Teacher Content Knowledge

Student-Adaptive Pedagogy for Elementary Teachers: Promoting Multiplicative and Fractional Reasoning to Improve Students' Preparedness for Middle School Mathematics

The project develops a teacher professional development intervention to support student-adaptive pedagogy for multiplicative and fractional reasoning. The idea is that classroom instruction should build on students' current conceptions and experiences. It focuses on students from urban, underserved and low-socioeconomic status populations who often fall behind in the elementary grades and are left underprepared for middle grades mathematics.

Lead Organization(s): 
Award Number: 
1503206
Funding Period: 
Wed, 07/15/2015 to Sun, 06/30/2019
Full Description: 

The project develops a teacher professional development intervention to support student-adaptive pedagogy for multiplicative and fractional reasoning. The idea is that classroom instruction should build on students' current conceptions and experiences. The context for the study is grades 3-5 teachers in Aurora Public Schools. It focuses on students from urban, underserved and low-socioeconomic status populations who often fall behind in the elementary grades and are left underprepared for middle grades mathematics. It includes a summer workshop and academic year follow-up including teacher collaboration. The project provides tools for capitalizing on successful, school-based research for promoting teachers' buy-in, adoption, and sustaining of student-adaptive pedagogy. The project also includes measurement of student understanding of the concepts. An extensive plan to share tools and resources for teachers and instructional coaches (scalable to district/state levels) and of research instruments and findings, will promote sharing project outcomes with a wide community of stakeholders (teachers, administrators, researchers, parents, policy makers) responsible for students' growth. This is a Full Design & Development project within the DRK-12 Program's Learning Strand. The Discovery Research K-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.

The project aims to implement and study a professional development intervention designed to shift upper-elementary teachers' mathematics teaching toward a constructivist approach, called student-adaptive pedagogy (AdPed), which adapts teaching goals and activities based on students' conceptions and experiences. The project focuses on multiplicative and fractional reasoning--critical for students' success in key areas of middle school mathematics (e.g., ratio, proportion, and function). The project seeks to design an instrument for measuring teachers' implementation of AdPed, a clinical interview rubric for students' multiplicative reasoning and then an analysis of teachers' content knowledge and the implementation of AdPed following the professional development. The research design is rooted in an innovative, cohesive framework that integrates four research-based components: (i) a model of mathematics learning and knowing, (ii) models of progressions in students' multiplicative and fractional reasoning, (iii) a model of teaching (AdPed) to promote such learning, and (iv) a mathematics teacher development continuum. Capitalizing on successful preliminary efforts in the Denver Metro area to refine a PD intervention and student-adaptive tools that challenge and transform current practices, the project will first validate and test instruments to measure (a) teacher growth toward adaptive pedagogy and (b) students' growth in multiplicative reasoning. Using these new instruments, along with available measures, the project will then promote school-wide teacher professional development (grades 3-5) in multiple schools in an urban district with large underserved student populations and study the professional development benefits for teacher practices and student outcomes. The mixed methods study includes classroom-based data (e.g., video analysis, lesson observations, teacher interviews) and measures of students' multiplicative reasoning specifically and mathematical understanding generally.

Visual Access to Mathematics: Professional Development for Teachers of English Learners

This project addresses a critical need, developing professional development materials to address the teachers of ELLs. The project will create resources to help teachers build ELLs' mathematical proficiency through the design and development of professional development materials building on visual representations (VRs) for mathematical reasoning across a range of mathematical topics.

Award Number: 
1503057
Funding Period: 
Sat, 08/01/2015 to Wed, 07/31/2019
Full Description: 

The demands placed on mathematics teachers of all students have increased with the introduction of college and career readiness standards. At the same time, the mathematics achievement of English Language Learners (ELLs) lags behind that of their peers. This project addresses a critical need, developing professional development materials to address the teachers of ELLs. The project will create resources to help teachers build ELLs' mathematical proficiency through the design and development of professional development materials building on visual representations (VRs) for mathematical reasoning across a range of mathematical topics. The project will study how to enhance teachers' pedagogical content knowledge that is critical to fostering ELLs' mathematical problem solving and communication to help support fluency in using VRs among teachers and students. To broaden the participation of students who have traditionally not demonstrated high levels of achievement in mathematics, a critical underpinning to further success in the sciences and engineering, there will need to be greater support for teachers of these students using techniques that have been demonstrated to improve student learning. 

