The Technology of the Development of Dialogical Speech Skills of the Students Based on Foreign Language Communicative Online Training

. The topic of the article is quite acute as there exists a need to search for new online educational technologies that will further increase the efficiency of foreign language educational process at modern universities in Russia. The purpose of the article is to present the methodological founda-tions of foreign language communicative preparation and analyze the quality of the influence of foreign language communicative online training on the development of dialogical speech skills of the students. The leading method of studying this issue is an experimental teaching method. The study was carried out among bachelor's degree students majoring in 44.03.01 «Pedagogical education» with a minor of «English as a foreign language» at Linguistics University of Nizhny Novgorod, Russia and allowed to reveal the positive dynamics in the experimental groups. The article proves that foreign language communicative online training is a modern educational technology that aims at active development of students' dialogical speech skills and sig-nificantly differs from ordinary communicative training in the following features: the presence of certain stages correlated with the developed dialogical speech skills of students, ensuring active social preparation of students to further implementation of foreign language communication in the field of interpersonal and professional interaction; creation of conditions for expanding individual foreign language communicative experience. The materials presented in the article contribute to the integration of the procedural com-ponent of foreign language communicative online training in foreign language classes at the university.

Introduction
A modern Russian University is a social institution that should create necessary educational conditions for the development of a harmonious socially interactive person. This goal may be achieved at Foreign language classes, where a tutor will be able to create a special educational environment that will contribute to personal communicative development of every student. To realize this idea a tutor must be in a permanent search of new methods of training and education, educational technologies that ensure the development of basic skills and abilities of students, increasing their motivation to learn and involvement in the educational process.
This problem of searching for new educational technologies is relevant both for Russian and foreign researchers. For example, M. N. Norbahira and A. R. Radzuwan consider three main theoretical aspects of learning and mastering the first and second languages and suggest several original educational technologies for their development [10]. M. Bolognesi and P. Vernillo research the role of metonymy in the representation of abstract concepts in the analysis of verbal and visual metaphors of the language. Such deep analysis helps students to go deeper into the understanding of underneath meanings and hidden context in the dialogue with a native speaker [1]. S. Leher & K. S. See study different methods of language learning based on the proportion of quantity and quality of language material presented [7].
However, COVID-19 Global pandemic deprived all educational institutions of a chance to conduct offline classes. Present-day reality motivates us to re-examine all the modern educational technologies from the point of their successful integration into online teaching and learning process.
One of such technologies that became widely used in Russian educational space that was greatly modified by SARS-CoV-2 infection is communicative training technology. This type of technology «grew up» from psychological training and is an effective form of developing of communicative skills [13].
The analysis of modern Russian research literature dedicated to the problems of the usage of communicative training technology in higher education indicates a constant increase of scientific interest of this problem [12]. However, almost no research papers in this area concentrates on studying its impact on foreign language education [14]. Most of the researchers consider communicative training to be a form of synthesis of various methods and techniques for providing theoretical and practical communicative training of students within their native society [4]. The question of using the technology of communicative training for the development of foreign-language dialogic skills is studied rather insufficiently. Thus, the purpose of our research is to study and test foreign language communicative training as a separate specific educational technology that accelerates the development of dialogical speech skills of bachelor's degree students majoring in 44.03.01 «Pedagogical education» with a minor of «English as a foreign language» at Linguistics University of Nizhny Novgorod, Russia.
In our research we define foreign language communicative training as a modern educational technology that aims at active development of foreign language dialogic speech skills in the process of intensive interpersonal online interaction. This special type of training is aimed at developing communicative competence as the ability to establish and maintain social contacts, resolve conflict situations that arise in the process of communication, as well as to select various means of communication according to the goals and conditions of communication. Unlike classical training foreign language communicative training aims at developing the components of foreign language communicative competence of student's skills of dialogical speech, and modeled with rules, regulations, policies of social and communicative behavior of foreign society.
To add to this, as a kind of pedagogical technology, a foreign language communicative training has several characteristics common to this pedagogical category, among which are the following: conceptuality, consistency, manageability, efficiency, reproducibility. It is important for us to mention these characteristics as they also let this technology to be effective in online learning process [11]. Let us look at some of them in more detail. Modern researchers classify training technologies as a part of «action learning» method («learning through action», «learning by meaningful action»), the founder of which is R. Revans [6]. Learning through action is generally performed using The Revans-Marquardt's formula, which looks like this: L=P+Q+R (1) where L -stands for learning, P -stands for programmed knowledge, Qstands for asking a question to create insight, and R -stands for reflection [2]. 2. Consistency. This quality of foreign language communicative training is manifested in the presence of an invariant system of principles necessary for creating an effective educational environment. 3. Manageability. This characteristic is universal for pedagogical technology and assumes «the possibility of diagnostic goal-setting, planning, designing the learning process, step-by-step diagnostics, varying tools and methods to correct the results» [9]. These characteristics are also realized through its format, that presupposes the existence of six following stages: 1) introduction; 2) initial analysis of the communicative situation; 3) search for the new effective ways of communicative interaction; 4) development of communicative abilities at the micro-level; 5) development of communicative abilities at the macrolevel; 6) reflection. 4. Reproducibility. The availability to transfer the technology of foreign language communicative training to any other university educational program is explained by its clear, understandable, and effective structure. In general, the composition of any training involves three basic parts: the introductory part, the main part, and the final part. The basis for building many modern trainings is learning cycles, which effectiveness has been repeatedly confirmed in the scientific works of foreign and domestic researchers [8]. The content of the technology of foreign language communicative training presupposes the implementation of special types of tasks that were developed based on psychological and pedagogical features of modern university students and include set of personally significant topics and situations. The developed types of exercises include the following: 1) communicative-stimulating; 2) communicative-analytical; 3) communicative-constructing; 4) communicative-fixing; 5) communicative-developing; 6) communicative-reflexive.
Since we believe that foreign language communicative training has a very high potential for online foreign language learning and acquisition, let us briefly characterize the main difference between online and offline communication. Virtual communication differs significantly from real one and has the following unique characteristics: 1) high degree of efficiency; 2) anonymous nature of communication; 3) absence of stress factors of the real socializing environment.
Let us consider these features in more detail. 1. High degree of efficiency.
The development of various social networks and instant messaging services (Vk.com, Facebook, WhatsApp, Viber, etc.) has led to the blurring of space-time boundaries between communicants. As a result, the communicative space of the interlocutors becomes autonomous, which allows them not to depend on time, as an online resource is available 24 hours a day. although the dialogue in the network «preserves the chronology, but this chronology records only the moment of sending and does not reflect the logical sequence of elements of communication» [15]. 2. Anonymous nature of communication.
The lack of personal contact between the interlocutors and the restriction in the use of verbal means of communication on the Internet create conditions for distorting the process of network communication. Computer-mediated communication allows the Internet user to self-model their personality. To do this, they can use a pseudonym instead of a real name or post information that does not correspond to reality, which leads to erosion of the real identity of the communicants. Moreover, in conditions of virtual communication with a minimum of data about the communication partner, the interlocutor independently creates his image for himself, trying to simultaneously imagine how his words are perceived in a joint dialogue. Thus, the real addressee is absent and can only be «completed» in the sender's mind on the basis of his personal social and communicative experience. 3. Absence of stress factors of a real socializing environment.
In the process of interacting with society, a person experiences a certain level of social pressure in the form of special norms of behavior, certain rules, and principles of interpersonal interaction, approved by this society. Some of them may conflict with their needs. To achieve a balance between these two processes, society offers a person a set of ready-made statuses and roles that he can realize during his life. According to the theory of roles, one of the characteristics of a formed personality is its belonging to certain types of social roles inherent in each society. The virtual space, represented by the Internet and perceived by a person as «not real», does not carry any social danger in its content. However, such freedom of expression of can grow into impunity. Using this, any user can falsify information and «slander other people or organizations or insult and humiliate without fear of responsibility for their behavior» [3].

