Academic journal article Educational Technology & Society

# Effects of Worked Examples Using Manipulatives on Fifth Graders' Learning Performance and Attitude toward Mathematics

Academic journal article Educational Technology & Society

# Effects of Worked Examples Using Manipulatives on Fifth Graders' Learning Performance and Attitude toward Mathematics

## Article excerpt

Introduction

The concept of equivalence plays an important role in learning fractions. Students must first be equipped with basic concepts related to fractions before they can learn the meaning of equivalent fractions and it is only after these two steps that the concept of rational numbers can be further developed. The equivalence relation of fractions must be taken into consideration when comparing the order relation between two fractions. An understanding of the concept of equivalent fractions is the basis for performing the four arithmetic operations (addition, subtraction, multiplication and division) on fractions with different denominators. Equivalent fractions are the most difficult of all sub-concepts related to fractions, requiring that students have flexibility in their thought processes and a willingness to solve problems by advancing from concrete operations into formal operations. However, among elementary school students, the comprehension of the concept of equivalent fractions tends to be quite weak (Kamii & Clark, 1995). Elementary school students in Taiwan also have this problem; in fact, many students are unable to fathom that one half is equal to two quarters, even if they have previously studied equivalent fractions (Yu & Leu, 2002). An incomplete understanding of fractions or overly rigid thinking can prevent students from solving problems related to equivalent fractions.

Most elementary school students are at the stage of concrete operations, in which action and iconic representation can only be formed through actual practice. Therefore, physical manipulatives are commonly used in mathematics education to make abstract ideas and symbols more meaningful and comprehensible to students (Durmus & Karakirik, 2006). Developing a comprehension of concepts related to equivalent fractions requires that objects be split into different portions; however, physical manipulatives are ill-suited to the arbitrary splitting of objects. Moyer, Bolyard, and Spikell (2002) recently defined virtual manipulatives as interactive, web-based visual representations of a dynamic object capable of facilitating the development of mathematical concepts by students. Virtual manipulatives allow the splitting of objects into different portions to facilitate the learning of concepts associated with equivalent fractions. This enables students to visualize specific, abstract mathematical concepts and the content of learning can be broken down for presentation purposes (Chang, Yuan, Lee, Chen, & Huang, 2013). This makes virtual manipulatives excellent tools to facilitate the learning of concepts associated with equivalent fractions.

Worked examples have been successfully applied in the instruction of computer programming, algebra, and geometry (Carroll, 1994; Paas & van Merrienboer, 1994). Students with experience using worked examples as an instructional strategy adopt problem-solving techniques more quickly and present heightened problem solving performance (Chandler & Sweller, 1991). The provision of appropriate worked examples can aid in the formation of concepts by learners. Virtual manipulatives and worked examples offer exciting new possibilities as learning aids; however, there's a noticeable lack in the literature of the large-scale validation of these strategies and few studies have explored the practical implementation of combining worked examples with virtual manipulatives. Understanding the properties of worked examples with virtual manipulatives and how these relate to learning is important in predicting which material will be more beneficial and can help to inform the design of new learning materials. This study explores how different approaches to example integration influence the learning performance of fifth grade students.

Literature review

Factors affecting the learning of equivalent fractions

A failure to learn the concept of equivalent fractions is due mainly to overly rigid thinking (Peng & Leu, 1998). …

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