Jinfa Cai - Papers

Publications (since 1994)

Research Monograph

Cai, J. (2007). A series of empirical studies of U.S. and Chinese students’ learning of mathematics. Beijing, China: Educational Sciences Publishing House.

Cai, J. (1995). A cognitive analysis of U.S. and Chinese students' mathematical performance on tasks involving computation, simple problem solving, and complex problem solving. ( Journal for Research in Mathematics Education monograph series 7), Reston, VA: National Council of Teachers of Mathematics. 160 pages.

Journal Special Issues Edited

Cai, J. (ed.) (2004). Developing algebraic thinking in the earlier grades: Case studies of the Chinese, Russian, Singaporean, South Korean, and U.S. school mathematics. Journal of Mathematics Educators ( Singapore), 8(1). Invited Guest Editor for the Special Issue.

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.

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. (accepted, in preparation to be published in the second issue of 2007). What is Effective Mathematics Teaching? A Dialogue between East and West. Zentralblatt fuer Didaktik der Mathematik ( International Review on Mathematics Education). Invited Guest Editor for the Special Issue.

Refereed Journal Articles

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. & Brooke, M. (2006). New perspectives of looking back in mathematical problem solving. Mathematics Teaching, 196, 42-45.

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. (2004). Developing algebraic thinking in the earlier grades: A case study of the Chinese mathematics curriculum. Journal of Mathematics Educators ( Singapore), 8(1), 107-130.

Cai, J. (2004). Introduction to the Special Issue on developing algebraic thinking in the earlier grades from an international perspective. Journal of Mathematics Educators ( Singapore), 8(1), 1-5.

Lo, J. J., Watanabe, T., & Cai, J. (2004). The development of ratio concepts: An Asian perspective. Mathematics Teaching in Middle School, 9 (7), 362-367.

Moyer, J. C., Huinker, D., & Cai, J. (2004). Developing algebraic thinking in the earlier grades: A case study of the U.S.Investigation series. Journal of Mathematics Educators ( Singapore), 8(1), 6-38.

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.

Cai, J. (2003). Investigating parental roles in students’ learning of mathematics from a cross-national perspective. Mathematics Education Research Journal, 15 (2), 87-106.

Cai, J. & Sloyer, C. W. (2003). Making indirect reasoning accessible: A problem-based learning approach. EduMath, 17, 2-15.

Cai, J. (2003). Setting the record straight or setting up a research agenda? A review of “Standards-Based School Mathematics Curricula: What Are They? What Do Students Learn?” Journal for Research in Mathematics Education, 34(3), 260-265.

Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students’mathematical problem solving and problem posing. Journal of Mathematical Behavior. 21(4), 401-421.

Cai, J., Lo, J. J. & Watanabe, T. (2002). Intended treatments of arithmetic average in U.S. and Asian school mathematics. School Science and Mathematics. 102(8), 391-404.

Cai, J. (2002). Assessing and understanding U.S. and Chinese students’ mathematical thinking: Some insights from cross-national studies. Zentralblatt fuer Didaktik der Mathematik ( International Review on Mathematics Education). 34(6), 278 – 290.

Cai, J. (2002). Exploring gender differences of U.S. and Chinese students in their solution processes of solving routine and nonroutine mathematical problems. Research in Middle Level Education ON_LINE. 26(1), 1-23.

Cai, J. (2001). Improving mathematics learning: Lessons from cross-national studies of U.S. and Chinese students. Phi Delta Kappan, 82(5), 400-405.

Cai, J. (2000). Understanding and representing the arithmetic averaging algorithm: An analysis and comparison of U.S. and Chinese students' responses. International Journal of Mathematical Education in Science and Technology, 31(6), 839-855.

Cai, J. (2000). Mathematical thinking involved in U.S. and Chinese students' solving process-constrained and process-open problems. Mathematical Thinking and Learning: An International Journal, 2, 309-340.

Cai, J. & Kenney, P. A. (2000). Fostering mathematical thinking through multiple solutions. Mathematics Teaching in the Middle School, 5(8), 534-539.

Cai, J., Moyer, J. C., Wang, N. (1999). Parental roles in students' learning of mathematics: An exploratory study. Research in Middle Level Education, 22(3), 1-18.

Cai, J., Moyer, J. C., & Grochowski, N. J. (1999). Making the mean meaningful: An instructional study. Research in Middle Level Education, 22 (4), 1-24.

Cai, J. (1998). An investigation of U.S. and Chinese students' mathematical problem posing and problem solving. Mathematics Education Research Journal, 10(1), 37-50.

