with students' learning progression, much less is known about how teachers learn. Another implication is that the STM approach allows machine scoring of natural language in a way that highlights strengths and weaknesses in reasoning rather than simply returning a score. For formative use, this is information that is more helpful as it highlights areas for further instruction. A third implication is that DCMs will allow to assess teacher knowledge at a finer-grained understanding than is typically available, thus allowing for careful refinement of PD as well as a tool for showing overall growth in PD. A fourth implication is that a more systematic approach will be followed to capture the kinds of knowledge teachers need. Assessments developed using DCMs and STMs have the potential to serve as models for developing further instruments in other STEM content areas. Such assessments have the potential to not only help identify successful PD programs, but also to provide PD providers with rich data from which they can make instructional decisions.

Professional Development Supports for Teaching Bioinformatics through Mobile Learning

This project will investigate the professional development supports needed for teaching bioinformatics at the high school level. The project team will work with biology and mathematics teachers to co-design instructional modules to engage students with core bioinformatics concepts and computational literacies, by focusing on local community health issues supported through mobile learning activities.

Lead Organization(s): 
Award Number: 
1812738
Funding Period: 
Sat, 09/01/2018 to Mon, 02/28/2022
Full Description: 

Bioinformatics is an emerging area of research that develops new knowledge through computational analysis of vast biological and biomedical data. This project will investigate the professional development supports needed for teaching bioinformatics at the high school level. Building from a robust literature in professional development design research, project team will work with biology and mathematics teachers to co-design instructional modules to engage students with core bioinformatics concepts and computational literacies, by focusing on local community health issues supported through mobile learning activities. The overarching goal of the project is to help create an engage population of informatics-informed students who are capable of critically analyzing information and able to solve local problems related to their health and well-being.

The project team will use a design-based implementation research approach to identify the curricular and instructional supports needed to achieve the teaching and learning goals through iterative project revisions, employing mixed methods to evaluate teacher and student learning processes and outcomes. Teachers from local high needs schools will participate in a three-week summer workshop, where they will learn about state-of-the-art bioinformatics content, project-based pedagogies that promote computational literacy, and strategies integrate mobile technologies into instruction.  They will implement the instructional units during the year, and the summer workshop will be revised and delivered to an expanded cohort of teachers the following summer. The data collection and analysis conducted on teachers' enactment of these modules will reveal the professional development and implementation areas needed to support particular populations, specifically underrepresented groups in STEM, to engage with bioinformatics learning and take authentic action on local community issues.

Understanding the Role of Simulations in K-12 Science and Mathematics Teacher Education

This project will develop and implement a working conference for scholars and practitioners to articulate current use cases and theories of action regarding the use of simulations in PreK-12 science and mathematics teacher education. The conference will be structured to provide opportunities for attendees to share their current research, theoretical models, conceptual views, and use cases focused on the design and use of digital and non-digital simulations for building and assessing K-12 science and mathematics teacher competencies.

Lead Organization(s): 
Award Number: 
1813476
Funding Period: 
Sat, 09/01/2018 to Sat, 08/31/2019
Full Description: 

The recent emergence of updated learning standards in science and mathematics, coupled with increasingly diverse school students across the nation, has highlighted the importance of updating professional learning opportunities for science and mathematics teachers. One promising approach that has emerged is the use of simulations to engage teachers in approximations of practice where the focus is on helping them learn how to engage in ambitious content teaching. In particular, recent technological advances have supported the emergence of new kinds of digital simulations and have brought increased attention to simulations as a tool to enhance teacher learning. This project will develop and implement a working conference for scholars and practitioners to articulate current use cases and theories of action regarding the use of simulations in PreK-12 science and mathematics teacher education. The conference will be structured to provide opportunities for attendees to share their current research, theoretical models, conceptual views, and use cases focused on the design and use of digital and non-digital simulations for building and assessing K-12 science and mathematics teacher competencies.

