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Member Profile

Jinfa Cai


    • Roles: Project Researcher


  • Higher Ed: Mathematics, Higher Ed: Education 


Jinfa Cai is a Professor and Director of Secondary Mathematics Education at the University of Delaware. In 2000-2001, he was invited to Harvard University as a visiting Professor. In 1994, he earned a Ph. D. in the area of mathematics education from the University of Pittsburgh. His research interest is related to students's learning and mathematical problem solving. In particular, he is interested in how students learn mathematics and solve problems as well as how teachers and teaching impact students's learning and mathematical thinking. He has explored these questions in various educational contexts, both within and across nations. His work has been published in various research journals, including Journal for Research in Mathematics Education, Educational Studies in Mathematics, Journal of Mathematical Behavior, Mathematical Thinking and Learning, Mathematics Education Research Journal, International Review on Mathematics Education, International Journal of Mathematical Education in Science and Technology, International Journal of Educational Research, Research in Middle Level Education, Educational Measurement: Issues and Practice, and Phi Delta Kappan.

Jinfa has served on the Executive Board of American Educational Research Association's Special Interest Group for Research in Mathematics Education (2000-2002) and currently serves on the Editorial Boards of the Journal for Research in Mathematics Education (USA), Mathematics Education Research Journal (Australia), Zentralblatt fuer Didaktik der Mathematik (Germany), and International Journal of Mathematics Education (Singapore). He has chaired or organized over 10 symposiums or conferences, including 10th International Congress in Mathematics Instruction's Topic Study Group on Problem Solving Research in Mathematics Education, Copenhagen, Denmark, 4-11 July 2004. 


Cognitive studies of the teaching and learning of mathematics, studies of mathematical curriculum, Mathematical assessment, Cross-cultural studies, Problem solving, and Teacher education. 


Cai, J., Mamona, J. & Weber, K. (eds.) (2005). Mathematical problem solving research: What we know and where we are going. Journal of Mathematical Behavior, 24(3-4). Invited Guest Editors for the two Special Issues.

Cai, J. & Knuth, E. (ed.) (2005). Developing algebraic thinking: Multiple perspectives. Zentralblatt fuer Didaktik der Mathematik (International Review on Mathematics Education), 37(1). Invited Guest Editors for the Special Issue.

Fan, L., Wong, N-Y., Cai, J. & Li, S. (2004) (Eds.). How Chinese learn mathematics: Perspectives from insiders. Singapore: World Scientific Publishers.

Cai, J. & Wang, T. (2006). U.S. and Chinese teachers' conceptions and constructions of representations: A case of teaching ratio concept. International Journal of Mathematics and Science Education, 4, 145-186.

Cai, J. & Lester, F. A. (2005). Solution and pedagogical representations in Chinese and U.S. mathematics classroom. Journal of Mathematical Behavior, 24 (3-4), 221-237.

Cifarelli, V & Cai, J. (2005). The evolution of mathematical explorations in open-ended problem solving situations. Journal of Mathematical Behavior, 24(3-4), 302-324.

Cai, J. & Cifarelli, V (2005). Exploring mathematical exploration: How do two college students formulate and solve their own mathematical problems? FOCUS on Learning Problems in Mathematics, 27(3), 43-72.

Silver, E. A. & Cai, J. (2005). Assessing students' mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.

Cai, J. (2005). U.S. and Chinese teachers' knowing, evaluating, and constructing representations in mathematics instruction. Mathematical thinking and Learning: An International Journal, 7(2), 135-169.

Cai, J. & Knuth, E. J. (2005). The development of students' algebraic thinking in earlier grades from curricular, instructional, and learning perspectives. Zentralblatt fuer Didaktik der Mathematik (International Review on Mathematics Education), 37(1), 1-4.

Cai, J., Lew, H. C., Morris, A., Moyer, J. C., Ng, S. F. & Schmittau, J. (2005). The Development of Students' Algebraic Thinking in Earlier Grades: A Cross-Cultural Comparative Perspective. Zentralblatt fuer Didaktik der Mathematik (International Review on Mathematics Education), 37(1), 5-15.

Cai, J. (2004). Why do U.S. and Chinese students think differently in mathematical problem solving? Exploring the impact of early algebra learning and teachers' beliefs. Journal of Mathematical Behavior, 23, 135-167.

Cai, J. (2003). Singaporean students' mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737.