Professional Development

CAREER: Designing and Enacting Mathematically Captivating Learning Experiences for High School Mathematics

This project explores how secondary mathematics teachers can plan and enact learning experiences that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere (referred to as "mathematically captivating learning experiences" or "MCLEs"). The study will examine how high school teachers can design lessons so that mathematical content itself is the source of student intrigue, pursuit, and passion.

Lead Organization(s): 
Award Number: 
1652513
Funding Period: 
Wed, 02/15/2017 to Mon, 01/31/2022
Full Description: 

This design and development project explores how secondary mathematics teachers can plan and enact learning experiences that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere (referred to as "mathematically captivating learning experiences" or "MCLEs"). This study is important because of persistent disinterest by secondary students in mathematics in the United States. This study will examine how high school teachers can design lessons so that mathematical content itself is the source of student intrigue, pursuit, and passion. To do this, the content within mathematical lessons (both planned and enacted) is framed as mathematical stories and the felt tension between how information is revealed and withheld from students as the mathematical story unfolds is framed as its mathematical plot. The Mathematical Story Framework (Dietiker, 2013, 2015) foregrounds both the coherence (does the story make sense?) and aesthetic (does it stimulate anticipation for what is to come, and if so, how?) dimensions of mathematics lessons. The project will generate principles for lesson design usable by teachers in other settings and exemplar lessons that can be shared.

Specifically, this project draws from prior curriculum research and design to (a) develop a theory of teacher MCLE design and enactment with the Mathematical Story Framework, (b) increase the understanding(s) of the aesthetic nature of mathematics curriculum by both researchers and teachers, and (c) generate detailed MCLE exemplars that demonstrate curricular coherence, cognitive demand, and aesthetic dimensions of mathematical lessons. The project is grounded in a design-based research framework for education research. A team of experienced high school teachers will design and test MCLEs (four per teacher) with researchers through three year-long cycles. Prior to the first cycle, data will be collected (interview, observations) to record initial teacher curricular strategies regarding student dispositions toward mathematics. Then, a professional development experience will introduce the Mathematical Story Framework, along with other curricular frameworks to support the planning and enacting of lessons (i.e., cognitive demand and coherence). During the design cycles, videotaped observations and student aesthetic measures (surveys and interviews) for both MCLEs and a non-MCLEs (randomly selected to be the lesson before or after the MCLE) will be collected to enable comparison. Also, student dispositional measures, collected at the beginning and end of each cycle, will be used to learn whether and how student attitudes in mathematics change over time. Of the MCLEs designed and tested, a sample will be selected (based on aesthetic and mathematical differences) and developed into models, complete with the rationale for and description of aesthetic dimensions.

Readiness through Integrative Science and Engineering: Refining and Testing a Co-constructed Curriculum Approach with Head Start Partners

Building upon prior research on Head Start curriculum, this phase of Readiness through Integrative Science and Engineering (RISE) will be expanded to include classroom coaches and community experts to enable implementation and assessment of RISE in a larger sample of classrooms. The goal is to improve school readiness for culturally and linguistically diverse, urban-residing children from low-income families, and the focus on science, technology, and engineering will address a gap in early STEM education.

Lead Organization(s): 
Award Number: 
1621161
Funding Period: 
Sat, 10/01/2016 to Wed, 09/30/2020
Full Description: 

Readiness through Integrative Science and Engineering (RISE) is a late stage design and development project that will build upon the results of an earlier NSF-funded design and development study in which a co-construction process for curriculum development was designed by a team of education researchers with a small group of Head Start educators and parent leaders. In this phase, the design team will be expanded to include Classroom Coaches and Community Experts to enable implementation and assessment of the RISE model in a larger sample of Head Start classrooms. In this current phase, an iterative design process will further develop the science, technology, and engineering curricular materials as well continue to refine supports for teachers to access families' funds of knowledge related to science, technology, and engineering in order to build on children's prior knowledge as home-school connections. The ultimate goal of the project is to improve school readiness for culturally and linguistically diverse, urban-residing children from low-income families who tend to be underrepresented in curriculum development studies even though they are most at-risk for later school adjustment difficulties. The focus on science, technology, and engineering will address a gap in early STEM education.

The proposed group-randomized design, consisting of 90 teachers/classrooms (45 RISE/45 Control), will allow for assessment of the impact of a 2-year RISE intervention compared with a no-intervention control group. Year 1 will consist of recruitment, induction, and training of Classroom Coaches and Community Experts in the full RISE model, as well as preparation of integrative curricular materials and resources. In Year 2, participating teachers will implement the RISE curriculum approach supported by Classroom Coaches and Community Experts; data on teacher practice, classroom quality, and implementation fidelity will be collected, and these formative assessments will inform redesign and any refinements for Year 3. During Year 2, project-specific measures of learning for science, technology, and engineering concepts and skills will also be tested and refined. In Year 3, pre-post data on teachers (as in Year 2) as well as on 10 randomly selected children in each classroom (N = 900) will be collected. When child outcomes are assessed, multilevel modeling will be used to account for nesting of children in classrooms. In addition, several moderators will be examined in final summative analyses (e.g., teacher education, part or full-day classroom, parent demographics, implementation fidelity). At the end of this project, all materials will be finalized and the RISE co-construction approach will be ready for scale-up and replication studies in other communities.