The project will use an iterative design and development process to develop a blended learning model of professional development on using VRs with a 30-hour face-to-face summer institute and sixteen 2-hour online learning sessions. Teachers and teacher-leaders will help support the development of the professional development materials. A cluster randomized control trial will study the piloting of the materials and their impact on teacher outcomes. Thirty middle schools from Massachusetts and Maine serving high numbers of ELLs, with approximately 120 teachers, will be randomly assigned to receive the treatment or control conditions. Using a two-level random intercepts hierarchical linear model, the study will explore the impact of participation in the professional development on teachers' mathematical knowledge for teaching and instructional practice. The pilot study will also explore the feasibility of delivering the professional development model more broadly. It builds on prior work that has shown efficacy in geometry, but expands the work beyond a single area in mathematics. At the same time, they will test the model for feasibility of broad implementation.

The Discovery Research K-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.

Learning Labs: Using Videos, Exemplary STEM Instruction and Online Teacher Collaboration to Enhance K-2 Mathematics and Science Practice and Classroom Discourse

This project will develop and study two sets of instructional materials for K-2 teacher professional development in mathematics and science that are aligned with the CCSS and NGSS. Teachers will be able to review the materials online, watch video of exemplary teaching practice, and then upload their own examples and students' work to be critiqued by other teachers enrolled in professional learning communities as well as expert coaches.

Lead Organization(s): 
Award Number: 
1417757
Funding Period: 
Wed, 04/15/2015 to Sat, 03/31/2018
Full Description: 

The Discovery Research K-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. The investigators of this study propose to develop and study two sets of instructional materials for K-2 teacher professional development in mathematics and science that are aligned with the Common Core State Standards in Mathematics (CCSS) and the Next Generation Science Standards (NGSS). They will develop two modules in each subject area and an introductory module that prefaces and integrates the science and mathematics materials. Teachers will be able to review the materials online, watch video of exemplary teaching practice, and then upload their own examples and students' work to be critiqued by other teachers enrolled in professional learning communities as well as expert coaches. New instructional materials aligned with the standards are needed to assist teachers in meeting the challenging instructional practices recommended. To date, scant few resources of this type exist and, given many school districts have limited resources, more cost-effective forms of development such as this must be found. A particular strength of this project is that teachers will be able to engage in the courses online, on an ongoing basis and integrate what they have learned into their daily teaching practice.

The investigators propose a program of design research to develop and improve the modules. The central hypothesis is a test of the Teaching Channel model--that the modules and professional learning communities result in significant changes in the quality of instructional practice. Text analytics will be performed on the online discussion to detect changes in group discourse over time. Changes in instructional quality and vision will be measured by observing the videos posted by teachers. Pre-post tests of student work will be performed. The findings of the research will be disseminated through conference presentations, publications, and the Teaching Channel website.

An Efficacy Study of the Learning and Teaching Geometry PD Materials: Examining Impact and Context-Based Adaptations

This study will examine the impact of the Learning and Teaching Geometry (LTG) professional development for secondary mathematics teachers on the teachers' knowledge and classroom instruction, as well as on their students' learning. As the nation invests vast resources in the professional development of teachers to meet new curriculum and instruction challenges, exploring the efficacy of professional development is important to understand how best to direct those resources.

Lead Organization(s): 
Award Number: 
1503399
Funding Period: 
Wed, 07/01/2015 to Sun, 06/30/2019
Full Description: 

The Discovery Research K-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. There are few examples of research that demonstrates causal impacts of professional development on teachers' knowledge and practice and student learning. This study will examine the impact of the Learning and Teaching Geometry (LTG) professional development for secondary mathematics teachers on the teachers' knowledge and classroom instruction, as well as on their students' learning. As the nation invests vast resources in the professional development of teachers to meet new curriculum and instruction challenges, exploring the efficacy of professional development is important to understand how best to direct those resources.

Using a cluster randomized design, the project will sample from 132 teachers (66 per condition) from 28 middle and high schools to participate in a 2-year implementation of the LTG professional development, facilitated by highly trained facilitators to study the efficacy of the materials. The project will monitor the fiedity of implementation of the LTG using a professional development session logging tool and Facilitator Interview Protocol. Outcome measures include measures of teacher knowledge, teaching practice, and student learning of geometry. Analyses will include two- and three-level hierarchical linear models to estimate the effects of participation in the LTG professional development and growth over time.

