D EVELOPMENT OF M ULTIPLE R EPRESENTATION T RANSLATING M EASUREMENT T OOL AND E XAMINATION OF 9 TH G RADE S TUDENTS ’ M ULTIPLE R EPRESENTATION T RANSLATE S KILLS IN A LGEBRA

: In this study, it was aimed to examine 9th grade students' multiple representation translate skills in algebra learning area and the relationship between these representations translate skills. The study employs survey design. Selected through purposive sampling method, 637 ninth grade students in a socio-economically medium level province in Turkey participated to the study. Within the scope of the study, Multiple Representation Translating Measurement Tool (MRTMT) including four factors (verbal- graph- algebraic- table) was developed and data were collected through this instrument. The validity and reliability of the scale was tested with Rasch analysis and confirmatory factor analysis (CFA). Cronbach Alpha value was calculated as .88. The findings show that students’ skills of translating between representations level is low. In addition, students were most successful in expressing the situation with other representations when the table representation was given, but had difficulty in translating it to other representations when given an algebraic representation. Furthermore, it is found out that there is a significant relationship between students’ translating skills to verbal- graph- algebraic- table representations. Accordingly, it can be suggested that each representation should be used in an interrelated and holistic way in algebra teaching.


Introduction
Mathematics is an abstract discipline and has its own terminology. Algebra is a learning area where we use this terminology most in mathematics. In the most general sense, algebra is the language of mathematics and this language consists of meanings and operations (Baki, 2018). In addition, algebra has been recognized as a critical turning point in students' mathematics learning (Wang, 2015). On the other hand, it is important to teach algebra with understandable representations since it is considered incomprehensible and abstract. Accordingly, because algebra is perceived as abstract by students, it is stated that there is a need to use multiple representations effectively and to associate these representations in algebra teaching (Sarpkaya Aktaş, 2019). As a matter of fact, the conceptual learning desired in mathematics teaching is possible by understanding the problem situation with various representations and translating the knowledge to different representations (Bossé, Adu-Gyamfi & Chandler, 2014;Keller & Hirsch, 1998;Ural, 2012). Multiple representations are used extensively in mathematics (Gagatsis & Shiakalli, 2004). The use of multiple representations in many fields of mathematics education and the investigation of translate skills give important clues about the conceptual and meaningful learning of the subject studied.
In the literature, we often come across studies investigating translate skills between multiple representations in algebra teaching. A review of literature suggests that the studies mostly focus on elementary education (Akkuş & Çakıroğlu, 2006;Demir & Cansız Aktaş, 2019;Deniz, 2016;Gurbuz & Sahin, 2015;Mourad, 2005;Sarıhan Musan, 2012;Sert, 2007) and higher education levels (Andrá, Lindström, Arzarello, Holmqvist, Robutti & Sabena, 2015;Bal, 2015;De Bock, Van Dooren & Verschaffel, 2015;Galbraith & Heines, 2000;Ipek & Okumus, 2012;Kardes, Aydin & Delice, 2012;Presmeg & Nenduradu, 2005). In these studies, multiple representation translates were generally identified by adopting qualitative methods (Deniz, 2016;Fonger, Davis, Rohwer & Lou, 2018;Gurbuz & Sahin, 2015;Huntley & Davis, 2008;Ipek & Okumus, 2012;Presmeg & Nenduradu, 2005;Rahmawati, Purwanto, Subanji, Hidayanto & Anwar, 2017). Multiple representation translate tests developed in mathematical contexts in the field of algebra (Bal, 2015;Demir & Cansız Aktaş, 2019;Kardeş et al., 2012;Ozhan-Turan, 2011) are available in the literature. However, a valid and reliable instrument that verifies the multiple representation components (verbal-graph-algebraic-table) at secondary education level is not available in the literature, to the researcher's best knowledge. On the other hand, in secondary education curricula, there are many learning outcome guidelines that encourage the use of instructional technologies with which we can easily integrate multiple representations in algebra teaching (MoNE, 2018;NCTM, 2000) because secondary level students are ready for this. It is believed that it is sufficient for a high school student to show skill only in algebraic operations. However, it is important to get them provide not only operational mechanics but also translates between representations for conceptual learning (Duval, 2006). Many researchers draw attention to the importance of representations in mathematical understanding and associate the understanding of mathematical knowledge with representations (Adiguzel & Akpinar, 2004;Goldin, 2003;Janvier, 1987;Parrot & Leong,2018;Schultz & Waters, 2000). This study focuses on translate skills between multiple representations, which are stated to have an important role in critical mathematical skills such as conceptual learning, problem solving, and relating (Bossé et al., 2014;Keller & Hirsch, 1998;Ural, 2012). Since students experience challenges in algebra which is thought to be abstract (Lew, 2004;van Ameron, 2002;Witzel, Mercer, & Miller, 2003), the current research has been carried out on the examination of multiple representations and their translate, which is a method to overcome these difficulties.
In this study, the process of the original development of the multiple representation translate test for 9th grade students and examination of 9th grade students' multiple representation translate skills in the field of algebra learning through the quantitative research method-unlike previous research-are reported. Multiple Representation Translating Measurement Tool was originally developed in this study based on verbal-graph-algebraic-table multiple representation components (Bossé, Adu-Gyamfi & Cheetham, 2011a;Heinze, Star & Verschaffel, 2009;Waisman, Leikin, Shaul & Leikin, 2014;Wilkie, 2016) in line with equations and disequilibrium sub-learning areas in secondary education 9th grade curriculum (MoNE, 2018). In addition, it was sought to answer the following research questions: "What is 9th grade students' level of multiple representation translate skills in algebra learning area?" and "Are there relationships among 9th grade students' verbalgraph-algebraic-table multiple representation skills in algebra learning area?"