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 Classes: Identifying and Addressing Challenges to Improve Instruction for Struggling Learners

The purpose of this project is to improve mathematics instruction for struggling learners by focusing on the quality of instruction occurring in mathematics intervention classrooms. The study will focus on how intervention class time is spent, what mathematics content is emphasized, which evidence-based instructional practices are used, and what challenges are faced by teachers.

Partner Organization(s): 
Award Number: 
1621294
Funding Period: 
Thu, 09/15/2016 to Mon, 08/31/2020
Full Description: 

Given the adoption of more rigorous mathematics standards, U.S. school districts face a pressing need to improve instruction for struggling learners who are not reaching proficiency on standardized assessments. In response to low performance, a common district solution is to add mathematics intervention classes which aim to provide struggling students with time for more intensive and targeted instruction. Researchers have begun to identify effective mathematics intervention practices, but few studies have examined if intervention teachers are actually implementing these approaches with students. Very little is known about how intervention class time is spent, what mathematics content is emphasized, which evidence-based instructional practices are used, and what challenges are faced by teachers.

The purpose of this project is to improve mathematics instruction for struggling learners by focusing on the quality of instruction occurring in mathematics intervention classrooms. The investigators will conduct observations and interviews with teachers and district leaders to understand current practices and challenges. This will be followed by a national survey of 300 teachers to document challenges across the country in terms of providing mathematics intervention. 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.

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.

Understanding and Improving Learning from Online Mathematics Classroom Videos

The purpose of this project is to investigate issues in the design and implementation of effective virtual learning communities (VLCs) for teachers and to examine the relation between teachers' reflective engagement with VLCs and their students' mathematics learning outcomes. Findings from this project will be used to build and share effective ways to support teacher learning online.

 

Award Number: 
1621253
Funding Period: 
Mon, 08/15/2016 to Fri, 07/31/2020
Full Description: 

U.S. elementary teachers face many challenges. They are asked to teach all subjects to students with different needs and abilities. To do this well, they need good professional learning opportunities. Many teachers look online for such opportunities, but little is known about the quality of those opportunities and how they can be improved to help teachers meet their challenges. The goals of this project are to learn more about how teachers use one popular website for elementary mathematics teachers and how this website and similar ones can be adapted to better support teacher learning. Specifically, the project will (1) interview teachers about their use of the website, (2) investigate how to improve the ways teachers interact with video resources on the site by testing different ways of guiding their attention, and (3) examine how teachers' interactions with these video resources are related to their students' learning of mathematics. Findings from this project will be used to build and share effective ways to support teacher learning online. The project will thus benefit teachers who use the popular website, teachers who use similar websites, researchers who study how teachers learn from such websites, and the students of teachers who learn from such websites.

Video-based learning has been the focus of much professional development research over the past decade. As video-based learning has been found to be effective, many professional developers have taken this learning to scale through the online space. A number of high profile and popular virtual learning communities (VLCs) have emerged to allow teachers to interact with video, but the scant number of studies on the effectiveness of such VLCs show some difficulties in engaging teachers in sustained, reflective professional learning. The purpose of this project is to investigate several major issues in the design and implementation of effective VLCs for teachers and to examine the relation between teachers' reflective engagement with VLCs and their students' mathematics learning outcomes. The investigators propose 3 studies, which build on each other, to address these issues. This project will (1) interview teachers who are members of a popular VLC, to investigate what they learn and how they contribute to community; (2) investigate conditions that impact the posting of reflective commentary about video cases through iterative experiments, as reflective commentary has the potential to build community and to support teacher learning; and (3) investigate the relation between reflective reactions to video cases and student mathematics outcomes. Through these investigations, this project will explore issues that impact the scalability of teachers learning asynchronously from online video. Results will be used to develop guided pathways - a prototype of an innovation that will be based on the results from the research - on one widely used VLC. Thus, this project will provide both a contribution to the field of STEM teacher education research and an immediate, research-based product that can be disseminated to thousands of teachers through an existing VLC.

Improving the Implementation of Rigorous Instructional Materials in Middle-Grades Mathematics: Developing a System of Practical Measures and Routines (Collaborative Research: Smith)

The goal of this project is to improve the implementation of rigorous instructional materials in middle-grades mathematics at scale through a system of practical measures and routines for collecting and using data that both assesses and supports implementation.

