Hispanics/Latinos

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.

Quality Urban Ecology Science Teaching for Diverse Learners

This project will examine the relationship between teacher professional development associated with newly developed modules in urban ecology and the achievement and engagement of long-term English learners (LTEL).  Existing Urban Ecology learning modules will be enhanced to accommodate the needs of LTELs, and teachers will participate in professional development aimed at using the new materials to effectively integrate academic science discourse and literacy development for LTELs.

Lead Organization(s): 
Award Number: 
1503519
Funding Period: 
Sat, 08/01/2015 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. This exploratory research project will examine the relationship between teacher professional development associated with newly developed modules in urban ecology and the achievement and engagement of long-term English learners (LTEL). Participants in the project will include students in grades 4-8 in a large urban school district, elementary school teachers, middle school science teachers, and middle school teachers of English language arts. Existing Urban Ecology learning modules will be enhanced to accommodate the needs of LTELs, and teachers will participate in professional development aimed at using the new materials to effectively integrate academic science discourse and literacy development for LTELs.

The project will develop two enhanced urban ecology modules (47 lessons) for English learners in grades 4-8; science language and literacy assessments for English language learners (ELLs); an ELL STEM career awareness inventory; an urban ecology for ELLs teacher knowledge scale, and an urban ecology for ELLs pedagogy observation protocol. The materials will be tested with a stratified random sample of students identified by achievement level (low, medium, and high) and linguistic background (mainstream, LTEL, and "at risk" of becoming LTEL). A mixed-methods research design will be used to test the hypothesis that the quantity and quality of LTEL science language and literacy achievement will increase as a result of teacher participation in implementing the newly developed transdisciplinary framework for Urban Ecology for English Learners.

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.

PBS NewsHour STEM Student Reporting Labs: Broad Expansion of Youth Journalism to Support Increased STEM Literacy Among Underserved Student Populations and Their Communities

The production of news stories and student-oriented instruction in the classroom are designed to increase student learning of STEM content through student-centered inquiry and reflections on metacognition. This project scales up the PBS NewsHour Student Reporting Labs (SRL), a model that trains teens to produce video reports on important STEM issues from a youth perspective.

Award Number: 
1503315
Funding Period: 
Sat, 08/01/2015 to Wed, 07/31/2019
Full Description: 

The Discovery Research K-12 program (DR-K12) 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 scales up the PBS NewsHour Student Reporting Labs (SRL), a model that trains teens to produce video reports on important STEM issues from a youth perspective. Participating schools receive a SRL journalism and digital media literacy curriculum, a mentor for students from a local PBS affiliate, professional development for educators, and support from the PBS NewsHour team. The production of news stories and student-oriented instruction in the classroom are designed to increase student learning of STEM content through student-centered inquiry and reflections on metacognition. Students will develop a deep understanding of the material to choose the best strategy to teach or tell the STEM story to others through digital media. Over the 4 years of the project, the model will be expanded from the current 70 schools to 150 in 40 states targeting schools with high populations of underrepresented youth. New components will be added to the model including STEM professional mentors and a social media and media analytics component. Project partners include local PBS stations, Project Lead the Way, and Share My Lesson educators.

The research study conducted by New Knowledge, LLC will add new knowledge about the growing field of youth science journalism and digital media. Front-end evaluation will assess students' understanding of contemporary STEM issues by deploying a web-based survey to crowd-source youth reactions, interest, questions, and thoughts about current science issues. A subset of questions will explore students' tendencies to pass newly-acquired information to members of the larger social networks. Formative evaluation will include qualitative and quantitative studies of multiple stakeholders at the Student Reporting Labs to refine the implementation of the program. Summative evaluation will track learning outcomes/changes such as: How does student reporting on STEM news increase their STEM literacy competencies? How does it affect their interest in STEM careers? Which strategies are most effective with underrepresented students? How do youth communicate with each other about science content, informing news media best practices? The research team will use data from pre/post and post-delayed surveys taken by 1700 students in the STEM Student Reporting Labs and 1700 from control groups. In addition, interviews with teachers will assess the curriculum and impressions of student engagement.


Project Videos

2019 STEM for All Video Showcase

Title: How Video Storytelling Reengages Teenagers in STEM Learning

Presenter(s): Leah Clapman & William Swift

2018 STEM for All Video Showcase

Title: PBS NewsHour's STEM SRL Transforms Classrooms into Newsrooms

Presenter(s): Leah Clapman & William Swift

2017 STEM for All Video Showcase

Title: PBS is Building the Next Generation of STEM Communicators

Presenter(s): Leah Clapman, John Fraser, Su-Jen Roberts, & Bill Swift


SimScientists Games: Development of Simulation-Based Game Designs to Enhance Formative Assessment and Deep Science Learning in Middle School

This project will focus on understanding how educational games, designed according to research-based learning and assessment design principles, can better assess and promote students' science knowledge, application of science process skills, and motivation and engagement in learning.