STEM Practice-Rich Investigations for NGSS Teaching (SPRINT)

This is an exploratory project that will research and develop resources and a model for professional learning needed to meet the demand of implementing the Next Generation Science Standards (NGSS). The Exploratorium Teacher Institute will engage middle school science teachers in a one-year professional learning program to study how familiar routines and classroom tools, specifically hands-on science activities, can serve as starting points for teacher learning.

Lead Organization(s): 
Award Number: 
1503153
Funding Period: 
Mon, 06/01/2015 to Wed, 05/31/2017
Full Description: 

The Discovery Research K-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.

STEM Practice-rich Investigations for NGSS Teaching (SPRINT) is an exploratory project that will research and develop resources and a model for professional learning needed to meet the demand of implementing the Next Generation Science Standards (NGSS). The Exploratorium Teacher Institute will engage middle school science teachers in a one-year professional learning program to study how familiar routines and classroom tools, specifically hands-on science activities, can serve as starting points for teacher learning. The Teacher Institute will use existing hands-on activities as the basis for developing "practice-rich investigations" that provide teachers and students with opportunities for deep engagement with science and engineering practices. The results of this project will include: (1) empirical evidence from professional learning experiences that support teacher uptake of practice-rich investigations in workshops and their classrooms; (2) a portfolio of STEM practice-rich investigations developed from existing hands-on activities that are shown to enhance teacher understanding of NGSS; and (3) a design tool that supports teachers in modifying existing activities to align with NGSS.

SPRINT conjectures that to address the immediate challenge of supporting teachers to implement NGSS, professional learning models should engage teachers in the same active learning experiences they are expected to provide for their students and that building on teachers' existing strengths and understanding through an asset-based approach could lead to a more sustainable implementation. SPRINT will use design-based research methods to study (a) how creating NGSS-aligned, practice-rich investigations from teachers' existing resources provides them with experiences for three-dimensional science learning and (b) how engaging in these investigations and reflecting on classroom practice can support teachers in understanding and implementing NGSS learning experiences.

SmartCAD: Guiding Engineering Design with Science Simulations (Collaborative Research: Magana-de-Leon)

This project investigates how real time formative feedback can be automatically composed from the results of computational analysis of student design artifacts and processes with the envisioned SmartCAD software. The project conducts design-based research on SmartCAD, which supports secondary science and engineering with three embedded computational engines capable of simulating the mechanical, thermal, and solar performance of the built environment.

Lead Organization(s): 
Award Number: 
1503436
Funding Period: 
Mon, 06/15/2015 to Fri, 05/31/2019
Full Description: 

The Discovery Research K-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. 

In this project, SmartCAD: Guiding Engineering Design with Science Simulations, the Concord Consortium (lead), Purdue University, and the University of Virginia investigate how real time formative feedback can be automatically composed from the results of computational analysis of student design artifacts and processes with the envisioned SmartCAD software. Through automatic feedback based on visual analytic science simulations, SmartCAD is able to guide every student at a fine-grained level, allowing teachers to focus on high-level instruction. Considering the ubiquity of CAD software in the workplace and their diffusion into precollege classrooms, this research provides timely results that could motivate the development of an entire genre of CAD-based learning environments and materials to accelerate and scale up K-12 engineering education. The project conducts design-based research on SmartCAD, which supports secondary science and engineering with three embedded computational engines capable of simulating the mechanical, thermal, and solar performance of the built environment. These engines allow SmartCAD to analyze student design artifacts on a scientific basis and provide automatic formative feedback in forms such as numbers, graphs, and visualizations to guide student design processes on an ongoing basis. 

