Classroom talk and the legacy of Confucian culture in mathematics classroom

Teaching and Teacher Education 88 (2020) 102964

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Classroom talk and the legacy of Confucian culture in mathematics classroom Emily S.W. Sum*, Oh Nam Kwon Department of Mathematics Education, College of Education, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 151-748, South Korea

h i g h l i g h t s
Revoicing orchestrates mathematical arguments despite the honorific-encoded utterance in the hierarchical Confucian classroom.
Revoicing foster classroom discussion while keeping students’ social face and Confucian ethnics.
Knowledge is co-constructed and co-owner by the students in the collectivist classroom.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 July 2018 Received in revised form 8 September 2019 Accepted 28 October 2019 Available online xxx

Korean students have been performing well in international assessments of mathematics. Nevertheless, classrooms have often been described as teacher-dominated and silence is valued as a pedagogical strategy to cultivate thinking. Previous studies have attributed this phenomenon to the ideology of Confucianism. This paper examines the sociocultural aspects of classroom talk for developing students’ mathematical processes. Our findings show teacher revoicing facilities discussions/dialogues in the hierarchical classroom. It orchestrates multiple voices of honorifics and different speech styles/levels, both individual and choral responses. It promotes classroom talk without the sociocultural framing, and creates a learning environment necessary for implementing recent curriculum initiatives. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Teacher revoicing Classroom talk Confucianism Korean classroom

1. Introduction Korean elementary students have been performing well in recent international studies of mathematics achievements over the past two decades, such as TIMSS 2011 (Mullis, Martin, Foy, & Arora, 2012) and TIMSS 2015 (Mullis, Martin, Foy, & Hooper, 2016). Yet, research using classroom video-based analysis generally describes the teaching in East Asian countries to be “very traditional and oldfashioned” (Leung, 2001, p. 35). As observed in the Learner’s Perspective Study (Clarke, Keitel, & Shimizu, 2006; Kaur, Anthony, Ohtani, & Clarke, 2013), Korean classrooms are teacherdominated with minimal oral interactions. Students are reticent and rarely speak/communicate their mathematical ideas (Park & Leung, 2006). Their responses are often in choral mode and restricted to an agreement with the mathematical statement/position given by the teacher (Clarke, Xu, & Wan, 2013a, 2013b).

* Corresponding author. E-mail addresses: [email protected] (O.N. Kwon).

(E.S.W.

https://doi.org/10.1016/j.tate.2019.102964 0742-051X/© 2019 Elsevier Ltd. All rights reserved.

Sum),

[email protected]

Grow-Maienza, Hahn, and Joo (2001) analyse the mathematical practices in elementary schools and identify the systematic patterns of instruction including public evaluation and choral response (CR). Ju & Kwon (2007), p. 277) argue that “the students seemed reluctant to talk about their ideas because their answers might be incorrect”. Similarly, Lee and Sriraman (2013, p. 163) also point out that students are “quite sensitive about making mistakes in public” and “seriously afraid of losing face in front of peers when answering teachers’ questions”. This socio-culture psychological concept of face/chemyon (체면) (Choi & Lee, 2002; Kim & Yang, 2011) is based on the moral feeling/ethnical emotion of Confucianism that influences student behaviour and their participation in class. Koreans themselves are critical of their own educational policies and practices despite their remarkable educational achievement internationally. Rounds of education reforms have been initiated since 1995 (Kim, 2004). New policies are introduced by each new government from the presidential election every five years, which aim to tailor for the needs of economic development and national competitiveness. Major direction of the curriculum design includes “a student-centred curriculum aiming to facilitate students’

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autonomy and creativity … as two of the most important abilities required for leadership in the 21st-century era of globalization and information technology” (Kim, 2003, p. 146). Correspondingly, mathematics curriculum has shifted its focus on content knowledge to core competencies, with increased emphasis upon the teaching of problem-solving strategies, developing students’ higher-order reasoning and thinking skills, and communicating mathematically (Ministry of Education, Science, and Technology, 2009). In fact, Korean educators and policy makers are aware of the importance of classroom talk in students’ mathematical development, where teaching practices and instructional strategies have started to change in the recent years (e.g. Kim, Han, Park, & Lee, 2013; Pang, 2012). Based on the classroom video-data from our larger study on children’s development of the concept of multiplication, revoicing was evident as a scaffolding strategy adopted by teachers. Teacher revoicing (O’Connor & Michaels, 1993) is a concept originated from Anglophone context, in which the teacher reutters a student’s contribution (spoken/written) through repeating, rephrasing, reporting and expanding during discussion (Forman, LarreamendyJoerns, Stein, & Brown, 1998). Our research question is, how does revoicing support students’ development of the mathematical processes such as reasoning and communication in a Confucian classroom? To answer our question, we analysed the classroom interactions and mathematical discourse of the video-records. The episodes presented below contain many of the typical and consequential characteristics of the classroom’s discussion. Our intention to provide such a long example is to give the reader a better idea of what it means to participate in a Korean classroom, and how students’ multiplicative reasoning gradually developed as the lesson progressed.

