Achievement/Growth

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.

Zoombinis: The Full Development Implementation Research Study of a Computational Thinking Game for Upper Elementary and Middle School Learners

This project leverages an existing game by embedding tools for studying patterns of students' decision-making and problem solving in the environment. This allows researchers to understand how students learn about computational thinking within a tool that bridges informal and formal learning settings to engage a wide variety of students. The project will also develop tools and resources for classroom teachers.

Lead Organization(s): 
Award Number: 
1502882
Funding Period: 
Wed, 07/15/2015 to Sat, 06/30/2018
Full Description: 

The Logical Journey of the Zoombinis implementation research study examines the development of computational thinking for upper elementary and middle grades students. Computational thinking is the set of ideas and practices considered vital for computer science skills and has been attracting increased attention over the past several years in K-12 education. This project leverages an existing game by embedding tools for studying patterns of students' decision-making and problem solving in the environment. This allows researchers to understand how students learn about computational thinking within a tool that bridges informal and formal learning settings to engage a wide variety of students. The project will also develop tools and resources for classroom teachers. 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 research examines three questions. First, what strategies do players develop during Zoombinis gameplay that may provide evidence of implicit computational thinking? Second, how can teachers leverage implicit knowledge of computational thinking developed in Zoombinis to improve formal (explicit) learning? Third, how can a large-scale commercial game be used for broad and equitable improvement of computational thinking? The research uses and develops educational data mining techniques to assess students' learning in conjunction with pre-post computational thinking assessments (external to the game), teacher interviews, classroom observations, and case studies of classroom use. The goal is to understand both students' learning of computational thinking and how to bridge the formal and informal learning via classroom implementation of the Zoombinis game.

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.

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

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

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

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

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

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

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

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

Lead Organization(s): 
Award Number: 
1453493
Funding Period: 
Wed, 07/15/2015 to Tue, 08/31/2021
Full Description: 

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

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

 

CAREER: Exploring Beginning Mathematics Teachers' Career Patterns

Research increasingly provides insights into the magnitude of mathematics teacher turnover, but has identified only a limited number of factors that influence teachers' career decisions and often fails to capture the complexity of the teacher labor market. This project will address these issues, building evidence-based theories of ways to improve the quality and equity of the distribution of the mathematics teaching workforce. 

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1506494
Funding Period: 
Fri, 08/15/2014 to Fri, 07/31/2020
Full Description: 

Recruiting and retaining effective mathematics teachers has been emphasized in national reports as a top priority in educational policy initiatives. Research indicates that the average turnover rate is nearly 23% for beginning teachers (compared to 15% for veteran instructors); turnover rates for beginning mathematics teachers are even higher. Many mathematics teachers with three or fewer years' experience begin their careers in high-needs schools and often transfer to low-need schools at their first opportunity. This reshuffling, as effective teachers move from high- to low-need schools, exacerbates the unequal distribution of teacher quality, with important implications for disparities in student achievement. Research increasingly provides insights into the magnitude of mathematics teacher turnover, but has identified only a limited number of factors that influence teachers' career decisions and often fails to capture the complexity of the teacher labor market. Thus, it is essential to understand the features, practices, and local contexts that are relevant to beginning teachers' career decisions in order to identify relevant strategies for retention. This project will address these issues, building evidence-based theories of ways to improve the quality and equity of the distribution of the mathematics teaching workforce. This support for an early CAREER scholar in mathematics policy will enhance capacity to address issues in the future.

This work will be guided by three research objectives, to: (1) explore patterns in mathematics teachers' career movements, comparing patterns between elementary and middle school teachers, and between high- and low-need schools; (2) compare qualifications and effectiveness of teachers on different career paths (e.g., movement in/out of school, district, field); and (3) test a conceptual model of how policy-malleable factors influence beginning math teachers' performance improvement and career movements. The PI will use large-scale federal and state longitudinal data on a cohort of teachers who were first-year teachers in 2007-08 and taught mathematics in grades 3-8. Three samples will be analyzed separately and then collectively: a nationally representative sample from the Beginning Teacher Longitudinal Study (about 870 teachers who represent a national population of nearly 85,970); about 4,220 Florida teachers; and about 2,410 North Carolina teachers. In addition, the PI will collaborate with Education Policy Initiative at Carolina (EPIC) at UNC-Chapel Hill to collect new data from the 2015-16 cohort of first-year teachers in NC (about 800 teachers) and follow them for 2 years. The new data collection will provide detailed and reliable measures on the quality of both pre- and in-service teacher supports in order to understand how they may be linked to teachers' career movements and performance.

The original award # of this project was 1350158.

CAREER: L-MAP: Pre-service Middle School Teachers' Knowledge of Mathematical Argumentation and Proving

This program of research will examine how middle school pre-service teachers' knowledge of mathematical argumentation and proving develops in teacher preparation programs. The project explores the research question: What conceptions of mathematical reasoning and proving do middle school preservice teachers hold in situations that foster reasoning about change, proportionality, and proportional relationships, as they enter their mathematics course sequence in their teacher preparation program, and how do these conceptions evolve throughout the program?

