This paper probes into qualities aiming at improving students’ creativity in mathematics learning and attempts to share Chinese experience of mathematical teaching. Based on the “Youth Innovation Competence Model”, we put forward six principles of mathematics creative teaching as follow s: 1) encourage creative thinking; 2) make full use of representations and transformation of mathematical knowledge; 3) establish motivation, self-efficacy, and self-concept within students; 4) help students become self-regulated; 5) promote group interactions; and 6) implement open learning environment. With the utilization of six principles in mathematical teaching in Chinese classroom, the lesson Understanding of Long Cuboid and Cube of fifth grade shows that these principles can be perfectly implemented in driving problem, anchor task, and diagnostic assignment in mathematical teaching. Most importantly, students’ competence in innovation is greatly improved.
Ainsworth, S. (1999). The Functions of Multiple Representations. Computers & Education, 33, 131-152. https://doi.org/10.1016/S0360-1315(99)00029-9
Ainsworth, S., & Peevers, G. (2003). The Interaction between Informational and Computational Properties of External Representations on Problem-Solving and Learning. In Proceedings of the Annual Meeting of the Cognitive Science Society (p. 25). https://escholarship.org/uc/item/8qg8x7bw
Ainsworth, S., Bibby, P., & Wood, D. (2002). Examining the Effects of Different Multiple Representational Systems in Learning Primary Mathematics. Journal of the Learning Sciences, 11, 25-61. https://doi.org/10.1207/S15327809JLS1101_2
Amabile, T. M. (1996). Creativity in Context. Boulder, CO: Westview.
Ames, C. (1992). Achievement Goals and the Classroom Motivational Climate. In D. H. Schunk, & J. L. Meece (Eds.), Student Perceptions in the Classroom (pp. 25-57). Hillsdale, NJ: Lawrence Erlbaum.
Askew, M. (2013). Issues in Teaching for and Assessment of Creativity in Mathematics and Science. In D. Corrigan, R. Gunstone, & A. Jones (Eds.), Valuing Assessment in Science Education: Pedagogy, Curriculum, Policy (pp. 169-182). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-6668-6_9
Balka, D. S. (1974). Creative Ability in Mathematics. Arithmetic Teacher, 21, 633-636.
Bandura, A. (1997). Self-Efficacy: The Exercise of Control. New York: W.H. Freeman and Company.
Beghetto, R. (2007). Does Creativity Have a Place in Classroom Discussions? Prospective Teachers’ Response Preferences. Thinking Skills and Creativity, 2, 1-9. https://doi.org/10.1016/j.tsc.2006.09.002
Beghetto, R. A., & Kaufman, J. C. (2014). Classroom Contexts for Creativity. High Ability Studies, 25, 53-69. https://doi.org/10.1080/13598139.2014.905247
Benware, C. A., & Deci, E. L. (1984). Quality of Learning with an Active versus Passive Motivational Set. American Educational Research Journal, 21, 755-765. https://doi.org/10.3102/00028312021004755
Blumenfeld, P. C. (1992). Classroom Learning and Motivation. Journal of Educational Psychology, 84, 272-281. https://doi.org/10.1037/0022-0663.84.3.272
Boden, M. (2004). The Creative Mind: Myths and Mechanisms (2nd ed.). London: Routledge. https://doi.org/10.4324/9780203508527
Boyatzis, R. E. (1982). The Competent Manager: A Model for Effective Performance (pp. 80-82). Hoboken, NJ: John Wiley & Sons Ltd.