Materials and Methods
Practical research was carried out and objectively assessed in the course of a training experiment on the basis of Linguistics University of Nizhny Novgorod, Russia in the framework of the main educational program 44.03.01 «Pedagogical education» with a minor of «English as a foreign language».
The organization of the pilot test was carried out in the academic year 2019-2020. The total number of participants was 60 people. This article provides data for two groups, each of which consisted of 12 people.
To maintain the consistency and clarity of the experiment, we designated one of them as group No. 1 -the experimental group (hereinafter referred to as the EG), and the second was designated as group No. 2 -the control group (hereinafter referred to as the CG).
The number of non-variable conditions of the experiment included: the same amount of time allotted for the assimilation of educational material; duration of classes (90 minutes); regularity of the lessons (3 lessons 3 times per week) the number of subjects in the EG and the CG; approximately the same starting level of development of universal competencies in the EG and CG at the moment of the beginning of experimental training; the content of the ascertaining and final diagnostics; uniform assessment criteria; a unified form of processing statistical data of the experiment.
The number of variable conditions of the experiment included: different teachers teaching in the EG and CG; leading teaching technology; the form of organizing and conducting classes.
We tried to evaluate student's dialogical speech performance twice: first before the experimental learning and second after the experiment. For the most effective assessment of the initial and final indicators that allow you to clearly track the dynamics of the development of certain foreign language skills of dialogic speech, a special system of criteria was developed, based on the theory of three sides of communication, highlighted by G. M. Andreeva [5].
The communicative side of dialogical communication assumed an assessment of the level of development of foreign language skills of dialogical speech of high school students using the following quantitative criteria: 1) the number of replicas from each interlocutor; 2) the number of different types of dialogical units; 3) the number of hesitation pauses. Qualitative indicators of the level of development of foreign language skills of dialogical speech of high school students in the framework of the communicative side of dialogical communication were evaluated using the following qualitative criteria: 1) compliance of the contents of the dialogic utterance set of communicative tasks; 2) lexico-grammatical and phonetic correctness of the utterances; 3) pragmatism and emotion in building a dialogical statement.
The perceptual side of dialogical communication was supposed to assess the level of development of foreign language skills of dialogical speech of high school students using the following quantitative criteria: 1) the amount of time spent actively listening to the interlocutor; 2) the number of clarifying questions asked to the interlocutor; 3) the number of replicas that express the speaker's attitude to the interlocutor's statement. Qualitative indicators of the level of development of foreign language skills of dialogical speech of high school students in the framework of the perceptual side of dialogical communication were measured using the following criteria: 1) perception and interpretation of information about verbal signals from the communication partner received during the dialogue; 2) ability to act in various roles; 3) ability to predict possible reactions of the partner in the process of communication.
The interactive side of dialogical communication was supposed to assess the level of development of foreign language skills of dialogical speech of high school students using the following quantitative criteria: 1) the number of replicas aimed at maintaining dialogical unity on the part of each interlocutor; 2) the number of specific speech tools (conversational formulas, clichés, formulas of speech etiquette) used in the dialogue by each of the interlocutors; 3) the number of arguments given in the process of dialogical communication by each of the interlocutors. Qualitative indicators of the level of development of foreign language skills of dialogical speech of high school students within the interactive side of dialogical communication were measured using the following criteria: 1) flexibility in the development of the topic and subject of communication; 2) the use of cooperation strategies in the dialogue; 3) the ability to predict possible conflicts and resolve them.

Results
After the completion of the learning experiment, we evaluated both qualitative and quantitative indicators of the progress in EG and CG. For the most effective assessment of the initial and final indicators of the development of foreign language dialogical speech skills, a special system of criteria has been developed. Verbal answers of the students were studied and evaluated according to 3 quantitative and 3 qualitative criteria for each of communication units that were previously mentioned. According to the primary data, we calculated the overall average score of the qualitative and quantitative indicators in the EG and CG before the experiment. Then we evaluated the success rate of the performance of students both in EG and CG, according to the formula of Bespalko: Where «a» stands for the number of students who showed a generally positive result and «n» is a total number of students in the group. The results for both groups before learning experiment was 0.5 with an average acceptable score of 0.7, which indicates an extremely low level of the development of the foreign language speech skills within the groups. After the learning experiment we also calculated the overall average score of the qualitative and quantitative indicators in the EG and CG and then evaluated the success rate of the performance of the students in the EG and CG, according to the formula of Bespalko. The results for the CG was 0.583 whereas the result of the EG was 1.0 withan average acceptable score of 0.7, which indicates a high level of the development of foreign language dialogical speech skills in EG and low average in CG. A comparative analysis of the data of ascertaining and final periods demonstrates an intensive positive dynamic change among qualitative and quantitative indicators of the level of the development of dialogical speech skills in foreign language in the EG. (see Fig. 1). The obtained data allow us to draw a conclusion about the intensive positive dynamics of changes in qualitative and quantitative indicators of the level of development of foreign language dialogic speech skills in the EG based on the results of the learning experiment.
In the EG several students with high level of the foreign language communicative competence development increased up to 42%. The number of students with an average level increased to 33%. The number of students with the minimum level decreased up to 25%. Students in the CG did not show such significant results as students in the EG. The number of students with the minimum level increased to 33%, however, the number of students with an average level stayed the same, while the number of students with a high level of performance remained at zero.
Thus, a comparative analysis of the results of the ascertaining and control stages of the study confirms the effectiveness of the foreign language communicative online training created by us for the development of dialogical speech skills of university students.

Discussion
The relevance of the development of foreign language dialogic speech skills within the university is determined not only by the requirements of the Federal Educational Standard for the professional results of gathering the bachelor's degree in program 44.03.01 «Pedagogical education» with a minor of «English as a foreign language», but also by the indicators of the level of development of the personal characteristics of the graduate -the future teacher of a foreign language, who must be able to conduct a constructive conversation with any interlocutor and always achieve mutual understanding in the process of communication. Based on these requirements, the orientation of the process of foreign language education to the simultaneous development of students' skills in communicative, interactive, and perceptual aspects of dialogical speech in a foreign language is of particular importance.
To achieve this goal, the list of skills required for development in foreign language classes at the university was clarified in accordance with the three sides of dialogical communication: the communicative side of dialogical communication (the ability to establish contact, the ability to achieve the set communication goal, the ability to argue your point of view); the perceptual side of dialogical communication (the ability to actively listen to a partner; the ability to understand and accept the point of view of the interlocutor; the ability to assess and predict the verbal behavior of the partner; the interactive side of dialogical communication (the ability to navigate in a communication situation, the ability to assess the effectiveness of one's own communicative behavior, the ability to communicate in conflict situations).
Modern students are representatives of generations «Z» and «Alpha». The emerging information society had a significant impact on the processes of their personal formation and development. Under the influence of high technologies and virtual communication, the process of the development of their communication skills becomes more difficult as students have relatively little experience of communication in live conditions, which leads to the fact that they are poorly oriented in situations of real dialogical interaction and it is difficult for them to interpret the communicative behavior of the interlocutor.
The study of the conceptual provisions of the «action learning» methodology, as well as the general theory of training, made it possible to clarify the concept of a foreign language communicative online training. Regarding the process of the development of students' dialogical speech skills in foreign language lessons at a specialized university, foreign language communicative online training is a modern teaching technology aimed at actively developing the skills of dialogical speech in a foreign language in the process of intense intercultural online interaction.
The key features of a foreign language communicative online training, which distinguishes it from other types of communication training are: 1) focus on the integrated development of general communicative, special perceptual and interactive skills of dialogic speech; 2) creation of conditions for active secondary socialization of the individual in a foreign language society; 3) usage of a foreign language as the main means of teaching.
The main distinguishing features of the technology of foreign language communicative online training, contributing to an increase in the effectiveness of teaching students a foreign language is: 1) orientation towards the social development of the individual; 2) creating conditions for expanding the communicative experience in a foreign language; 3) creating conditions for the development of foreign language communicative skills of dialogical speech.