While the use of simulations in teacher education is neither new nor limited to digital simulation, emerging technological capabilities have enabled digital simulations to become practical in ways not formerly available. The current literature base, however, is dated and the field lacks clear theoretic models or articulated theories of action regarding what teachers could or should learn via simulations, and the essential components of effective learning trajectories. This working conference will be structured to provide opportunities for attending, teacher educators, researchers, professional development facilitators, policy makers, preservice and inservice teachers, and school district leaders to share their current research, theoretical models, conceptual views, and use cases regarding the role of simulations in K-12 science and mathematics teacher education. The conference will be organized around four major goals, including: (1) Define how simulations (digital and non-digital) are conceptualized, operationalized, and utilized in K-12 science and mathematics teacher education; (2) Document and determine the challenges and affordances of the varied contexts, audiences, and purposes for which simulations are used in K-12 science and mathematics teacher education and the variety of investigation methods and research questions employed to investigate the use of simulations in these settings; (3) Make explicit the theories of action and conceptual views undergirding the various simulation models being used in K-12 science and mathematics teacher education; and (4) Determine implications of the current research and development work in this space and establish an agenda for studying the use of simulations in K-12 science and mathematics teacher education. The project will produce a white paper that presents the research and development agenda developed by the working conference, describes a series of use cases describing current and emergent practice, and identifies promising directions for future research and development in this area. Conference outcomes are expected to advance understanding of the varied ways in which digital and non-digital simulations can be used to foster and assess K-12 science and mathematics teacher competencies and initiate a research and development agenda for examining the role of simulations in K-12 science and mathematics teacher education.


Project Videos

2019 STEM for All Video Showcase

Title: Understanding the Role of Simulations in Teacher Preparation

Presenter(s): Lisa Dieker, Angelica Fulchini Scruggs, Heather Howell, Michael Hynes, & Jamie Mikeska


Prospective Elementary Teachers Making for Mathematical Learning

This study takes an innovative approach to documenting how teacher knowledge can be enhanced by incorporating a design experience into pre-service mathematics education. Teachers will use digital and fabrication technologies (e.g., 3D printers and laser cutters) to design and use manipulatives for K-6 mathematics learning. The goals of the project include describing how this experience influences the prospective teachers' knowledge and identities while creating curriculum for teacher education.

Lead Organization(s): 
Award Number: 
1812887
Funding Period: 
Sat, 09/01/2018 to Mon, 08/31/2020
Full Description: 

What teachers know and believe is central to what they can do in classrooms. This study takes an innovative approach to documenting how teacher knowledge can be enhanced by incorporating a design experience into pre-service mathematics education. The study's participating prospective teachers will use digital and fabrication technologies (e.g., 3D printers and laser cutters) to design and use manipulatives for K-6 mathematics learning. The goals of the project include describing how this experience influences the prospective teachers' knowledge and identities while creating curriculum for teacher education. Also, because more schools and students have access to 3D fabrication capabilities, teacher education can utilize these capabilities to prepare teachers to take advantage of these resources. Prior research by the team demonstrated how the process of making a manipulative can support prospective teachers in learning about mathematics and how to teach elementary mathematics concepts. The project will generate resources for other elementary teacher education programs and research about how prospective elementary teachers learn mathematics for teaching.

The project includes three research questions. First, what forms of knowledge are brought to bear as prospective elementary teachers make new manipulatives and write corresponding tasks to support the teaching and learning of mathematics? Second, how does prospective elementary teachers' knowledge for teaching mathematics develop as they make new manipulatives and write tasks to support the teaching and learning of mathematics? Third, as prospective elementary teachers make new manipulatives and write tasks to support the teaching and learning of mathematics, how do they see themselves in relation to the making, the mathematics, and the mathematics teaching? The project will employ a design-based research methodology with cycles of design, enactment, analysis and redesign to create curriculum modules for teacher education focused on making mathematics manipulatives. Data collection will include video recording of class sessions, participant observation, field notes, artifacts from the participants' design of manipulatives, and assessments of mathematical knowledge for teaching. A qualitative analysis will use multiple frameworks from prior research on mathematics teacher knowledge and identity development.

Design and Development of a K-12 STEM Observation Protocol (Collaborative Research: Roehrig)

This project will design and develop a new K-12 classroom observation protocol for integrated STEM instruction (STEM-OP). The STEM-OP will inform the instruction of integrated STEM in many contexts with the goal of improving integrated STEM education.

Award Number: 
1813342
Funding Period: 
Sat, 09/01/2018 to Wed, 08/31/2022
Full Description: 

This project will design and develop a new K-12 classroom observation protocol for integrated STEM instruction (STEM-OP). The STEM-OP will be developed for use in K-12 STEM settings. While the importance of integrated STEM education is established, there remains disagreement on models and effective approaches for integrated STEM instruction. This issue is confounded by the lack of observation protocols sensitive to integrated STEM teaching and learning to inform research to the effectiveness of new models and strategies. Existing instruments were not developed for use in integrated STEM learning environments. The STEM-OP will be designed to be used effectively by multiple stakeholders in a variety of contexts. Researchers will benefit from having the STEM-OP available for them to carry out research and continue to improve STEM education in a variety of ways. Existing instruments were not developed for use in integrated STEM learning environments.  The STEM-OP and associated training materials will be available for use by other education stakeholders, such as K-12 teachers and district administrators, through a publicly available online platform. In brief, the STEM-OP will inform the instruction of integrated STEM in many contexts with the goal of improving integrated STEM education.

