Academic journal article Educational Technology & Society

Assessment of Animated Self-Directed Learning Activities Modules for Children's Number Sense Development

Academic journal article Educational Technology & Society

Assessment of Animated Self-Directed Learning Activities Modules for Children's Number Sense Development

Article excerpt

Introduction

Number sense has been considered as one of the most important topics in mathematics education (Dunphy, 2007; Jordan, Glutting, & Ramineni, 2010; National Council of Teachers of Mathematics, [NCTM], 2000; Verschaffel, Greer, & De Corte, 2007; Yang & Tsai, 2010). However, several number sense studies showed that not only middle and elementary school children (Markovits & Sowder, 1994; Mcintosh, B. Reys, R. Reys, Bana, & Farrel, 1997; Menon, 2004a; Reys & Yang, 1998; Yang & Li, 2008) but also preservice teachers performed poorly in solving problems related to number sense (Menon, 2004b; Yang, Reys, & Reys, 2009). Mathematics educators have found that children's inflexibility in handling number sense problems may be related to the inappropriate design of mathematics textbooks and the rule-based instruction of school mathematics (Markovits & Sowder, 1994; Menon, 2004a; Reys & Yang, 1998; Yang & Li, 2008). For example, previous studies showed that traditional instruction, which focuses primarily on standard written computation rather than conceptual understanding, may result in children's difficulties in using number sense flexibly and efficiently (Menon, 2004a; Yang & Li, 2008). Helping children develop number sense has been highlighted in school mathematics by many reports and studies (Bobis, 2004; Dunphy, 2007; Mcintosh et al., 1997; NCTM, 2000). Seeking an effective learning material that would facilitate children's development of number sense is an urgent issue for current mathematics education.

Previous studies and reports have strongly suggested that technology should be integrated into mathematics teaching and learning, since technology is a promising means for providing conceptual understanding (Dick, 2007; Inamdar & Kulkarni, 2007; NCTM, 2000; Ruthven, 2007; Vulis & Small, 2007; Yang & Tsai, 2010; Zbiek, Heid, Blume, & Dick, 2007). For example, NCTM (2000) highlights that the integration of technology into mathematics classroom settings can enhance children's mathematics learning and promote conceptual understanding. In addition, Olive and Lobato (2008) state that "providing technological tools that enable children to enact their own mathematical operations can be a very powerful aid to children's learning" (p. 43). Technology can provide dynamic visualization, immediate feedback, and interactivity that can help children learn mathematics effectively (Gegner, Mackay, & Mayer, 2009; Suh & Moyer-Packenham, 2007). Therefore, it is reasonable to believe that technology should play a key role in helping children learn mathematics.

Accordingly, the purpose of this study was to examine the effectiveness of computer animation self-directed learning number sense-based activities compared with a corresponding paper-version approach. The specific research questions are as follows:

* Are there any significant differences in students' performance on number sense across the two self-directed learning approaches after the experiment?

* Are there any differences in methods used by students to solve number sense problems across the two self-directed learning approaches after the experiment?

Background

Number sense framework

What is number sense? Number sense refers to an individual's general understanding of numbers, operations, and the relationship between number and operation, and the ability to handle daily-life situations that include numbers (Markovits & Sowder, 1994; Reys & Yang, 1998; Yang & Tsai, 2010). During the past two decades, due to the importance of number sense, several research studies and reports have been produced (Markovits & Sowder, 1994; NCTM, 2000; Reys & Yang, 1998; Verschaffel et al., 2007; Yang & Li, 2008; Yang & Tsai, 2010). Even though these studies and reports defined number sense from different perspectives, they have included the following major common components: (a) Understanding the basic meanings of numbers; (b) recognizing number size; (c) Being able to use multiple representations; d) Recognizing the relative effect of operation on numbers; and e) Being able to judge the reasonableness of a computational result via estimation or mental computation (Markovits & Sowder, 1994; NCTM, 2000; Reys & Yang, 1998; Verschaffel et al. …

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