Bransford, J. D., & Schwartz, D. L. (1999). Rethinking Transfer: A Simple Proposal with Multiple Implications. Review of Research in Education, 24, 61-100. https://doi.org/10.2307/1167267
Butler, D. L., & Winne, P. H. (1995). Feedback and Self-Regulated Learning: A Theoretical Synthesis. Review of Educational Research, 65, 245. https://doi.org/10.3102/00346543065003245
Cai, J., & Hwang, S. (2002). Generalized and Generative Thinking in US and Chinese Students’ Mathematical Problem Solving and Problem Posing. Mathematical Behavior, 21, 401-421. https://doi.org/10.1016/S0732-3123(02)00142-6
Chan, S., & Yuen, M. I. (2014). Personal and Environmental Factors Affecting Teachers’ Creativity-Fostering Practices in Hongkong. Thinking Skills and Creativity, 12, 69-77. https://doi.org/10.1016/j.tsc.2014.02.003
Chan, Y. (2016). Teaching Design Based on Cultivating Middle School Students’ Mathematical Creativity. Company in Mathematics, 6, 8-10.
Covington, M. V. (1992). Making the Grade: A Self-Worth Perspective on Motivation and School Reform. New York: Cambridge University Press. https://doi.org/10.1017/CBO9781139173582
Crick, R. D., Huang, S., Shafi, A. A., & Goldspink, C. (2015). Developing Resilient Agency in Learning: The Internal Structure of Learning Power. British Journal of Educational Studies, 63, 121-160. https://doi.org/10.1080/00071005.2015.1006574
Csikszentmihalyi, M. (1997). Finding Flow: The Psychology of Engagement with Everyday Life. New York: Basic Books.
Cuoco, A. A., & Curcio, F. R. (2001). The Roles of Representation in School Mathematics (2001 Yearbook). Reston, VA: National Council of Teachers of Mat.
Daly, I., Bourgaize, J., & Vernitski, A. (2019). Mathematical Mindsets Increase Student Motivation: Evidence from the EEG. Trends in Neuroscience and Education, 15, 8-28. https://doi.org/10.1016/j.tine.2019.02.005
Daniel, H. T., & Laura, I. (2020). Creativity and Education: A Bibliometric Mapping of the Research Literature (1975-2019). Thinking Skills and Creativity, 35, Article ID: 100625. https://doi.org/10.1016/j.tsc.2019.100625
Davies, D., Jindal-Snape, D., Collier, C., Digby, R., Hay, P., & Howe, A. (2013). Creative Learning Environments in Education: A Systematic Literature Review. Thinking Skills and Creativity, 8, 80-91. https://doi.org/10.1016/j.tsc.2012.07.004
Debellis, V. A., & Goldin, G. A. (2006). Affect and Meta-Affect in Mathematical Problem Solving: A Representational Perspective. Educational Studies in Mathematics, 63, 131-147. https://doi.org/10.1007/s10649-006-9026-4
Deci, E. L., Vallerand, R. J., Pelletier, L. G., & Ryan, R. M. (1991). Motivation and Education: The Self-Determination Perspective. Educational Psychologist, 26, 325-346. https://doi.org/10.1207/s15326985ep2603&4_6
Deci, E., & Ryan, R. (1985). Intrinsic Motivation and Self-Determination in Human Behavior (Perspectives in Social Psychology). New York: Plenum Press. https://doi.org/10.1007/978-1-4899-2271-7
Denissen, J. J. A., Zarrett, N. R., & Eccles, J. S. (2007). I Like to Do It, I’m Able, and I Know I Am: Longitudinal Couplings between Domain-Specific Achievement, Self-Concept, and Interest. Child Development, 78, 430-447. https://doi.org/10.1111/j.1467-8624.2007.01007.x
Dienes, Z. (1973). The Six Stages in the Process of Learning Mathematics. Slough: NFER Nelson.
Dweck, C. S. (1999). Self-Theories: Their Role in Motivation, Personality, and Development. Hove: Psychology Press.
Elliott, E. S., & Dweck, C. S. (1988). Goals: An Approach to Motivation and Achievement. Journal of Personality & Social Psychology, 54, 5-12. https://doi.org/10.1037/0022-3514.54.1.5
Ervynck, G. (1991). Mathematical Creativity. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 42-52). New York: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47203-1_3
Garon-Carrier, G., Boivin, M., Guay, F., Kovas, Y., Dionne, G., Tremblay, R. E. et al. (2016). Intrinsic Motivation and Achievement in Mathematics in Elementary School: A Longitudinal Investigation of Their Association. Child Development, 87, 165-175. https://doi.org/10.1111/cdev.12458
Goldin, G. A. (1998). Representational Systems, Learning, and Problem Solving in Mathematics. Journal of Mathematical Behavior, 17, 137-165. https://doi.org/10.1016/S0364-0213(99)80056-1
Graham, S., & Weiner, B. (1996). Theories and Principles of Motivation. In D. C. Berliner, & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 63-84). London: Macmillan.