The primary product of this project is the new observation protocol called STEM-OP for K-12 classrooms implementing integrated STEM lessons. The project will use over 500 integrated STEM classroom videos to design the STEM-OP. Using exploratory and confirmatory factor analysis, the STEM-OP will be a valid and reliable instrument for use in a variety of educational contexts. The research will explore the different ways that elementary, middle, and high school science teachers enact integrated STEM instruction. This study will shed light on the nature of STEM instruction in each of these grade bands and provide information building towards an understanding of learning progressions for engineering practices across grade bands. Research exploring how the nature of STEM integration changes from day to day over the course of a unit will provide critical information about the different sequencing and trajectories of STEM units. Examining how integrated STEM instruction unfolds over a full unit of instruction will inform the understanding of integrated STEM practices at both micro- and macro- levels of analysis. The STEM-OP and associated training materials will be available for use by other education stakeholders, such as K-12 teachers and district administrators, through a publicly available, which will be distributed via a publicly available, online platform that includes a training manual and classroom video for practice scoring.

Design and Development of a K-12 STEM Observation Protocol (Collaborative Research: Dare)

This project will design and develop a new K-12 classroom observation protocol for integrated STEM instruction (STEM-OP). The STEM-OP will inform the instruction of integrated STEM in many contexts with the goal of improving integrated STEM education.

Lead Organization(s): 
Award Number: 
1854801
Funding Period: 
Sat, 09/01/2018 to Wed, 08/31/2022
Full Description: 

This project will design and develop a new K-12 classroom observation protocol for integrated STEM instruction (STEM-OP). The STEM-OP will be developed for use in K-12 STEM settings. While the importance of integrated STEM education is established, there remains disagreement on models and effective approaches for integrated STEM instruction. This issue is confounded by the lack of observation protocols sensitive to integrated STEM teaching and learning to inform research to the effectiveness of new models and strategies. Existing instruments were not developed for use in integrated STEM learning environments. The STEM-OP will be designed to be used effectively by multiple stakeholders in a variety of contexts. Researchers will benefit from having the STEM-OP available for them to carry out research and continue to improve STEM education in a variety of ways. Existing instruments were not developed for use in integrated STEM learning environments.  The STEM-OP and associated training materials will be available for use by other education stakeholders, such as K-12 teachers and district administrators, through a publicly available online platform. In brief, the STEM-OP will inform the instruction of integrated STEM in many contexts with the goal of improving integrated STEM education.

The primary product of this project is the new observation protocol called STEM-OP for K-12 classrooms implementing integrated STEM lessons. The project will use over 500 integrated STEM classroom videos to design the STEM-OP. Using exploratory and confirmatory factor analysis, the STEM-OP will be a valid and reliable instrument for use in a variety of educational contexts. The research will explore the different ways that elementary, middle, and high school science teachers enact integrated STEM instruction. This study will shed light on the nature of STEM instruction in each of these grade bands and provide information building towards an understanding of learning progressions for engineering practices across grade bands. Research exploring how the nature of STEM integration changes from day to day over the course of a unit will provide critical information about the different sequencing and trajectories of STEM units. Examining how integrated STEM instruction unfolds over a full unit of instruction will inform the understanding of integrated STEM practices at both micro- and macro- levels of analysis. The STEM-OP and associated training materials will be available for use by other education stakeholders, such as K-12 teachers and district administrators, through a publicly available, which will be distributed via a publicly available, online platform that includes a training manual and classroom video for practice scoring.

Design and Development of a K-12 STEM Observation Protocol (Collaborative Research: Ring-Whalen)

This project will design and develop a new K-12 classroom observation protocol for integrated STEM instruction (STEM-OP). The STEM-OP will inform the instruction of integrated STEM in many contexts with the goal of improving integrated STEM education.

