Low Socio-economic Status Students

Playing with the Data: Developing Digital Supports for Middle School Science Teachers using Game-based Formative Assessment

This project will use cycles of design-based research to build new knowledge about how to facilitate teachers' interpretation and use of digital game-based formative assessment data. The research will also inform the revision and expansion of Playfully, an existing, online data-reporting dashboard that can be used with multiple digital games.

Award Number: 
1503255
Funding Period: 
Wed, 07/01/2015 to Sat, 06/30/2018
Full Description: 

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.

This project will use cycles of design-based research to build new knowledge about how to facilitate teachers' interpretation and use of digital game-based formative assessment data. The research will also inform the revision and expansion of Playfully, an existing, online data-reporting dashboard that can be used with multiple digital games. The project is a collaboration between researchers at Education Development Center Inc.'s Center for Children and Technology (EDC|CCT) and the assessment and game development teams at GlassLab. The research and development teams will engage in a three-year partnership with 60 middle-grade science teachers working in diverse school settings in different parts of the country. The aim of the project is to refine an online formative assessment platform that utilizes data from a video game designed to teach argumentation at the middle school level. It provides rigorous research on the design features of data tools and associated materials available to teachers to inform their ongoing instruction (i.e., formative assessment tools) when using game-based platforms.

Dissemination of the results of this project will include practical, evidence-based suggestions for supporting middle school science teachers' use of digital games for assessment, and for the design and implementation of data dashboards. Key audiences include educational game designers, game-based assessment developers, formative assessment experts, and leaders in middle grade science teaching and learning.

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

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

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

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

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

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.

Tools for Teaching and Learning Engineering Practices: Pathways Towards Productive Identity Work in Engineering

Identifying with engineering is critical to help students pursue engineering careers. This project responds to this persistent large-scale problem. The I-Engineering framework and tools address both the learning problem (supporting students in learning engineering design) and the identity problem (supporting students in recognizing that they belong in engineering). 

Lead Organization(s): 
Award Number: 
1502755
Funding Period: 
Fri, 05/01/2015 to Tue, 04/30/2019
Full Description: 

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. Identifying with engineering is critical to help students pursue engineering careers. This project responds to this persistent large-scale problem. The I-Engineering framework and tools address both the learning problem (supporting students in learning engineering design) and the identity problem (supporting students in recognizing that they belong in engineering). I-Engineering will support identity development as a part of learning two core practices in engineering: 1) defining problems and 2) designing solutions. In particular, the I-Engineering framework and tools will help middle grades teachers and students engage in the engineering design process using meaningful, authentic and often youth-driven contexts. The project will ground this work in two engineering design challenges: 1) safe and green commutes and 2) portable energy, both of which exemplify engineering for sustainable communities. The objectives are to: 1) To develop research-based understandings of how to support identity development among middle school students from underrepresented backgrounds in the context of learning engineering. 2) To develop and refine a framework and tools (I-Engineering) in support of student learning and identity development in engineering with a focus on sustainability. 3) To collaborate with grades 6 and 7 teachers to implement and refine I-Engineering for classroom use. 4) To study whether the I-Engineering framework/tools support identity development in engineering among middle school students from underrepresented backgrounds. 

The project draws upon design-based implementation research to develop and test the I-Engineering framework and tools among students and teachers in grades 6 and 7. Using social practice theory, how aspects of the learning environment shape identity development will be identified, yielding information on the impact of the instructional tools generated. The research questions are grounded in two areas: supporting identity development in engineering, understanding how students progress in their engineering development and patterns across implementation of the I-Engineering resources. Studies will shed light on mechanisms that support identity development in engineering, how that might be scaffolded, and how such scaffolds can transport across context. The mixed-method student- and classroom-level studies will allow for empirical claims regarding how and under what conditions youth from underrepresented backgrounds may progress in their identity development in engineering. The research plan includes student case studies drawing on task-based interviews, observations and student work and classroom studies using observations, student and teacher interviews, an engineering identity survey, student work and formative assessments of engineering practices. I-Engineering will reach over 500 students and their teachers in schools that serve predominantly underrepresented populations. The project team will disseminate the findings, framework and tools in support of teaching engineering practices, and promoting understanding of the importance of identity development in broadening participation.

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.

Precision Math: Using Interactive Gaming Technology to Build Student Proficiency in the Foundational Concepts and Problem Solving Skills of Measurement and Data Analysis

The purpose of this 4-year project is to improve student mathematics achievement by developing a mathematics intervention focused on key measurement and data analysis skills. The PM intervention will be designed for first and second grade students who are experiencing mathematics difficulties. To increase student mathematics achievement, the intervention will include: (a) a technology-based component and (b) hands-on activities.