1. Representation, Multiple Representation, Translate
Representation is a structure that replaces another one, such as a word for an object, a sentence for a situation, a scheme for the arrangement of things, a picture for a scene (McKendree, Small, Stenning & Conlon, 2002). Visual representations can differ in various design dimensions: they can be concrete or abstract; they can be physical (i.e. visual features are concrete) or virtual (i.e. visual features are presented on a digital display); they can be static or animated (i.e. visual properties change during the learning experience); and they can be interactive (Rau, 2017). There are different classifications of the concept of representation in the literature. One of these classifications is the classification made by Lesh, Post & Behr (1987) consisting of pictures and diagrams, manipulatives, verbal symbols, written symbols and real life situations components. Kaput (1998) stated that such a classification is cognitive in essence and does not take into account other perspectives related to thinking and learning (cognitive, behavioral, etc.). Lesh, Post & Behr (1987) expresses representation as external practices of students ' inner understanding. While Wileman (1980) claims that there is no difference between internal (mental) representations and external representations, and internal representation is the image of the external representation in the mind (cited in: Bayik, 2010), some researchers believe that students' mental development is directly related to their ability to work (Pape & Tchoshanov, 2001). Students can be more actively involved in learning to construct and interpret representations by discussing the properties of representations, including their advantages and limitations. (Greeno & Hall, 1997, p. 362).
The concept of multiple representations in mathematics education is emphasized by many researchers (Aviles-Garay, 2001;Bieda & Nathan, 2009;Dundar, 2015;Even, 1998;Gagatsis & Shiakalli, 2004;Hitt, 2002;Kaya, 2015). Researchers stated that learning with multiple representations is necessary for a conceptual understanding of mathematics (Adu-Gyamfi et al., 2015;Bossé et al., 2014;Dreher, Kuntze & Lerman, 2015;Keller & Hirsch, 1998). The reason why multiple representations are emphasized by researchers is that a single representation cannot express a mathematical item clearly and saliently. At this point, it was suggested that in order to learn a concept, it should be constructed by diversifying the concept with its external representations as much as possible, and that more opportunities should be given for translate between representations (Hitt, 2002).
Translate is defined as the transition from one representation style to another (Janvier, 1987) and "movement required by an interpretation into a different modality of representation" (Roth & Bowen, 2001, p. 161). What is translated is not the representation itself, but the ideas or structures expressed through representations (Adu-Gyamfi, Stiff & Bossé, 2012). The term translate is the successful transformation of the information and relationships expressed by a mathematical representation into a target representation. The term translates used in this study refers to matching the structures of a mathematical representation with another representation. An example of this process is to take a statement presented in tabular form and express it graphically while maintaining its rule or relationship. Thus, the translate process includes two forms of representation, an initial (input) representation and a target (output) representation (Adu-Gyamfi et al., 2012). The translate will be successful if the basic elements or structures expressed in the initial representation are successfully expressed through the structures in the target representation.