Conclusion
Based on the results of the experimental training, it can be concluded that foreign language communicative online training has a positive impact on the social and communicative development of the personality of bachelor's degree students majoring in 44.03.01 «Pedagogical education» with a minor of «English as a foreign language» at Linguistics University of Nizhny Novgorod, Russia.
By the means of the indicated technology, these students accumulate previously acquired experience of social interaction with the newly acquired one, which contributes not only to the development of social competence, but also to the formation of such significant personality traits as self-awareness and self-esteem, which help to form their own identity.
Thus, a foreign language communicative online training cancover the deficit of live communication observed because of the development of Internet technologies. Itis able to give an impetus to university students to rethink and rework the results of their activities in various


Does Teacher Education Matter? Comparison of Education and Science Major Teachers’ Assessment Literacy

The purpose of this study was to investigate science teachers' assessment literacy having different majors (education versus science) and compare those teachers' assessment literacy. A multiple-case study, one of the qualitative research designs, was utilized to fulfill the aim. Four science teachers, two from each major, who were teaching at public schools during the 2017-2018 semesters, participated in the study. Preinterviews, observations, post-interviews, and documents were used as data collection tools during the investigation. Content analysis was conducted using science teachers' assessment literacy model that exists in the literature. The findings of the study revealed that science teachers were similar and different from each other with respect to several dimensions of assessment literacy, which are views about learning, assessment purposes, assessment strategies, what to assess, and assessment interpretation. Recommendations for science education research and implications for science teacher education are provided.

Introduction
What are the activities that in-service teachers engage in throughout their instructional time? Activities conducted for assessment purposes take at least one-third of the instructional time (Stiggins, 1991). More importantly, research indicated that quality of assessment is linked to students' learning and enhancement of teaching (Box, 2008;Stiggins, 1999). For increasing assessment's influence on learning and teaching, "effectively designed learning environments must be assessment-centered" (Bransford, Brown & Cocking, 2000, p. 127). How can teachers design an assessment-centered learning environment? "…Teachers pay attention to the knowledge and beliefs that learners bring to a learning task, use this knowledge as a starting point for new instruction, and monitor students' changing conceptions as instruction proceeds" (Bransford et al., 2000, p. 11). That is, teachers should develop assessment literacy, which requires not only understanding theoretical and philosophical foundations of educational assessment but also effective utilization of assessment practices (Stiggins, 1991(Stiggins, , 2002Volante & Fazio, 2007). Knowledge and skills required to develop assessment literacy have been also defined as a part of teachers' pedagogical professional knowledge (Abell & Siegel, 2011;Magnusson, Krajcik & Borko, 1999).
Although assessment literacy is an important dimension of teachers' knowledge and teachers' assessment practices influenced by their literacy take considerable time of their instruction, there has been scarcity of studies investigating in-service science teachers' assessment literacy using qualitative measures. Most of the studies used an inventory to investigate teachers' assessment literacy and examined several factors affecting literacy such as teaching experience, attitude, efficacy, and conceptions of assessment (e.g., Levy-Vered & Nasser-Abu Alhija, 2015;Mertler, 2005;Quilter & Gallini, 2000;Volante & Fazio, 2007). Given the factors affecting assessment literacy, there has been a need for studies investigating whether education-related major area makes a difference in science teachers' assessment literacy. Studies using qualitative measures differed in their type. Some focused on the change in pre and in-service teachers' assessment literacy after participating in a professional development program or a course (DeLuca, Chavez, Bellara & Cao, 2013;Deneen & Brown, 2016;Koh, 2011) and relied on teachers' documents to reveal their assessment literacy without using observations. Other qualitative studies examined middle school science (Gottheiner & Siegel, 2012), chemistry (Izci & Siegel, 2019), pre-service physics (Ogan-Bekiroglu & Suzuk, 2014), and pre-service secondary (Siegel & Wissehr, 2011) teachers' assessment literacy during the planning and teaching a science topic. Even though there has been an increase in the number of research on assessment literacy relying on qualitative data, there has been scarcity of studies focusing on both knowledge and practice level of assessment literacy with its all dimensions (e.g., İzci, 2018). Therefore, the purpose of this study was to investigate science teachers' assessment literacy having different majors (education versus science) and compare those teachers' assessment literacy. Specifically, this study sought to answer the research question of "In what ways is assessment literacy different for science teachers with different majors (education versus science)?" This study utilized Science Teacher Assessment Literacy (STAL) model (Abell & Siegel, 2011). There have been several reasons for this. First, the model is specific to science teachers. Second, the model was proposed based on the empirical and theoretical literature on teachers' assessment knowledge and practices. Lastly, literature provided empirical evidence for the applicability of the model for investigating both pre and inservice science teachers' assessment literacy (Gottheiner & Siegel, 2012;İzci & Siegel, 2019;Siegel & Wissehr, 2011). STAL model defines assessment literacy as assessment knowledge and skills, which teachers require while designing an assessment-centered learning environment (Abell & Siegel, 2011). In an assessment-centered learning environment, teachers investigate students' knowledge and skills, interpret the assessment results, and utilize the results to increase students' learning and teaching practice (Abell & Siegel, 2011;Xu & Brown, 2016). Figure 1 shows STAL model guiding this study. A Model for Science Teacher Assessment Literacy (Abell & Siegel, 2011, p. 212).
STAL model consists of five components. Assessment values and views of learning as a whole is central to the model and this core component influences other four components, which are knowledge of assessment purposes, what to assess, assessment strategies, and assessment interpretation and action-taking.
Teachers' view of learning has a shaping effect on how teachers conceptualize and utilize assessment throughout instruction (Abell & Siegel, 2011;Xu & Brown, 2016). A teacher whose view of learning is constructivist use assessment for revealing, monitoring, and developing students' learning throughout his/her teaching while a teacher with a traditional view of learning prefers to utilize assessment to determine the degree to which students mastered what they are expected to learn at the end of his/her teaching. Assessment values and principles are based on both teachers' views of learning (Shepard, 2000) and assessment experiences in science teaching (Abell & Siegel, 2011). These values and principles are the fundamental ideas and beliefs that lead teachers during assessment decisions they make in their science classroom (Abell & Siegel, 2011).
STAL model (Abell & Siegel, 2011;Xu & Brown, 2016) advocates that an assessment literate teacher should possess a complete understanding about assessment purposes, what to assess, assessment strategies, interpretation, and utilization of assessment results. Knowledge of assessment purposes refers to teachers' reasons for assessing students. Why teachers assess students can be categorized as diagnostic, formative, summative, and metacognitive (Abell & Siegel, 2011). Diagnostic assessment is the assessment occurring at the beginning of teaching for both eliciting students' prior conceptions, knowledge, and beliefs about the topic being taught and using those to regulate teaching (Abell & Siegel, 2011). Formative assessment is the assessment occurring throughout the instruction for giving feedback to both students and teachers about learning and teaching for enhancement of them (Abell & Siegel, 2011). Summative assessment is the assessment occurring at the end of a class, unit or semester to document students' learning and mostly giving course grades. It also provides feedback to teachers about their teaching (Abell & Siegel, 2011). Lastly, metacognitive assessment is the assessment conducted to increase students' awareness about their learning as well as monitor it. Knowledge of what to assess refers to dimensions of learning that teachers believed to be important to assess and based on teachers' assessment values and views of learning (Abell & Siegel, 2011). Students' attainment of curricular objectives, scientific and engineering practices, and nature of science can be included in the assessment tasks that teachers used. Knowledge of assessment strategies refers to the various ways teachers used to assess. Assessment strategies can be categorized as formal and informal (Abell & Siegel, 2011). Formal strategies include exams, lab reports, quizzes, homework, tests, advance organizers, etc. Formal strategies are the ones that teachers use to evaluate students throughout instruction. Informal strategies include classroom discussions and observation of students, and teachers' primary aim is not to give grades to students. Knowledge of assessment interpretation and action taking refers to what teachers do with the assessment data (Abell & Siegel, 2011). Eliciting students' existing knowledge, providing feedback to students, monitoring students' learning, controlling and regulating teaching, giving grades, etc. are examples of how a teacher can interpret and act upon assessment results.
Literature review on science teachers' assessment literacy revealed that studies could be grouped as (1) studies using quantitative data sources, (2) qualitative studies, and (3) studies investigating the impact of an intervention on assessment literacy.
Studies in the first category used quantitative data sources to determine either preservice (Gul, 2011;Ogan-Bekiroglu & Suzuk, 2014) or in-service teachers' (Davidheiser, 2013) assessment literacy in different areas of science using an already existing instrument (Gul, 2011) or an instrument developed by the researcher (Ogan-Bekiroglu & Suzuk, 2014). Participants of the studies conducted with pre-service teachers were science (Gul, 2011) and physics (Ogan-Bekiroglu & Suzuk, 2014). Results of these studies indicated that pre-service science teachers' assessment literacy level was low, and they have difficulties especially in communicating assessment results. Moreover, they were not highly capable of selecting and developing appropriate assessment methods and interpreting and using assessment results. A study conducted with pre-service physics teachers categorized participants in terms of the degree to which their assessment literacy is constructivist (Ogan-Bekiroglu & Suzuk, 2014). Pre-service physics teachers' assessment literacy levels were identified as close to constructivist in terms of types of assessments, evaluation criteria, and cognitive levels of assessments. However, in-service science teachers' assessment literacy levels were found as high (Davidheiser, 2013) with regard to selecting and developing appropriate assessment methods, and interpreting, using and communicating assessment results based on data obtained from an existing instrument in literature. While results obtained from quantitative studies provide insight about teachers' assessment literacy level, it was advocated that reliability and usability supporting measures of assessment literacy is weak (DeLuca, LaPointe-McEwan & Luhanga, 2016) since the construct is multidimensional in nature. This study comes into prominence since it uses qualitative data to reveal teachers' assessment literacy both in the theoretical and practical realm.
Qualitative studies on assessment literacy mostly focused on either pre-service (i.e., Ogan-Bekiroglu & Suzuk, 2014;Siegel & Wissehr, 2011) or in-service (i.e., Gottheiner & Siegel, 2012;İzci & Siegel, 2019) science teachers' literacy. One study in this category conducted a descriptive content analysis on empirical studies investigating secondary science teachers' assessment knowledge and practice using the assessment literacy framework (İzci, 2018). Most of the studies utilized an existing theoretical framework (e.g., STAL) while two studies developed their own framework (Ogan-Bekiroglu & Suzuk, 2014;Siegel & Wissehr, 2011). One study defined assessment literacy as types of assessments, evaluation criteria, and cognitive levels of assessment, considering dimensions about assessment as defined by others (Ogan-Bekiroglu & Suzuk, 2014), and another study advocated that assessment literacy included assessment principles, purposes, and tools of assessment (Siegel & Wissehr, 2011). Results of the studies conducted with pre-service teachers revealed that although preservice teachers' assessment literacy was close to constructivist view, in theory, their assessment practices were more traditional. Studies conducted with in-service teachers yielded similar findings (Gottheiner & Siegel, 2012;İzci & Siegel, 2019). Content analysis of studies regarding assessment knowledge and practice (İzci, 2018) indicated that there have not been longitudinal studies on assessment literacy. Moreover, it was revealed that most of the studies investigated assessment knowledge and perception, and focused on espoused assessment instead of enacted one. Therefore, this study is valuable since assessment literacy with its all dimensions was investigated both in theoretical and practical realm through the use of observational and interview data collected during the teaching of matter, and its change unit spanned four weeks.
Studies in the third category investigated the effect of either a course on pre-service science teachers' assessment literacy (Akdağ-Gürsoy, 2015;Buldur, 2009) or a professional development program on in-service science teachers' assessment literacy (Koh, 2011). One of the courses designed for pre-service teachers was a content and implementation-based assessment course (Akdağ-Gürsoy, 2015) and the other was a theoretical and practical course on alternative assessment (Buldur, 2009). Both courses were found to be effective in increasing pre-service science teachers' assessment literacy (Akdağ-Gürsoy, 2015;Buldur, 2009), attitudes (Akdağ-Gürsoy, 2015, and self-efficacy (Buldur, 2009). Professional development program designed for in-service science teachers included authentic task design and rubric development for assessment (Koh, 2011). Results of this study revealed that professional development program increased the intellectual quality of both teachers' and students' assessment tasks.

