Sources of Differences in Children's Understandings of Mathematical Equality: Comparative Analysis of Teacher Guides and Student Texts in China and the United States

REFERENCES

• Anderson , C. W. and Smith , E. L. 1987 . “ Teaching science ” . In Educators' handbook: A research perspective , Edited by: ichardson-Koehler , V. 84 – 111 . New York : Longman .
   Google Scholar
• Baroody , A. J. and Ginsburg , H. P. 1983 . The effects of instruction on children's understanding of the “equals” sign . The Elementary School Journal , 84 : 199 – 212 .
   Web of Science ®Google Scholar
• Behr , M. , Erlwanger , S. and Nichols , E. 1980 . How children view the equals sign . Mathematics Teaching. , 92 : 13 – 15 .
   Google Scholar
• Capraro , R. M. and Capraro , M. M. Underlying structures of mathematical representation: A Theoretical Perspective . Paper presented at the annual meeting of the American Educational Research Association . San Francisco, CA. April .
   Google Scholar
• Carpenter , T. P. , Franke , L. P. and Levi , L. 2003 . Thinking mathematically: Integrating arithmetic & algebra in elementary school , Portsmouth, NH : Heinemann .
   Google Scholar
• Cathcart , W. , Pothier , Y. , Vance , J. and Bezuk , N. 2006 . Learning mathematics in elementary mathematics and middle schools, , 4th ed , Columbus, OH : Merrill Prentice Hall .
   Google Scholar
• Confrey , J. and Stohl , V. 2004 . On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations , Washington, DC : The National Academies .
   Google Scholar
• Curriculum Research Center and Elementary Mathematics Curriculum Research . 2005 . Elementary mathematics teacher guide book (vol. 1) , Beijing : People's Education Press .
   Google Scholar
• Denmark , T. , Barco , E. and Voran , J. 1976 . Final report: A teaching experiment on equality , Tallahassee : Florida State University: Project for the Mathematical Development of Children . (PMDC Technical Report No. 6). (ERIC Document Reproduction Service No. ED144805)
   Google Scholar
• Ding , M. and Li , X. Errors in students' transition from verbal to symbolic understanding: Case study . Paper presented at the 33rd annual meeting of the Research Council on Mathematic Learning . Feb. . University of Nevada Las Vegas .
   Google Scholar
• Falkner , K. P. , Levi , L. and Carpenter , T. P. 1999 . Children's understanding of equality: A foundation for algebra . Teaching Children Mathematics , 6 : 232 – 236 .
   Google Scholar
• Hatfield , M. , Edwards , N. , Bitter , G. and Morrow , J. 2005 . Mathematics methods for elementary and middle school teachers, , 5th ed. , Hoboken, NJ : Wiley Josey-Bass .
   Google Scholar
• Kieran , C. 1981 . Concepts associated with the equality symbol . Educational Studies in Mathematics , 12 : 317 – 326 .
   Google Scholar
• Knuth , E. J. , Stephens , A. C. , McNeil , N. M. and Alibali , M. W. 2006 . Does understanding the equal sign matter? Evidence from solving equations . Journal for Research in Mathematics Education. , 37 : 297 – 312 .
   Web of Science ®Google Scholar
• Li , J. 2004 . “ Through understanding of the textbook: A significant feature of Chinese teacher manuals ” . In How Chinese learn mathematics: Perspectives from insiders , Edited by: Fang , L. , Wong , N. Y. , Cai , J. and Li , S. Hackensack, NJ : World Scientific .
   Google Scholar
• Lu , J. and Yang , G. 2005 . Elementary mathematics book (vol. 1) , Beijing : People's Education Press .
   Google Scholar
• Ma , L. 1999 . Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States , Mahwah, NJ : Erlbaum .
   Google Scholar
• McNeil , N. M. , Grandau , L. , Knuth , E. J. , Alibali , M. W. , Stephens , A. C. Hattikudur , S. 2006 . Middle-school students' understanding of the equal sign: The books they read can't help . Cognition and Instruction , 24 : 367 – 385 .
   Web of Science ®Google Scholar
• Ministry of Education . 2001 . National mathematics standards (experimental edition) , China : Beijing Normal University Press .
