Blacks/African Americans

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.

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.

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.

CAREER: Multilevel Mediation Models to Study the Impact of Teacher Development on Student Achievement in Mathematics

This project will develop a comprehensive framework to inform and guide the analytic design of teacher professional development studies in mathematics. An essential goal of the research is to advance a science of teaching and learning in ways that traverse both research and education.

Lead Organization(s): 
Award Number: 
1552535
Funding Period: 
Thu, 09/01/2016 to Tue, 08/31/2021
Full Description: 

This is a Faculty Early Career Development Program (CAREER) project. The CAREER program is a National Science Foundation-wide activity that offers the most prestigious awards in support of junior faculty who exemplify the role of teacher-scholars through outstanding research, excellent education and the integration of education and research. The intellectual merit and broader impacts of this study lie in two complementary contributions of the project. First, the development of the statistical framework for the design of multilevel mediation studies has significant potential for broad impact because it develops a core platform that is transferable to other STEM (science, technology, engineering, and mathematics) education areas and STEM disciplines. Second, the development of software and curricular materials to implement this framework further capitalize on the promise of this work because it distributes the results in an accessible manner to diverse sets of research and practitioner groups across STEM education areas and STEM disciplines. Together, the components of this project will substantially expand the scope and quality of evidence generated through mathematics professional development and, more generally, multilevel mediation studies throughout STEM areas by increasing researchers' capacity to design valid and comprehensive studies of the theories of action and change that underlie research programs.

This project will develop a comprehensive framework to inform and guide the analytic design of teacher professional development studies in mathematics. The proposed framework incorporates four integrated research and education components: (1) develop statistical formulas and tools to guide the optimal design of experimental and non-experimental multilevel mediation studies in the presence of measurement error, (2) develop empirical estimates of the parameters needed to implement these formulas to design teacher development studies in mathematics, (3) develop free and accessible software to execute this framework, and (4) develop training materials and conduct workshops on the framework to improve the capacity of the field to design effective and efficient studies of teacher development. An essential goal of the research is to advance a science of teaching and learning in ways that traverse both research and education.

Science, Technology, Engineering and Mathematics Scholars Teacher Academy Resident System

This project will investigate the effectiveness of a teacher academy resident model to recruit, license, induct, employ, and retain middle school and secondary teachers for high-need schools in the South. It will prepare new, highly-qualified science and mathematics teachers from historically Black universities in high-needs urban and rural schools with the goal of increasing teacher retention and diversity rates.

Lead Organization(s): 
Award Number: 
1621325
Funding Period: 
Fri, 07/15/2016 to Wed, 06/30/2021
Full Description: 

This project at Jackson State University will investigate the effectiveness of a teacher academy resident model to recruit, license, induct, employ, and retain middle school and secondary science and mathematics teachers for high-need schools in the South. It will prepare new, highly-qualified science and mathematics teachers from historically Black universities in high-needs urban and rural schools. The project involves a partnership among three historically Black universities (Jackson, State University, Xavier University of Louisiana, and the University of Arkansas at Pine Bluff), and diverse urban and rural school districts in Jackson, Mississippi; New Orleans, Louisiana; and Pine Bluff Arkansas region that serve more than 175,000 students.

Participants will include 150 middle and secondary school teacher residents who will gain clinical mentored experience and develop familiarity with local schools. The 150 teacher residents supported by the program to National Board certification will obtain: state licensure/certification in science teaching, a master's degree, and initiation. The goal is to increase teacher retention and diversity rates. The research question guiding this focus is: Will training STEM graduates have a significant effect on the quality of K-12 instruction, teacher efficacy and satisfaction, STEM teacher retention, and students? Science and mathematics achievement? A quasi-experimental design will be used to evaluate project's effectiveness.

Supporting Teacher Practice to Facilitate and Assess Oral Scientific Argumentation: Embedding a Real-Time Assessment of Speaking and Listening into an Argumentation-Rich Curriculum (Collaborative Research: Henderson)

The fundamental purpose of this project is to support teacher practice and professional learning around oral scientific argumentation in order to improve the quality of this practice in classrooms. The key outcome of this work will be a research-informed and field-tested prototype to improve the quality of teaching and learning argumentation in middle school science classrooms usable in different learning environments.