Cai, J. (1998). Exploring students' conceptual understanding of the averaging algorithm. School Science and Mathematics, 98(2), 93-98.

Cai, J. (1998). Research into practice: Developing algebraic reasoning in the elementary grades. Teaching Children Mathematics, 5(4), 225-229.

Cai, J. (1997). Beyond computation and correctness: Contributions of open-ended tasks in examining U.S. and Chinese students' mathematical performance. Educational Measurement: Issues and Practice, 16(1), 5-11.

Cai, J. (1997). Learning mathematics through inventing in classroom. EduMath, 4, 51-62.

Parke, C. & Cai, J. (1997). Does the task truly measure what was intended? Mathematics Teaching in the Middle School, 3(1), 74-82.

Cai, J., Jakabcsin, S. M., & Lane, S. (1996). Assessing students' mathematical communication. School Science and Mathematics, 96(5), 238-246.

Cai, J., Magone, M., Wang, N., & Lane, S. (1996). A cognitive analysis of QUASAR's performance assessments and their sensitivity to measuring changes in middle school students' thinking. Research in Middle Level Education Quarterly, 19(3), 63-94.

Silver, E. A. & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539.

Cai, J., Magone, M., Wang, N., & Lane, S. (1996). Assessment: Describing student performance qualitatively. Mathematics Teaching in the Middle School, 1 (10), 828-835.

Cai, J. & Silver, E. A. (1995). Solution processes and interpretations of solutions in solving a division-with-remainder story problem: Do Chinese and U.S. students have similar difficulties? Journal for Research in Mathematics Education, 26(5), 491-497.

Silver, E. A., Leung, S. S., & Cai, J. (1995). Generating multiple solutions for a problem: A comparison of the responses of U.S. and Japanese students. Educational Studies in Mathematics, 28(1), 35-54.

Cai, J. (1994). A protocol-analytic study of metacognition in mathematical problem solving. Mathematics Education Research Journal, 6(2), 166-183.

Magone, M., Cai, J., Silver, E. A., & Wang, N., (1994). Validating the cognitive complexity and content quality of a mathematics performance assessment. International Journal of Educational Research, 12(3), 317-340.

Book Chapters

Cai, J. & Moyer, J. C. (In Press). Developing algebraic thinking in earlier grades: Some insights from international comparative studies. 2008 National Council of Teachers of Mathematics Yearbook.

Cai, J. & Lester, F. (in press). Contributions from cross-national comparative studies to the internationalization of mathematics education: Studies of Chinese and U.S. classrooms . In Bill Atweh (Ed.), Internationalisation and Globalisation in Mathematics and Science Education. New York, NY: Springer.

Cai, J. (2006). U .S. and Chinese teachers’ cultural values of representations in mathematics education. In F. K. S. Leung, K. D. Graf, & F. Lopez-Real (Eds), Mathematics education in different cultural traditions: A comparative study of East Asian and the West (pp. 465-482). New York, NY: Springer.

Cai, J. & Clark, J. (2005). Solving a pizza ratio problem: Searching for evidence why U.S. and Chinese students think differently. In Wong , N.Y. (Ed) (2005), Revisiting Mathematics Education in Hong Kong for the New Millennium (pp. 254-281). Hong Kong: Hong Kong Association for Mathematics Education.

Fan, L., Wong, N-Y., Cai, J. & Li, S. (2004). Focusing on Chinese way of learning: An introduction. In Fan, L., Wong, N-Y., Cai, J. & Li, S. (Eds.). How Chinese learn mathematics: Perspectives from insiders (pp. vii-xii)). Singapore: World Scientific Publishers.

Cai, J. & Cifarelli , V. (2004). Thinking mathematically by Chinese learners: An international comparative perspective. In Fan, L., Wong, N-Y., Cai, J. & Li, S. (Eds.). How Chinese learn mathematics: Perspectives from insiders (pp. 71-106). Singapore: World Scientific Publishers.

Cai, J., F-L Lin, & L. Fan (2004). Characterizing Chinese learners: Evidence-based insights and future research directions. In Fan, L., Wong, N-Y., Cai, J. & Li, S. (Eds.). How Chinese learn mathematics: Perspectives from insiders (pp. 535-554). Singapore: World Scientific Publishers.

Garddis, K., Lo, J., & Cai, J. (2004). Recommended resources in mathematics education. In K. K. Fowler, Using the mathematics literature (pp. 327-356). Marcel Dekker Publisher.