Lead Organization(s): 
Award Number: 
1503481
Funding Period: 
Sat, 08/01/2015 to Wed, 07/31/2019
Full Description: 

The Discovery Research K-12 (DRK-12) program 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. This project is a four-year design and development study submitted to the assessment strand of the program. It will focus on understanding how educational games, designed according to research-based learning and assessment design principles, can better assess and promote students' science knowledge, application of science process skills, and motivation and engagement in learning. The project will develop a new genre of games to serve as formative assessment resources designed to collect evidence of science learning during gameplay, provide feedback and coaching in the form of hints, and reinforce middle grade (6th-8th) students' life science concepts and investigation practices about ecosystems described in the Next Generation Science Standards (NGSS) (Achieve, 2013). The games will build on the designs of the simulation-based, curriculum-embedded assessments developed in previous NSF-funded efforts, which include student progress reports and reflection activities that allow teachers to provide feedback to students and adjust instruction. The design of the games will draw from multiple lines of research, such as cognition, particularly model-based learning; principled assessment design; and motivation. Intended to provide engaging activities for understanding and investigating the system components, roles, interactions, and population dynamics of ecosystems, the project will produce two sets of comprehensive games: (1) Organisms and Interactions, and (2) Emergent Population Levels: Managing an Ecosystem. Each game will consist of progressively advanced mini-games. Twenty-four California Bay Area middle school teachers will participate in the study. Teacher professional development (PD) will include face-to-face sessions and an online platform that permits a wide range of interactions among participants and the facilitators. The PD will emphasize the alignment of the ecosystem simulation-based curriculum modules with their state standards, instructional materials, and the new games. 

The project will address six research questions: (1) How well do the games align with the ecosystem crosscutting concepts, core ideas, and inquiry practices in the NGSS?; (2) How well do game components meet quality standards?; (3) How well do the games integrate with the existing simulation-based curriculum modules and the teachers' existing instructional sequence?; (4) What effect does the use of the games have on students' understanding of the science concepts, scientific practices, and collaboration skills?; (5) How does success in gameplay relate to improved performance on the external outcome measures comprised of the simulation-based benchmark and the pre/posttest?; and (6) How does the use of the games affect students' engagement in science learning? In a Year 1 usability study, the project will test, analyze, and revise alpha versions of the games. In Year 2, a classroom feasibility study of beta versions will inform further revisions. In Year 3, six teachers will pilot-test the games. A second pilot test in Year 4 will examine the effectiveness of the games by comparing student performance in classes using the existing simulation-based curriculum-embedded assessments and reflection activities with classes using the curriculum-embedded assessments plus the new games. Data collection and analysis strategies include: (a) alignment reviews; (b) focus groups and usability testing; (c) cognitive labs for construct validity and usability; (d) game reports (badges); (e) pre/posttest of American Association for the Advancement of Science (AAAS) items; (f) benchmark assessment data; (g) student interest in the games and science; (h) teacher surveys; (i) case studies; (j) game quality analysis; (k) differential item functioning; (l) analysis of covariance; and (m) analysis of variance on posttest scores (outcome variable) to compare the means across student groups (by intervention mode) and their prior science achievement levels.

Developing Teachers' Capacity to Promote Argumentation in Secondary Science

This project will produce insights into the challenges teachers face in modifying their teaching in the substantial and complex ways demanded by the Next Generation Science Standards. This project will develop and study a program of professional development to help middle and high school science teachers support their students to learn to argue scientifically. 

Award Number: 
1503511
Funding Period: 
Wed, 07/01/2015 to Sun, 06/30/2019
Full Description: 

This project will produce insights into the challenges teachers face in modifying their teaching in the substantial and complex ways demanded by the Next Generation Science Standards. This project will develop and study a program of professional development to help middle and high school science teachers support their students to learn to argue scientifically. The program includes strategies for organizing science activities to create contexts where students have something to argue about and teaching practices that promote sustained, productive argumentation among students. Results will document what aspects of these new practices teachers find easier and more difficult to implement, and how challenges are influenced by the urban schooling contexts in which project teachers work. The project will also further our understanding of how site-based professional development can be structured to support teacher learning and improvement.

