Skills of Using and Transform Multiple Representations of the Prospective Teachers

Multiple Representations in 8th Grade Mathematics Textbook and the Extent to which Teachers Implement Them

“…Moreover, results of low representation by real life situations are in agreement with the results of the study of Yan and Lianghuo (2004) which cited that it is a common in most textbooks in the world the lack of real life situations representations such as the Unites States of America and China. Results of this study also align with the study of Bal (2015) that there is a lack in the use of representations in the curricula; and that the presentation of the curricula is still controlled by the traditional way.…”

“…Many international researchers who are interested in mathematics such as (Cai & Lester, 2005;Dreher & Kuntze, 2015;Dwi, Subanji, Hidayanto & Anwar, 2017;You & Quinn, 2010) consider mathematical representations as the basic feature to teach and learn math, whereas researchers mentioned that mathematical representations are closely improving students' learning and understanding of math (Anthony & Walshaw, 2009;Greeno & Hall, 1997;Santulli, 2009;Tripathi, 2008). Nonetheless, there are only few studies that highlighted the role of the textbook and teachers in facilitating students' understanding through using mathematical representations (Bal, 2015;Bayazit, 2011;Yan & Lianghuo, 2006;Ulu, 2017) Reviewing the literature concerning mathematical representations; the work of Lesh, Post, and Behr (1987) was one of the most important in this area, they constructed a model of the various elements in which mathematical representations are structured. This model is consisted of five elements (Figure 1); (1) representations by written symbols such as writing numbers or symbols to express the math concept, (2) spoken representations which indicate expressing the math concept by words which allows often for more rephrasing the words and linking the concepts with other areas and life situations.…”

Alteration Representation in the Process of Translation Graphic to Graphic

“…In their study, they found that students have not been able to translate from a physical context to a graphic instead of making a verbal translation to a graphic. While Bal (2015), in a study conducted with 134 primary school teachers prior to service in state universities in Turkey, they found that they generally were not successful in translating verbal representations to other representations. The teachers reported that several representations help to better understand the problems and produce some solutions.…”

“…He said that "part of what we mean when we say that 'understanding' students are that: (1) you can recognize the idea embedded in a variety of different systems of representation qualitatively, (2) which can be flexible to manipulate ideas in certain systems of representation, and (3) can accurately translate ideas from one system to another." Translation activities from one representation to another are very important in the learning process to express mathematical ideas (Duval, 2006;Bal, 2015;Bossé, Adu-Gyamfi, & Cheetham, 2011). In addition, NCTM (2000) suggests that students "choose, apply and translate mathematical representations to solve problems".…”

“…However, reality shows that the ability to translate representations between verbal, tables, graphical and symbolic relationships in mathematical relationships is still low (Gagatsis & Shiakalli, 2004). Previous research related to the translation of mathematical representations has been carried out at all levels of education, both in secondary education (Çelik & Sağlam-Arslan, 2012; Bossé, Adu-Gyamfi, & Chandler, 2014; Rahmawati, Purwanto, Subanji, Hidayanto, & Anwar, 2017) and higher (İpek & Okumuş, 2012;Bal, 2015). İpek & Okumuş, (2012) to conduct research on future primary school teachers in the use of representations that can not translate between representations.…”