Pedagogical Content Knowledge

Learning Labs: Using Videos, Exemplary STEM Instruction and Online Teacher Collaboration to Enhance K-2 Mathematics and Science Practice and Classroom Discourse

This project will develop and study two sets of instructional materials for K-2 teacher professional development in mathematics and science that are aligned with the CCSS and NGSS. Teachers will be able to review the materials online, watch video of exemplary teaching practice, and then upload their own examples and students' work to be critiqued by other teachers enrolled in professional learning communities as well as expert coaches.

Lead Organization(s): 
Award Number: 
1417757
Funding Period: 
Wed, 04/15/2015 to Sat, 03/31/2018
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. The investigators of this study propose to develop and study two sets of instructional materials for K-2 teacher professional development in mathematics and science that are aligned with the Common Core State Standards in Mathematics (CCSS) and the Next Generation Science Standards (NGSS). They will develop two modules in each subject area and an introductory module that prefaces and integrates the science and mathematics materials. Teachers will be able to review the materials online, watch video of exemplary teaching practice, and then upload their own examples and students' work to be critiqued by other teachers enrolled in professional learning communities as well as expert coaches. New instructional materials aligned with the standards are needed to assist teachers in meeting the challenging instructional practices recommended. To date, scant few resources of this type exist and, given many school districts have limited resources, more cost-effective forms of development such as this must be found. A particular strength of this project is that teachers will be able to engage in the courses online, on an ongoing basis and integrate what they have learned into their daily teaching practice.

The investigators propose a program of design research to develop and improve the modules. The central hypothesis is a test of the Teaching Channel model--that the modules and professional learning communities result in significant changes in the quality of instructional practice. Text analytics will be performed on the online discussion to detect changes in group discourse over time. Changes in instructional quality and vision will be measured by observing the videos posted by teachers. Pre-post tests of student work will be performed. The findings of the research will be disseminated through conference presentations, publications, and the Teaching Channel website.

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.

An Efficacy Study of the Learning and Teaching Geometry PD Materials: Examining Impact and Context-Based Adaptations

This study will examine the impact of the Learning and Teaching Geometry (LTG) professional development for secondary mathematics teachers on the teachers' knowledge and classroom instruction, as well as on their students' learning. As the nation invests vast resources in the professional development of teachers to meet new curriculum and instruction challenges, exploring the efficacy of professional development is important to understand how best to direct those resources.

Lead Organization(s): 
Award Number: 
1503399
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 (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. There are few examples of research that demonstrates causal impacts of professional development on teachers' knowledge and practice and student learning. This study will examine the impact of the Learning and Teaching Geometry (LTG) professional development for secondary mathematics teachers on the teachers' knowledge and classroom instruction, as well as on their students' learning. As the nation invests vast resources in the professional development of teachers to meet new curriculum and instruction challenges, exploring the efficacy of professional development is important to understand how best to direct those resources.

Using a cluster randomized design, the project will sample from 132 teachers (66 per condition) from 28 middle and high schools to participate in a 2-year implementation of the LTG professional development, facilitated by highly trained facilitators to study the efficacy of the materials. The project will monitor the fiedity of implementation of the LTG using a professional development session logging tool and Facilitator Interview Protocol. Outcome measures include measures of teacher knowledge, teaching practice, and student learning of geometry. Analyses will include two- and three-level hierarchical linear models to estimate the effects of participation in the LTG professional development and growth over time.

SmartCAD: Guiding Engineering Design with Science Simulations (Collaborative Research: Magana-de-Leon)

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: 
1503436
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.

Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods

This project will convene mathematics teacher educators with different theoretical perspectives to develop a shared menu of research-supported practices and new research questions to explore that could improve mathematics methods courses.

Award Number: 
1503358
Funding Period: 
Mon, 06/01/2015 to Tue, 05/31/2016
Full Description: 

Mathematics methods courses are a critical component of mathematics teacher education. One criticism of mathematics methods courses is that they vary widely across institutions and states. Mathematics methods courses differ with respect to what is taught, how it is taught, the intended learning goals, and how those learning goals are assessed. This variation is due, in part, to the different theoretical perspectives of mathematics teacher educators who teach these courses. The investigators of this Conference and Workshop grant propose to convene mathematics teacher educators with different theoretical perspectives to develop a shared menu of research-supported practices and new research questions to explore that could improve mathematics methods courses. The investigators' hypothesis is that by drawing from the research knowledge base when designing methods courses (using scholarly practices) and by studying these courses to add to the research knowledge base (conducting scholarly inquiry), mathematics teacher educators of any theoretical perspective can contribute to collective efforts to improve the quality and coherence of mathematics methods courses. The investigators intend to disseminate the conference findings to mathematics teacher educators and mathematics education researchers through conference presentations, publications, teacher educator association websites, and the project website. A particular strength of this work is that it addresses a need to prioritize scholarly practices and scholarly inquiry that could improve the quality and coherence of mathematics methods courses across theoretical perspectives, mathematics teacher educators, institutions, and states. 