Award Number: 
1621238
Funding Period: 
Sat, 10/01/2016 to Thu, 09/30/2021
Full Description: 

The goal of this 5-year research project is to improve the implementation of rigorous instructional materials in middle-grades mathematics at scale. Many projects seek to improve mathematics instruction, but are not able to easily track their efforts at improvement. The primary product of this project will be a system of practical measures and routines for collecting and using data that both assesses and supports the implementation of rigorous instructional materials in middle-grades mathematics. In contrast to research and accountability measures, practical measures are assessments that require little time to administer and can thus be used frequently. The data can be analyzed rapidly so that teachers can receive prompt feedback on their progress, and instructional leaders can use the data to decide where to target resources to support improvement in the quality of instruction and student learning. The system of practical measures and routines will include 1) measures of high-leverage aspects of teachers' instructional practices that have been linked to student learning (e.g., rigor of tasks, quality of students' discourse) and attend to equitable student participation; and 2) measures of high-leverage aspects of key supports for improving the quality of teachers' practice (e.g., quality of professional development; coaching); and 3) a set of routines regarding how to use the resulting data to engage in rapid, improvement efforts. A key principle of the proposed project is that the system of measures and routines can be adapted to a wide range of school and district contexts. This project is supported by the Discovery Research preK-12 (DRK-12) program. The DRK-12 program supports research and development of STEM education innovations and approaches in assessment, learning, and teaching.

The project will establish three research-practice partnerships with five districts, in three different states, that are currently implementing rigorous instructional materials in middle-grades mathematics. Year 1 will focus on the development of a set of practical measures of classroom instruction. Year 2 will focus on testing the use of the classroom measures in the context of supports for teachers' learning, and the development of practical measures of key supports for teachers' learning. Years 3-4 will focus on how the project can "learn our way to scale" (Bryk et al., 2015), which requires strategically implementing measures and routines in increasingly diverse conditions. The project will engage in rapid improvement cycles in which researchers will work alongside district leaders and professional development (PD) facilitators to analyze the data from the measures of both classroom instruction and the quality of support for teacher learning to test the effectiveness of improvements in intended supports for teacher learning and to adjust the design of the support based on data. Across Years 1-4, the project will use recent developments in technology and information visualization to test and improve 1) the collection of practical measures in situ and 2) the design of data representations (or visualizations) that support teachers and leaders to make instructional improvement decisions. In Year 5, the project will conduct formal analyses of the relations between supports for teachers' learning; teachers' knowledge and classroom practices; and student learning.

Doing the Math with Paraeducators: A Research and Development Project

This project will design and pilot professional development that focuses on developing the confidence, mathematical knowledge, and teaching strategies of paraeducators using classroom activities that they are expected to implement. The planned professional development will enable them to make a greater difference in the classroom, but it will also increase their access to continuing education and workplace opportunities.

Lead Organization(s): 
Award Number: 
1621151
Funding Period: 
Thu, 09/15/2016 to Sat, 08/31/2019
Full Description: 

Over one million paraeducators (teaching assistants and volunteers) currently assist in classrooms, and another 100,000 are likely to be added in the next ten years. Paraeducators (paras) are often required to teach content, such as mathematics, but there are few efforts to provide them with the knowledge or supervision they need to be effective when working with a range of students, including those with disabilities and for whom English is a second language. The project will focus on developing the confidence, mathematical knowledge, and teaching strategies of paras using classroom activities that they are expected to implement. The planned professional development will enable them to make a greater difference in the classroom, but it will also increase their access to continuing education and workplace opportunities. The work will be conducted in the Boston Public Schools (BPS) and will focus on grades K-3, where the largest numbers of paras are employed. Given the importance of early math learning in predicting mathematical achievement, supporting paras who work in the early grades is particularly important.

The project will design and pilot professional development that supports paraeducator knowledge development and addresses instructional challenges in teaching mathematics. The project will address the following goals: research the current roles of paras in mathematics instruction, the preparation of their collaborating teachers, and the opportunities for collaboration and planning between supervising teachers and paras in BPS; pilot, develop, implement, and research a model for professional development program for paras that targets specific activities they can implement that are key to student learning in number and operation in K-3; document how paras assume new roles that increase student engagement and empower them as mathematical learners; pilot, develop, implement, and research a supervisory component to help teachers set expectations, and structures for debriefing and reflecting along with their paras; and identify next steps for an early stage development study based on our findings. A needs assessment survey will investigate the context in which paras work. The iterative process of design-based research will develop, test, and implement the targeted professional development with paras, measuring how prepared they feel to implement new ideas and how they translate their learning into new pedagogical practices. Crosscase analyses, descriptive statistics, tallies and coded behaviors from observations, and themes from paras, and teacher and administrator interviews will be collected, coded, and analyzed. Furthermore, an efficacy survey will be administered periodically to document longitudinal changes in paras, which will be integrated in the crosscase analyses.

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