Proportional reasoning, an essential part of learning and understanding science and mathematics, has been investigated in numerous studies in many countries ( Karplus, Karplus, Formisano, & Paulsen, 1977 and 1978; Karplus, 1978). As part of an effort to exchange information regarding the development of reasoning with scholars in the People's Republic of China, the author administered the Paper Clips task ( Karplus, 1978). In this task students had to deduce a scale factor from given and measured data to predict the height of a hypothetical figure ( Comrade Tall). The task included two similar items.
Forty-nine fourth- and fifth-grade students from the laboratory school of Shanghai Teachers University participated in the investigation. They included 22 girls and 27 boys, who were studying the fifth-grade mathematics syllabus that included concern with ratio and proportions. Most were the children of professional workers such as teachers at the University itself. The 14 fourth graders were gifted students who had been moved one year ahead in their mathematics studies. The 35 fifth graders were selected by their teachers from the school's total fifth-grade enrollment of about twice that number.
The Paper Clips task was administered in the usual fashion, using Chinese paper clips and a suitably scaled illustration of "Comrade Short" so his height would be about six and one-half paper clips. An instructor from the University's foreign language department translated the author's oral explanations and instructions. The papers were handed in by the students after five to 20 minutes of effort, whenever they had completed their work.
Forty-six of the 49 students used proportional reasoning by applying ratios successfully on at least one of the two items of the task, and 37 used this approach on both items. No student used the incorrect additive reasoning that had been observed in many student samples in the United States and Europe ( Karplus , et al., 1977; Karplus, 1978). For comparative purposes, therefore, the percentages of students using ratios on the first of the two items (which was the____________________