Lead Organization(s): 
Award Number: 
1812794
Funding Period: 
Sat, 09/01/2018 to Wed, 08/31/2022
Full Description: 

This project will design and develop a new K-12 classroom observation protocol for integrated STEM instruction (STEM-OP). The STEM-OP will be developed for use in K-12 STEM settings. While the importance of integrated STEM education is established, there remains disagreement on models and effective approaches for integrated STEM instruction. This issue is confounded by the lack of observation protocols sensitive to integrated STEM teaching and learning to inform research to the effectiveness of new models and strategies. Existing instruments were not developed for use in integrated STEM learning environments. The STEM-OP will be designed to be used effectively by multiple stakeholders in a variety of contexts. Researchers will benefit from having the STEM-OP available for them to carry out research and continue to improve STEM education in a variety of ways. Existing instruments were not developed for use in integrated STEM learning environments.  The STEM-OP and associated training materials will be available for use by other education stakeholders, such as K-12 teachers and district administrators, through a publicly available online platform. In brief, the STEM-OP will inform the instruction of integrated STEM in many contexts with the goal of improving integrated STEM education.

The primary product of this project is the new observation protocol called STEM-OP for K-12 classrooms implementing integrated STEM lessons. The project will use over 500 integrated STEM classroom videos to design the STEM-OP. Using exploratory and confirmatory factor analysis, the STEM-OP will be a valid and reliable instrument for use in a variety of educational contexts. The research will explore the different ways that elementary, middle, and high school science teachers enact integrated STEM instruction. This study will shed light on the nature of STEM instruction in each of these grade bands and provide information building towards an understanding of learning progressions for engineering practices across grade bands. Research exploring how the nature of STEM integration changes from day to day over the course of a unit will provide critical information about the different sequencing and trajectories of STEM units. Examining how integrated STEM instruction unfolds over a full unit of instruction will inform the understanding of integrated STEM practices at both micro- and macro- levels of analysis. The STEM-OP and associated training materials will be available for use by other education stakeholders, such as K-12 teachers and district administrators, through a publicly available, which will be distributed via a publicly available, online platform that includes a training manual and classroom video for practice scoring.

Testing the Efficacy of the Strategic Observation and Reflection (SOAR) for Math Professional Learning Program

The purpose of this project is to develop, implement and test a professional development program, SOAR for Math, to build capacity for mentors and teachers to improve English learner's academic language development and mathematical content understanding.

Award Number: 
1814356
Funding Period: 
Sat, 09/01/2018 to Wed, 08/31/2022
Full Description: 
Professional development is an important way for teachers who are currently in classrooms to learn about new best practices in mathematics teaching and learning and improve their practice. Little is known about what types of professional development (PD) and teacher mentoring programs support teachers' improved practices and ultimately lead to gains in student learning. The purpose of this project is to develop, implement and test a professional development program, SOAR for Math, to build capacity for mentors and teachers to improve English learner's academic language development and mathematical content understanding.
 
This study will test the efficacy of the Strategic Observation and Reflection (SOAR) for Math professional development program. The mixed methods study is designed to answer several research questions: (1) What is the impact of teachers' participation in SOAR for Math on student achievement outcomes for current and recent grade 3-6 English learner students in treatment schools? (2) What is the impact of SOAR for Math on treatment school teachers' knowledge and practices related to their academic language and literacy development instruction for current and recent English learner students, specifically scores on the Knowledge/Use Scale? (3) What is the impact of SOAR for Math on treatment mentors' knowledge and practices related to their academic language and math instruction? A randomized controlled trial will be conducted in 80 elementary schools in one California school district. Schools serving third- through sixth-grade general education students will be eligible to participate. The research team will randomly assign 40 schools to provide SOAR for Math training to mentor teachers and 40 schools to comprise a control group receiving business-as-usual professional development. Two mentors per school will participate in the study. Measures will include state math scores and a variety of observations and questionnaires to assess fidelity of implementation. Data will be analyzed using hierarchical linear modeling to account for the nested data structure.

Development and Validation of a Mobile, Web-based Coaching Tool to Improve PreK Classroom Practices to Enhance Learning

This project will promote pre-K teachers' use of specific teaching strategies that have been shown to enhance young children's learning and social skills. To enhance teachers' use of these practices, the project will develop a new practitioner-friendly version of the Classroom Quality Real-time Empirically-based Feedback (CQ-REF) tool for instructional coaches who work with pre-K teachers.