Grégoire, J. (2016). Understanding Creativity in Mathematics for Improving Mathematical Education. Journal of Cognitive Education and Psychology, 15, 24-36. https://doi.org/10.1891/1945-8959.15.1.24
Guilford, J. P. (1967). The Nature of Human Intelligence. New York: McGraw-Hill.
Haylock, D. (1978). An Investigation into the Relationship between Divergent Thinking in Non-Mathematical and Mathematical Situations. Mathematics in School, 7, 25-25. http://www.jstor.org/stable/30213375
Hiatt, A. A. (1970). Assessing Mathematical Thinking Abilities of Sixth, Ninth, and Twelfth Grade Students. Unpublished Doctoral Dissertation, Oakland, CA: University of California.
Hiebert, J., & Carpenter, T. P. (1992). Learning and Teaching with Understanding: Handbook of Research on Mathematics Teaching and Learning. New York: Macmillan.
Hwang, W. Y., Chan, N. S., Dung, J. J., & Yang, Y. L. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving Using a Multimedia Whiteboard System. Educational Technology & Society, 10, 191-212.
Ivcevic, Z., & Nusbaum, E. C. (2017). From Having an Idea to Doing Something with it: Self-Regulation for Creativity. In M. Karwowski, & J. C. Kaufman (Eds.), The Creative Self (pp. 343-365). San Diego, CA: Academic Press. https://doi.org/10.1016/B978-0-12-809790-8.00020-0
Janvier, C. (1987). Representation and Understanding: The Notion of Function as an Example. Hillsdale, NJ: Lawrence Erlbaum.
Jindal-Snape, D., Davies, D., Collier, C., Howe, A., Digby, R., & Hay, P. (2013). The Impact of Creative Learning Environments on Learners: A Systematic Literature Review. Improving Schools, 16, 21-31. https://doi.org/10.1177/1365480213478461
Kaput, J. (1998). Representations, Inscriptions, Descriptions and Learning: A Kaleidoscope of Windows. Journal of Mathematical Behavior, 17, 265-261. https://doi.org/10.1016/S0364-0213(99)80062-7
Kaufman, J. C., & Beghetto, R. A. (2009). Beyond Big and Little: The Four C Model of Creativity. Review of General Psychology, 13, 1-12. https://doi.org/10.1037/a0013688
Kim, M. K., Roh, I. S., & Cho, M. K. (2016). Creativity of Gifted Students in an Integrated Math-Science Instruction. Thinking Skills & Creativity, 19, 38-48. https://doi.org/10.1016/j.tsc.2015.07.004
Kozbelt, B. A., Beghetto, R. A., & Runco, M. A. (2010). Theories of Creativity (pp. 321-447). New York: Cambridge University Press.
Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in School Children. Chicago, IL: University of Chicago Press.
Kwon, O. N., Park, J. H., & Park, J. S. (2006). Cultivating Divergent Thinking in Mathematics through an Open-Ended Approach. Asia Pacific Education Review, 7, 51-61. https://doi.org/10.1007/BF03036784
Larson, B. E. (2000). Classroom Discussion: A Method of Instruction and a Curriculum Outcome. Teaching and Teacher Education, 16, 661-677. https://doi.org/10.1016/S0742-051X(00)00013-5
Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and Mathematics Education: The State of the Art. ZDM International Journal on Mathematics Education, 45, 159-166. https://doi.org/10.1007/s11858-012-0459-1
Leikin, R., & Sriraman, B. (2016). Creativity and Giftedness. Interdisciplinary Perspectives from Mathematics and Beyond. Columbus, OH: Ohio Library and Information Network. https://doi.org/10.1007/978-3-319-38840-3
Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 33-40). Hillsdale, NJ: Erlbaum.