Research Design
This study is qualitative (Marshall & Rossman, 2011) since teachers' assessment literacy is implicit (Loughran, Mulhall & Berry, 2004) and complex in nature (Abell & Siegel, 2011). Qualitative research has the potential to make science teachers' assessment literacy explicit and understandable. Among qualitative research designs, case study guided the study. Case study is the study of an issue investigated through one or more cases within a bounded system (i.e., setting, a context) (Creswell, 2007) and provides an in-depth portrayal and analysis of a particular practice, process, or event (Yin, 2009). Science teachers' assessment literacy (i.e., practice and knowledge) within the context of "Matter and its Change" unit (i.e., bounded system) was investigated in this study. Case study also purposes to expand theories (Yin, 2009) and this case study aimed to expand STAL proposed by Abell and Siegel (2011). Considering the size of the bounded case, this study is an example of multiple-case study. Multiple-case study is conducted for either predicting similar results (a literal replication) or predicting contrasting results (a theoretical replication) through the use of different cases, which are different from each other in some respect (e.g., experienced teachers and beginning teachers) (Yin, 2009). In this study, science teachers were grouped into two, of which each was unique in terms of their major degrees (i.e., education and science) and hence these groups constituted different cases. This study aimed to predict to what degree major is central in science teachers' assessment literacy through the use of those contrasting cases. The unit of analysis of this multiple case study was the assessment literacies of science teachers with different majors. Analysis of participants' assessment literacies in both knowledge and practice level was considered in this study. Therefore, assessment literacy in knowledge level and assessment literacy in practice level constituted an embedded unit of analysis of this study.

Participants
Four in-service science teachers, who were volunteers and information-rich cases, participated in the study ( Table 1). Two of the participants graduated from science teacher education (Oguz * and Ahu) program at a faculty of education and the other two (Sarp and Miray) graduated from the faculty of arts and science with a focus on chemistry.

Context of the Study
The study was conducted in two public middle schools in Safranbolu county of Karabük, Turkey. Achievement rankings of the schools were better than other schools in the county. The socioeconomic status of students in the schools was high and the schools had necessary facilities for teachers and students (e.g., laboratory with its materials and equipment). In each of the schools, there was one education major and one science major teacher. Oguz and Sarp were studying at one school while Ahu and Miray were in the other. The contexts where observations were conducted will be explained below.
Oguz teaches science in class and laboratory. There were 29 students in his science class and two students sit in each row. There were nine desks in the laboratory and students work in predetermined groups at those desks. Although the laboratory has basic materials, there has not been sufficient equipment for each student. Therefore, Oguz has to prefer demonstrations instead of making students conduct experiments. Both the class and laboratory have smartboards.
Sarp teaches science in class and laboratory. There were 29 students in his science class and two students sit in each row. There were seven desks in the laboratory and students work in predetermined groups at those desks. Although the laboratory has basic materials, there has not been sufficient equipment for each student. However, Sarp enables his students to conduct experiments. Both class and laboratory have smartboards.
Ahu teaches science in class and laboratory. There were 32 students in her science class and two students sit in some rows while one sits in others. There were three desks in the laboratory and 10 students can work at each of those desks. The laboratory has a majority of materials required for experiments and observations. However, Ahu prefers using demonstrations since the class is crowded. Both class and laboratory have smartboards.
Miray teaches science in class and laboratory. There were 33 students in her science class and two students sit in each row. There were three desks in the laboratory and 11 students can work at each of those desks. Although the laboratory has basic materials, there has not been sufficient equipment for each student. Because of the lack of materials and crowded class, Miray prefers demonstrations. Both class and laboratory have smartboards.

Data Collection Sources
Qualitative data sources were used in this study to reveal and compare science teachers' assessment literacy having different majors, as summarized in Figure 2.

Flowchart for Data Collection
Semi-structured pre-interviews were conducted with four participants before they teach the unit of Matter and its Change. Semi-structured interview questions were prepared based on STAL model (Abell & Siegel, 2011) guiding the study and empirical studies on assessment literacy (İzci, 2018). Pre-interview questions focused on teachers' demographic information, assessment values and views of learning as a whole, knowledge of assessment purposes, knowledge of what to assess, knowledge of assessment strategies, and knowledge of assessment interpretation and action-taking (see Appendix A for selected questions).
Observations were used to collect data about participants' assessment literacy in practice level throughout their teachings of Matter and its Change unit. There were several reasons for selecting "Matter and its Change" unit. First, one of the researchers was an expert on chemistry education, which enabled her to capture science teachers' assessment literacy in this unit. Second, this unit was suitable for using various assessment methods that provided opportunity for science teachers to enact their assessment literacy and hence to collect rich information. Lastly, conducting the study during the teaching of this unit was convenient for researchers. The second researcher as a non-participant observer used an observation protocol (see Appendix B) and took field notes considering STAL model (Abell & Siegel, 2011)  To reveal science teachers' assessment literacy in practice level assessment purposes during teaching were collected to gain in-depth information about teachers' assessment literacy in practice level. Examinations, textbooks that teachers utilize for assessment activities, educational websites used by teachers for teaching and assessment purposes, homework, and science laboratory reports prepared for students and assessed by teachers were the main documents used in this study.
Post-interviews were conducted to collect additional data about participants' assessment literacy in practice level after teaching of Matter and its Change unit. Questions in post-interviews were peculiar to each participant since their assessment practices were different from each other. Observations and field notes were considered during the preparation of post-interview questions (see Appendix A).

