Problem Posing and Its Relationship with Teaching Experience of Elementary School Mathematics Teachers from Ethnic Minority Area in Southwest China

This study examined characteristics of problem posing and its relationship with the teaching experience of elementary school mathematics teachers from ethnic minority areas in the Southwest of China. Eighty-one ( N = 81) elementary school mathematics teachers responded to a task-based questionnaire and posed mathematical problems based on given problem situations. Characteristics of their mathematical problem posing were observed through the total numbers, appropriateness, difficultly, and flexibility levels of the problems posed by the teachers. Results show that elementary school mathematics teachers were capable of posing a considerable number of appropriate mathematical problems. Significant differences were found in the flexibility of the posed problems among the teachers with different years of teaching experience. This finding suggests that teachers ’ capability in mathematical problem posing may not necessarily grow along with teaching experience. Limitations of the study and implications in developing teachers ’ mathematical problem posing are discussed.

[1]  Peter Liljedahl,et al.  Empirical research on problem solving and problem posing: a look at the state of the art , 2021, ZDM – Mathematics Education.

[2]  Benjamin Rott,et al.  Developing a framework for characterising problem-posing activities: a review , 2021, Research in Mathematics Education.

[3]  Jinfa Cai,et al.  Publisher Correction to: Teachers as redesigners of curriculum to teach mathematics through problem posing: conceptualization and initial findings of a problem‑posing project , 2021, ZDM – Mathematics Education.

[4]  A. Leavy,et al.  Balancing competing demands: Enhancing the mathematical problem posing skills of prospective teachers through a mathematical letter writing initiative , 2021, Journal of Mathematics Teacher Education.

[5]  Lukas Baumanns,et al.  Rethinking Problem-Posing Situations: A Review , 2020 .

[6]  Li Cao,et al.  Reciprocal Learning in Mathematics Problem Posing and Problem Solving: An Interactive Study between Canadian and Chinese Elementary School Students , 2020, Eurasia Journal of Mathematics, Science and Technology Education.

[7]  Jinfa Cai,et al.  Affect in mathematical problem posing: conceptualization, advances, and future directions for research , 2020, Educational Studies in Mathematics.

[8]  F. Leung,et al.  Affective determinants of mathematical problem posing: the case of Chinese Miao students , 2020, Educational Studies in Mathematics.

[9]  R. Leikin,et al.  Opening mathematical problems for posing open mathematical tasks: what do teachers do and feel? , 2020, Educational Studies in Mathematics.

[10]  Shin-Yi Lee Research Status of Mathematical Problem Posing in Mathematics Education Journals , 2020, International Journal of Science and Mathematics Education.

[11]  Jinfa Cai,et al.  Learning to teach mathematics through problem posing: teachers’ beliefs and performance on problem posing , 2020, Educational Studies in Mathematics.

[12]  A. Leavy,et al.  Posing mathematically worthwhile problems: developing the problem-posing skills of prospective teachers , 2020, Journal of Mathematics Teacher Education.

[13]  Jinfa Cai,et al.  Teachers’ Beliefs about Mathematics, Learning, Teaching, Students, and Teachers: Perspectives from Chinese High School In-Service Mathematics Teachers , 2020 .

[14]  Jinfa Cai,et al.  Teachers’ Beliefs about Mathematics, Learning, Teaching, Students, and Teachers: Perspectives from Chinese High School In-Service Mathematics Teachers , 2020, International Journal of Science and Mathematics Education.

[15]  Jinfa Cai,et al.  Posing Researchable Questions in Mathematics and Science Education: Purposefully Questioning the Questions for Investigation , 2020, International Journal of Science and Mathematics Education.

[16]  Marta Molina,et al.  Meanings given to algebraic symbolism in problem-posing , 2018 .

[17]  J. Lederman,et al.  Implications of Informal Education Experiences for Mathematics Teachers' Ability to Make Connections Beyond Formal Classroom , 2015 .

[18]  Aihui Peng,et al.  The Status Quo and Development of Mathematics Education for Ethnic Minorities in China , 2014 .

[19]  A. Hošpesová,et al.  Developing teachers’ subject didactic competence through problem posing , 2013 .

[20]  Bharath Sriraman,et al.  Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA , 2013 .

[21]  Xenia Xistouri,et al.  Field dependence/independence cognitive style and problem posing: an investigation with sixth grade students , 2011 .

[22]  Carrie R. Leana,et al.  Applying Organizational Research to Public School Reform: The Effects of Teacher Human and Social Capital on Student Performance , 2009 .

[23]  Edd V. Taylor,et al.  Culture and Mathematics in School: Boundaries Between “Cultural” and “Domain” Knowledge in the Mathematics Classroom and Beyond , 2008 .

[24]  E. Silver,et al.  Assessing Students' Mathematical Problem Posing. , 2005 .

[25]  Sandra Crespo,et al.  Learning to pose mathematical problems: Exploring changes in preservice teachers' practices , 2003 .

[26]  Edward A. Silver,et al.  An Analysis of Arithmetic Problem Posing by Middle School Students. , 1996 .

[27]  E. Corte,et al.  An empirical test of the impact of primitive intuitive models of operations on solving word problems with a multiplicative structure , 1996 .

[28]  J. Ogbu,et al.  Understanding Cultural Diversity and Learning , 1992 .

[29]  Alan H. Schoenfeld,et al.  Explorations of Students' Mathematical Beliefs and Behavior. , 1989 .

[30]  B. Graham Mathematical education and Aboriginal children , 1988 .

[31]  Lyn D. English,et al.  Teaching and learning through mathematical problem posing: commentary , 2020 .

[32]  Jinfa Cai,et al.  Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research , 2020 .

[33]  Jinfa Cai,et al.  Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ conceptions on problem posing and lesson design , 2020 .

[34]  Mike Askew,et al.  Mediating primary mathematics: theory, concepts, and a framework for studying practice , 2018 .

[35]  Florence Mihaela Singer,et al.  Mathematical problem posing : from research to effective practice , 2015 .

[36]  B. Koichu,et al.  What Do High School Teachers Mean by Saying “I Pose My Own Problems”? , 2015 .

[37]  N. Schmitt The Effects of Teaching Experience on High School Education: A Statistical Model on Factors of Educational Achievement in Math and Science , 2013 .

[38]  Zulbiye Toluk-Ucar Developing pre-service teachers understanding of fractions through problem posing , 2009 .

[39]  Jinfa Cai,et al.  Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing , 2002 .

[40]  Stephen I. Brown Reconstructing School Mathematics: Problems with Problems and the Real World , 2001 .

[41]  Roger Howe Knowing and Teaching Elementary Mathematics , 1999 .

[42]  G. Goldin Representational systems, learning, and problem solving in mathematics , 1998 .

[43]  E. Silver On Mathematical Problem Posing. , 1994 .

[44]  Don S. Balka Creative Ability in Mathematics. , 1974 .

[45]  J. A. Crowther The Evolution of Physics: , 1938, Nature.