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Investigating Productive Use of High-Leverage Student Mathematical Thinking Collaborative Research: Stockero)

This project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. The study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks.

Lead Organization(s): 
Award Number: 
1720566
Funding Period: 
Thu, 06/01/2017 to Mon, 05/31/2021
Full Description: 

The project will examine how secondary mathematics teachers respond to and use students' thinking during whole class discussion. An ongoing challenge for teachers is making the best use of students' emerging mathematical ideas during whole class discussion. Teachers need to draw on the ideas students have developed in order to create opportunities for learning about significant mathematical concepts. This study will create tasks specifically designed to generate opportunities for teachers to build on students' thinking and then use classroom observation and analysis of classroom video to develop tools to support teachers in leading whole class discussion.

The project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. This study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks. The project engages teacher-researchers in exploring the building practice. The teacher-researchers will use the project-designed tasks in their classrooms and then engage in a cycle of analysis of their own teaching with the research team. Data collection and analysis will rely on video analysis of classrooms, teachers' reflections on task enactment, and data collected during research team meetings convened with teacher-researchers to analyze practice.

Investigating Productive Use of High-Leverage Student Mathematical Thinking (Collaborative Research: Peterson)

This project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. The study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks.

Lead Organization(s): 
Award Number: 
1720410
Funding Period: 
Sat, 07/01/2017 to Mon, 05/31/2021
Full Description: 

The project will examine how secondary mathematics teachers respond to and use students' thinking during whole class discussion. An ongoing challenge for teachers is making the best use of students' emerging mathematical ideas during whole class discussion. Teachers need to draw on the ideas students have developed in order to create opportunities for learning about significant mathematical concepts. This study will create tasks specifically designed to generate opportunities for teachers to build on students' thinking and then use classroom observation and analysis of classroom video to develop tools to support teachers in leading whole class discussion.

The project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. This study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks. The project engages teacher-researchers in exploring the building practice. The teacher-researchers will use the project-designed tasks in their classrooms and then engage in a cycle of analysis of their own teaching with the research team. Data collection and analysis will rely on video analysis of classrooms, teachers' reflections on task enactment, and data collected during research team meetings convened with teacher-researchers to analyze practice.

High School Students' Climate Literacy Through Epistemology of Scientific Modeling (Collaborative Research: Chandler)

This project will focus on learning about model based reasoning in science, and will develop, implement, study, and refine a 6-week climate science module for high school students. The module will feature use of a web-based climate modeling application, and the project team will collect and analyze evidence of model-based reasoning about climate phenomena among students.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1719872
Funding Period: 
Fri, 09/01/2017 to Fri, 12/31/2021
Full Description: 

This project will focus on learning about model based reasoning in science, and will develop, implement, study, and refine a 6-week climate science module for high school students. The module will feature use of a web-based climate modeling application, and the project team will collect and analyze evidence of model-based reasoning about climate phenomena among students. Scientists routinely use data-intensive, computer-based models to study complex natural phenomena, and modeling has become a core objective of current science curriculum standards. The project will provide new insights about student use of scientific models to understand natural phenomena, and advance knowledge about curriculum, instruction, and assessment practices that promote model-based reasoning among students.

This 4-year Design and Development project will examine use of a web-based climate modeling tool designed to provide non-scientists experiences with climate modeling in high school geoscience classrooms. A theoretically-grounded and empirically tested approach to design-based research, instructional design, and assessment development will be used in an iterative cycle of instructional innovation and education research to find answers to two research questions: 1) How do secondary students develop epistemic and conceptual knowledge about climate? And 2) How do secondary science teachers support student use of climate modeling application to develop epistemic and conceptual knowledge about climate? Data associated with conceptual and epistemic knowledge, curriculum-embedded modeling tasks, interviews, and videorecorded observations of instruction will be used to study impacts of the new curriculum module on 55 high school science teachers and 3,000 students. Project participants include students from low socioeconomic populations and other groups underrepresented in STEM fields. The curriculum will also serve as a resource for an existing, online professional development course at the American Museum of Natural History that engages teachers nationwide.

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.

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.

Development of the Electronic Test of Early Numeracy

The project will develop and refine an electronic Test of Early Numeracy (e-TEN) in English and Spanish that will assess informal and formal knowledge of number and operations in domains including verbal counting, numbering, numerical relationships, and mental addition/subtraction. The overarching goal of the assessment design is to create a measure that is more accurate, more accessible to a wider range of children, and easier to administer than existing measures.