Multiple Representation and Algebra
Students perceive algebra as a very difficult lesson (Egodawatte, 2011;Kalaivani & Tarmizi, 2014). In particular, teaching algebra as a subject dealing only with abstract symbols supports students' belief that mathematics does not make sense (Lew, 2004). The concept of variable which involves symbols is considered one of the most difficult and important concepts in algebra. Therefore, students have difficulty in learning this subject conceptually. If abstract concepts are taught to students in a concrete way, this difficulty can be eliminated or reduced (Kalkan, 2014). At this point, teachers can encourage students to think by choosing problems involving meaningful real-life situations and a teaching method that encourages students to think in different ways.
The purpose of supporting translates between multiple representations is to enable students to build their representations onto each other's to develop strong mathematical ideas, instead of making mathematical discussions with different methods using separate representations to solve a specific problem (Stein, Engle, Smith & Hughes, 2008). Translating multiple representations in mathematics teaching gives the opportunity to conceptualize, express and observe mathematical concepts in different ways. Hitt (1998) supported this view and stated that the main purpose of teaching mathematics is to enable students to pass from one representation type to another without falling into contradictions. Many teaching approaches have been proposed by the mathematics education community to address this current problem. The key role of learning mathematics, emphasized by many researchers in the field of mathematics education, is also expressed in the current national standards of many countries (e.g. NCTM, 2000;Education Minister Confererence-Kultus Minister Konferenz [KMK], 2003). As a component of mathematical competency, KMK expressed using mathematical representations as: • Implementing, interpreting and distinguishing different representations for mathematical objects and situations, • Recognizing the connections between representations and • Choosing different representations and changing between them depending on the conditions and purpose (KMK, 2003, p. 8).
In studies on algebra, we usually see the multiple representation components as verbal-graph-algebraictable representations (Bossé et al., 2011a;Heinze et al., 2009;Waisman et al., 2014;Wilkie 2016). For this reason, in this study, the research was conducted with a measurement tool which was verified by referencing these four representations.
The purpose of this study is to examine 9th grade students' multiple representation translate skills in algebra learning area and the relationship between these representations translate skills by the original developed tool (MRTMT). The researh questions were determined as; -What is 9th grade students' level of multiple representation translating skills in algebra learning area? -Are there relationships among 9th grade students' verbalgraph-algebraic -table multiple representation skills in algebra learning area?

Research Design
In this study, 9th grade students translate skills between representations in algebra were examined through survey model within the scope of quantitative research methods. Survey design research studies are mostly carried out with descriptive purposes and put forth the picture of a case at a specific time (Robson, 2017). This study reveals 9th grade students' level of translate skills between multiple representations in algebra without experimental intervention to conditions, objects and individuals.