Cai, J. (2003). What research tells us about teaching mathematics through problem solving. In F. Lester (Ed.), Research and issues in teaching mathematics through problem solving (pp. 241-254). Reston, VA: National Council of Teachers of Mathematics.

Cai, J. & Sun, W. (2002). Developing students’ proportional reasoning: A Chinese perspective. In B. H. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios and proportions (pp. 195-205). National Council of Teachers of Mathematics 2002 Yearbook. Reston, VA: NCTM.

Cai, J. (2001). Having abilities to solve routine problems does not necessarily mean having abilities to solve nonroutine problems. In S. S. Leung (Ed.), Holistic review of the mathematics curriculum: What’s next? (pp. 70-82). Hong Kong: The Chinese University of Hong Kong and the Hong Kong Association for Mathematics Education.

Cai, J. (2001). Problem-based mathematics instruction: Challenges and Promises. In E. Pehkonen (ed.), Problem solving around the world (pp. 23-34). Faculty of Education, University of Turku, Finland, Report Series C: 14.

Cai, J., & Long, Y. (1999). Examining the differences of U.S. and Chinese students' mathematical cognition. In H. Zhang, Cai, J., & Wang, B. (Eds.), Cross-cultural studies in mathematics education (pp. 17-41). Guizhou Educational Press.

Cai, J. (1998). Building foundations for conceptual understanding of arithmetic average in the middle grades classroom. In Larry Leutzinger (Ed.), Mathematics in the Middle (pp. 201-215). Reston, VA: National Council of Teachers of Mathematics.

Cai, J. Moyer, J. C., Laughlin, C. (1998). Algorithms in solving non-routine mathematical problems. In L. J. Morrow (Ed.), The teaching and learning of algorithms in school mathematics (pp. 218 - 229). 1998 Yearbook of the National Council of Teachers of Mathematics. Reston, VA: NCTM.

Moyer, J. C., Cai, J., & Grampp, J. (1997). The gift of diversity in learning through mathematical exploration. In J. Trentacosta (Ed.), Multicultral and gender equity in the mathematics classroom: The gift of diversity (pp. 151-163). 1996 Yearbook of the National Council of Teachers of Mathematics. Reston, VA: NCTM.

Cai, J., Lane, S., & Jakabcsin, M. S. (1996). The role of open-ended tasks and holistic scoring rubrics: Assessing students' mathematical reasoning and communication. In P. C. Elliott (Ed.), Communication in mathematics: K-12 and beyond (pp. 137-145). 1996 Yearbook of the National Council of Teachers of Mathematics. Reston, VA: NCTM.

Edited Books

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

Fan, L., Wong, N-Y., Cai, J. & Li, S. (2005) (Eds.). How Chinese learn mathematics: Perspectives from insiders. Jiangsu Education Press. [(Chinese version of the Fan et al. (2004)]

Zhang, H., Cai, J., & Wang, B. (Eds.) (1999). Cross-cultural studies in mathematics education. Guizhou Educational Press.

Cao, C.& Cai, J. (Eds.) (1989/1995). Mathematics pedagogy (second printing). Jiangsu Education Press.

Refereed Articles or Invited Lectures for Conference Proceedings

Cai, J., Mamona-Downs, J., Ambrus, A., Iwasaki, H., & Icasuriaga, A. V. (in press). Topic Study Group 18: Problem solving in mathematics education. In M. Niss (Ed.), Proceedings of the 10 th International Congress on Mathematics Education. Kluwer Academic Publishers.

Cai, J. (in press). Intended, implemented/planned, and achieved mathematical curricula in U.S. and China: Some highlights from a decade of research. In Z. Usiskin (Ed.), Proceedings of the first International Mathematics Curriculum Study. Reston, VA: National Council of Teachers of mathematics.

Cifarelli, V.. & Cai, J. (2006). The role of self-generated problem posing in mathematical exploration. In J., Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the Thirtieth Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 369-376). Prague, Czech Republic: Charles University in Prague.

Wang, N. & Cai, J. (2006). An investigation of factors influencing teachers’ scoring student responses to mathematics constructed-response assessment tasks. In J., Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the Thirtieth Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 313-320). Prague, Czech Republic: Charles University in Prague.

Cai, J. (2005). Critical features of effective mathematics instruction: Issues and Practice. In Lam, L. (Ed.), Recent Advances in Mathematics Education Research and Teaching Practices (Proceedings of the International Conference on Mathematics Education). Hong Kong, China: The Hong Kong Institute of Education, July 6-8, 2005.

