Instructional Practice

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

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

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

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

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

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.

Longitudinal Learning of Viable Argument in Mathematics for Adolescents

This project builds on a prior study that demonstrated increases in students' knowledge of argumentation and their performance on mathematics assessments. The project will extend the use of the argumentation intervention into all eighth grade content areas, with a specific focus on students' learning of reasoning and proof, and contribute to understanding how students' learning about mathematical practices that can help them learn mathematics better.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1621438
Funding Period: 
Thu, 09/01/2016 to Mon, 08/31/2020
Full Description: 

The project will examine learning in eighth grade mathematics with a specific focus on students' learning of reasoning and proof. The intervention builds on a prior study in algebra that demonstrated increases in students' knowledge of argumentation and their performance on mathematics assessments. This project will extend the use of the argumentation intervention into all eighth grade content areas. The investigators will also address support for teachers in the form of teacher materials that link the argumentation content with mathematics standards and state-wide assessments, and a learning progression to engage students in proving tasks. The project will use assessments of mathematics learning and additional data from teachers and students to understand the impact of the argumentation intervention on teachers and students. The project contributes to understanding how students can learn about mathematical practices, such as proving, that can help them learn mathematics better. A significant contribution will be the definition of aspects of proving and descriptions of student outcomes that can be used to measure how well students have achieved these components of proving. The Discovery Research PreK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. This project is also supported by NSF's EHR Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.

The project suggests twelve conceptual pillars that are combined with classroom processes and assessable outcomes to examine the use of argumentation practices in the teaching of eighth grade mathematics content. The investigation of classroom support for argumentation includes research questions that focus on improvement on state-level assessments, students' ability to construct mathematical arguments, and the conceptual progression that supports students' understanding of argumentation and proof. In addition, the study will examine teachers' role in argumentation in the classroom and their perception of potential challenges for classroom implementation. The study will use an experimental design to examine an intervention for mathematical reasoning and proof in eighth grade. The project includes a treatment group of teachers that will participate in professional development including a summer institute followed by instructional coaching over a two year period.

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:

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.

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.

Organizing to Learn Practice: Teacher Learning in Classroom-Focused Professional Development

This project addresses the fundamental challenge of how to support teachers to improve their practice. The approach uses a "live mathematics classroom" as a common text for working on practice, where participants are not only watching and discussing but are engaged in developing and learning practice. The project will generate new knowledge regarding ways in which elementary teachers of mathematics can be supported to learn effective teaching practice.

Lead Organization(s): 
Award Number: 
1621104
Funding Period: 
Thu, 09/01/2016 to Mon, 08/31/2020
Full Description: 

Growing evidence about the powerful effects of skillful teaching on students' learning creates a need to for professional development that impacts teachers' actual practice. Just as other professions (e.g., nursing, social work, law) have centered practitioners' learning in "live" practice with structures that support learning in context, the project will investigate whether and how this can be accomplished in teaching. The approach uses a "live mathematics classroom" as a common text for working on practice, where participants are not only watching and discussing but are engaged in developing and learning practice. The project also explores the following variations in practice-based professional development: (1) on-site and remote participation of teachers; and (2) the addition of supplementary practice-focused professional development. The project will generate new knowledge regarding ways in which elementary teachers of mathematics can be supported to learn effective teaching practice.

This project addresses a fundamental challenge for professional development, that is, how to support teachers to improve their practice. Teachers profit from well-designed opportunities to develop new visions for practice, learn more about students' thinking, or work on specific mathematical topics or tasks. Still, such opportunities are often insufficient to support teachers with the complexity of classroom teaching. These kinds of professional opportunities focus on critical resources for instruction but not on the details of teaching practice itself. This practice-centered professional development is situated within a summer mathematics program for fifth graders. The proposed research will explore the impact on teachers' practice, as well as on their knowledge and dispositions, from participating in these structured ways. Three studies will resolve the following three sets of questions: (1) What do teachers learn from structured participation in the class? Does their participation impact their own teaching practice, and if so, in what ways? (2) Does the setting of the peripheral participation matter? Does this form of participation impact their own teaching practice, and if so, in what ways? (3) Does the addition of professional development focused on a particular teaching practice impact teachers' own practice, and if so, in what ways? How does the addition of professional development focused on a specific instructional practice compare across the in-person and online forms of participation in terms of impact on teachers' own practice? The project will collect and analyze several types of data pre- and post-intervention, including measures of mathematical knowledge for teaching, measures of language for talking about the work of teaching and students, and skill with leading a mathematics discussion, and the mathematical quality of instruction. The project will generate new knowledge related to to organizing professional learning around supports that teachers need to learn practice as well as ways to study their learning of teaching practice.

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