Participants
Selected through purposive sampling method, 637 ninth grade students studying at different types of high school in a socio-economically medium level province in Turkey participated to the study. Accordingly, the criteria were studying at ninth grade and different types of high schools. Participants' distribution in terms of gender is presented in Table 1. According toTable 1. 332 (52.1%) female and 305 (47.9%) male students participated in the study. In addition, the school distribution of the students participating in the study is given in Table 2. As is given in Table 2, of the participants in the study, 84 (13.2%) were from the first high school, 110 (17.2%) were from the second high school, 55 (8.6%) were from the third high school, 92 (14.5%) were from the fourth high school, 42 (6.6%) were from the fifth high school, 98 (15.4%) were from the first sixth school, 76 (12%) were from the seventh high school, 41 (6.4%) were from the eighth high school, 39 (6.1%) were from the ninth high school. Considering the research questions, school types were not expressed here as students' schools are not differentiated in the analysis.

Data Collection
The data were collected from participants who voluntarily accepted to participate to the study. The data collection was held in a mathematics lesson in the spring semester of 2018-2019. It took about 45 minutes. All ethic rules were followed and taken ethic permission from the authorities.

Development of the instrument
Due to the lack of a valid and reliable Multi-representation Translating Measurement Tool at the 9th grade level in the literature, it was decided to develop the MRTMT originally to search for answers to research questions. The measurement tool was developed in six phases. In the first phase, the researcher and field specialists agreed on develop content for the learning outcome "Practices are performed on algebraic, graphical and numerical representations of the relationships in verbal expressions representing real life situations.", which is present in numbers and algebra learning area of MoNE secondary education mathematics curriculum (MoNE, 2018, p.21). To this end, a group of specialists was formed. The group consisted of a faculty member who has a PhD in mathematics teaching, a faculty member who has a PhD in algebra, a Turkish language specialist and a high school mathematics teacher.
In the second phase, the group came together and identified the outcomes needed in multiple representations translates. Accordingly, they agreed on 16 questions. In the third phase, a Turkish language specialist controlled the questions. In the fourth phase, the questions were presented to prospective elementary school mathematics teachers. Face validity of the questions were ensured by controlling their clarity and intelligibility. In the fifth phase, the researchers came together and revised the questions based on the feedback from prospective teachers and Turkish language specialist. After the discussion, 4 questions were discarded since they measured the same aspects. In the sixth phase, the test including 12 questions was presented to two high school mathematics teachers. Following the teachers' examination, multiple representations translating measurement tool was formed. In order to finalize the draft scale after statistical procedures, a pilot study was carried out. First, the measurement tool was implemented with 97 high school students and the Cronbach alpha value was calculated as .88.
MRTMT including 12 open ended questions consists of four parts. In the first part, students are provided with a verbal problem and the students are asked to express this problem in algebraic, table and graph forms. In the second part, students are asked to express a problem given in the form of a graph in verbal, algebraic and tabular forms. In the third part, students are asked to express the problem given in algebraic form in verbal, table and graph forms, and in the last part, they are asked to express the problem given in the table representation in verbal, algebraic and graph forms (see Annex).

