The initial treatment of the concept of function in the selected secondary school mathematics textbooks in the US and China

References

• Mullis IVS, Martin MO, Minnich CA, et al. TIMSS 2011 encyclopedia: education policy and curriculum in mathematics and science. Vols. 1 and 2. Chestnut Hill (MA): TIMSS & PIRLS International Study Center, Boston College; 2012.
   Google Scholar
• Lemke M, Sen A, Pahlke E, et al. International outcomes of learning in mathematics literacy and problem solving: PISA 2003 results from the US perspective (NCES 2005–003). Washington (DC): National Center for Education Statistics, US Department of Education; 2004.
   Google Scholar
• Osborn JH, Jones BF, Stein M. The case for improving textbooks. Educ Leadersh. 1985;12:9–16.
   Google Scholar
• Stigler JW, Hiebert J. The teaching gap: best ideas from the world's teachers for improving education in the classroom. New York: Free Press; 1999.
   Google Scholar
• Reys BJ, Reys RE, Chavez O. Why mathematics textbooks matter. Educ Leadersh. 2004;61(5):61–66.
   Web of Science ®Google Scholar
• Schmidt WH, McKnight CC, Raizen SA. A splintered vision: an investigation of US science and mathematics education. Dordrecht: Kluwer; 1997.
   Google Scholar
• Son J, Senk S. How reform curricula in the USA and Korea present multiplication and division of fractions. Educ Stud Math. 2010;74(2):117–142.
   Google Scholar
• Valverde GA, Bianchi LJ, Wolfe RG, et al. According to the Book. Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht: Kluwer Academic Publishers; 2002.
   Google Scholar
• Fuson KC, Stigler JW, Bartsch K. Grade placement of addition and subtraction topics in China, Japan, the Soviet Union, Taiwan, and the United States. J Res Math Educ. 1988;19:449–458.
   Web of Science ®Google Scholar
• Son J. A cross-national comparison of reform curricula in Korea and the US in terms of cognitive complexity: the case of fraction addition and subtraction. ZDM Int J Math Educ. 2012;44(2):161–174.
   Google Scholar
• Stigler JW, Fuson KC, Ham M, et al. An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cogn Instruct. 1986;3:153–171.
   Google Scholar
• Kilpatrick J, Swafford J, Findell B. Adding it up: helping children learn mathematics. Washington (DC): National Academy Press; 2001.
   Google Scholar
• Valverde GA, Schmidt WH. Greater expectations: learning from other nations in the quest for ‘world-class standards’ in US school mathematics and science. J Curriculum Stud. 2000;32(5):651–687.
   Web of Science ®Google Scholar
• Usiskin Z, Willmore E. Mathematics curriculum in Pacific rim countries – China, Japan, Korea, and Singapore: proceedings of a conference. Charlotte (NC): Information Age; 2007.
   Google Scholar
• NCTM. Principles and standards for school mathematics. Reston (VA): NCTM; 2000.
   Google Scholar
• Fuson KC, Carroll WM, Drueck JV. Achievement results for second and third graders using the standards-based curriculum Everyday Mathematics. J Res Math Educ. 2000;31(3):277–295.
   Web of Science ®Google Scholar
• Huntley MA, Rasmussen CL, Villarubi RV, et al. Effects of standards-based mathematics education: a study of the Core-plus mathematics project algebra and functions strand. J Res Math Educ. 2000;31(3):328–361.
   Web of Science ®Google Scholar
• Xu B. The development of school mathematics textbooks in China since 1950. ZDM Int J Math Educ. 45(5):725–736.
   Google Scholar
• Zhong QQ. Curriculum reform in China: challenges and reflections. Front Educ China. 2006;3:370–382.
   Google Scholar
• Charalambous C, Delaney S, Hui-Yu H, et al. A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Math Think Learn. 2010;12:117–151.
   Web of Science ®Google Scholar
• Cai J, Moyer JC. The teaching of equation solving: approaches in standards-based and traditional curricula in the United States. Pedagogies. 2010;5(3):170–186.
   Google Scholar
• Li Y. A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. J Res Math Educ. 2000;31(2):234–241.
   Web of Science ®Google Scholar
• Nie B, Cai J, Moyer JC. How a standards-based mathematics curriculum differs from traditional curriculum: with a focus on intended treatments of the ideas of variable. ZDM Int J Math Educ. 2009;41(6):777–792.
   Google Scholar
• Dubinsky E, Harel G. The nature of the process conception of function. In: Harel G, Dubinsky E, editors. The concept of function: aspects of epistemology and pedagogy. MAA notes 25. Washington (DC): The Mathematical Association of America; 1992. p. 85–106.
   Google Scholar
• Even R. Subject matter knowledge for teaching and the case of functions. Educ Stud Math. 1990;21(6):521–554.
   Google Scholar
• Dreyfus T, Eisenberg T. Intuitive functional concepts: a baseline study on intuitions. J Res Math Educ. 1982;13:360–380.
   Google Scholar
• Markovits Z, Eylon BS, Bruckheimer M. Difficulties students have with the function concept. In: Coxford AF, Shulte AP, editors. The ideas of algebra, K–12, 1988 yearbook of the National Council of Teachers of Mathematics (NCTM). Reston (VA): NCTM; 1988; p. 43–60.