Pehkonen, E., Choe, Y. H., Cai, J., Ishida, J., & Stacey, K. (2004). Topic Study Group 11: Problem solving in mathematics education. In H. Fujita, Y. Hashimoto, B. R. Hodgson, P. Y. Lee, S. Lerman, & T. Sawada (Eds.), Proceedings of the 9 th International Congress on Mathematics Education (pp. 325 – 336). Kluwer Academic Publishers.

Cai, J. & Hwang, S. (2003). A perspective of investigating the direct link between mathematical problem solving and problem posing. Paper published in the Proceedings of the Joint Annual Meeting of the PME and PME/NA, (Volume 3, pp. 103-110). Honolulu, HI: University of Hawaii, July 13-18, 2003.

Cai, J. (2002). Impact of teachers’ conceptions of pedagogical representations on U.S. and Chinese students’ thinking. In F. Lopez-Real et al. (Eds.), Proceedings of the International Congress of Mathematics Instruction (ICMI) Comparative Study Conference (pp. 115-124). The University of Hong Kong, Hong Kong, China. October 20-25, 2002.

Cai, J. (2002). Assessing and understanding students’ mathematical thinking: Some insights from cross-national studies in mathematics. In D. Edge & B. H. Yeap (Eds.), Mathematics education for a knowledge-based era: Proceedings of International Congress of Mathematics Instruction’s Second East Asian Regional Conference on Mathematics Education (Volume 1: Plenary and Regular lectures) (pp. 65-79). Association of Mathematics Educators and National Institute of Education in Singapore. May 27-31, 2002.

Cai, J. & Gorowara, C. C. (2002). Teachers’ conceptions and constructions of pedagogical representations in teaching statistics: A case of arithmetic average. In B. Phillips (Ed.), Developing a statistically literate society: Proceedings of the Sixth International Conference on Teaching Statistics (pp. 401-406). International Association for Statistical Education (IASE).

Lo, J. J., Cai, J., & Watanabe, T. (2001). A comparative study of the selected textbooks from China, Japan, Taiwan, and the United States on the teaching of ratio and proportion concepts. In R. Speiser, C. A., Maher, & C. N. Walter (Eds.), Proceedings of the Twenty-Third Annual Meeting of the North American Chapter of the International Group of the Psychology of Mathematics Education (pp. 509-520). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Cai, J. (1999). Instructional impact on students' selection of strategies and representations in problem solving. In F. Hitt & M. Santos (Eds.), Proceedings of the Twenty-first Annual Meeting of the North American Chapter of the International Group of the Psychology of Mathematics Education (pp. 538-546). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Cai, J. (1997). Generating multiple solutions to mathematical problems by prospective secondary teachers. In J. A. Dossey, J. O. Swafford, M. Parmantie, & A. E. Dossey (Eds.), Proceedings of the Nineteenth Annual Meeting of the North American Chapter of the International Group of the Psychology of Mathematics Education (pp. 323-330). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Cai, J., Moyer, J. C., & Wang, N. (1996). The development of an instrument for assessing parental involvement in students' learning of mathematics. In Jakubowski, E., Watkins, D., & Biske, H. (Eds.), Proceedings of the Eighteenth Annual Meeting of the North American Chapter of the International Group of the Psychology of Mathematics Education (Vol. 1 pp. 115-120). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Moyer, J. C., Cai, J., Pustejovsky, S. (1996). Inner city middle school students' understanding of speed. In E. Jakubowski, D. Watkins, & H. Biske (Eds.), Proceedings of the Eighteenth Annual Meeting of the North American Chapter of the International Group of the Psychology of Mathematics Education (Vol. 1 pp. 100-106). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Cai, J. (1995). Beyond the computational algorithm: Students' understanding of the arithmetic average concept. In L. Meira & D. Carraher (Eds.), Proceedings of the Nineteenth Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 144-151). Recife, Brazil: Universidade Federal de Pernambuco.

Cai, J. (1995). Exploring gender differences in solving open-ended mathematical problems. In D. T. Owens, M. K. Reed, and G. M. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group of the Psychology of Mathematics Education (Vol. 2, pp. 24-30). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Cai, J. & Moyer, J. C. (1995). Middle school students' understanding of average: A problem solving approach. In D. T. Owens, M. K. Reed, and G. M. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group of the Psychology of Mathematics Education (Vol. 1, pp. 359-364). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Cai, J. & Silver, E. A. (1994). A cognitive analysis of Chinese students' mathematical problem solving: An exploratory study. In D. Kirshner (Ed.), Proceedings of the Sixteenth Annual Meeting of North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 3-9). Louisiana State University, Baton Rouge, Louisiana.

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