# Errors in Solving Word Problems about Speed: A Case in Singapore and Mainland China

## Article excerpt

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The study of pupils' problem-solving errors in different topics is a prominent field in mathematics education (Ashlock, 1998; Babbitt, 1990; Booth, 1983; Cox, 1975; Engelhardt, 1977; Olivier, 1989; Radatz, 1979, 1980; Roberts, 1968). Errors lead to wrong answers. They are systematic when that they are applied regularly in the same circumstances (Olivier, 1989), and they can be resistant to casual re-education (Booth, 1983). Such errors are caused by underlying conceptual structures which are called misconceptions (Olivier, 1989). Students' errors are not simply a result of ignorance or carelessness. They are often caused by an overgeneralization of previous knowledge that is correct in an earlier domain to an extended domain that is not valid (Olivier, 1989; Radatz, 1980). Diagnostic error analysis not only provides information about individuals' mathematics learning, but also provides practical help for teachers with regard to individualized instruction. These kinds of analysis remind teachers to be sensitive to the effects of individuals' previous learning and to make an effort to connect new knowledge to previous learning (Olivier, 1989; Radatz, 1979). This study investigates errors students make when solving word problems about speed at the elementary level.

The topic of word problems about speed was selected for study because these problems apply various mathematical concepts from the primary to the university level (Bowers & Nickerson, 2000; Ministry of Education (MOE) (Singapore), 2000a, 2000b; Nichols, 1996; People's Education Press (PEP), 1994; Teh & Looi, 2002a, 2002b; Tylee, 1997). Several studies have included rate problems as a specific model of multiplication and division (Bell, Fischbein, & Greer, 1984; Fischbein, Deri, Nello, & Marino, 1985; Greer, 1992). However, the word problems about speed included in these studies were from only the simplest category of the 13 categories of motion (speed) problems that Mayer (1981) identified. Mayer analyzed algebraic word problems including those about speed in secondary school mathematics textbooks, but Mayer did not investigate how students actually solve the problems and what difficulties they may have. This study seeks in part to fill these gaps.

The participants in this study came from grades 6-8 because similar word problems about speed are presented in the mathematics textbooks for these three grades (L. Jiang, 1998a, 1998b; PEP, 1992, 1993a, 1993b; MOE (Singapore), 2000a, 2000b; Teh & Looi, 2002a, 2002b).

This study also endeavored to reveal the similarities and differences between the students in the two different contexts (Singapore and China). Cross-national studies provide us with an opportunity to ascertain the strengths and weaknesses of educational systems (Robitaille & Travers, 1992), and consequently provide information about how to improve the teaching and learning of mathematics (Cai, 2000a, 2004; Robitaille & Travers, 1992). Children from Singapore and China have performed exceptionally well in international comparative studies in mathematics (Mullís, I. V. S., Martin, M. O., Beaton, A. E., Gonzalez, E. J., Kelly, D. L., & Smith, T. A., 1997; Zhang, 1998). Singapore was ranked first to third in mathematics among the participating countries for grades 4 and 8 in the Trends in International Mathematics and Science Studies (TIMSS) in 1995, 1999, 2003, and 2007 (Beaton, A., Mullís, I., Martin, M., Gonzalez, E., Kelly, D. & Smith, T., 1996; Mullís et al., 1997; Mullís, Martin, & Foy, 2008; Mullís, Martin, Gonzalez, & Chrostowski, 2004; Mullís, I. V. S., Martin, M. O., Gonzalez, E. J., Gregory, K. D., Garden, R. A., O'Connor, K. M., et al., 2000). In the Second International Assessment of Education Progress (SIAEP), China was ranked first among the twenty-one participating countries for 13-year-olds (Zhang, 1998). The Programme for International Student Assessment (PISA) found that Chinese students from Shanghai performed the best (OECD, 2010). …

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