Data Analysis
Data obtained from pre-interviews, observations, post-interviews, and documents were analyzed using both deductive and inductive analysis (Patton, 2002). Deductive analysis was the main analysis method while inductive analysis was utilized as required during the analysis of science teachers' assessment literacy. Comparing assessment literacy of science teachers with different majors was also inductive and required using the constant comparative method (Glaser & Strauss, 1967). Analysis of participants' STAL in both knowledge and practice level was conducted primarily deductive. STAL model (Abell & Siegel, 2011) and empirical study on assessment literacy (İzci, 2018) provided codes for deductive analysis of STAL components, namely, assessment values and views of learning as a whole, knowledge of assessment purposes, knowledge of what to assess, knowledge of assessment strategies, and knowledge of assessment interpretation and action-taking. Moreover, researcher-created codes were used for the inductive analysis of data when existing codes were not appropriate to code. Preinterviews were the main data sources while analyzing STAL in knowledge level whereas observations, post-interviews, and documents provided data during analysis of STAL in practice level (see Table 2 for the coding scheme and selected data analysis examples. Codes written in italics indicate researcher created codes). Comparing STAL of science teachers with different majors was inductive in nature, which is defined as ''discovering patterns, themes, and categories in one's data'' (Patton, 2002, p. 453). The researchers used the constant comparative method during inductive analysis (Glaser & Strauss, 1967). The constant comparative method involves comparing two segments of data to determine similarities and differences (Merriam, 2002). Coded data regarding science teachers' STAL in practice level was compared and contrasted to find similarities and differences between STAL of participants with different majors. The same procedure was applied for comparing and contrasting coded data for science teachers' STAL in knowledge level.  Teaching what is planned to teach "Purpose of education is to teach a planned idea, planned part to students." (Oguz, preinterview)  Teacher role  Encourage students for their learning  Ensure active participation of students in the learning process  Guide students to support their learning "My role during teaching is to ensure students' active participation in the class and be a guide for them. In the past, it was not like that; we were active during teaching. Within the context of a changed system, I believe that encouraging students' active participation will give positive results in terms of learning." (Oguz, pre-interview)  Student role  Be prepared for teaching  Active participation  Be responsible and effective individuals "Students' roles during teaching are being prepared for the class by bringing textbooks and notebooks, answering questions in class, and being effective individuals who are aware of their responsibilities." (Sarp, pre-interview)  Teaching sequence  Teaching topic  Using question-answer method  If the topic is related to topics learned in previous grades, using the question-answer method to elicit students' prior knowledge  Implementing assessment tasks in textbooks (Miray, observation)  Teaching sequence in laboratory  Asking questions to elicit students' prior knowledge about the topic  Giving feedback based on students' responses  Performing experiments as demonstrations  Making students conduct experiments if necessary materials exist  Making students watch a video of experiments if it is not applicable to conduct in the laboratory  Asking questions about the experiment  Giving feedback based on students' responses (Oguz, observation) Perception of assessment  Assessment for teachers  Eliciting students' prior knowledge  Determining whether learning is achieved or not  Grading students "Assessment is to seek answers to the questions of What do students remember from previous grades related to the topic? Could students learn what I teach? Does learning occur? The first thing that comes to my mind about assessment is to grade students." (Miray, pre-interview)  Assessment for students  Ensuring students' learning through the use of assessment  Determining students' level of learning for the topic  Providing the opportunity to students to check their learning difficulties and misconceptions if exists "Assessment should be designed considering students' level if the assessment is expected to be appropriate to its aim. Because students' levels are different from each other and you cannot assess students if you stick with one method. When I determine students' difficulties or misconceptions, I am trying to learn the degree to which learning occurred". (Miray, preinterview) Purpose of assessment  Diagnostic  Eliciting students' prior knowledge "My purpose of assessment is to elicit students' prior knowledge." (Miray, pre-interview)  Formative  Eliciting students' learning difficulties and misconceptions  Giving feedback to students by encouraging them to learn  Creating a context for students' learning  Helping students to develop their learning  Helping teachers to monitor students' learning level  Helping teachers to check their teaching "My formative assessment purposes are to determine students' learning difficulties and misconceptions, to develop students' learning and encourage for learning, to create a context where students organize their learning, to monitor students' level of learning, and to check my teaching." (Oguz, pre-interview)  Summative  Determining students' achievement level of objectives  Grading students "My summative assessment purposes are to determine students' achievement level of objectives and grade students." (Ahu, pre-interview) Informal  Teacher observation "Think that I ask a question to a successful student and the answer was wrong. After a while, I will ask a question at the same difficulty level to that student. The student's answer might be right or wrong. If the answer was wrong, I did not evaluate the student as s/he did not know the right answer. The student might be sick or forget the answer. I consider these kinds of situations. I use observations throughout my all teaching practices." (Ahu, post-interview) Assessment interpretation and actiontaking Ahu: Well done, Kübra. I give you "+" (Ahu, observations, questions, and grades given as "+" )  Grading  Homework in textbook Which one of the following is not a symbol of an element?
Exam question Information about X, Y, and Z is given as follows. X: Symbols are used to represent X. Y: Formulas are used to represent Y. Z: Neither symbols nor formulas are used to represent Z. Which of the following is true for X, Y, and Z?
Compound Mixture Element (Oguz, documents, questions used in exams for grading)

Credibility and Ethical Issues of the Study
The researchers utilized triangulation, prolonged engagement, and member checks to ensure credibility. Triangulation of sources and analyst/investigator triangulation were used to increase credibility (Patton, 2002). Using data from multiple sources (i.e., preinterviews, observations, documents, and post-interviews) for data collection and analysis helped us to ensure triangulation of source. Analyst/investigator triangulation was achieved through independent analysis of data by two analysts. The second researcher spent six weeks in the research setting and with the participants, which ensures prolonged engagement. Her entry began with introducing the study with permissions from the Institutional Review Board, Ministry of National Education, school administrators, and participants. Then, the researcher conducted pre-interviews, observations, and post-interviews by being present in the research site all the time. After analysis of data, findings about teachers' assessment literacy in both knowledge and practice level were shared with the participants. Participants agreed with the findings and hence we assured member checks.
All research activities were conducted in alignment with the permission of the Zonguldak Bülent Ecevit University Institutional Review Board (Date: 30.11.2017, Protocol number: 269) and Ministry of National Education. The voluntary participation of all teachers was ensured through a written consent form. Participants were told to withdraw from the study whenever they want and that no one except researchers had access to data. Moreover, participants were informed that pseudonyms would be used when reporting the study. Through this, issues regarding ethics in research, such as protection of the participants from harm, and confidentiality were assured (Fraenkel & Wallen, 2006).