Mann, E. L. (2006). Creativity: The Essence of Mathematics. Journal for the Education of the Gifted, 30, 236-260. https://doi.org/10.4219/jeg-2006-264
Marsh, H. W., & Craven, R. (1997). Academic Self-Concept: Beyond the Dustbowl. In G. Phye (Ed.), Handbook of Classroom Assessment: Learning, Achievement, and Adjustment (pp. 131-198). Orlando, FL: Academic Press. https://doi.org/10.1016/B978-012554155-8/50008-9
Maxwell, A. A. (1974). An Exploratory Study of Secondary School Geometry Students: Problem Solving Related to Convergent-Divergent Production. Unpublished Doctoral Dissertation, Knoxville, TN: University of Tennessee.
Mayer, R. E., & Anderson, R. B. (1992). The Instructive Animation: Helping Students Build Connections between Words and Pictures in Multimedia Learning. Journal of Educational Psychology, 84, 444-452. https://doi.org/10.1037/0022-0663.84.4.444
National Governors Association Center for Best Practices, Council of Chief State School Officers (2010). Common Core State Standards for English Language Arts. Washington DC: National Governors Association Center for Best Practices, Council of Chief State School Officers.
Newell, A., & Simon, H. (1972). Human Problem Solving. Englewood Cliffs, NJ: Prentice-Hall.
Nie, S. (2017). On the “Fertile Ground” of Cultivating Creative Thinking Ability in Mathematics Classroom—Cultivating Creative Thinking Ability of Elementary School Students in Mathematics Teaching. New Course (Elementary), 7.
Ott, N., Brünken, R., Vogel, M., & Malone, S. (2018). Multiple Symbolic Representations: The Combination of Formula and Text Supports Problem Solving in the Mathematical Field of Propositional Logic. Learning and Instruction, 58, 88-105. https://doi.org/10.1016/j.learninstruc.2018.04.010
Partnership for 21st Century Skills (2019). Framework for 21st Century Learning Definitions. Partnership for 21st Century Skills. http://static.battelleforkids.org/documents/p21/P21_Framework_DefinitionsBFK.pdf
Pei, D. (2016). Learning Power: New Vision of Interpreting Students Learning and Development. Curriculum, Teaching Material and Method, 7, 3-9.
Poincaré, H. (1948). Science and Method. New York: Dover.
Poincaré, H. (1956). Mathematical Creation. In J. R. Newman (Ed.), The World of Mathematics (pp. 2041-2050). New York: Simon and Schuster.
Richardson, C., & Mishra, P. (2018). Learning Environments that Support Student Creativity: Developing the SCALE. Thinking Skills and Creativity, 27, 45-54. https://doi.org/10.1016/j.tsc.2017.11.004
Runco, M. A., & Jaeger, G. J. (2012). The Standard Definition of Creativity. Creativity Research Journal, 24, 92-96. https://doi.org/10.1080/10400419.2012.650092
Sawada, T. (1997). Developing Lesson Plans. In J. Becker, & S. Shimada (Eds.), The Open-Ended Approach: A New Proposal for Teaching Mathematics (pp. 1-9). Reston, VA: National Council of Teachers of Mathematics.