Lead Organization(s): 
Award Number: 
1621496
Funding Period: 
Thu, 09/01/2016 to Mon, 08/31/2020
Full Description: 

This is an early-stage design and development collaborative study submitted to the assessment strand of the Discovery Research PreK-12 (DRK-12) program, in response to Program Solicitation NSF 15-592. The fundamental purpose of this project is to support teacher practice and professional learning around oral scientific argumentation in order to improve the quality of this practice in classrooms. To achieve this purpose, the project will examine the validity of a new technology-based formative assessment tool for classroom argumentation--"Diagnosing the Argumentation Levels of Groups" (DiALoG)--for which psychometric validation work has been conducted in a laboratory setting. The DiALoG assessment tool allows teachers to document classroom talk and display scores across multiple dimensions--both intrapersonal and interpersonal--for formative assessment purposes. The project will work with 6th-8th grade science teachers to monitor and support argumentation through real-time formative assessment data generated by the DiALoG instrument. DiALoG will be used in conjunction with "Amplify Science", a Lawrence Hall of Science-developed curriculum that incorporates the science practice of engaging in argument from evidence, and a suite of newly developed Responsive Mini-Lessons (RMLs), which consist of 20-30 minute instructional strategies designed to assist teachers to provide feedback to students' thinking and follow-up to argumentation episodes that the DiALoG tool identifies in need of further support. The study will allow the refinement and expansion of DiALoG and evaluation of its impact on teacher pedagogical content knowledge and formative assessment practices in widespread classroom use.

The project will address two specific research questions: (1) How can DiALoG be refined to provide a formative assessment tool for oral argumentation that is reliable, practical, and useful in middle school classrooms?; and (2) How does the use of DiALoG affect teacher formative assessment practices around evidence-based argumentation, when implementing science units designed to support oral argumentation? In order to answer these questions, the project will conduct a randomized control trial with 100 teachers: 50 will teach argumentation-focused curriculum with DiALoG, 50 will teach the same curriculum without DiALoG. Both control and treatment teachers will receive all digital and physical materials needed to teach three Amplify Science curriculum units. Treatment teachers will be provided also with the most recent version of DiALoG, including the linked RMLs, as well as support materials for using DiALoG with the Amplify curriculum. A subgroup of focus teachers (5 from the treatment group, and 5 from the control group) will be the subject of additional data collection and analysis. Three focus lessons, in which students are engaging in small-group or whole-class oral argumentation, will be selected from each of the three Amplify Science curricular units. Teacher measures for the randomized control trial will include validated instruments, such as (a) a pre- and post-assessment of teacher pedagogical content knowledge; (b) post-lesson and post-unit surveys in which teachers will self-report on their formative assessment practices; and (c) video recordings of selected lessons in the focus classrooms. In order to observe potential differences in formative assessment practices between treatment and control, protocols will be used to analyze the video recordings of focus classrooms, including (a) Reformed Teaching Observation Protocol; (b) Assessment of Scientific Argumentation inside the Classroom; and (c) Formative Assessment for Teachers and Students. The key outcome of this work will be a research-informed and field-tested prototype to improve the quality of teaching and learning argumentation in middle school science classrooms usable in different learning environments.

CAREER: Designing Learning Environments to Foster Productive and Powerful Discussions Among Linguistically Diverse Students in Secondary Mathematics

Lead Organization(s): 
Award Number: 
1553708
Funding Period: 
Mon, 02/01/2016 to Sun, 01/31/2021
Full Description: 

The project will design and investigate learning environments in secondary mathematics classrooms focused on meeting the needs of English language learners. An ongoing challenge for mathematics teachers is promoting deep mathematics learning among linguistically diverse groups of students while taking into consideration how students' language background influences their classroom experiences and the mathematical understandings they develop. In response to this challenge, this project will design and develop specialized instructional materials and guidelines for teaching fundamental topics in secondary algebra in linguistically diverse classrooms. The materials will incorporate insights from current research on student learning in mathematics as well as insights from research on the role of language in students' mathematical thinking and learning. A significant contribution of the work will be connecting research on mathematics learning generally with research on the mathematics learning of English language learners. In addition to advancing theoretical understandings, the research will also contribute practical resources and guidance for mathematics teachers who teach English language learners. The Faculty Early Career Development (CAREER) program is a National Science Foundation (NSF)-wide activity that offers awards in support of junior faculty who exemplify the role of teacher-scholars through outstanding research, excellent education, and the integration of education and research within the context of the mission of their organizations.

