Understanding and representing the arithmetic averaging algorithm: an analysis and comparison of US and Chinese students' responses

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U.S. and Chinese Teachers' Constructing, Knowing, and Evaluating Representations to Teach Mathematics (2005, methodology): “All of these problems except one are directly adopted from the studies of U.S. and Chinese students’ thinking (e.g., Cai, 2000a; Cai & Hwang, 2002).”
Preservice Elementary Teachers' Conceptual and Procedural Knowledge of Mean, Median, and Mode (2006, background): “The thinking exhibited by preservice teachers in this study strongly resembles the thinking of elementary and middle school children in the research literature summarized earlier (Cai, 2000; Jones et al., 2000; Mokros & Russell, 1995; Mooney, 2002; Watson & Moritz, 2000).”
Preservice Teachers Understanding of the Mean: Moving Beyond the Arithmetic Average (2006, background): “Important indicators of conceptual understanding of the mean include (but are not limited to) recognition of contexts where the mean is a suitable measure (Watson & Moritz, 2000), the ability to solve weighted mean problems (Mevarech, 1983; Pollatsek et al., 1981), recognition of the mean as a repre”