Comparison of Teachers' View of Learning and Perception of Assessment
Teachers' views of learning were compared considering their views about goals for teaching, teacher role, student role, teaching sequence, and laboratory teaching sequence (Table 3). With respect to goals for teaching, education major teachers had topic and concept teaching-related goals whereas science major teachers' goals focused on helping students to become individuals who have knowledge and skills of both society and era. When teachers' views about their roles during teaching were compared, it was revealed that education major teachers adopted the guide role who encourage students for both their learning and active participation. However, science major teachers had affective variable-focused goals such as increasing students' interest in science lessons and being role models for students. Considering student roles, all participating teachers believed that students should be active and responsible for their learning. In terms of teaching sequence emphasizing the importance of the topic, informing students about the topic's relation to previous topics, and using the questioning method were the common activities conducted by all participants. However, education major teachers elicited students' prior knowledge at the beginning of instruction through questioning right after informing students about the importance and relation of the topic whereas only one science major teacher (Miray) did after teaching the topic. The teaching of the topic occurred at the beginning of instruction in science major teachers' instructions while education major teachers taught the topic after emphasizing the topic's importance and eliciting students' prior knowledge. Using an online educational platform (e.g., MorpaKampüs and Eba) purposively for both teaching and assessment occurred only in education major participants' classes. With respect to teaching sequence in the laboratory, education major teacher Sarp was the one who designed instruction to enhance students' learning in the laboratory.
Teachers' perceptions of assessment were compared considering assessment for teachers and assessment for students (Table 4). All participating teachers perceived assessment as a vehicle to elicit students' prior knowledge. However, only education major teachers viewed assessment as a way to elicit students' difficulties and misconceptions. Interestingly, determining students' level of learning existed in one education major (Oguz) and one science major (Sarp) teacher's perception of assessment for teachers. Using assessment for grading was more prevalent among science major teachers. With respect to assessment for learner, all teachers believed in using a variety of assessment methods. Using assessment as a way to encourage students for learning was emphasized by all education major teachers and one science major teacher (Miray). One education major (Ahu) and one science major (Sarp) teacher considered assessment as a tool to help students achieve objectives. Similarly, the idea of using assessment to provide feedback to students about their learning was observed in education major (Oguz) and one science major (Miray) teacher. Table 3.

Comparison of teachers' assessment literacy in knowledge level
Teachers will be compared considering assessment purposes, assessment strategies, what teachers assessed, and how teachers interpreted assessment and took action ( Table 5). In terms of purposes, all teachers believed in using assessment for diagnostic, formative, and summative purposes. Determining students' achievement level of objectives was the main focus of all teachers' summative assessments. Grading was also prevalent among teachers. However, only one education major teacher (Oguz) considered its use for learning. Teachers were also similar in the sense that they planned to use diagnostic assessment for eliciting students' prior knowledge. With regard to formative assessment, education major teachers (Oguz and Ahu) were more knowledgeable about the ways that assessment could be used for formative purposes. Also, only these teachers had the idea of using formative assessment for determining students' learning level. Checking teaching during formative assessment was embraced by all education major teachers (Oguz and Ahu) and one science major (Miray) teacher. Interestingly, one education major (Oguz) and one science major (Miray) teacher believed in utilizing formative assessment for helping students to develop learning. Similarly, one education major (Oguz) and one science major (Sarp) shared the idea of using formative assessment for encouraging students to learn.
When teachers' assessment strategies were compared, it was revealed that education major teachers were more knowledgeable about formal assessment strategies, especially about alternative ones. All teachers stated that they used smartboard, examination, test (fill in the blanks, matching, true-false, and multiple-choice questions), questioning, homework, and lab reports as formal assessments. However, education major teachers had the idea of using advance organizers, classroom assessment, project, peer assessment, and group assessment. In terms of informal strategies, all teachers mentioned that they utilized teacher observation. All teachers except one, a science major (Miray), had the idea of using discussion.
Teachers were the same in terms of including factual, conceptual, and procedural knowledge in what to assess. Interestingly, nature of science was emphasized by one education major (Ahu) and one science major (Miray) teacher. Comparison of teachers' knowledge about assessment interpretation and action taking did not reveal any clear-cut differences among teachers with different majors. In general, all teachers were knowledgeable about using assessment results to collect data about students' learning, difficulties, and misconceptions. However, using assessment data to improve teaching and to improve students' learning through feedback were stated by all teachers except one, science major (Sarp). Table 5. Oguz stated that he uses assessment results to elicit students' prior knowledge, to determine students' difficulties and misconceptions, to provide feedback to students by encouraging them to learn, to create a context for students' learning, to help students to develop their learning, to monitor students' learning, to check his teaching, to help students to achieve objectives, to grade for students' learning during preinterview.

Comparison of Participant Teachers' Assessment Literarcy in Knowledge Level
Ahu stated that she uses assessment results to elicit students' prior knowledge, to determine students' difficulties and misconceptions, to determine students' learning level, to provide feedback to students, to check her teaching, to determine students' achievement level of objectives, and to grade during pre-interview.
Sarp stated that he uses assessment results to elicit students' prior knowledge, to determine students' difficulties and misconceptions, to encourage students to learn, to help students achieve objectives, and to grade during preinterview.
Miray stated that she uses assessment results to elicit students' prior knowledge, to determine students' misconceptions, to provide feedback to students, to help students to develop their learning, to check her teaching, to help students to achieve objectives, and to grade during pre-interview.

Comparison of Teachers' Assessment Literacy in Practice Level
Teachers' practices were compared considering assessment purposes, assessment strategies, what teachers assessed, and how teachers interpreted assessment and took action ( Table 6). All teachers used summative assessment to determine students' achievement level of objectives. However, education major teachers utilized summative assessment to grade students' learning whereas science major teachers used it for grading. Three teachers (Oguz, Ahu, and Miray) elicited students' prior knowledge through summative assessment while one science major teacher (Sarp) did not perform the summative assessment for that purpose. In terms of formative assessment, all teachers elicited students' misconceptions and difficulties, provided feedback to students, and checked their teaching. However, education major teachers utilized formative assessment for a wider range of purposes than science teachers did and for ensuring students' learning as well. Monitoring students' learning level and checking teaching purposes came together only in education major teachers' practices.
When teachers were compared in terms of strategies, it was revealed that all teachers used smart board, examination, test (fill in the blanks, matching, true-false, and multiple-choice questions), questioning, and homework as formal assessments. Nevertheless, education major teachers utilized more variety of methods, especially alternative ones (e.g., advance organizer and peer assessment), than science majors did. All participating teachers used teacher observation as an informal strategy.
Teachers were similar to each other in the sense that they all assessed factual, conceptual, and procedural knowledge. Interestingly, one education major (Ahu) and one science (Miray) teacher focused on assessing nature of science during their practices.
Teachers' assessment practices in terms of how they interpreted assessment results and took action did not differ to a certain degree. All participating teachers used assessment results to get information regarding students' learning in terms of objectives, difficulties, and misconceptions. Moreover, all teachers provided feedback to students and checked their teaching. However, science major teachers' feedbacks were not as good as education major teachers' in terms of informing and supporting students' learning. Their feedback included saying "right and wrong" to students' responses. One education major teacher, Oguz, among others utilized assessment results for a wide variety of ways than other teachers did. Oguz used assessment results to elicit students' prior knowledge, to determine students' difficulties and misconceptions, to provide feedback to students by encouraging them to learn, to create a context for students' learning, to encourage students' peer and self-learning, to help students to develop their learning, to check his teaching, to help students to achieve objectives, to grade for students' learning during his teaching.
Ahu used assessment results to elicit students' prior knowledge, to determine students' difficulties and misconceptions, to determine students' learning level, to provide feedback to students, to determine students' achievement level of objectives, and to grade for students' learning during her teaching.
Sarp used assessment results to determine students' difficulties and misconceptions, to provide feedback to students, to check his teaching, to help students achieve objectives, and to grade during his teaching.
Miray used assessment results to elicit students' prior knowledge, to determine students' learning difficulties and misconceptions, to provide feedback (i.e., yes and no) to students, to check her teaching, to help students to achieve objectives, and to grade during her teaching.

