The Mathematics Education I and II Courses' Effect on Teacher Candidates' Development of Number Sense

Article excerpt

(ProQuest: ... denotes formulae omitted)

Number sense has been recognized as one of the major objectives of the elementary school mathematics in the "Everybody Counts" document created by the National Research Council in 1989 (National Research Council [NRC], 1989). In addition, the importance of number sense in mathematics education has been much more emphasized by specifying it as a standard in the document, "Curriculum and Evaluation Standards for School Mathematics," presented by the National Council of Teachers of Mathematics (Chow, 2001; Markovits & Sowder, 1994; National Council of Teachers of Mathematics [NCTM], 1989). Along with these documents, teachers, researchers and curriculum writers have taken a growing interest in number sense (Hope, 1989; Howden, 1989, Markovits & Sowder, 1994; McIntosh, Reys, & Reys, 1992; Pike & Forrester, 1996; Reys & Yang, 1998).

In the NCTMs "Principles and Standards for School Mathematics" (2000), number sense is identified as one of the fundamental ideas of mathematics for students. This document indicates that students need to: "(/') understand numbers, ways of representing numbers, relationships among numbers, and number systems; (it) understand the meanings of operations and how they relate to one another, and (Hi) compute fluently and make reasonable estimates" (p. 32). It points out that, in mathematics courses, children are mostly directed to use standard algorithms, and that mathematical education does not support the development of number sense (Reys et al, 1999).

Although Turkeys Elementary Education (First-Fifth Grades) Mathematics Curriculum1 (Ministry of National Education- Milli Egitim Bakanligi [MoNE], 2009) contains a "Numbers" learning topic, there are no direct statements regarding number sense. Only the descriptions in the operational estimation section under the subject of estimation strategies can be associated with number sense. Moreover, some information concerning the use of reference points is provided in the special numbers section (pp. 17-18). The Middle School (Fifth-Eighth Grades) Mathematics Curriculum was renewed in 2013. Two of its indicators for reasoning skill in mathematics are related to the results of operations, and the indicators for measurement considering a reference point are associated with number sense (MoNE, 2013, p. v).

Number Sense

Although it is difficult to precisely define number sense, different researchers have offered various definitions. Hope (1989) has described number sense as a feeling of being able to make reasonable estimations about the various uses of numbers, being able to recognize arithmetic errors, being able to select the most effective computing method, and being able to notice number patterns. Number sense is also defined as "a good intuition about the numbers and their relationships" (Howden, 1989, p. 11). Reys and Yang (1998), on the other hand, defined number sense as "a persons general understanding regarding numbers and operations" (pp. 225-226). In fact, they argue that there should be flexibility in the use of this concept, which they define as the ability and tendency to make mathematical decisions and to develop useful strategies for numbers and operations. Number sense is also defined as "using numbers in a flexible manner, thinking practically about operations with numbers, choosing the most effective and convenient solutions, sometimes finding nonstandard solutions to problems, benefiting from a reference point that simplifies the problem, and using conceptual thinking for fractions and different forms of representation for fractions" (Kayhan Altay & Umay, 2013, p. 251). Greeno (1991) claims, "number sense is a term that requires a theoretical analysis, rather than a definition" (p. 170) and that number sense is a form of cognitive expertise. According to him, number sense means knowing what resources are offered by an environment, how to find these resources in activities and how to use them, and to understand and comprehend hidden patterns. …

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