The Strategies of Mathematics Teachers When Solving Number Sense Problems

Number sense refers to a person’s general understanding of numbers, operations and their relationships and using this understanding to handle daily-life situations related to numbers. Number sense is used to develop practical, flexible, and efficient strategies (including mental computation and estimation) to handle numerical situations (McIntosh, Reys, & Reys, 1992; Yang, 2003). Students with good number sense can use numbers (like compose/decompose) flexibly when mentally computing, estimating, recognizing the magnitude of numbers, judging the reasonableness of computational results, recognizing the relative effect of operation on numbers, developing benchmarks about measurements and magnitudes, moving between number representations and relating the numbers, symbols and operations (Burns, 2007; Gersten & Chard, 1999; Markovits & Sowder, 1994; Shumway, 2011; Sowder & Kelin, 1993). In the literature, many studies and reports point to the necessity and importance of improving number sense of students (National Council of Teachers of Mathematics, 2000; Anghileri, 2006). However; the research in the literature show that students have an inclination to use rule based methods and standard written algorithms and generally have low number sense (Alsawaie, 2011; Reys et al. , 1999; Yang, 2005; Yang & Li, 2008; Yang, Li, & Lin, 2008). There are some possible reasons of this failure situation and Yang et al. (2009) pointed to one of them. They indicated that children’s lack of number sense may be partly due to their teachers’ lack of number sense. If the teachers design a good learning environment with communication, thinking, reasoning, and discussion while using number sense activities, they can improve their students’ number sense (Crites, 1994; Markovits & Sowder, 1994; Tsao, 2004; Yang, 2003; Yang, Hsu, & Huang, 2004). The aim of this study is to investigate the strategies that are used by mathematics teachers while solving the number sense-related problems. To develop a number sense test, the literature is reviewed. The total of 12 questions from four number sense components are selected from different studies (Yang, 2007; Yang, Reys & Reys, 2009; Tsao, 2005). The number sense components are: a) understanding the meaning of numbers, operations and their relationships, b) recognizing relative number size, c) developing and using benchmarks appropriately, d) judging the reasonableness of a computational result by using the strategies of estimation. Two experts reviewed the questions and both agreed that they are appropriate. A pilot study is conducted with four mathematics teachers. In this study, 11 mathematics teachers (5 female and 6 male) from a graduate program in education participated. Each participant is given the number sense test and asked to explain their solution strategy after solving the problems. In data analysis, 132 responses from 11 participants are examined. At first the answers are evaluated for correctness. In the second part of data analysis, the strategies teachers used are analyzed. The strategies are assessed as number sense strategy or rule based strategy. The results of the data analysis show that the 84.1% of the teachers’ provided correct answers consistently and 15.9% gave incorrect answers. In the 54.9% of the correct answers, number sense strategies are used and in the 45.1% of the correct answers rule-based strategies are used. When the correct and incorrect answers are analyzed together, in the 46.2% of the answers number sense strategies, and in 53.8% of the answers the rule-based strategies are used. The results of this study show that even though teachers may use the number sense strategies at some, but not at the desired level. Teachers tended to use the rule-based strategies and standard written algorithms.