Validity and Reliability of the Measurement Tool
The Rasch Measurement model was used to determine the item difficulty and reliability values, item discrimination values of the items and validity and reliability of MRTMT, developed within the scope of the research (Rasch, 1980). The Rasch model examines whether the data fit to the model (Linacre, 2008), the difficulty level of the items, and the linear relationship between item difficulty and items (Dervent, Devrilmez, İnce & Ward, 2018). Rasch analysis was analyzed with Winstep 3.72.4 and its findings are shown in Table 3. In Table 3, item numbers are in the first column; total scores of correct answers are in the second column and item difficulty index is in the third column. The fourth column includes standard error regarding difficulty of the questions. The fifth and sixth columns present the internal and external fit indices. Internal fit is sensitive to expected responses, while external fit is sensitive to unexpected responses (Linacre, 2008). The fit indices section provides the content validity of the measurement tool by showing the consistency between the questions. In the chart of fit index, the questions from top to bottom are listed from hard to easy. Mean square values (MNSQ) show how the obtained responses form a pattern of test items with regard to model fit. MNSQ is expected to be between 0.5 and 1.5 (Linacre, 2008).
Standardized distribution values (ZSTD) indicate the meaningful compatibility levels of test items with each other. According to Bond and Fox (2015), this value should be between +2 and -2. The last column gives the score-measurement correlation values. The positive values indicate that the correlation is in the expected direction.
According to Table 3, it is seen that 11 items of the 12-question test provide the expected MNSQ and ZSTD values. Only in the external fit of test item number 4, the MNSQ value is slightly above the expected value. Internal fit is more sensitive than external fit and is more important for the validity and reliability of test items (Bond & Fox, 2015). Therefore, it seems that the 4th test item does not need to be removed from the test. In addition, all of the score-measurement correlation values are positive.  Table 4 shows the difficulty and reliability values of the questions and their score-measurement correlations. Boone, Staver & Yale (2014) propose that the real RMSE values are more consistent than the model RMSE values in research and they should be used.
The representativeness of the items is determined by the item discrimination value. This value is expected to be 2.0 and above (Baghaei & Amrahi, 2011). According to the table, the item discrimination value was determined as 2.81. This value shows that the discrimination level of the items in the test is at the expected level. The item reliability value in Table 4 is accepted as equivalent to the Cronbach alpha value. The reliability of the items is at the expected level with .90. This value indicates that the internal consistency level of the test is high. Person-item map (Wright Map) presented in Figure 1 shows item and person measurements that are in the same direction (Linacre, 2008). The map shows the distribution of items according to their difficulty and the level of matching of these questions with persons. The last column lists the difficulty levels of the items. In this column, item difficulty increases as you go from bottom to top. Accordingly, it can be said that item number seven is the most difficult question and item number four is the easiest question.
On the other hand, confirmatory factor analysis (CFA) was performed with Lisrel 8.80 program to check whether the determined factors work in the measurement tool. For this, normality assumptions were provided first and it was decided to analyze 637 data in total. The KMO value was found to be .89, and the Cronbach Alpha value was .88.
CFA enables the researcher to test whether the data is consistent with the previously determined factor structure (Meydan & Şeşen, 2016). As the developed MRTMT was defined as including four factors which are verbal-graph-algebraic-table multiple representation dimensions as given in the literature (Bossé et al., 2011a;Heinze et al., 2009;Waisman et al., 2014;Wilkie 2016), confirmatory analysis was performed. CFA diagram is provided in Figure 2. There are some index types used in the literature to reveal whether the model examined in CFA fit to the data or not. They are (x 2 )/sd, CFI, RMSEA, GFI, AGFI, NFI, NNFI and SRMR indices (Marsh & Hocevar, 1988). The values obtained from MRTMT, which are evaluated according to these indices, are given in the table below.  Jöreskog and Sörbom (1996), states that, the absence of red arrows in the t values indicates that all items are significant at the .05. No items had to be removed from the test.
Thus, the findings of Rasch analysis and the values obtained from CFA reveal that the developed MRTMT is a valid and reliable instrument.

Data Analysis
Descriptive statistics (mean, standard deviation) were used to explain the level of multiple representation translate skills of 9th grade students. Accordingly, SPSS 21.00 program was used. In addition, to answer the research question "Are there relationships among 9th grade students' verbalgraph-algebraic-table multiple representation skills in algebra learning area?", correlation statistics were run and the data were analyzed through SPSS 21.0. The repeated measures ANOVA was performed to explain the significant differences between factors.
Quantitative data consist of responses obtained from 12 open ended questions in the MRTMT. Analytical scoring key developed for the measurement tool is presented in Table 6.  (Cetin, & Ertekin, 2011) The highest score that can be obtained from the scale is 36 and the lowest score is 0. Within the scope of the analysis, mean and standard deviation values were examined in order to obtain descriptive statistics of the data.
On the other hand, the correlations were examined separately in order to reveal the relationships between students' translate skills of graph, table, verbal and algebraic representations in the field of algebra. The relationship between students' ability to translate between representations was determined by calculating the "Pearson Correlation" coefficients based on the relationships between the verbal-algebraic, verbal-