Lead Organization(s): 
Award Number: 
1813008
Funding Period: 
Wed, 08/01/2018 to Sun, 07/31/2022
Full Description: 

Children from low-income families often enter kindergarten academically behind their more economically affluent peers. Advancing pre-kindergarten (pre-K) teachers' ability to provide all students with high-quality early math learning experiences has potential to minimize this gap in school readiness. This project will promote pre-K teachers' use of specific teaching strategies, such as spending more time on math content and listening to children during instructional activities, that have been shown to enhance young children's learning and social skills. To enhance teachers' use of these practices, the project takes a novel approach--a mobile website that helps instructional coaches who work with pre-K teachers. The Classroom Quality Real-time Empirically-based Feedback tool (CQ-REF) will guide coaches' ability to observe specific teacher practices in their classrooms and then provide feedback to help teachers evaluate their practices and set goals for improvement.  Practically, the CQ-REF addresses the need for accessible, real-time feedback on high quality pre-K classroom teaching.

This project focuses on developing a new practitioner-friendly version of the CQ-REF, originally designed as a research tool for evaluating the quality of classroom teaching, for use by coaches and teachers. At the beginning of the four-year project, the team will collect examples of high-quality classroom teaching and coaching strategies. These will be used to create a library of video and other materials that teachers and coaches can use to establish a shared definition of what effective pre-K teaching looks like. In year three of the project, the team will pilot the CQ-REF with a diverse range of pre-K teachers and their coaches to determine the tool's usability and relevance. In this validation study coaches will be randomly assigned to either use the CQ-REF tool or coach in their usual manner. After one year, the CQ-REF's impact on teacher practices and student outcomes will be assessed. Outcomes of interest include teacher and student classroom behavior and children's executive function and ability in mathematics, literacy and science. Concurrently, an external evaluation team will examine how the coaching is being conducted and used, and participants' impressions of the coaching process. In the fourth and final year, the team will focus on refining the tool based on results from prior work and on disseminating the findings to research and practitioner audiences.

Design and Development of Transmedia Narrative-based Curricula to Engage Children in Scientific Thinking and Engineering Design (Collaborative Research: Ellis)

This project will address the need for engineering resources by applying an innovative pedagogy called Imaginative Education (IE) to create middle school engineering curricula. In IE, developmentally appropriate narratives are used to design learning environments that help learners engage with content and organize their knowledge productively. This project will combine IE with transmedia storytelling.

Lead Organization(s): 
Award Number: 
1814033
Funding Period: 
Sun, 07/15/2018 to Thu, 06/30/2022
Full Description: 

Engineering is an important component of the Next Generation Science Standards (NGSS). However, resources for supporting teachers in implementing these standards are scarce. This project will address the need for resources by applying an innovative pedagogy called Imaginative Education (IE) to create middle school engineering curricula. In IE, developmentally appropriate narratives are used to design learning environments that help learners engage with content and organize their knowledge productively. To fully exploit the potential of this pedagogy, this project will combine IE with transmedia storytelling. In transmedia storytelling, different elements of a narrative are spread across a variety of formats (such as books, websites, new articles, videos and other media) in a way that creates a coordinated experience for the user. Once created, the curricula will be implemented in classrooms to research its impact on (1) increasing learners' capacities to engage in both innovative and direct application of engineering concepts, and (2) improving learners' science, technology, engineering, and mathematics (STEM) identity. 

This research will be led by Smith College and Springfield Technical Community College in collaboration with Springfield (MA) Public Schools (SPS). Additional expertise in evaluating the findings will be provided by the Collaborative for Educational Services and an external advisory board of leaders in STEM education and transmedia storytelling. The project will result in the development of a transmedia learning environment that includes two NGSS-aligned, interdisciplinary engineering units and seven lessons that integrate science and engineering. The research study will be implemented in four phases in eight SPS middle schools. Approximately 900 students will participate each year. In Phase 1, the project team will collaborate with SPS teachers to create engineering units, lessons, and standards-based achievement measures. In Phase 2, teachers in the treatment group will participate in professional development (PD) workshops covering IE, transmedia learning environments, structure of the curriculum, and connections to NGSS. In Phase 3 the curricula will be implemented in treatment classrooms and both treatment and control group students will be assessed. In Phase 4, testing and assessment will continue in SPS schools and will be expanded to rural and suburban classrooms. Teachers in these classrooms will use online multimedia PD that will ensure scalability and mirrors the structure and content of in-person PD. Data analysis will provide evidence of whether this imaginative and transmedia educational approach improves students' capacities for using engineering concepts and enhances their STEM identity.


Project Videos

2019 STEM for All Video Showcase

Title: Transforming Engineering Education for Middle School (TEEMS)

Presenter(s): Beth McGinnis-Cavanaugh, Sonia Ellis, & Crystal Ford


Pages

Subscribe to Mathematics