Discussion
Findings were discussed considering teachers' perception of assessment influenced by their views of learning first and then teachers' assessment literacy in knowledge and practice level.
Teachers' views of learning included several dimensions. With respect to goals for teaching, education major science teachers' goals were subject matter goals (i.e., teaching science) whereas science major teachers' goals were schooling (i.e., preparation for life). This finding is compatible with the nature of teachers' orientation indicating that teachers have a variety of goals such as schooling, affective, and subject matter (Friedrichsen & Dana, 2005). Differences between teachers with different majors might be related to the differences in their undergraduate education (Avraamidou, 2013;Mansoor, 2009). Teacher education programs' focus is "teaching science knowledge meaningfully to students" while the focus of the program in arts and science faculty is "contributing to use of science knowledge for research and industrial purposes". Differences in the focuses of programs might provide a baseline for how they interpret their experiences (Mansour, 2009) and how they see their profession (Friedrichsen & Dana, 2005). Participants with different majors were also different from each other in terms of their views about teacher roles. Education major teachers embraced the role of a guide during learning whereas science major teachers believed that their role was to help students' development of positive attitudes towards science. This difference might also be explained by knowledge and experiences that they gained during undergraduate education (Avraamidou, 2013;Mansoor, 2009), which has the potential to influence how teachers see their profession (Friedrichsen & Dana, 2005). Teachers' goals for teaching were compatible with their role during teaching, which is consistent with the fact that teachers' orientation is an interrelated set of beliefs (Friedrichsen, van Driel & Abell, 2011). In terms of students roles, there was no difference between teachers with different majors. All teachers stated that students should be active during learning. This finding is expectable considering the fact that participating teachers have taught science based on a national science curriculum (Ministry of National Education, 2018) adopting constructivism (Friedrichsen & Dana, 2005). There was a discernible difference in the teaching sequence of teachers with different majors. Education major teachers were better at designing instruction that ensured student-learning than science majors did. This might be stemmed from differences in teachers' pedagogical content knowledge. Pedagogical content knowledge is the knowledge that ensures teachers' teaching of the topic in a way that is understandable by students (Shulman, 1986). Courses taken during teacher education are one of the major sources for pedagogical content knowledge development (Grossman, 1990). Although teachers were not so much different from each other in terms of their teaching experience, another source of pedagogical content knowledge (Abell, 2007), courses taken at education faculty by education major teachers might constitute a baseline for their professional development (Demirdogen, Hanuscin, Uzuntiryaki-Kondakci & Koseoglu, 2016). With respect to perception, all teachers considered assessment as a tool for eliciting students' prior knowledge. Similarity between teachers might be explained by teachers' teaching science based on a national science curriculum (Sen, Oztekin & Demirdogen, 2018), which has spiral nature, and curriculum is one of the factors affecting teachers' assessment decisions (Tomanek, Talanquer & Novodvorsky, 2008). However, perceiving assessment as a way to reveal students' misconceptions was only observed in education major teachers. This might be explained by the interaction between "knowledge of learner" and "knowledge of assessment" components of pedagogical content knowledge (Aydin, Demirdogen, Akin, Uzuntiryaki-Kondakci & Tarkin, 2015;Demirdogen et al., 2016), which might be strengthened by courses during taken teacher education (Bell & Cowie, 2001;Grossman, 1990) and subsequent teaching experience (Abell, 2007).
Teachers' assessment literacy was discussed considering its components (e.g., purposes and strategies). Teachers were not different from each other in terms of the type of assessment purposes that existed in knowledge and practice level. That is, they all understood and enacted assessments for diagnostic, formative, and summative purposes. Teaching experience (i.e., at least 20 years of experience) might influence science major teachers' pedagogical professional knowledge (Abell, 2007) and assessment practices (Tomanek et al., 2008), and hence they might have the same purposes as education major teachers. However, how teachers translated their purposes into practice was different for education and science major teachers. Grading and determining students' achievement level of objectives existed in all participating teachers' summative purposes in both knowledge and practice level. This finding is compatible with the finding of other studies in the literature (Nazlıçiçek & Akarsu, 2008;Volante & Fazio, 2007). Teachers' having summative purposes in knowledge and practice level might be related to the fact that teachers feel responsible for ensuring students' both objective achievement and being successful at state-wide exams (Bell & Cowie, 2001;Tomanek et al., 2008). However, only one education major teacher (Oguz) perceived and enacted summative assessment as a means to grade learning, which might be related to the nature of that teacher's pedagogical professional knowledge base. Oguz had nine years of teaching experience and courses that he took during teacher education were mostly influenced by constructivism, which might influence his assessment knowledge and practice (Grossman, 1990). In terms of diagnostic assessment, all teachers except one (science major teacher, Sarp) transfered their purpose of eliciting prior knowledge to their practices. The gap in teachers' beliefs and practices might be the reason for Sarp's inability to transfer that purpose to practice (Demirdogen et al. 2016;Uzuntiryaki, Boz, Kirbulut & Bektas, 2010). Moreover, Sarp did not define his role as a guide during teaching and preferred to lecture after informing students about the objectives. Sarp's views of learning might affect both his purposes (Abell & Siegel, 2011) and practices (Bell & Cowie, 2001) of assessment. Interestingly, all participating teachers were able to transfer all of their formative assessment purposes to their practices, which is in line with the studies indicating that teachers have formative assessment practices (Ruiz-Promo & Furtak, 2007). This is also compatible with the fact that teachers' pedagogical professional knowledge has both understanding and enactment dimensions (Park & Chen, 2012). Teacher education courses (Bell & Cowie, 2001;Grossman, 1990), teaching experience (Abell, 2007;Box, 2008), and curriculum (Tomanek et al., 2008) might result in the observation of formative assessment practices in all teachers. However, the quality of teachers' formative assessment practices differed; science major teachers' feedbacks provided for students' learning were observed as "right and wrong". Education major teachers encouraged students learn from peers when providing feedback. Since science major teachers did not take any course on assessment, their poor formative assessment practices were expectable (Bell & Cowie, 2001).
Teachers mostly preferred to use formal assessment strategies in both knowledge and practice level, which is compatible with the studies indicating that teachers favor traditional assessment since they might feel knowledgeable about those (Gelbal & Kelecioğlu, 2007), responsible for preparing students for statewide exams (Black & Wiliam, 2004;Box, 2008), and have low self-efficacy about formative assessment (Box, 2008;Gelbal & Kelecioğlu, 2007). However, education major teachers used advance organizers and classroom assessment during teaching as opposed to science teachers. Teacher education courses (Bell & Cowie, 2001;Grossman, 1990) and teaching experience (Abell, 2007;Box, 2008) might explain this difference.
With regard to what to assess, all teachers believed in assessing factual, conceptual, and procedural knowledge and assessed those in practice. This is expectable considering the fact that curriculum (Tomanek et al., 2008) and feelings responsible for preparing students for statewide exams (Bell & Cowie, 2001;Box, 2008;Tomanek et al., 2008) influence teachers' assessment practices.
Teachers' assessment knowledge and practices in terms of how they interpreted assessment results and took action did not differ to a certain degree. In general, all teachers used assessment results to collect data about students' learning in terms of objectives, difficulties, and misconceptions as they stated during pre-interview. Furthermore, all participating teachers were able to provide feedback to students and check their teaching. Nevertheless, science major teachers' feedbacks were not qualified enough to inform and enhance students' learning. Also, one education major teacher, Oguz, among others utilized assessment results for a wide variety of ways than other teachers did. Education major teachers might have more developed pedagogical content knowledge than science majors might have (Aydin et al., 2015;Demirdogen et al., 2016;Shulman, 1986) because of teacher education courses (Bell & Cowie, 2001;Grossman, 1990) and teaching experience (Abell, 2007;Box, 2008).

Implications for Research and Teacher Education
The findings of the study have implications for teacher education and research. Science teachers' assessment literacy, one of the components of pedagogical professional knowledge of teachers, is implicit (Loughran et al., 2004) and complex (Abell & Siegel, 2011) in nature. Therefore, teacher education courses and professional development programs should provide opportunities where pre-service and in-service teachers think about their assessment knowledge in an explicit and reflective manner. Therefore, these contexts should encourage pre and in-service teachers to provide their answers to the questions of "Why do I conduct assessment during teaching? What are my purposes for assessment? To what degree my assessment purposes and views of learning are compatible? How do I interpret assessment results? Do I use evaluation to improve teaching and learning?" Science method and practicum courses have the potential for helping pre-service teachers to create their answers to these questions. Inservice teachers also need professional development programs, as they stated during the study, which aim to increase both their knowledge and practices of assessment and evaluation.
This study has been one of the first attempts investigating education and science major teachers' assessment literacy within the context of teaching "Matter and its Change" unit at public schools. Teachers' subject matter knowledge and contexts of teaching might influence their assessment knowledge and practices (Magnusson et al., 1999). Therefore, there is a need to conduct studies with teachers both having different levels of subject matter knowledge and teaching in different contexts (i.e., private versus public). Another research might be the determination of science teachers' assessment literacy enacted during the teaching of different disciplines of science (e.g., physics and biology). These kinds of studies might contribute to understanding the nature of science teachers' assessment literacy.