Findings
To answer the research question "What is 9th grade students' level of multiple representation translate skills in algebra learning area?", means and standard deviations of translate between representations were calculated and the results are provided in Table 7. According to the findings of descriptive statistics performed in order to identify 9th grade students' multiple representations translate skills in algebra, as provided in Table 7, students are more successful in translating from table representation to other representations compared to other representation translates. Another translate that student generally succeed in is translating from graph representation to other representations, while students have difficulty in translating from algebraic representation to other representations.
In order to identify whether there is a statistically significant difference between multiple representations translate score means in the factors or not, repeated measures ANOVA test was performed. Since the sphericity assumption, which is one of the assumptions of this test, was not met, the F value obtained from the Greenhouse and Geisser correction (cited in: Abdi, 2010) was used in the reporting. The results of this test, which is conducted to determine whether the difference in scores between factors is statistically significant, are provided in Table 8.  (Cohen, 1988).
Then, comparisons were made with the paired t test in order to see the differences in success in detail and it was seen that there is a significant difference between all factors except the skills of translating from graph representation to other representations and the skill of translating from table representation to other representations. While the significant difference between students' translate skill from algebraic representation to other representations and their translate skill from table representation to other representations is the greatest (4> 3), the difference between their translate skill from verbal representation to other representations and their translate skill from graph representation to other representations is the smallest (2> 1).
As a result of the descriptive analysis, the means and standard deviations for each item of the factors are presented in Table 9. According to Table 9, the value of translate from verbal representation to algebraic representation is (X =1.11; SD =1.08), to table representation is (X =.82; SD =1.23), to graph representation is (X =.96; SD =1.19). While translating from verbal representation, the item that students are most successful in is item 1, which requires translate to algebraic representation, while the item they have the most difficulty is item 3, which requires translate to graph representation.
According to Table 9, the value of translate form graph representation to verbal representation is (X =1.67; SD =1.37), to algebraic representation is (X =.42; SD = .97), to table representation is (X =1.06; SD = 1.33). While translating from graph representation, the item that students were most successful in was the 4th item that requires translate to verbal representation, while the item they had the most difficulty with was the 6th item that required translate to the table representation.
The value of translate from algebraic representation to verbal representation is (X =.56; SD =.98), to table representation is (X =.75; SD =.97), to graph representation is (X = .58; SD =.87). While translating from algebraic representation, the item that students are most successful in is the 7th item, which requires translate to the table representation, the item they had the most difficulty with was the 9th item that requires the translate to verbal representation.
The value of translate from table representation to verbal representation is (X =1.32; SD =1.24), to algebraic representation is (X =.74; SD =1.11), to graph representation is (X =1.25; SD =1.28). While translating from table representation, the item that students were most successful in was item 10, which requires translate to verbal representation, the item they had the most difficulty with was the 11th item, which requires translate to algebraic representation.
In general, it is seen that the translate form in which students are most successful when translating between representations in the equations and disequilibrium sub-learning area is translate from graph representation to verbal representation (M1), while the translate form in which they most unsuccessful is translate from algebraic representation to graph representation (M9).
To answer the research question "Are there relationships among 9th grade students' verbalgraphalgebraic-table multiple representation skills in algebra learning area?", Pearson Correlation coefficients were calculated for each representations through translate scores and the results are provided in Table 10.  Cohen (1988) states that the r value obtained in the correlation analysis indicates a low level relationship between .10 and .29, a moderate relationship between .30 and .49, and a high level between .50 and 1.0.
As a result of the Pearson correlation analysis, a significant and high level relationship was found between 9th grade students' skills of translating to algebraic representation and translating to verbal representation in the sub-learning area of equations and disequilibrium (r=.52, p<.01). Therefore, it can be suggested that as students' translate skills to algebraic representation increase, their translate skills to verbal representation will increase.
Besides, a significant and high level relationship was also found between 9th grade students' skills of translating to table representation and translating to verbal representation (r=.60, p<.01) and translating to algebraic representation (r=.70, p<.01) in the sub-learning area of equations and disequilibrium. Accordingly, it can be said that if students' translate skills to table representation increase, their translate skills to verbal and algebraic representations will increase.
Lastly, a significant and high level relationship was also found between 9th grade students' skills of translating to table representation and translating to verbal representation(r=.58, p<.01), translating to algebraic representation (r=.68, p<.01) and translating to table representation (r=.75, p<.01) in the sublearning area of equations and disequilibrium. Accordingly, it can be said that if students' translate skills to graph representation increase, their translate skills to verbal, algebraic and table representations will increase.