Lead Organization(s): 
Award Number: 
1503161
Funding Period: 
Wed, 07/01/2015 to Sun, 06/30/2019
Full Description: 

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools. 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.

Strong knowledge of measurement and data analysis is essential to ensure competiveness of the nation as a whole and full access to educational and work opportunities for all students. Despite this importance, a considerable number of U.S. students, particularly students from poor and minority backgrounds, struggle with these two areas of mathematics. The purpose of this 4-year Research and Development project, Precision Mathematics (PM): Building Student Proficiency in the Foundational Concepts and Problem Solving Skills of Measurement and Data Analysis, is to improve student mathematics achievement by developing a mathematics intervention focused on key measurement and data analysis skills. The PM intervention will be designed for first and second grade students who are experiencing mathematics difficulties. To increase student mathematics achievement, the intervention will include: (a) a technology-based component that will provide students with individualized instruction and (b) hands-on activities that will offer opportunities for students to interact with their teacher and peers around critical measurement and data analysis concepts. Primary activities of the project will include intervention development, pilot testing, data analysis, and intervention revision. One primary benefit of PM is that it will provide struggling learners with meaningful access to critical concepts and skills identified in the Common Core State Standards Initiative. Another benefit is that will be designed to serve as a foundation for students to understand more advanced mathematical concepts introduced in the later grades. PM has the potential to address a concerning gap in U.S. education. To date, intervention research focused on measurement and data analysis is scant.

Proficiency with measurement and data analysis is essential for obtaining occupations in the STEM fields. A primary aim of this project is to develop PM, a mathematics intervention designed to teach key concepts of measurement and data analysis to at-risk 1st and 2nd grade students. Comprising the intervention will be technology-based and collaborative problem-solving activities. At each grade, the intervention will provide 20 hours of instruction focused on topics identified in the Common Core State Standards. A primary aim of the project is to develop the intervention using a design science approach, including a mix of qualitative and quantitative research methods that will guide iterative testing and revision cycles. A second primary aim is to test the promise of the intervention to improve student mathematics achievement. Rigorous pilot studies (i.e., randomized controlled trials) will be conducted in 1st and 2nd grade classrooms involving over 700 at-risk students. Within classrooms, students will be randomly assigned to treatment (PM) or control conditions (business as usual). Two research questions will be addressed: (a) What is the potential promise of the intervention when delivered in authentic education settings? (b) Based on empirical evidence, are revisions to the intervention's theory of change necessary? Tests of main effects of intervention effects will be conducted using analysis of covariance models, adjusting for pretest scores. Generated findings are anticipated to contribute to the knowledge base on early STEM learning for at-risk learners.

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.

CAREER: Algebraic Knowledge for Teaching: A Cross-Cultural Perspective

The goal of this CAREER program of research is to identify, from a cross-cultural perspective, essential Algebraic Knowledge for Teaching (AKT) that will enable elementary teachers to better develop students' algebraic thinking. This study explores AKT based on integrated insights of the U.S. and Chinese expert teachers' classroom performance.

Lead Organization(s): 
Award Number: 
1350068
Funding Period: 
Fri, 08/15/2014 to Wed, 07/31/2019
Full Description: 

What content knowledge is needed for the teaching of mathematics? What practices are more effective for realizing student success? These questions have received considerable attention in the mathematics education community. The goal of this CAREER program of research is to identify, from a cross-cultural perspective, essential Algebraic Knowledge for Teaching (AKT) that will enable elementary teachers to better develop students' algebraic thinking. Focusing on two fundamental mathematical ideas recently emphasized by the Common Core State Standards - inverse relations and properties of operations - this study explores AKT based on integrated insights of the U.S. and Chinese expert teachers' classroom performance. It will be focused on three objectives: (1) identify AKT that facilitates algebraic thinking and develop preliminary findings into teaching materials; (2) refine research-based teaching materials based on the evaluative data; and (3) integrate research with education through course development at Temple University and teacher outreach in Philadelphia.

The model underlying this research program is that improved pedagogy will improve student learning, both directly and indirectly. A design-based research method will be used to accomplish objectives #1 and #2. Cross-cultural videotaped lessons will be first analyzed to identify AKT, focusing on teachers' use of worked examples, representations, and deep questions. This initial set of findings will then be developed into teaching materials. The U.S. and Chinese expert teachers will re-teach the lessons as part of the refinement process. Data sources will include: baseline and updated survey data (control, context, and process variables), observation, documents, videos, and interviews. The statistical techniques will include descriptive and inferential statistics and HLM will to address the hierarchical nature of the data.

