Reasoning Skills

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.

SmartCAD: Guiding Engineering Design with Science Simulations (Collaborative Research: Xie)

This project investigates how real time formative feedback can be automatically composed from the results of computational analysis of student design artifacts and processes with the envisioned SmartCAD software. The project conducts design-based research on SmartCAD, which supports secondary science and engineering with three embedded computational engines capable of simulating the mechanical, thermal, and solar performance of the built environment.

Lead Organization(s): 
Award Number: 
1503196
Funding Period: 
Mon, 06/15/2015 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. 

In this project, SmartCAD: Guiding Engineering Design with Science Simulations, the Concord Consortium (lead), Purdue University, and the University of Virginia investigate how real time formative feedback can be automatically composed from the results of computational analysis of student design artifacts and processes with the envisioned SmartCAD software. Through automatic feedback based on visual analytic science simulations, SmartCAD is able to guide every student at a fine-grained level, allowing teachers to focus on high-level instruction. Considering the ubiquity of CAD software in the workplace and their diffusion into precollege classrooms, this research provides timely results that could motivate the development of an entire genre of CAD-based learning environments and materials to accelerate and scale up K-12 engineering education. The project conducts design-based research on SmartCAD, which supports secondary science and engineering with three embedded computational engines capable of simulating the mechanical, thermal, and solar performance of the built environment. These engines allow SmartCAD to analyze student design artifacts on a scientific basis and provide automatic formative feedback in forms such as numbers, graphs, and visualizations to guide student design processes on an ongoing basis. 

The research hypothesis is that appropriate applications of SmartCAD in the classroom results in three learning outcomes: 1) Science knowledge gains as indicated by a deeper understanding of the involved science concepts and their integration at the completion of a design project; 2) Design competency gains as indicated by the increase of iterations, informed design decisions, and systems thinking over time; and 3) Design performance improvements as indicated by a greater chance to succeed in designing a product that meets all the specifications within a given period of time. While measuring these learning outcomes, this project also probes two research questions: 1) What types of feedback from simulations to students are effective in helping them attain the outcomes? and 2) Under what conditions do these types of feedback help students attain the outcomes? To test the research hypothesis and answer the research questions, this project develops three curriculum modules based on the Learning by Design (LBD) Framework to support three selected design challenges: Solar Farms, Green Homes, and Quake-Proof Bridges. This integration of SmartCAD and LBD situate the research in the LBD context and shed light on how SmartCAD can be used to enhance established pedagogical models such as LBD. Research instruments include knowledge integration assessments, data mining, embedded assessments, classroom observations, participant interviews, and student questionnaires. This research is carried out in Indiana, Massachusetts, and Virginia simultaneously, involving more than 2,000 secondary students at a number of socioeconomically diverse schools. Professional development workshops are provided to familiarize teachers with SmartCAD materials and implementation strategies prior to the field tests. An external Critical Review Committee consisting of five engineering education researchers and practitioners oversee and evaluate this project formatively and summative. Project materials and results are disseminated through publications, presentations, partnerships, and the Internet.

Scientific Data in Schools: Measuring the Efficacy of an Innovative Approach to Integrating Quantitative Reasoning in Secondary Science (Collaborative Research: Stuhlsatz)

Lead Organization(s): 
Award Number: 
1503005
Funding Period: 
Wed, 07/15/2015 to Fri, 05/31/2019
Project Evaluator: 
Kristin Bass
Full Description: 

The goal of this project is to investigate whether the integration of real data from cutting-edge scientific research in grade 6-10 classrooms will increase students’ quantitative reasoning ability in the context of science. Data Nuggets are activity-based resources that address current needs in STEM education and were developed by science graduate students and science teachers at Michigan State University through prior support from the NSF GK-12 program and the BEACON Center for the Study of Evolution in Action. The goal of Data Nuggets is to engage students in the practices of science through an innovative approach that combines scientific content from authentic research with key concepts in quantitative reasoning. Partners from Michigan State University and BSCS will adapt the materials to address current science and mathematics standards, create a professional development program for teachers, and test the efficacy of the materials through a cluster-randomized trial in the classrooms of 30 teachers in Michigan, Colorado, and California.

The project will study whether short, targeted interventions of classroom activities embedded within a typical curriculum can impact student outcomes. Prior to the study teachers will participate in professional development. Classrooms of the teachers in the study will be randomly assigned to either a treatment or comparison condition. Student outcome measures will include understanding of quantitative reasoning in the context of science, understanding of the practices and processes of science, student engagement and motivation, and interest in science.

In order to adequately train the next generation of citizens and scientists, research is needed on how quantitative reasoning skills build upon each other throughout K-16 science education Students need to experience activities that emphasize how science is conducted, and apply their understandings of how scientists reason quantitatively. Establishing the efficacy of Data Nuggets could provide the field with information about supplementing existing curriculum with short interventions targeted at particular scientific practices. By facilitating student access to authentic science, Data Nuggets bridge the gap between scientists and the public. Scientists who create Data Nuggets practice their communication skills and share both the process of science and research findings with K-12 students (and perhaps their families), undergraduates, and teachers, improving the understanding of science in society.

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: Advancing Secondary Mathematics Teachers' Quantitative Reasoning

Advancing Reasoning addresses the lack of materials for teacher education by investigating pre-service secondary mathematics teachers' quantitative reasoning in the context of secondary mathematics concepts including function and algebra. The project extends prior research in quantitative reasoning to develop differentiated instructional experiences and curriculum that support prospective teachers' quantitative reasoning and produce shifts in their knowledge.