The research hypothesis is that appropriate applications of SmartCAD in the classroom results in three learning outcomes: 1) Science knowledge gains as indicated by a deeper understanding of the involved science concepts and their integration at the completion of a design project; 2) Design competency gains as indicated by the increase of iterations, informed design decisions, and systems thinking over time; and 3) Design performance improvements as indicated by a greater chance to succeed in designing a product that meets all the specifications within a given period of time. While measuring these learning outcomes, this project also probes two research questions: 1) What types of feedback from simulations to students are effective in helping them attain the outcomes? and 2) Under what conditions do these types of feedback help students attain the outcomes? To test the research hypothesis and answer the research questions, this project develops three curriculum modules based on the Learning by Design (LBD) Framework to support three selected design challenges: Solar Farms, Green Homes, and Quake-Proof Bridges. This integration of SmartCAD and LBD situate the research in the LBD context and shed light on how SmartCAD can be used to enhance established pedagogical models such as LBD. Research instruments include knowledge integration assessments, data mining, embedded assessments, classroom observations, participant interviews, and student questionnaires. This research is carried out in Indiana, Massachusetts, and Virginia simultaneously, involving more than 2,000 secondary students at a number of socioeconomically diverse schools. Professional development workshops are provided to familiarize teachers with SmartCAD materials and implementation strategies prior to the field tests. An external Critical Review Committee consisting of five engineering education researchers and practitioners oversee and evaluate this project formatively and summative. Project materials and results are disseminated through publications, presentations, partnerships, and the Internet.

Fostering STEM Trajectories: Bridging ECE Research, Practice, and Policy

This project will convene stakeholders in STEM and early childhood education to discuss better integration of STEM in the early grades. PIs will begin with a phase of background research to surface critical issues in teaching and learning in early childhood education and STEM.  A number of reports will be produced including commissioned papers, vision papers, and a forum synthesis report.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1417878
Funding Period: 
Mon, 06/15/2015 to Tue, 05/31/2016
Full Description: 

Early childhood education is at the forefront of the minds of parents, teachers, policymakers as well as the general public. A strong early childhood foundation is critical for lifelong learning. The National Science Foundation has made a number of early childhood grants in science, technology, engineering and mathematics (STEM) over the years and the knowledge generated from this work has benefitted researchers. Early childhood teachers and administrators, however, have little awareness of this knowledge since there is little research that is translated and disseminated into practice, according to the National Research Council. In addition, policies for both STEM and early childhood education has shifted in the last decade. 

The Joan Ganz Cooney Center and the New America Foundation are working together to highlight early childhood STEM education initiatives. Specifically, the PIs will convene stakeholders in STEM and early childhood education to discuss better integration of STEM in the early grades. PIs will begin with a phase of background research to surface critical issues in teaching and learning in early childhood education and STEM. The papers will be used as anchor topics to organize a forum with a broad range of stakeholders including policymakers as well as early childhood researchers and practitioners. A number of reports will be produced including commissioned papers, vision papers, and a forum synthesis report. The synthesis report will be widely disseminated by the Joan Ganz Cooney Center and the New America Foundation.

The Discovery Research K-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 project.

Design Technology and Engineering Education for English Learner Students: Project DTEEL

One significant challenge facing elementary STEM education is the varied preparation of English-language learners. The project addresses this with an innovative use of engineering curriculum to build on the English-language learners' prior experiences. The project will support teachers' learning about strategies for teaching English-language learners and using engineering design tasks as learning opportunities for mathematics, science and communication skills. 

Lead Organization(s): 
Award Number: 
1503428
Funding Period: 
Mon, 06/01/2015 to Thu, 05/31/2018
Full Description: 

The Discovery Research K-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. One significant challenge facing elementary STEM education is the varied preparation of English-language learners. The project addresses this with an innovative use of engineering curriculum to build on the English-language learners' prior experiences. The project will support teachers' learning about strategies for teaching English-language learners and using engineering design tasks as learning opportunities for mathematics, science and communication skills. 

The project's cross-disciplinary approach is grounded in both inquiry-based science education research and bilingual cognition research. These complementary foci bridge research areas to highlight how engineering experiences for students can capitalize on bilingual students' experiences as problem solvers. The project will develop teachers' ability and instructional efficacy for both STEM and bilingual student instruction. The project adapts a previously developed curriculum for engineering education by adding resources and tools to support bilingual students. The research design primarily measures teacher-level phenomenon such as implementation of instructional strategies, STEM self-efficacy and ability to address the academic development of bilingual students through engineering design activities. Data collected include classroom observations, teacher surveys, focus groups, and teacher interviews. Student assessments will be piloted in the final year of the project.

Refining a Model with Tools to Develop Math PD Leaders: An Implementation Study

This project will work with middle school mathematics teachers in San Francisco Unified School District to develop their capacity to conduct professional development for the teachers in their schools. A central goal of this project is to develop models and resources for effective professional development and preparation of professional development leaders in mathematics with special attention to students who are English language learners.