This project involves students and teachers at various levels (elementary, undergraduate, and graduate) at Temple University and the School District of Philadelphia (SDP) in the U.S. and Nanjing Normal University and Nantong School District in China. A total of 600 current and future elementary teachers and many of their students will benefit directly or indirectly from this project. Project findings will be disseminated through various venues. Activities of the project will promote school district-university collaboration, a novice-expert teacher network, and cross-disciplinary and international collaboration. It is anticipated that the videos of expert teaching will also be useful future research by cognitive researchers studying ways to improve mathematics learning.

Publications
G indicates graduate student author; U indicates undergraduate student author

Journal Articles in English

  1. Ding, M., G Chen, W., & G Hassler, R. (2019). Linear quantity models in the US and Chinese elementary mathematics classrooms. Mathematical Thinking and Learning, 21, 105-130 doi: 10.1080/10986065.2019.1570834 . PDF
  2. Barnett, E., & Ding, M. (2019). Teaching of the associative property: A natural classroom investigation. Investigations of Mathematics Learning, 11, 148-166. doi: 10.1080/19477503.2018.1425592  PDF
  3. Ding, M., & G Heffernan, K. (2018). Transferring specialized content knowledge to elementary classrooms: Preservice teachers’ learning to teach the associative property. International Journal of Mathematics Educational in Science and Technology, 49, 899-921.doi: 10.1080/0020739X.2018.1426793 PDF
  4. Ding, M. (2018). Modeling with tape diagrams. Teaching Children Mathematics25, 158-165. doi: 10.5951/teacchilmath.25.3.0158  PDF
  5. G Chen, W., & Ding, M.* (2018). Transitioning from mathematics textbook to classroom instruction: The case of a Chinese expert teacher. Frontiers of Education in China, 13, 601-632. doi: 10.1007/s11516-018-0031-z (*Both authors contributed equally). PDF
  6. Ding, M., & G Auxter, A. (2017). Children’s strategies to solving additive inverse problems: A preliminary analysis. Mathematics Education Research Journal, 29, 73-92. doi:10.1007/s13394-017-0188-4  PDF
  7. Ding, M. (2016).  Developing preservice elementary teachers’ specialized content knowledge for teaching fundamental mathematical ideas: The case of associative property. International Journal of STEM Education, 3(9), 1-19doi: 10.1186/s40594-016-0041-4  PDF
  8. Ding, M. (2016). Opportunities to learn: Inverse operations in U.S. and Chinese elementary mathematics textbooks. Mathematical Thinking and Learning, 18, 45-68. doi: 10.1080/10986065.2016.1107819  PDF

Journal Articles in Chinese
Note: The Chinese journals Educational Research and Evaluation (Elementary Education and Instruction教育研究与评论 (小学教育教学) and Curriculum and Instructional Methods (课程教材教法) are both official, core journals in mathematics education field in China.

  1. Chen, W. (2018). Strategies to deal with mathematical representations – an analysis of expert’s classroom instruction. Curriculum and Instructional Methods. 数学教学的表征处理策略——基于专家教师的课堂教学分析. 课程教材教法. PDF
  2. Ma, F. ( 2018) – Necessary algebraic knowledge for elementary teachers- an ongoing cross-cultural study. Educational Research and Evaluation (Elementary Education and Instruction), 2, 5-7.  小学教师必备的代数学科知识-跨文化研究进行时。教育研究与评论 (小学教育教学), 2, 5-7. PDF
  3. Chen, J. (2018) Infusion and development of children’s early algebraic thinking – a comparative study of the US and Chinese elementary mathematics teaching. Educational Research and Evaluation (Elementary Education and Instruction), 2, 8-13.  儿童早期代数思维的渗透与培养-中美小学数学教学比较研究。教育研究与评论(小学教育教学),28-13.  PDF
  4. Zong, L. (2018). A comparative study on the infusion of inverse relations in the US and Chinese classroom teaching. Educational Research and Evaluation (Elementary Education and Instruction), 2, 14-19.  中美逆运算渗透教学对比研究。教育研究与评论(小学教育教学,2,14-19.  PDF
  5. Wu, X. (2018). Mathematical representations and development of children’s mathematical thinking: A perspective of US-Chinese comparison. Educational Research and Evaluation (Elementary Education and Instruction), 2, 20-24.  数学表征与儿童数学思维发展-基于中美比较视角。教育研究与评论(小学教育教学,2, 20-24.  PDF

Dissertations

  1. Hassler, R. (2016). Mathematical comprehension facilitated by situation models: Learning opportunities for inverse relations in elementary school.Published dissertation, Temple University, Philadelphia, PA. (Chair: Dr. Meixia Ding)  PDF
  2. Chen, W. (2018). Elementary mathematics teachers’ professional growth: A perspectives of TPACK (TPACK 视角下小学数学教师专业发展的研究). Dissertation, Nanjing Normal University. Nanjing, China. PDF

