Abstract
The aim of this study is to reveal teacher candidates’ preference regarding uses of verbal, symbolic, number line, and/or model representations of fraction divisions, and to investigate their skill of transferring from one representation type to the others. Case study was used as the research method in this study. The case that is examined within the scope of the study involves the performances of students in transiting between different representations of the fraction division. The study group consisted a total of 71 mathematics teacher candidates who were students in a university in Turkey. Among the results of the study were that the comparison of the performances of the pre-service teachers in transitions between representations reveals that the pre-service teachers were quite successful in expressing a fraction whose verbal or numeric (symbolic) expression was provided through other types of representation, but they were very unsuccessful in representing the fractions that were provided via models or on number lines through other types of representation. Key words: Multiple representations, division of fractions, mathematics teacher candidates.
Highlights
The representations that one uses when solving mathematical problems provide us with a gateway to understanding his/her thinking (NCTM, 2000)
Utilizing multiple representations during problem solving provides opportunities for the students to engage with the problem from the different aspects and to investigate deeply (Driscoll, 1999; McGowan and Tall, 2001)
This study investigated the preferences of pre-service teachers for using multiple representations such as verbal representation, symbolic representation, number line representation and model representation in division in fractions and their competences for using such representations and transiting between such representations
Summary
The representations that one uses when solving mathematical problems provide us with a gateway to understanding his/her thinking (NCTM, 2000). Utilizing multiple representations during problem solving provides opportunities for the students to engage with the problem from the different aspects and to investigate deeply (Driscoll, 1999; McGowan and Tall, 2001). This is, in turn, beneficiary for robust understanding of the concepts. One theory of learning in mathematics is the multiple representations can be utilized to help students develop deeper, more flexible understanding of the concepts and processes (Even, 1998; Hiebert and Carpenter, 1992; Keller and Hirsch 1998; Piez and Voxman, 1997).
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