Partner Organization(s): 
Award Number: 
1621470
Funding Period: 
Thu, 09/15/2016 to Tue, 08/31/2021
Full Description: 

The project will develop and refine an electronic Test of Early Numeracy (e-TEN) in English and Spanish, focused on number and operations. The assessment will incorporate a learning trajectory that describes students' development of the understanding of number. The electronic assessment will allow for the test to adapt to students' responses and incorporate games to increase children's engagement with the tasks. These features take advantage of the electronic format. The achievement test will be designed to be efficient, user-friendly, affordable, and accessible for a variety of learning environments and a broad age range (3 to 8 years old). The overarching goal of the assessment design is to create a measure that is more accurate, more accessible to a wider range of children, and easier to administer than existing measures. This project is funded by the Discovery Research Pre-K-12 Program, which funds research and development of STEM innovations and approaches in assessment, teaching and learning.

The e-TEN will assess informal and formal knowledge of number and operations in domains including verbal counting, numbering, numerical relationships, and mental addition/subtraction. The items will be designed using domain-based learning trajectories that describe students' development of understanding of the topics. The test will be designed with some key characteristics. First, it will be semi-adaptive over six-month age spans. Second, it will have an electronic format that allows for uniform implementation and an efficient, user-friendly administration. The test will also be accessible to Spanish speakers using an inclusive assessment model. Finally, the game-based aspect should increase children's engagement and present more meaningful questions. The user-friendly aspect includes simplifying the assessment process compared to other tests of numeracy in early-childhood. The first phase of the development will test a preliminary version of the e-TEN to test its functionality and feasibility. The second phase will focus on norming of the items, reliability and validity. Reliability will be assessed using Item Response Theory methods and test-retest reliability measures. Validity will be examined using criterion-prediction validity and construct validity. The final phase of the work will include creating a Spanish version of the test including collecting data from bilingual children using both versions of the e-TEN.

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.

Algebra Project Mathematics Content and Pedagogy Initiative

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

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

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

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

InquirySpace 2: Broadening Access to Integrated Science Practices

This project will create technology-enhanced classroom activities and resources that increase student learning of science practices in high school biology, chemistry, and physics. InquirySpace will incorporate several innovative technological and pedagogical features that will enable students to undertake scientific experimentation that closely mirrors current science research and learn what it means to be a scientist.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1621301
Funding Period: 
Thu, 09/15/2016 to Tue, 08/31/2021
Full Description: 

This project will create technology-enhanced classroom activities and resources that increase student learning of science practices in high school biology, chemistry, and physics courses. The project addresses the urgent national priority to improve science education as envisioned in the Next Generation Science Standards (NGSS) by focusing less on learning facts and equations and instead providing students with the time, skills, and resources to experience the conduct of science and what it means to be a scientist. This project builds on prior work that created a sequence of physics activities that significantly improved students' abilities to undertake data-based experiments and led to productive independent investigations. The goal of the InquirySpace project is to improve this physics sequence, extend the approach to biology and chemistry, and adapt the materials to the needs of diverse students by integrating tailored formative feedback in real time. The result will be student and teacher materials that any school can use to allow students to experience the excitement and essence of scientific investigations as an integral part of science instruction. The project plans to create and iteratively revise learning materials and technologies, and will be tested in 48 diverse classroom settings. The educational impact of the project's approach will be compared with that of business-as-usual approaches used by teachers to investigate to what extent it empowers students to undertake self-directed experiments. To facilitate the widest possible use of the project, a complete set of materials, software, teacher professional development resources, and curriculum design documents will be available online at the project website, an online teacher professional development course, and teacher community sites. 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.

InquirySpace will incorporate several innovative technological and pedagogical features that will enable students to undertake scientific experimentation that closely mirrors current science research. These features will include (1) educational games to teach data analysis and interpretation skills needed in the approach, (2) reduced dependence on reading and writing through the use of screencast instructions and reports, (3) increased reliance on graphical analysis that can make equations unnecessary, and (4) extensive use of formative feedback generated from student logs. The project uses an overarching framework called Parameter Space Reasoning (PSR) to scaffold students through a type of experimentation applicable to a very large class of experiments. PSR involves an integrated set of science practices related to a question that can be answered with a series of data collection runs for different values of independent variables. Data can be collected from sensors attached to the computer, analysis of videos, scientific databases, or computational models. A variety of visual analytic tools will be provided to reveal patterns in the graphs. Research will be conducted in three phases: design and development of technology-enhanced learning materials through design-based research, estimation of educational impact using a quasi-experimental design, and feasibility testing across diverse classroom settings. The project will use two analytical algorithms to diagnose students' learning of data analysis and interpretation practices so that teachers and students can modify their actions based on formative feedback in real time. These algorithms use computationally optimized calculations to model the growth of student thinking and investigation patterns and provide actionable information to teachers and students almost instantly. Because formative feedback can improve instruction in any field, this is a major development that has wide potential.

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