   Google Scholar
• Schwingendorf K, Hawks J, Beineke J. Horizontal and vertical growth of the student's conception of function. In: Harel G, Dubinsky E, editors. The concept of function aspects of epistemology and pedagogy. Washington (DC): Mathematical Association of America; 1992. p. 133–149.
   Google Scholar
• Sfard A. Operational origins of mathematical objects and the quandary of reification – the case of function. In: Harel G, Dubinsky E, editors. The concept of function aspects of epistemology and pedagogy. Washington (DC): Mathematical Association of America; 1992. p. 59–84.
   Google Scholar
• Vinner S, Dreyfus T. Images and definitions for the concept of function. J Res Math Educ. 1989;20(4):356–366.
   Web of Science ®Google Scholar
• Carlson M. A cross-sectional investigation of the development of the function concept. In: Dubinsky E, Schoenfeld AH, Kaput JJ, editors. Research in collegiate mathematics education, III. Issues in mathematics education. Vol. 7. USA: American Mathematical Society; 1998. p. 115–162.
   Google Scholar
• Carlson MP, Oehrtman MC, Thompson PW. Foundational reasoning abilities that promote coherence in student’s function understanding. In: Carlson MP, Rasmussen C, editors. Key aspects of knowing and learning the concept of function in making the connection: research and practice in undergraduate mathematics. Washington (DC): Mathematical Association of America; 2005.
   Google Scholar
• Eisenberg T, Dreyfus T. On understanding how students learn to visualize function transformations. In: Dubinsky E, Schoenfeld A, Kaput J, editors. Research in collegiate mathematics education. Vol. 1. Providence (RI): American Mathematical Society; 1994. p. 45–68.
   Google Scholar
• Hartter BJ. A function or not a function? That is the question. Math Teach. 2009;103(3):200–205.
   Google Scholar
• Cai JF, Lo JJ, Watanabe T. Intended treatments of arithmetic average in US and Asian school mathematics textbook. School Sci Math. 2002;102(8):391–404.
   Google Scholar
• Stein MK, Kim G. The role of mathematics curriculum materials in large-scale urban reform: an analysis of demands and opportunities for teacher learning. In: Remillard J, Herbel-Eisenmann B, Lloyd G, editors. Mathematics teachers at work: connecting curriculum materials and classroom instruction. New York (NY): Routledge; 2009. p. 37–55.
   Google Scholar
• Fan LH, Zhu Y. Focus on representation of problem types in intended curriculum: a comparison of selected mathematics textbooks from mainland China and the United States. Int J Sci Math Educ. 2006;4:609–626.
   Google Scholar
• Cai JF, Ng SF, Moyer JC. Developing students’ algebraic thinking in earlier grades: lessons from China and Singapore. In: Cai J, Knuth E, editors. Early algebraization. Berlin: Springer; 2011. p. 25–41.
   Google Scholar
• Cai JF, Lew HC, Morris A, et al. The development of students’ algebraic thinking in earlier grades. ZDM Int J Math Educ. 2005;37(1):5–15.
   Google Scholar
• Lappan G, Fey JT, Fitzgerald WM, et al. Variables and patterns: teachers’ guide. Upper Saddle River (NJ): Prentice Hall; 2006.
   Google Scholar
• Bailey R, Day R, Frey P, et al. Mathematics: applications and concepts (Tennessee edition), course 2. Columbus (OH): The McGraw-Hill Company; 2006.
   Google Scholar
• Carter J, Gilbert GJ, Day R, et al. Math connects (Tennessee edition), course 3. Columbus (OH): The McGraw-Hill Company; 2012.
   Google Scholar
• Research Center for Middle School Mathematics Curriculum. Shu Xue. Beijing: People's Education Press; 2008.
   Google Scholar
• Dossey J, Halvorsen K, McCrone S. Mathematics education in the United States 2008: a capsule summary fact book. Report presented at: The 11th International Congress on Mathematics Education; 2008; Monterrey, Mexico.
   Google Scholar
• Tabachneck HJM, Koedinger KR, NathanMJ. An analysis of the task demands of algebra and the cognitive processes needed to meet them. Proceedings of the 1995 annual meeting of the Cognitive Science Society. Hillsdale (NJ): Lawrence Erlbaum Associates Inc.; 1995. p. 397–402.
   Google Scholar
• NCTM. A framework for constructing a vision of algebra. Algebra working group document. Reston (VA): NCTM; 1997.
   Google Scholar
• Bednarz N, Kieran C, Lee L, editors. Approaches to algebra: perspectives for research and teaching. Dordrecht: Kluwer; 1996.
   Google Scholar
• Ferrini-Mundy J, Graham K. Research in calculus learning: understanding limits, derivatives, and integrals. In: Kaput JJ, Dubinsky E, editors. Research issues in undergraduate mathematics learning. MAA notes 33. Washington (DC): The Mathematical Association of America; 1994. p. 31–45.
   Google Scholar
• Sliver EA. Cross-national comparisons of mathematics curriculum materials: what might we learn? ZDM Int J Math Educ. 2009;41(6):827–832.
   Google Scholar
• Stevenson HW, Bartsch K. An analysis of Japanese and American textbooks in mathematics. In: Leetsman R, Walberg HJ, editors. Japanese educational productivity. Greenwich (CT): JAI Press; 1992. p. 103–134.
   Google Scholar
• Cai JF. Improving mathematics learning: lessons from cross-national studies of Chinese and US students. Phi Delta Kappan. 2001;82(5):400–404.
   Web of Science ®Google Scholar