Discussion
An examination of the answers given by the students to the Multiple Representation Translating Measurement Tool, which was originally developed in the current study to investigate students' translate skills between multiple representations in algebra, reveals that students' skills of translating between representations are at a low level. This finding is in line with the studies in the literature (Akkus & Cakiroglu, 2006;Bossé et al., 2014;De Bock et al., 2015;Demir & Cansiz-Aktas, 2018;Gurbuz & Sahin, 2015;Ipek & Okumus, 2012;Kardes et al., 2012;Mourad, 2005;Sert, 2007).
The findings of the current study suggest that the translate of representation that students are most successful in is the translate from graph representation to verbal representation (X = 1.67), while the translate of the representation they have the most difficulty with is the translate from graph representation to algebraic representation (X = .42) and from algebraic representation to verbal representation (X = .56). Similarly, it is highlighted in the literature that the translate form that students are most successful with is transformation of graph-verbal (Andrá et al., 2015) and the translate form they have most difficulty with is transformation of verbal-algebraic (De Bock et al., 2015;Delice & Sevimli, 2010;Galbraith & Haines, 2000). On the other hand, although the students were quite successful in translating from graph representation to verbal representation, they were not so successful in the opposite direction. It is thought that this problem of the students may stem from the need for more than one representation translate such as symbolic, equation, schematic and numerical in the translate of verbal representation to graph representation, as stated by Raviwati et al (2017).
It is thought that the reason why students have difficulty in graph-algebraic and algebraic-graph representation translate is their difficulty in analyzing the effect of changing parameters (De Bock et al., 2015). In addition, when all representation translates are considered, the finding that students have the most difficulty in translating algebraic and graph representations is supported by the finding by Bossé et al., (2014) that students switch graph features into algebraic formulas by going through a similar translate path.
The second translate that students find most difficult is the translate from algebraic representation to verbal representation. This finding is in line with Wang's (2015) study. On the other hand, Gurbuz & Sahin's (2015) finding that 8th grade students have problems in translating from graph and algebraic representation to verbal representation in equations and disequilibrium sub-learning area is in parallel with the algebraic-verbal translate performance in our study yet it contradicts with graph-verbal translate performance. This situation can be explained by the difference in difficulty level of the translate problems between representations prepared in both studies.
On the other hand, the verbal representation is the representation that students are most successful when translating from graph representation. This result is in line with the studies in the relevant literature (Andrá et al., 2015;İncikabı, 2016;Rahmawati et al., 2017). In the study in which İncikabı (2016) examined the types of representations which were used in the questions in the middle school mathematics textbooks and which were needed to solve the questions, it was found that verbal representation was requested as a solution in 68% of the questions containing graphics in their expressions.
The finding that the representation that students have the most difficulty in translating from algebraic representation is the verbal representation is supported by Andrá et al. (2015). As Mourad (2005) states, algebraic representation can cause difficulties and confusion for students. A student who is not proficient in algebraic representation cannot distinguish between the uses of representation, causing confusion and misunderstanding of concepts. On the other hand, the finding that the representation that students are most successful in translating from algebraic representation is the table representation is supported by the study of Bossé et al. (2011). The finding that the representation that students have the most difficulty in translating from table representation is algebraic representation is supported by the relevant literature (Adu-Gyamfi et al., 2012;Presmeg & Nenduradu, 2005).
The finding that students are successful in translating from table representation to other representations is in parallel with the studies in the literature (Akkus & Cakiroglu, 2006;Bal, 2015). The effective use of table representation in many lessons can be shown as the reason why students are successful in translating from table representation to other representations (Bal, 2015).
It has been found that students have difficulty in translating from algebraic representation to other representations. Many studies in the relevant literature support this finding (Andrá et al., 2015;Deniz, 2016;Ozhan-Turan, 2011). It is stated that the type of stimulus that challenges students the most is formula stimuli (Andra et al., 2015). The significant relationship determined between the students' graph representation translate skill in algebra and their ability to translate to verbal representation, expressed in the correlation analysis findings, is parallel to the finding of the study conducted by Adiguzel and Akpinar (2004) that success in finding and representing the graph representation increases the performance in algebra representation.