Award Number: 
1350342
Funding Period: 
Tue, 07/15/2014 to Tue, 06/30/2020
Full Description: 

Science, Technology, Engineering and Mathematics [STEM] and STEM education researchers and policy documents have directed mathematics educators at all levels to increase emphasis on quantitative reasoning so that students are prepared for continued studies in mathematics and other STEM fields. Often, teachers are not sufficiently prepared to support their students' quantitative reasoning. The products generated by this project fill a need for concrete materials at the pre-service level that embody research-based knowledge in the area of quantitative reasoning. The accessible collection of research and educational products provides a model program for changing prospective mathematics teachers' quantitative reasoning that is adoptable at other institutions across the nation. 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.

Advancing Reasoning addresses the lack of materials for teacher education by investigating pre-service secondary mathematics teachers' quantitative reasoning in the context of secondary mathematics concepts including function and algebra. The project extends prior research in quantitative reasoning to develop differentiated instructional experiences and curriculum that support prospective teachers' quantitative reasoning and produce shifts in their knowledge. Three interrelated research questions guide the project: (i) What aspects of quantitative reasoning provide support for prospective teachers' understanding of major secondary mathematics concepts such as function and algebra? (ii) How can instruction support prospective teachers' quantitative reasoning in the context of the teaching and learning of major secondary mathematics concepts such as function and algebra? (iii) How do the understandings prospective teachers hold upon entering a pre-service program support or inhibit their quantitative reasoning? Advancing Reasoning addresses these questions by enacting an iterative, multi-phase study with 200 prospective teachers enrolled in a secondary mathematics education content course over 5 years. The main phase of the study implements a series of classroom design experiments to produce knowledge on central aspects of prospective teachers' quantitative reasoning and the instructional experiences that support such reasoning. By drawing this knowledge from a classroom setting, Advancing Reasoning contributes research-based and practice-driven deliverables that improve the teaching and learning of mathematics.

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

Book

Journal Articles in English

  1. Ding, M., Li, X., G Hassler, R., & G Barnett, E. (2021). Understanding of the properties of operations: A cross-cultural analysis. International Journal of Mathematical Education in Science and Technology, 52(1), 39-64. doi: 10.1080/0020739X.2019.1657595. PDF
  2. Ding, M., G Hassler, R., & Li., X. (2020). Cognitive instructional principles in elementary mathematics classrooms: A case of teaching inverse relations. International Journal of Mathematical Education in Science and Technology. doi: 10.1080/0020739X.2020.1749319
  3. 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
  4. 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
  5. 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
  6. Ding, M. (2018). Modeling with tape diagrams. Teaching Children Mathematics25, 158-165. doi: 10.5951/teacchilmath.25.3.0158  PDF
  7. 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
  8. 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
  9. 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
  10. 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., G Spiro, B., & G Mochaourab, R. (2021). Promoting changes in elementary mathematics teaching: A case study. Presented at 2021 AERA annual conference (virtual).
  • Alibali, M. W., Ding, M., Yeo, A., Huang, H. & Meng, R. (2020, April) Linking Representations of Equality in First-Grade Mathematics Lessons in China [Roundtable Session]. AERA Annual Meeting San Francisco, CA http://tinyurl.com/sjs4ebe (Conference Canceled)
  • Ding, M. (2020, April). Worked examples in elementary mathematics classrooms: A cross-cultural analysis[Paper Session]. AERA Annual Meeting, San Francisco, CA (Conference Canceled).  Paper presented in AERA Interactive Presentation Gallery on July 31th 2020.
  • 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.

      Teacher Professional Development for Technology-enhanced Inquiry to Foster Students' 21st Century Learning

      This project will develop and evaluate a module for use in a 7th grade classroom that promotes student development of 21st Century skills with a particular focus on student development of scientific reasoning. The technology-enhanced curriculum will be designed to engage learners in deep and meaningful investigations to promote student learning of content in parallel with 21st century skills.

      Lead Organization(s): 
      Partner Organization(s): 
      Award Number: 
      1417983
      Funding Period: 
      Mon, 09/01/2014 to Fri, 08/31/2018
      Full Description: 

      The goal of this Exploratory Design and Development Teaching project is to develop and evaluate a module for use in a 7th grade classroom that promotes student development of 21st Century skills with a particular focus on student development of scientific reasoning. The technology-enhanced curriculum will be designed to engage learners in deep and meaningful investigations to promote student learning of content in parallel with 21st century skills. The module will be designed using principles of inquiry-based learning as well as the principles of universal design for learning (UDL). The motivation behind this project is that it will directly contribute to the limited research on the interventions that impact teachers' capacity to provide high quality 21st century STEM education to all students, with a specific focus on underrepresented minorities and those with disabilities. The classroom setting for which the curriculum will be delivered is within an urban district which includes a large number of minority students and over 20% students with specific learning disabilities. The project will catalyze students' deep understanding of content knowledge while developing 21st century skills in parallel; hence better preparing students for sustainable learning experiences into high school and beyond.

      A study will be conducted to determine the effectiveness of the learning modules on classroom practices as well as student learning. A mixed methods design involving multiple measures will provide insights into changes in teachers' content knowledge, teaching practices that include a focus on 21st century learning, and fidelity of use of the TI21 framework for implementation of the learning activities. Pre- and post-testing of students using a scientific reasoning assessment and surveys on attitudes towards STEM, along with validated and widely used concept inventories, will provide further measures. As part of this exploratory project, the design and validity of instruments for use with the targeted population, which includes students with specific learning disabilities, will be further tested. This will include administering some of the assessments through web-based apps to meet the needs of these students. The learning modules, with embedded assessments and web-based apps, will provide an innovative approach in which transferable 21st century skills can be developed and measured. Outcomes of this project will be disseminated throughout the urban school system and therefore have the ability to impact thousands of other students (mostly minorities and many with disabilities) and their science, math, and technology teachers. Project outcomes will also inform the development of future science and/or modules for use in similar urban classroom settings.

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