The project is focused on the design of specialized hypothetical learning trajectories that incorporate considerations for linguistically diverse students. One goal for the specialized trajectories is to foster productive and powerful mathematics discussions about linear and exponential rates in linguistically diverse classrooms. The specialized learning trajectories will include both mathematical and language development learning goals. While this project focuses on concepts related to reasoning with linear and exponential functions, the resulting framework should inform the design of specialized hypothetical learning trajectories in other topic areas. Additionally, the project will add to the field's understanding of how linguistically diverse students develop mathematical understandings of a key conceptual domain. The project uses a design-based research framework gathering classroom-based data, assessment data, and interviews with teachers and students to design and refine the learning trajectories. Consistent with a design-based approach, the project results will include development of theory about linguistically diverse students' mathematics learning and development of guidance and resources for secondary mathematics teachers. This research involves sustained collaboration with secondary mathematics teachers and the impacts will include developing capacity of teachers locally, and propagating the results of this work in professional development activities.


Project Videos

2019 STEM for All Video Showcase

Title: Fostering Math Discussions among English Learners

Presenter(s): William Zahner


Mathematical and Computational Methods for Planning a Sustainable Future II

The project will develop modules for grades 9-12 that integrate mathematics, computing and science in sustainability contexts. The project materials also include information about STEM careers in sustainability to increase the relevancy of the content for students and broaden their understanding of STEM workforce opportunities. It uses summer workshops to pilot test materials and online support and field testing in four states. 

Lead Organization(s): 
Award Number: 
1503414
Funding Period: 
Wed, 07/15/2015 to Sun, 06/30/2019
Full Description: 

The project will develop modules for grades 9-12 that integrate mathematics, computing and science in sustainability contexts. The project materials also include information about STEM careers in sustainability to increase the relevancy of the content for students and broaden their understanding of STEM workforce opportunities. It uses summer workshops to pilot test materials and online support and field testing in four states. Outcomes include the modules, tested and revised; strategies for transfer of learning embedded in the modules; and a compendium of green jobs, explicitly related to the modules. 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 STEM+Computing Partnerships (STEM+C) Program is a joint effort between the Directorate for Education & Human Resources (EHR) and Directorate Computer & Information Science & Engineering (CISE). Reflecting the increasing role of computational approaches in learning across the STEM disciplines, STEM+C supports research and development efforts that integrate computing within one or more STEM disciplines and/or integrate STEM learning in computer science; 2) advance multidisciplinary, collaborative approaches for integrating computing in STEM in and out of school, and 3) build capacity in K-12 computing education through foundational research and focused teacher preparation

The project is a full design and development project in the learning strand of DRK-12. The goal is to enhance transfer of knowledge in mathematics and science via sustainability tasks with an emphasis on mathematical and scientific practices. The research questions focus on how conceptual representations and the modules support students' learning and especially transfer to novel problems. The project design integrates the research with the curriculum development. It includes a mixed methods data collection and analysis from teachers and students (e.g., interviews, content exams, focus groups, implementation logs). Assessment of student work includes both short, focused problems in the content area and longer project-based tasks providing a range of assessments of student learning. The investigators will develop a rubric for scoring student work on the tasks. The curriculum design process includes iterations of the modules over time with feedback from teachers and using data collected from the implementation.

Collaborative Math: Creating Sustainable Excellence in Mathematics for Head Start Programs

This project will adapt and study a promising and replicable teacher professional development (PD) intervention, called Collaborative Math (CM), for use in early childhood programs. Prepared as generalists, preschool teachers typically acquire less math knowledge in pre-service training than their colleagues in upper grades, which reduces their effectiveness in teaching math. To address teacher PD needs, the project will simultaneously develop teacher content knowledge, confidence, and classroom practice by using a whole teacher approach.