Schoevers, E. M., Leseman, P. P. M., Slot, E. M., Bakker, A., Keijzer, R., & Kroesbergen, E. H. (2019). Promoting Pupils’ Creative Thinking in Primary School Mathematics: A Case Study. Thinking Skills and Creativity, 31, 323-334. https://doi.org/10.1016/j.tsc.2019.02.003
Schunk, D. H. (1982). Effects of Effort Attributional Feedback on Children’s Perceived Self-Efficacy and Achievement. Journal of Educational Psychology, 74, 548-556. https://doi.org/10.1037/0022-0663.74.4.548
Scott, G., Leritz, L. E., & Mumford, M. D. (2004). The Effectiveness of Creativity Training: A Quantitative Review. Creativity Research Journal, 16, 361-388. https://doi.org/10.1080/10400410409534549
Shapiro, Z. J. (1984). Social Justice and Educational Evaluation: Normative Implications of Alternative Criteria for Program Assessment. Educational Theory, 34, 137-149. https://doi.org/10.1111/j.1741-5446.1984.00137.x
Shavelson, R. J., Hubner, J. J., & Stanton, G. C. (1976) Self-Concept: Validation of Construct Interpretations. Review of Educational Research, 46, 407-441. https://doi.org/10.3102/00346543046003407
Singh, B. (1988). Teaching-Learning Strategies and Mathematical Creativity. New Delhi: Mittal Publications.
Spencer, L. M., & Spencer, S. M. (1993). Competence at Work: Models for Superior Performance. Hoboken, NJ: Wiley.
Sriraman, B. (2005). Are Giftedness and Creativity Synonyms in Mathematics? An Analysis of Constructs within the Professional and School Realms. The Journal of Secondary Gifted Education, 17, 20-36. https://doi.org/10.4219/jsge-2005-389
Sternberg, R. J., & Lubart, T. I. (1993). Creative Giftedness: A Multivariate Investment Approach. Gifted Child Quarterly, 37, 7-15. https://doi.org/10.1177/001698629303700102
Sternberg, R., & Lubart, T. (1999). The Concept of Creativity: Prospect and Paradigm. In R. Sternberg (Ed.), Handbook of Creativity (pp. 3-15). Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511807916.003
Tammadge, A. (1979). Creativity (Presidential Address to the Mathematical Association). Mathematical Gazette, 63, 145-163. https://doi.org/10.2307/3617885
Vallee, R. (1975). New Mathematics and Teaching. International Journal of Mathematical Education in Science and Technology, 6, 141-144. https://doi.org/10.1080/0020739750060201
Wallas, G. (1926). The Art of Thought. New York: Harcourt, Brace.
Wang, H. (2006). The Research Study of Mathematics and Creativity Cultivation. Journal of the Chinese Society of Education, 7, 77-78.
World Economic Forum (2016). The Future of Jobs: Employment, Skills and Workforce Strategy for the Fourth Industrial Revolution. Geneva: World Economic Forum. http://www3.weforum.org/docs/WEF_Future_of_Jobs.pdf
Wu, X., & Wang, D. (2002) Experiment on Developing Students’ Creating Ability in Mathematical Teaching. Journal of Mathematics Education, 11, 93-95.
Yerushalmy, M. (1997). Designing Representations: Reasoning about Functions of Two Variables. Journal for Research in Mathematics Education, 28, 431-466. https://doi.org/10.5951/jresematheduc.28.4.0431
Zhang, C., Chen, W., & Zhang, Z. (2020). Learning Process Analysis from Learners’ Perspective. Beijing: Beijing Normal University Press.
Zhang, C., Cheng, L., Wang, B., & Wang, Y. (2018). The Theoretical Construction of the Youth Innovation Competency Model. Journal of Beijing Institute of Education, 32, 28-34.
Zhang, J. J., & Norman, D. A. (1994). Representations in Distributed Cognitive Tasks. Cognitive Science, 18, 87-122. https://doi.org/10.1207/s15516709cog1801_3
Zimmerman, B. J. (2000). Attainment of Self-Regulation: A Social Cognitive Perspective. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of Self-Regulation (pp. 13-39). Cambridge, MA: Academic Press.
Zimmerman, B. J. (2001). Theories of Self-Regulated Learning and Academic Achievement: An Overview and Analysis. In D. H. Schunk, & B. J. Zimmerman (Eds.), Self-Regulated Learning and Academic Achievement: Theoretical Perspectives (pp. 1-37). Hillsdale, MI: Erlbaum.
Zimmerman, B. J. (2002). Becoming a Self-Regulated Learner: An Overview. Theory into Practice, 41, 64-70. https://doi.org/10.1207/s15430421tip4102_2