Conclusion
As a result, the students had the most difficulty in translating from other representations to algebraic representation and from algebraic representations to other representations. It has been observed that they generally cannot distinguish between table and graph representation.
When students learn certain algorithms, they can do operations (algebraic) quite easily. However, given an algebraic equation, they cannot illustrate the situation and interpret it from different aspects. In other words, the deficiency in understanding a mathematical sentence and explaining it with other representations also shows that they cannot learn conceptually and in a qualified way. For instance, as well as obtaining and solving the y = 2x equation, the student is expected to be able to explain what this mathematical sentence expresses with different representations suitable for a linear equation. In algebra teaching, solving equations successfully is possible through having students attain meaningful and conceptual learning by establishing mathematical relationships in also real-life situations as well as getting them to find the unknown. Therefore, the translate of representations to each other has a very critical place in algebra teaching.
According to another result of the study, there is a significant relationship between the verbal-graphalgebraic-table representation translate skills of the students. Based on these findings, it can be said that more emphasis should be placed on the use of representation in mathematics lessons. Therefore, teachers should encourage students to use representation and translate between representations. The idea that the use of multiple representations facilitates students' problem solving is supported by many studies (Deniz, 2016;Fonger et al., 2018;Huntley & Davis, 2008;Parrot & Leong, 2018;Sarıhan-Musan, 2012).

Recommendation
For the practitioners, it can be suggested that they should use multiple representations in classroom practices; students' expressing their thoughts should be encouraged through in-class discussion to let them understand how translating between representations are made; technology supported materials ensuring multiple thinking should be made use of rather than using only abstract symbolic language in algebra teaching.
For researchers, it can be suggested that they may examine the effects of different teaching methods in mathematics education on multiple representations translate skills; qualitative studies can be carried out regarding why multiple representations translate skills levels of students at various grades are low and why have difficulty in this; MRTMT, developed in this study for 9th grade students, can be used and its relationship with different learning areas/skills/performances can be examined. In addition, it can be suggested to investigate why students have difficulty in translating to some representation types while not having difficulty in some other representation types in terms of variables such as thinking structures, learning styles, etc.

Limitations
The research is limited to the descriptive findings of translating multiple representations obtained by the quantitative research method in the Equations and Inequalities subject in algebra unit.

Multiple Representation Transfer Test
This measurement tool has been prepared for use in a scientific study. These questions will not be used to evaluate you. Read the questions carefully and write your answers clearly in the blanks. Question 3: In a dairy, milk is stored in cold cabinets with a capacity of 920 liters. On Monday, there are 50 liters of milk in the refrigerator. The change in the amount of milk according to the days is expressed as y= 50+30x. In this expression, x is the amount of milk obtained from the cow in a day, and the variable y is the amount of milk in the refrigerator.

1) Express the equation verbally.
2) Since a cow gives 6 liters of milk a day, show the amount of milk in the refrigerator at the end of each day with a table.
3) Since 6 liters of milk are taken from a cow per day, draw a graph showing the amount of milk over time until the refrigerator is full.

Question 4:
In the table below, the scores of the students named Aylin, Batuhan, Can and Derya, who