The project is a longitudinal study of a cohort of 30 secondary science teachers from an urban school district in California. The professional development (PD) program will be organized around intensive summer institutes followed by 2 school-based lesson study cycles each year, facilitated by trained coaches. The PD work will be carried out over three years. All PD sessions will be recorded for interaction analysis to identify variations in coaching and teacher participation and the influences of such variation on teacher learning. Repeated measures of teachers' conceptions of argumentation will be given over 3 years as a measure of teacher learning. An observation protocol will be developed and used to measure teacher talk and its change over time. A sub-sample of teachers' classrooms will be video recorded to produce a longitudinal record for interaction analyses to link teacher talk to patterns of student argumentation. The third year of the project will add measures of student learning and link them to variations in teacher practice. The final year of the project will produce retrospective analyses that link pathways in teacher learning to features of the PD program and teachers' participation. 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.

Thinking Spatially about the Universe: A Physical and Virtual Laboratory for Middle School Science (Collaborative Research: Goodman)

This project will develop and study three week-long middle school lab units designed to teach spatial abilities using a blend of physical and virtual (computer-based) models. "ThinkSpace" labs will help students explore 3-dimensional astronomical phenomena in ways that will support both understanding of these topics and a more general spatial ability. Students will learn both through direct work with the lab unit interface and through succeeding discussions with their peers.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1503395
Funding Period: 
Wed, 07/01/2015 to Sat, 06/30/2018
Full Description: 

Critical breakthroughs in science (e.g., Einstein's Theory of General Relativity, and Watson & Crick's discovery of the structure of DNA), originated with those scientists' ability to think spatially, and research has shown that spatial ability correlates strongly with likelihood of entering a career in STEM. This project will develop and study three week-long middle school lab units designed to teach spatial abilities using a blend of physical and virtual (computer-based) models. "ThinkSpace" labs will help students explore 3-dimensional astronomical phenomena (moon phases and eclipses; planetary systems around stars other than the Sun; and celestial motions within the broader universe) in ways that will support both understanding of these topics and a more general spatial ability. Students will learn both through direct work with the lab unit interface and through succeeding discussions with their peers. The research program will determine which elements in the labs best promote both spatial skills and understanding of core ideas in astronomy; and how then to optimize interactive dynamic visualizations toward these ends. Virtual models of the sky and universe will be created using WorldWide Telescope, a free visualization tool that runs on desktop computers, tablets, and mobile devices. The ThinkSpace lab materials will be available at no cost on popular curriculum-sharing sites, including PBS Learning Media and BetterLesson.

The ThinkSpace team will address two main research questions: 1) How can spatial tasks that blend physical and virtual models be embedded into a STEM curriculum in ways that lead to significant improvements in spatial thinking? and 2) How can practitioners optimize design of interactive, dynamic visualizations for teaching spatially complex concepts? The first year of the study will examine two of the lab units with four teachers and about 320 students. The second year of the study will be similar. The third year of the study will test all three lab units in 10 classrooms. Over this study, each week-long ThinkSpace Lab will be formatively tested, using pre/post written assessments of astronomy content and spatial thinking; pre/post interviews with students; and in-class video of students using the lab activities. Scaffolded learning designs will support students in making connections between different spatial views of the phenomena, and will guide them to construct explanations and argue from evidence about how various phenomena (e.g. moon phases) arise in the real Universe, as Next Generation Science Standards demand. The impact of the ThinkSpace labs will be felt far beyond astronomy because the learning models being tested can transfer to other fields where spatial models are critical, and findings on optimization of dynamic visualizations can help to inform instructional design in the age of online learning. 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.

Development of Language-Focused Three-Dimensional Science Instructional Materials to Support English Language Learners in Fifth Grade (Collaborative Research: Valdes)

The main purpose of this project is to develop instructional materials for a year-long, fifth grade curriculum for all students, including ELLs. The planned curriculum will promote language-focused and three-dimensional science learning (through blending of science and engineering practices, crosscutting concepts, and disciplinary core ideas), aligned with the Framework for K-12 Science Education, the Next Generation Science Standards, and the Conceptual Framework for Language use in the Science Classroom.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1502507
Funding Period: 
Tue, 09/01/2015 to Sat, 08/31/2019
Full Description: 

This project is responsive to the societal challenges emerging from the nation's diverse and rapidly changing student demographics, including the rise of English language learners (ELLs), the fastest growing student population (see, for example, "U.S. school enrollment hits majority-minority milestone", Education Week, February 1, 2015). ELLs have grown exponentially: 1 in 5 students (21%) in the nation spoke a language other than English at home in 2011. The project's main purpose is to develop instructional materials for a year-long, fifth grade curriculum for all students, including ELLs. The planned curriculum will promote language-focused and three-dimensional science learning (through blending of science and engineering practices, crosscutting concepts, and disciplinary core ideas), aligned with the Framework for K-12 Science Education (National Research Council, 2012), the Next Generation Science Standards (Achieve, 2013), and the Conceptual Framework for Language use in the Science Classroom (Lee, Quinn & Valdés, 2013). The grade-level science content will target topics, such as structure and properties of matter, matter and energy in organisms and ecosystems, and Earth's and space systems, with engineering design embedded in each topic. The language approach will emphasize analytical science tasks aimed at making sense of and constructing scientific knowledge; and receptive (listening and reading) and productive (speaking and writing) language functions. Products and research results from this project will help to reduce the science achievement gaps between ELLs and non-ELLs, and enable all students to attain higher levels of proficiency in subsequent grade levels.