Lead Organization(s): 
Award Number: 
1350802
Funding Period: 
Tue, 07/15/2014 to Tue, 06/30/2020
Full Description: 

The field of mathematics teacher education needs a strong understanding of pre-service teachers' knowledge about the practice of mathematical argumentation and proof, including the development of this knowledge, to effectively move pre-service teachers toward a more sophisticated understanding and enactment of this practice with their own students. The integrated research and educational activities will contribute to the knowledge base teacher education programs need to effectively prepare middle school teachers for meeting the challenges of how to make reasoning and proof an integral aspect of instructional practice. The research results have the potential to guide teacher educators and educational researchers concerned with strengthening pre-service teachers' ability to make reasoning and proving an integral aspect of school mathematics. Consequently, pre-service teachers will be better equipped to develop mathematical reasoning skills in their future students and to support their students in learning mathematics with understanding. Given this country's growing need for a competent STEM workforce, helping all students learn mathematics in a way that supports deeper understanding is a priority. Additionally, the support of early CAREER scholars in mathematics education will add to the capacity of the country to address issues in mathematics education in the future.

The objective of this program of research is to examine how middle school pre-service teachers' knowledge of mathematical argumentation and proving develops in teacher preparation programs. The project explores the research question: What conceptions of mathematical reasoning and proving do middle school preservice teachers hold in situations that foster reasoning about change, proportionality, and proportional relationships, as they enter their mathematics course sequence in their teacher preparation program, and how do these conceptions evolve throughout the program? This development will be studied along three dimensions: (a) pre-service teachers' own ability to formulate mathematical arguments, (b) their ability to analyze mathematical arguments, and (c) their ability to analyze situations that engage students in mathematical argumentation and proving. Cross-sectional and longitudinal studies of 60 pre-service teachers' models, or systems of interpretation, of mathematical argumentation and proof in curricular context that foster reasoning about change, proportionality and proportional relationships will be conducted to provide an understanding of the trajectory that captures how pre-service teachers develop their knowledge of mathematical argumentation and proving throughout their university mathematics preparation program and into their student teaching.

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 Fri, 04/30/2021
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 Fri, 07/31/2020
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

      Learning about Ecosystems Science and Complex Causality through Experimentation in a Virtual World

      This project will develop a modified virtual world and accompanying curriculum for middle school students to help them learn to more deeply understand ecosystems patterns and the strengths and limitations of experimentation in ecosystems science. The project will build upon a computer world called EcoMUVE, a Multi-User Virtual Environment or MUVE, and will develop ways for students to conduct experiments within the virtual world and to see the results of those experiments.

      Project Email: 
      Lead Organization(s): 
      Award Number: 
      1416781
      Funding Period: 
      Mon, 09/01/2014 to Thu, 08/31/2017
      Full Description: 

      EcoXPT from videohall.com on Vimeo.

      Comprehending how ecosystems function is important knowledge for citizens in making decisions and for students who aspire to become scientists. This understanding requires deep thinking about complex causality, unintended side-effects, and the strengths and limitations of experimental science. These are difficult concepts to learn due to the many interacting components and non-linear interrelationships involved. Ecosystems dynamics is particularly difficult to teach in classrooms because ecosystems involve complexities such as phenomena distributed widely across space that change over long time frames. Learning when and how experimental science can provide useful information in understanding ecosystems dynamics requires moving beyond the limited affordances of classrooms. The project will: 1) advance understanding of experimentation in ecosystems as it can be applied to education; 2) show how student learning is affected by having opportunities to experiment in the virtual world that simulate what scientists do in the real world and with models; and 3) produce results comparing this form of teaching to earlier instructional approaches. This project will result in a learning environment that will support learning about the complexities of the earth's ecosystem.

      The project will build upon a computer world called EcoMUVE, a Multi-User Virtual Environment or MUVE, developed as part of an earlier NSF-funded project. A MUVE is a simulated world in which students can virtually walk around, make observations, talk to others, and collect data. EcoMUVE simulates a pond and a forest ecosystem. It offers an immersive context that makes it possible to teach about ecosystems in the classroom, allowing exploration of the complexities of large scale problems, extended time frames and and multiple causality. To more fully understand how ecosystems work, students need the opportunity to experiment and to observe what happens. This project will advance this earlier work by developing ways for students to conduct experiments within the virtual world and to see the results of those experiments. The project will work with ecosystem scientists to study the types of experiments that they conduct, informing knowledge in education about how ecosystem scientists think, and will build opportunities for students that mirror what scientists do. The project will develop a modified virtual world and accompanying curriculum for middle school students to help them learn to more deeply understand ecosystems patterns and the strengths and limitations of experimentation in ecosystems science. The resulting program will be tested against existing practice, the EcoMUVE program alone, and other programs that teach aspects of ecosystems dynamics to help teachers know how to best use these curricula in the classroom.

      Pages

      Subscribe to Achievement/Growth