Lead Organization(s): 
Award Number: 
1503486
Funding Period: 
Tue, 09/01/2015 to Sat, 08/31/2019
Full Description: 

This project was submitted to the Discovery Research K-12 (DRK-12) program that 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. 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 will adapt and study a promising and replicable teacher professional development (PD) intervention, called Collaborative Math (CM), for use in early childhood programs. CM content will focus on nine topics emphasized in preschool mathematics, including sets, number sense, counting, number operations, pattern, measurement, data analysis, spatial relationships, and shape. These concepts are organized around Big Ideas familiar in early math, are developmentally appropriate and foundational to a young child's understanding of mathematics. The project addresses the urgent need for improving early math instruction for low-income children. Prepared as generalists, preschool teachers typically acquire less math knowledge in pre-service training than their colleagues in upper grades, which reduces their effectiveness in teaching math. To address teacher PD needs, the project will simultaneously develop teacher content knowledge, confidence, and classroom practice by using a whole teacher approach. Likewise, the project will involve teachers, teacher aides, and administrators through a whole school approach in PD, which research has shown is more effective than involving only lead teachers. Through several phases of development and research, the project will investigate the contributions of project components on increases in teacher knowledge and classroom practices, student math knowledge, and overall implementation. The project will impact approximately 200 Head Start (HS) teaching staff, better preparing them to provide quality early math experiences to more than 3,000 HS children during the project period. Upon the completion of the project, a range of well-tested CM materials such as resource books and teaching videos will be widely available for early math PD use. Assessment tools that look at math knowledge, attitudes, and teacher practice will also be available. 

The project builds on Erikson Institute research and development work in fields of early math PD and curriculum. Over a 4-year span, project development and research will be implemented in 4 phases: (1) adapting the existing CM and research measures for HS context; (2) conducting a limited field study of revised CM in terms of fidelity and director, teacher/aide, and student outcomes, and study of business as usual (BAU) comparison groups; (3) a study of the promise of the intervention promise with the phase 3 BAU group (who offered baseline in phase 2) and (4) a test of the 2nd year sustainability intervention with phase 3 treatment group. The teacher and student measures are all published, frequently used measures in early childhood education and will be piloted and refined prior to full implementation. The project is a partnership between Erikson, SRI, and Chicago Head Start programs. Project research and resources will be widely disseminated to policy makers, researchers, and practitioners.

TRUmath and Lesson Study: Supporting Fundamental and Sustainable Improvement in High School Mathematics Teaching (Collaborative Research: Schoenfeld)

Given the changes in instructional practices needed to support high quality mathematics teaching and learning based on college and career readiness standards, school districts need to provide professional learning opportunities for teachers that support those changes. The project is based on the TRUmath framework and will build a coherent and scalable plan for providing these opportunities in high school mathematics departments, a traditionally difficult unit of organizational change.

Award Number: 
1503454
Funding Period: 
Wed, 07/01/2015 to Sun, 06/30/2019
Full Description: 

Given the changes in instructional practices needed to support high quality mathematics teaching and learning based on college and career readiness standards, school districts need to provide professional learning opportunities for teachers that support those changes. The project will build a coherent and scalable plan for providing these opportunities in high school mathematics departments, a traditionally difficult unit of organizational change. Based on the TRUmath framework, characterizing the five essential dimensions of powerful mathematics classrooms, the project brings together a focus on curricular materials that support teaching, Lesson Study protocols and materials, and a professional learning community-based professional development model. The project will design and revise professional development and coaching guides and lesson study mathematical resources built around the curricular materials. The project will study changes in instructional practice and impact on student learning. By documenting the supports used in the Oakland Unified School District where the research and development will be conducted, the resources can be used by other districts and in similar work by other research-practice partnerships.

This project hypothesizes that the quality of classroom instruction can be defined by five dimensions - quality of the mathematics; cognitive demand of the tasks; access to mathematics content in the classroom; student agency, authority, and identity; and uses of assessment. The project will use an iterative design process to develop and refine a suite of tool, including a conversation guide to support productive dialogue between teachers and coaches, support materials for building site-based professional learning materials, and formative assessment lessons using Lesson Study as a mechanism to enact reforms of these dimensions. The study will use a pre-post design and natural variation to student the relationships between these dimensions, changes in teachers' instructional practice, and student learning using hierarchical linear modeling with random intercept models with covariates. Qualitative of the changes in teachers' instructional practices will be based on coding of observations based on the TRUmath framework. The study will also use qualitative analysis techniques to identify themes from surveys and interviews on factors that promote or hinder the effectiveness of the intervention.

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