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. Scholarly Inquiry and Practices (SIP) Conference for Mathematics Education Methods is a Conference and Workshop project that builds from the investigators' prior studies, which revealed compelling questions mathematics teacher educators and mathematics education researchers need to address in order to improve mathematics methods courses. The project will convene forty mathematics teacher educators who identify with social-political, situated, or cognitive theoretical orientations to set a direction for building scholarly inquiry and practices in mathematics methods courses. Before the conference, participants will author abstracts and reflections about their methods courses and will survey local mathematics teachers to identify critical issues they perceive with mathematics teacher education. At the conference, participants will identify with a preferred theoretical orientation and participate in discussions around four themes: theoretical perspectives; building scholarly practices; research for informing practice; and assessing impact and residue. Some participants will be selected to present their abstracts in poster presentation format. Investigators will provide additional commentary that highlight common ideas that emerge across perspectives. Participants will organize in thematic research and writing teams and continue to work after the conference on co-authoring articles and conference presentations. The articles will be disseminated in a comprehensive monograph or special issue in a research-focused journal. Investigators have been invited to also publish articles in practitioner-focused journals. Presentations at research and practitioner conferences are also planned.

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.

Design Technology and Engineering Education for English Learner Students: Project DTEEL

One significant challenge facing elementary STEM education is the varied preparation of English-language learners. The project addresses this with an innovative use of engineering curriculum to build on the English-language learners' prior experiences. The project will support teachers' learning about strategies for teaching English-language learners and using engineering design tasks as learning opportunities for mathematics, science and communication skills. 

Lead Organization(s): 
Award Number: 
1503428
Funding Period: 
Mon, 06/01/2015 to Thu, 05/31/2018
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. One significant challenge facing elementary STEM education is the varied preparation of English-language learners. The project addresses this with an innovative use of engineering curriculum to build on the English-language learners' prior experiences. The project will support teachers' learning about strategies for teaching English-language learners and using engineering design tasks as learning opportunities for mathematics, science and communication skills. 

The project's cross-disciplinary approach is grounded in both inquiry-based science education research and bilingual cognition research. These complementary foci bridge research areas to highlight how engineering experiences for students can capitalize on bilingual students' experiences as problem solvers. The project will develop teachers' ability and instructional efficacy for both STEM and bilingual student instruction. The project adapts a previously developed curriculum for engineering education by adding resources and tools to support bilingual students. The research design primarily measures teacher-level phenomenon such as implementation of instructional strategies, STEM self-efficacy and ability to address the academic development of bilingual students through engineering design activities. Data collected include classroom observations, teacher surveys, focus groups, and teacher interviews. Student assessments will be piloted in the final year of the project.

Refining a Model with Tools to Develop Math PD Leaders: An Implementation Study

This project will work with middle school mathematics teachers in San Francisco Unified School District to develop their capacity to conduct professional development for the teachers in their schools. A central goal of this project is to develop models and resources for effective professional development and preparation of professional development leaders in mathematics with special attention to students who are English language learners.

Lead Organization(s): 
Award Number: 
1417261
Funding Period: 
Thu, 01/01/2015 to Tue, 12/31/2019
Full Description: 

There is increased demand for K-12 teacher professional development that yields improvements in student learning and achievement. This need is particularly high given widespread adoption of the Common Core State Standards (CCSS) in mathematics which challenges teachers to incorporate mathematical thinking and problem solving into their instruction. The professional development challenge is exacerbated as our nation's demographics continue to shift, increasing the number of English language learners in school districts throughout the U.S. To meet this demand, the educational community must develop large-scale, system-level professional development programs aligned with the CCSS that are scalable and sustainable. The project team from Stanford University will work with middle school mathematics teachers in San Francisco Unified School District to develop their capacity to conduct professional development for the teachers in their schools. A central goal of this project is to develop models and resources for effective professional development and preparation of professional development leaders in mathematics with special attention to students who are English language learners. These models and resources will: provide school districts with the tools to build local capacity and provide sustainable professional development to all middle school mathematics teachers; improve the quality of teaching and, in turn, make important progress toward ensuring that all students in middle school can achieve the mathematical skills and understandings identified in the new standards; and meet the needs of English language learners. In addition, the Stanford team will contribute to the knowledge base in mathematics education, professional development and English language learners.

In previous work, the team developed two interconnected models--the Problem-Solving Cycle (PSC) and the Mathematics Leadership Preparation (MLP) models for preparing professional development leaders. The PSC model consists of a series of interconnected workshops organized around a problem that can be solved using multiple representations and solutions and can be adapted for multiple grade levels. Each cycle focuses on a different math problem. During the first cycle, teachers collaboratively solve the focal math problem and develop plans for teaching it to their students. Teachers then teach the lesson in their classes and the lessons are videotaped. Subsequent workshops focus on participants' classroom experiences teaching the problem. The goals of these workshops are to help teachers learn how to build on student thinking and to explore a variety of instructional practices. They rely heavily on video clips from the PSC lesson to foster productive conversations and situate the conversations in teachers' classroom instruction. The MLP model is designed to prepare Math Leaders to facilitate the PSC. The MLP prepares teachers to lead professional development for their colleagues. These models showed promise of effectiveness in improving middle school mathematics teachers' knowledge and practice, developing math professional development leaders, and improving student achievement. Investigators intend to refine and test the design of the PSC and MLP models and develop resources that can be used by other schools and districts, as well as conduct an evaluation of the work.

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

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

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