Why do U.S. and Chinese students think differently in mathematical problem solving? Impact of early algebra learning and teachers' beliefs

By Jinfa Cai. 2004

100 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4b4d33867e6a9d1261d0dfc127cc798c6d9a72b7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Education

1. Meixia Ding
2. M. Carlson
3. Tao Wang
4. Xiaobao Li
5. Qiong Li
6. Xiaoqing Li
7. Zhonghua Zhang
8. Yujing Ni

In Statistics and Probability

1. Meixia Ding
2. M. Carlson
3. Tao Wang
4. Xiaobao Li
5. Qiong Li
6. Xiaoqing Li
7. Zhonghua Zhang
8. Yujing Ni

Citations in the corpus

• Effective mathematics teaching from teachers' perspectives : national and cross-national studies (2009, background): “A teacher’s manner of presenting mathematics is an indication of what he/she believes to be most essential, thereby influencing the ways that students understand and learn mathematics (Cai, 2004; Cooney, Shealy, & Arvold, 1998; Greeno, 1987; Thompson, 1992).”
• Transition from concrete to abstract representations: the distributive property in a Chinese textbook series (2014, background): “Recent studies (e.g., Cai, 2004; Koedinger, Alibali & Nathan, 2008) found that abstract representations have advantages over concrete representations in solving complex problems.”
• A Comparative Analysis of the Distributive Property in U.S. and Chinese Elementary Mathematics Textbooks (2010, background): “Empirical studies that directly compare early algebraic learning also demonstrate that Chinese elementary students have a better understanding of the concept of equivalence ( Li et al, 2008 ) and tend to solve word problems in abstract and algebraic ways ( Cai, 2004 ).”
• U.S. and Chinese Teachers' Conceptions and Constructions of Representations: A Case of Teaching Ratio Concept (2006, background): “students generated problems with pictures, but few Chinese students did ( Cai, 2004 ).”
• Elementary Teachers' Learning to Construct High-Quality Mathematics Lesson Plans (2013, background): “Teachers’ challenges were mainly related to connecting concrete to abstract, asking deep questions, and anticipating deep explanations, which are key factors in supporting students’ mathematical learning (Cai, 2004; Chi et al., 1994; NCTM, 2000).”
• Conceptions of effective mathematics teaching within a cultural context: perspectives of teachers from China and the United States (2010, background): “Thus, a solutionstrategythatlacksgeneralityshouldbediscouraged.Incontrast,U.S.teachersheavily emphasized the pragmatic nature of mathematics: as long as it works, students can choose whatever representations and strategies they like ( Cai 2004 ).”
• Influence of Curriculum Reform: An Analysis of Student Mathematics Achievement in Mainland China. (2011, background): “…of performance by U.S. students and Chinese students also suggest that some different instructional conditions are required for developing the competence in solving routine mathematics problems and for the competence in solving non-routine mathematics problems (Cai, 2004; Wang & Lin, 2005).”
• Problem solving in Chinese mathematics education: research and practice (2007, unknown): “The small-scale, in-depth studies include those by An (2004), Cai and his associates (e.g., Cai, 2000, 2004; Cai & Hwang, 2002; Cai & Lester, 2005), Clarke and his associates (e.g., Clarke, Keitel, & Shimizu, 2006), Geary and his associates (e.g., Geary, Bow-Thomas, Liu, & Siegler, 1996), Leung…”