Lead Organization(s): 
Award Number: 
1417261
Funding Period: 
Thu, 01/01/2015 to Mon, 12/31/2018
Full Description: 

There is increased demand for K-12 teacher professional development that yields improvements in student learning and achievement. This need is particularly high given widespread adoption of the Common Core State Standards (CCSS) in mathematics which challenges teachers to incorporate mathematical thinking and problem solving into their instruction. The professional development challenge is exacerbated as our nation's demographics continue to shift, increasing the number of English language learners in school districts throughout the U.S. To meet this demand, the educational community must develop large-scale, system-level professional development programs aligned with the CCSS that are scalable and sustainable. The project team from Stanford University will work with middle school mathematics teachers in San Francisco Unified School District to develop their capacity to conduct professional development for the teachers in their schools. A central goal of this project is to develop models and resources for effective professional development and preparation of professional development leaders in mathematics with special attention to students who are English language learners. These models and resources will: provide school districts with the tools to build local capacity and provide sustainable professional development to all middle school mathematics teachers; improve the quality of teaching and, in turn, make important progress toward ensuring that all students in middle school can achieve the mathematical skills and understandings identified in the new standards; and meet the needs of English language learners. In addition, the Stanford team will contribute to the knowledge base in mathematics education, professional development and English language learners.

In previous work, the team developed two interconnected models--the Problem-Solving Cycle (PSC) and the Mathematics Leadership Preparation (MLP) models for preparing professional development leaders. The PSC model consists of a series of interconnected workshops organized around a problem that can be solved using multiple representations and solutions and can be adapted for multiple grade levels. Each cycle focuses on a different math problem. During the first cycle, teachers collaboratively solve the focal math problem and develop plans for teaching it to their students. Teachers then teach the lesson in their classes and the lessons are videotaped. Subsequent workshops focus on participants' classroom experiences teaching the problem. The goals of these workshops are to help teachers learn how to build on student thinking and to explore a variety of instructional practices. They rely heavily on video clips from the PSC lesson to foster productive conversations and situate the conversations in teachers' classroom instruction. The MLP model is designed to prepare Math Leaders to facilitate the PSC. The MLP prepares teachers to lead professional development for their colleagues. These models showed promise of effectiveness in improving middle school mathematics teachers' knowledge and practice, developing math professional development leaders, and improving student achievement. Investigators intend to refine and test the design of the PSC and MLP models and develop resources that can be used by other schools and districts, as well as conduct an evaluation of the work.

CAREER: Proof in Secondary Classrooms: Decomposing a Central Mathematical Practice

This project will develop an intervention to support the teaching and learning of proof in the context of geometry.

Lead Organization(s): 
Award Number: 
1453493
Funding Period: 
Wed, 07/15/2015 to Tue, 06/30/2020
Full Description: 

This project, funded as part of the CAREER program, would add to the knowledge base on the teaching and learning of proof in the context of the most prevalent course/topic in which proof is taught in the K-12 curriculum, geometry. Given the centrality of the role of proof, and the persistent difficulties in teaching proof in the K-12 and undergraduate curriculum, the topic is of vital importance. The work is novel, focusing on an area of proof that is understudied, the introduction of students to the topic of proof. While building on prior work in proof, the project will tackle an important area of beginning to teach proof, which may lead to broader innovations at both the K-12 and undergraduate level. The project will produce a resource, a set of lessons, which can be used widely and are likely to be broadly disseminated based on the PI's previous NSF-supported work, which has been broadly disseminated to practitioner audiences. 

The goal of the project is to develop an intervention to support the teaching and learning of proof in the context of geometry. This study takes as its premise that if we introduce proof, by first teaching students particular sub-goals of proof, such as how to draw a conclusion from a given statement and a definition, then students will be more successful with constructing proofs on their own. The 5-year design and development study builds on the researcher's prior work from a Knowles Science Teaching Fellowship (KSTF) grant to study how teachers introduce proof to students. This study will build on the prior work to refine a framework for introducing proof developed in the KSTF study. Using this framework the researcher will work with five high school geometry teachers to develop lessons via Lesson Study methods to introduce sub-goals of proof. The PI will study the impact of the use of these lessons on students' ability to perform proofs, and compare to students of ten teachers who will not have participated in the intervention.

 

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