After the curriculum has been developed and field-tested during Years 1-3, a pilot study will be conducted in Year 4 to investigate promise of effectiveness. Using a randomized controlled trial design, the pilot study will address three research questions: (1) What is the impact of the intervention on science learning and language development for all students, including ELLs and former ELLs?; (2) What is the impact of the intervention on teachers' instructional practices?; and (3) To what extent are teachers able to implement the instructional materials with fidelity? To address research question 1, a sequence of multi-level models (MLMs) in which the posttest score for each student measure (the state/district science test score, and the science score and the language score on the researcher-developed assessment) will be regressed on a dummy variable representing condition (treatment or control) and pretest covariates. To examine whether the intervention is beneficial for students of varying levels of English proficiency, subgroup analyses will be conducted comparing ELLs in the treatment group against ELLs in the control group; former ELLs in the treatment group against former ELLs in the control group; and non-ELLs in the treatment group against non-ELLs in the control group, using the same MLMs. Exploratory analyses will be employed to examine the extent to which the level of English proficiency moderates the impact of the intervention on ELLs. To address research question 2, a 2-level model (teachers as level-1, and schools as level-2) in which the post-questionnaire scale score will be regressed on a dummy variable representing condition (treatment or control) will be conducted. To address research question 3, plans are to analyze ratings on coverage, adherence, and quality of instruction from classroom observations, along with ratings on program differentiation and participant responsiveness from the implementation and feedback form.

CAREER: Leveraging Contrasting Cases to Investigate Integer Understanding

Most students learn about negative numbers long after they have learned about positive numbers, and they have little time or opportunity to build on their prior understanding by contrasting the two concepts. The purpose of this CAREER project is to identify language factors and instructional sequences that contribute to improving elementary students' understanding of addition and subtraction problems involving negative integers. 

Lead Organization(s): 
Award Number: 
1350281
Funding Period: 
Thu, 05/15/2014 to Tue, 04/30/2019
Full Description: 

Currently, most students learn about negative numbers long after they have learned about positive numbers, and they have little time or opportunity to build on their prior understanding by contrasting the two concepts. Therefore, they struggle to make sense of negative integer concepts, which appear to conflict with their current understanding. The purpose of this CAREER project is to identify language factors and instructional sequences that contribute to improving elementary students' understanding of addition and subtraction problems involving negative integers. A second objective is to identify how elementary teachers interpret their students' integer understanding and use research findings to support their teaching of these concepts. This project is expected to contribute to theories regarding the development of integer understanding as well as what makes a useful contrasting case when learning new, related concepts. Moreover, the results of this project can contribute to our understanding of how to build on students? prior number knowledge rather than contradict it.

The principal investigator will conduct a series of four experimental studies involving a preparation for learning component with students randomly assigned to treatment or control groups. Study 1 will involve second and fourth graders and will test the language factors that support students' understanding of integers. Studies 2-4 will involve second and fifth graders and will test the optimal order in which integer addition and subtraction problems are presented in contrast with each other versus sequentially without contrasts. Using items that measure students? understanding of integers and integer operations, the PI will compare students' gains from pre-tests to post-tests between groups. Further, the investigator will qualitatively code students? solution strategies based on follow-up interviews and written work for additional information on the differences between groups. Following the experimental studies, the PI will work with elementary teachers over three lesson study cycles, during which teachers will implement instruction based on the prior studies? results. The PI will compare the performance of students who participate in the lesson study unit versus control classrooms to measure impact of the unit.

Videos of the lesson study unit, as well as the negative integer lesson plans will be made available for other teachers and teacher educators to use. Further, the investigator will incorporate the research results into an undergraduate mathematics methods course. To ensure that the results of this research reach a wider audience, the investigator will create an integer game and storybook, illustrating key concepts identified through the research, that parents can explore together with their children during family math nights and at home. On a broader scale, this project has the potential to illuminate ways to develop more coherence in the sequencing of mathematics topics to more effectively build on students? current understanding.

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