The goal of this CAREER program of research is to identify, from a crosscultural 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.
CAREER: Algebraic Knowledge for Teaching: A CrossCultural Perspective
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 crosscultural 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 researchbased 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 designbased research method will be used to accomplish objectives #1 and #2. Crosscultural 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 reteach 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 districtuniversity collaboration, a noviceexpert teacher network, and crossdisciplinary 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
 Ding, M. (2021). Teaching early algebra through examplebased problem solving: Insights from Chinese and U.S. elementary classrooms. New York, NY: Routledge. https://www.routledge.com/TeachingEarlyAlgebrathroughExampleBased…
Journal Articles in English
 Ding, M., Li, X., ^{G} Hassler, R., & ^{G} Barnett, E. (2021). Understanding of the properties of operations: A crosscultural analysis. International Journal of Mathematical Education in Science and Technology, 52(1), 3964. doi: 10.1080/0020739X.2019.1657595. PDF
 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
 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, 105130. doi: 10.1080/10986065.2019.1570834 . PDF
 ^{G }Barnett, E., & Ding, M. (2019). Teaching of the associative property: A natural classroom investigation. Investigations of Mathematics Learning, 11, 148166. doi: 10.1080/19477503.2018.1425592 PDF
 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, 899921.doi: 10.1080/0020739X.2018.1426793 PDF
 Ding, M. (2018). Modeling with tape diagrams. Teaching Children Mathematics, 25, 158165. doi: 10.5951/teacchilmath.25.3.0158 PDF
 ^{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, 601632. doi: 10.1007/s115160180031z (*Both authors contributed equally). PDF
 Ding, M., & ^{G} Auxter, A. (2017). Children’s strategies to solving additive inverse problems: A preliminary analysis. Mathematics Education Research Journal, 29, 7392. doi:10.1007/s1339401701884 PDF
 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), 119. doi: 10.1186/s4059401600414 PDF
 Ding, M. (2016). Opportunities to learn: Inverse operations in U.S. and Chinese elementary mathematics textbooks. Mathematical Thinking and Learning, 18, 4568. 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.
 ^{G }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
 Ma, F. ( 2018) – Necessary algebraic knowledge for elementary teachers an ongoing crosscultural study. Educational Research and Evaluation (Elementary Education and Instruction), 2, 57. 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, 57. PDF
 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, 813. 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)，2，813. PDF
 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, 1419. 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，2，1419. PDF
 Wu, X. (2018). Mathematical representations and development of children’s mathematical thinking: A perspective of USChinese comparison. Educational Research and Evaluation (Elementary Education and Instruction), 2, 2024. 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, 2024. PDF
Dissertations
 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
 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 FirstGrade 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 crosscultural 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 crosscultural 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 crosscultural opportunitypropensity 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 Crosscultural analysis. Paper presented at 2018 NCTM conference. Washington, DC. PPT
 ^{G}Barnett, 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 DRK12 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 crosscultural perspective. Poster presentation at the NSF PI meeting, Washington, DC. Poster
 Ding, M. (symposium organizer, 2016, April). Early algebraic in elementary school: A crosscultural 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
Project Videos
2022 STEM for All Video Showcase
Title: Teaching Early Algebra through ExampleBased Problem Solving
Presenter(s): Meixia Ding & Cassy Pressimone Beckowski 
2018 STEM for All Video Showcase
Title: Videos as a Tool to Support Crosscultural Teacher Learning
Presenter(s): Meixia Ding, Eli Barnett, & Monica Manfredonia 
2016 STEM for All Video Showcase
Title: CAREER: Algebraic Knowledge for Teaching
Presenter(s): Meixia Ding & Ryan Hassler 
2015 STEM for All Video Showcase
Title: Algebraic Knowledge for Teaching
Presenter(s): Meixia Ding & Ryan Hassler 