National Presentations
G indicates graduate student author; U indicates undergraduate student author

  • Ding, M (symposium organizer, 2019, April). Enhancing elementary mathematics instruction: A U.S.-China collaboration. Papers presented at NCTM research conference (Discussant: Jinfa Cai). (The following three action research papers were written by my NSF project teachers under my guidance).
      • Milewski Moskal, M., & Varano, A. (2019). The teaching of worked examples: Chinese approaches in U.S. classrooms. Paper 
      • Larese, T., Milewski Moskal, M., Ottinger, M., & Varano, A., (2019). Introducing Investigations math games in China: Successes and surprises. Paper
      • Murray, D., Seidman, J., Blackmon, E., Maimon, G., & Domsky, A. (2019). Mathematic instruction across two cultures: A teacher perspective. Paper
    • Ding, M., & Ying Y. (2018, June). CAREER: Algebraic knowledge for teaching: A cross-cultural perspective. Poster presentation at the National Science Foundation (NSF) PI meeting, Washington, DC.  Poster
    • Ding, M., Brynes, J., G Barnett, E., & Hassler, R. (2018, April). When classroom instruction predicts students’ learning of early algebra: A cross-cultural opportunity-propensity analysis. Paper presented at 2018 AERA conference. New York, NY.  Paper
    • Ding, M., Li, X., Manfredonia, M., & Luo, W. (2018, April). Video as a tool to support teacher learning: A Cross-cultural analysis. Paper presented at 2018 NCTM conference. Washington, DC.  PPT
    • GBarnett, E., & Ding, M. (2018, April). Teaching the basic properties of arithmetic: A natural classroom investigation of associativity. Poster presentation at 2018AERA conference, New York, NY.  Poster
    • Hassler, R., & Ding, M. (2018, April). The role of deep questions in promoting elementary students’ mathematical comprehension. Poster presentation at 2018AERA conference, New York, NY.
    • Ding, M., G Chen, W., G Hassler, R., Li, X., & G Barnett, E. (April, 2017). Comparisons in the US and Chinese elementary mathematics classrooms. Poster presentation at AERA 2017 conference (In the session of “Advancing Mathematics Education Through NSF’s DRK-12 Program”). San Antonio, TX. Poster
    • Ding, M., Li, X., G Hassler, R., & G Barnett, E. (April, 2017). Understanding the basic properties of operations in US and Chinese elementary School. Paper presented at AERA 2017 conference. San Antonio, TX.  Paper
    • Ding, M., G Chen, W., & G Hassler, R. (April, 2017). Tape diagrams in the US and Chinese elementary mathematics classrooms. Paper presented at NCTM 2017 conference. San Antonio, TX.  Paper
    • Ding, M., & G Hassler, R. (2016, June). CAREER: Algebraic knowledge for teaching in elementary school: A cross-cultural perspective. Poster presentation at the NSF PI meeting, Washington, DC. Poster
    • Ding, M. (symposium organizer, 2016, April). Early algebraic in elementary school: A cross-cultural perspective. Proposals presented at 2016 AERA conference, Washington, DC.
        • Ding, M. (2016, April). A comparative analysis of inverse operations in U.S. and Chinese elementary mathematics textbooks. Paper 
        • G Hassler, R. (2016, April). Elementary Textbooks to Classroom Teaching: A Situation Model Perspective. Paper
        • G Chen, W., & Ding, M. (2016, April). Transitioning textbooks into classroom teaching: An action research on Chinese elementary mathematics lessons. Paper
        • Li, X., G Hassler, R., & Ding, M. (2016, April). Elementary students’ understanding of inverse relations in the U.S. and China.  Paper
        • Stull, J., Ding, M., G Hassler, R., Li, X., & U George, C. (2016, April). The impact of algebraic knowledge for teaching on student learning: A Preliminary analysis. Paper
      • Ding, M., G Hassler, R., Li., X., & G Chen, W. (2016, April). Algebraic knowledge for teaching: An analysis of US experts' lessons on inverse relations. Paper presented at 2016 NCTM conference, San Francisco, CA. Paper
      • G Hassler. R., & Ding, M. (2016, April). Situation model perspective on mathematics classroom teaching: A case study on inverse relations. Paper presented at 2016 NCTM conference, San Francisco, CA.  Paper
      • Ding, M., & G Copeland, K. (2015, April). Transforming specialized content knowledge: Preservice elementary teachers’ learning to teach the associative property of multiplication. Paper presented at AERA 2015 conference, Chicago, IL. Paper PPT
      • Ding, M., & G Auxter, A. (2015, April). Children’s strategies to solving additive inverse problems: A preliminary analysis. Paper presented at AERA 2015 conference, Chicago, IL.  Paper

      Pages

      Subscribe to Low Socio-economic Status Students