Bounces of a marble and Zeno’s paradox

The coefficient of restitution of the bounces of a marble on a table is here studied and measured in terms of the total bouncing time. Interesting links arise with mathematics (geometric series) as well as philosophy (Zeno’s paradox), which make our proposal appealing for an interdisciplinary teaching-learning sequence. The relevance of this work for high school and undergraduate students is discussed with emphasis on students’ misconceptions when dealing with infinite processes.

Introduction
Convergent infinite series [1] arise as a mathematical tool in the solution of a lot of problems in physics. The issue of convergence of an infinite process and its application to concrete physics phenomena has been widely recognized to be a difficult one to deal with by high school as well as undergraduate students. Indeed recent studies pointed out students' difficulties in blending mathematics and physics [2,3].
In this contribution we propose an interdisciplinary teaching-learning sequence aimed to put together physics, mathematics and philosophy. The sequence is integrated by the proposal of simple experimental activities, where students have the opportunity to learn how to carry out measurements and perform data analysis in a concrete context. The designed activities are based on the use of built-in sensors and video cameras currently available on smartphones, according to the Bring Your Own Device (BYOD) paradigm. The core of our proposal is the study of the bouncing of a marble on a table by focusing on the progression of time intervals separating successive bounces. We find that, by measuring the total time of bouncing Δt, the coefficient of restitution ϵ can be estimated. In fact, in an inelastic collision the kinetic energy is not conserved, therefore the speed decreases. There is a simple relation between speeds vi and vf, before and after the collision, respectively, which defines ϵ: vf = ϵvi (ϵ < 1) [4]. By measuring the initial height h0 from which the marble is released, the coefficient of restitution ϵ can be expressed in terms of the total bouncing time as: where g is the gravity acceleration. The derivation of Eq. (1) allows us to talk about kinematics, mathematics and philosophy in a simple way and, then, to perform experiments. Indeed, obtaining the total bouncing time Δt requires the sum of a geometric series [1] and we show how, for the particular value  = ½, this is related to the solution of Zeno's paradox of Achilles and the turtle [5]. Finally we propose an experimental activity based on the BYOD paradigm, whose aim is to estimate the coefficient We point out that, in general, the coefficient of restitution exhibits a slight dependence on velocity [6] and, hence, on the initial release height. But this is really a tiny effect, which can be neglected as we assume in our experimental proposal. Further approximations are a vertical movement of the marble without spinning effects, a negligible time of contact with the floor at each bounce as well as a negligible effect of air drag and buoyancy.

The kinematics of bouncing bodies
In this Section we deal with successive bounces of a body (e.g. a marble) on the ground, and study the progression of the time intervals separating successive bounces. We show that, if the coefficient of restitution is assumed to be the same for all bounces, these times are in a geometric progression with ratio ϵ. This suggest a possible measure of the coefficient of restitution in terms of time intervals. In fact, we shall find that the coefficient of restitution is simply related to the total bouncing time. Alternative proposals of calculation and experimental measurement of the coefficient of restitution are reported in the literature (see for instance [7][8][9] and references therein).
Let us start by assuming that the body is initially at rest when released. At = 0 the body will be at height ℎ 0 with respect to the ground, so that its potential energy (assuming that the zero is on the ground) is 0 = ℎ 0 . Conservation of energy allows us to write that 0 will be equal to the kinetic energy immediately before the collision with the ground: After the collision the kinetic energy becomes and the body will reach a height ℎ 1 < ℎ 0 , which can be determined again by requiring conservation of energy: These two relations allow one to relate the coefficient of restitution to the ratio of the heights: The coefficients of restitution can be related with the times between collisions by means of the kinematic relation: where is the height of the body, measured from the ground. The time 0 from the release of the body to the first collision is given by ( 0 ) = 0, so that: The time needed to reach the height ℎ 1 after the first collision can be computed by considering that the body will start with velocity and be decelerated by gravity, so that one has to use the following kinematic relation: whose derivative with respect to time is: is defined by the condition ( 1 ) = 0, so that one gets:  (3) gives 2 = 2 ℎ 1 , so we get Therefore we express the coefficient of restitution as 11 00 ht ht   (11) which gives the following relation between bouncing times: 10 tt   (12) By iterating the same procedure for each bounce and assuming the same coefficient of restitution for all the bounces we therefore get: (14) which is the basis for the results of the following sections.

Computing the total bouncing time: the geometric series
The aim of this Section is to exploit the result obtained in equation (14) to compute the total time of bouncing. We shall see that the total time is finite even if there is an infinite number of bounces, thanks to the fact that the ratio ϵ is less than one [1]. This point is difficult to understand for most students. Indeed a widespread misconception among students is that a series with an infinite number of terms always diverges. The total bouncing time is: The series in round parentheses is a geometric series of ratio < 1, which is known to be convergent.
To compute the sum we follow the usual procedure: where the first equality in (16) relies on the fact that the series has an infinite number of terms. In this way the well-known expression for the sum of a geometric series has been recovered. By putting this result in equation (15), we get the total bouncing time It is a finite quantity, because the infinite number of bounces is balanced by the fact that they take less and less time. This is the key observation in order to understand the phenomenon and overcome the misconception that infinite bounces give infinite time.
Notice that the limiting case ϵ → 1 gives an infinite total time, which corresponds to the case of elastic bounces: in this situation the ball never stops as expected (at odds with the previous case here the balance does not take place). Solving the above equation with respect to ϵ we finally arrive at which, upon substituting equation (7), coincides with equation (1). Formula (19) allows one to estimate the coefficient of restitution starting from the knowledge of the initial height and the measurement of the total bouncing time.

Philosophy: Zeno's paradox
In this Section we give a geometric interpretation of the sum of the geometric series in equations (16), (17) for the particular case ϵ = 1 2 and relate the above results to Zeno's paradox [5]. In this way students have also the possibility to understand how and why it is not to be considered a paradox at all, thanks to the mathematics of infinite series. According to Zeno's paradox, Achilles and the turtle run on a path. We assume that Achilles starts running when the turtle reaches the middle point of the path, and that the turtle moves with half the velocity of Achilles. Then in the time Achilles will take to get to the middle point, the turtle will cover another quarter of the path. When Achilles will have covered this quarter, the turtle will cover another half of it, and so on. As a result, Achilles would never reach the slower turtle, and this is the usual statement of the paradox. This situation can be described as follows. We divide the path in two, then divide the second half in two, then divide the second half of the second half in two and so on. Then we clearly get Let us now consider the geometric series of ratio 1 2 , whose sum is: Thus the above strategy allowed us to compute the sum of the series without manipulating infinite series. This shows that Achilles reaches the turtle in a finite time, despite this takes an infinite number of steps.
As for the case of the bouncing marble, this happens by summing an infinite number of steps, which are shorter and shorter.

Experiment and data analysis
The set-up described in section 2 can be realized with a marble or a ball, which can be released from a certain height as bshown in figure 1. A meter is used to measure h0 while the total bouncing time can be measured by means of a phonometer. Several free apps are available for such a measurement, both on Android and iOS (for instance, Sound Analyzer App for Android [10]). We used the native iOS app, which has the advantage of being very sensitive, so that the time of every single bounce can be measured.
As an alternative, one can use his/her own ears and a chronometer and obtain quite accurate measurements as well.     figure 2. The growth of the error bars with height is due to various factors, such as air resistance (as also noticed in [7]), irregularities in the bouncing surfaces [12] and human errors in measuring times. Further uncertainties can be introduced by the release of the marble, which may give rise to unwanted spinning. In fact a careful initial release is crucial in order to improve the experimental conditions by minimizing lateral displacements of the marble. A detailed discussion of the effects of the errors on the experimental data has been given in [12].
The estimated value for the coefficient of restitution is 0.850 0.002.

Conclusions
A simple and common setup made of a marble bouncing on a table has been proposed, which allows us to estimate the coefficient of restitution ϵ in terms of the initial height h0 from which the ball is released and of the total bouncing time Δt. This issue is the core of an interdisciplinary teaching-learning sequence, aimed to put together physics, mathematics and philosophy. Indeed, we show how a kinematics topic can be related to a strictly mathematical subject, namely geometric series, and then provide a geometric interpretation of the sum of such series. Finally the argument utilized in Zeno's paradox is proven to be false. The focus of our proposal is on the convergence of infinite processes and its application to concrete examples borrowed from different fields, in order to make high school as well as undergraduate students to tackle and overcome their difficulties in blending mathematics and physics [2,3].