   Google Scholar
• National Council of Teachers of Mathematics . 2000 . Principles and standards for school mathematics , Reston, VA : Author .
   Google Scholar
• Porter , A. 1989 . A curriculum out of balance: The case of elementary school mathematics . Educational Researcher , 18 ( 5 ) : 9 – 1 .
   Google Scholar
• Research Group of National Mathematics Curriculum Standards for Compulsory Education . 2005a . Xinshiji xiaoxue shuxue jiaocai (New century elementary mathematics textbook) , China : Beijing Normal University Press .
   Google Scholar
• Research Group of National Mathematics Curriculum Standards for Compulsory Education . 2005b . Xinshiji xiaoxue shuxue jiaocai jiaoshi yongshu (New century elementary mathematics teacher guidebook) , China : Beijing Normal University Press .
   Google Scholar
• Reys , B. J. , Reys , R. E. and Chávez , O. 2004 . Why mathematics textbooks matter . Educational Leadership , 61 ( 5 ) : 61 – 66 .
   Web of Science ®Google Scholar
• Reys , R. E. , Lindquist , M. , Lambdin , D. , Smith , N. and Suydam , M. 2003 . Helping children learn mathematics: Active learning edition with integrated field activities, , 7th ed. , Hoboken, NJ : John Wiley & Sons .
   Google Scholar
• Rittle-Johnson , B. and Alibali , M. W. 1999 . Conceptual and procedural understanding: Does one lead to the other? . Journal of Educational Psychology , 91 : 175 – 189 .
   Web of Science ®Google Scholar
• Sáenz-Ludlow , A. and Walgamuth , C. 1998 . Third graders' interpretations of equality and the equal symbol . Educational Studies in Mathematics. , 35 : 153 – 187 .
   Google Scholar
• Schmidt , W. H. , McKnight , C. C. , Houang , R. T. , Wang , H. C. , Wiley , D. E. Cogan , L. S. 2001 . Why schools matter: A cross-national comparison of curriculum and learning , San Francisco : Jossey-Bass .
   Google Scholar
• Seo , K.-H. and Ginsburg , H. P. 2003 . “You've got to carefully read the math sentence…”: Classroom context and children's interpretations of the equal sign ” . In The development of arithmetic concepts and skills , Edited by: Baroody , A. J. and Dowwker , A. Mahwah, NJ : Erlbaum .
   Google Scholar
• Shen , B. and Liang , J. 1992 . Xiaoxue shuxue jiaoxue fa (Elementary mathematics teacher methods book) , Shanghai, Beijing : The Press of East China Normal University .
   Google Scholar
• Smith , S. 2001 . Early childhood mathematics, , 2nd ed. , Boston : Allyn & Bacon .
   Google Scholar
• Su , L. and Wang , N. 2005a . Elementary mathematics textbook (vols. 1–6) , Nanjing : Jiang Su Education Press .
   Google Scholar
• Su , L. and Wang , N. 2005b . Elementary mathematics teacher guidebook (vols. 1–6) , Nanjing : Jiang Su Education Press .
   Google Scholar
• Thompson , C. and Babcock , J. 1978 . A successful strategy for teaching missing addends . Arithmetic Teacher , 26 ( 4 ) : 38 – 41 .
   Google Scholar
• Tucker , B. , Singleton , A. and Weaver , T. 2006 . Teaching mathematics to all children: Designing and adapting instruction to meet the needs of diverse learners, , 2nd ed. , Columbus, OH : Merrill Prentice Hall .
   Google Scholar
• Van de Walle , J. 2004 . Elementary and middle school mathematics: Teaching developmentally, , 5th ed. , Boston, MA : Pearson .
   Google Scholar
• Wolters , M. A. The equal sign goes both ways. How mathematics instruction leads to the development of a common misconception . Proceedings of the Conference of the International Groups for the Psychology of Mathematics Education (PME), Italy, 3 . pp. 348 – 355 .
   Google Scholar
• Ye , Y. and Zhao , S. 2000 . Xiaoxue shuxue jiaocai jiaofa (Elementary mathematics teacher methods book) , Hangzhou, China : Zhe Jiang Jiao Xue Press .
   Google Scholar