Joseon. They explained the concepts of li (리: Principle/law) and ki (기: Energy/matter)4 through the theory of sadan5-chiljeong6 (사단 칠정: The Four Beginnings and Seven Emotions), which became specialized in a unique Korean way. To remain true to NeoConfucian thinking in all areas of daily life, scholars strictly followed the code of social ethics of sadan-chiljeong and samgangoryun (삼강오륜: The Three Bonds and Five Relationships). The Three Bonds are “loyalty of the retainer to his sovereign (군위신강), filial piety of the child to his parents (부위자강), and fidelity of the wife to her husband (부위부강)” (Cho, 2014, p. 7). Moreover, proper distinctions between people according to their social status must be made according to Five Relationships: Loyalty between king and subject (군신유의), closeness between father and son (부자유친), difference between husband and wife (부부유별), hierarchical order between old and young (장유유서), faithfulness between friends (붕 우유신). Harmonious social relationships can exist only when this set of code is followed (Kim, 2014). The most pronounced concept in the adaption of NeoConfucianism to the society is ye7 (예: Propriety), which builds the Korean version of the Neo-Confucian social system (Deuchler, 2004). Ye is “one of the major currents in Korean Neo-Confucian thought … set up on the premise of this innate li giving issuance” (Yu, 2016, p. 78). The embodiment of the ye is based on samgangoryun and the abstract concept was explained in storybooks disseminated widely during Joseon Korea so that even ‘naïve commoners8’ could understand the philosophy easily by looking at the pictures and reading the stories in hangul (한글) (Cho, 2014). Kim & Choi (2015) argue that the writing system of Korean alphabet, hangul, and the system of honorifics is entirely based upon jangyuyuseo (장유유서), as described: the virtue stresses preferential treatment of older persons and obliges younger persons to show respect to them, even in conversations and other types of communication. In this way, the Confucianism-imbued Korean language observes and reflects the rigidly hierarchical social structure and interactive patterns, constantly reminding and reinforcing those ideas subliminally (p. 176).

2. Korean Confucianism and its implication Korea is the “most Confucian part of the world” (Koh, 1996, p. 191). Teachers are highly respected in the society and classroom talk seems to go against the Confucian philosophical perspective, the teacher’s word is law. Rather than foster discussion, parents, teachers, and students all assume that the teacher’s proper role is to impart truth. It is a rare student that would question a teacher’s authority, whatever his or her private doubts (Sorensen, 1994, p. 27). Asking questions is considered a challenge to teacher’s authority. Therefore students rarely raise questions during the lesson. In fact, silence is a means of construing knowledge in Eastern philosophies, as seen in the Analects “the silent treasuring up of knowledge1” and in Tao Te Ching “those who know do not talk, those who talk do not know2”. Also, meditation has long been cultivated by Korean scholars, which is considered as valuable for higher-order thinking (Yu, 2016). The society of Joseon dynasty (1392e1897 CE) was built upon the ideology of Neo-Confucianism (성리학) that incorporated the metaphysical and cosmological tenets of Taoism and Buddhism. Although Neo-Confucianism originated in China, it was elevated to a higher philosophical level through Korean scholars like Toegye Yihwang (퇴계 이황) and Yulgok Yi-yi (율곡 이이).3 They were not just faithful transmitters but interpreters of Zhu Xi’ philosophy to

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默而識之e 論語述而 知者不言, 言者不知 e 道德經 3 Faces of Toegye Yi-hwang and Yulgok Yi-yi are on the Korean 1000-won and 5000-won notes respectively. 2

Unlike English and Chinese, there are six speech levels in contemporary Korean language that can be distinguished by different sentence endings (Lee & Ramsey, 2000). The grammatical forms of propriety involve an elaborate honorific system that is sensitive to who is speaking to whom (addressee) and who is speaking about whom (referent). The speaker must be constantly attentive to and adjust accordingly to the respective social status and age differences of the addressee/referent in different social settings. According to sadan-chiljeong, being humble and yielding to others is the beginning of propriety ye. Thus if one speaks to a

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Li (리) and ki (기) are two inseparable components of Neo-Confucianism. Four beginnings include feeling sorry for others or the heart of compassion/ commiseration (측은지심); the feeling of shame/dislike or being embarrassed by one’s own mistakes (수오지심); the feeling of courtesy/modesty/deference or being humble and yielding to others (사양지심); and the feeling of approving/disapproving or distinguishing between right and wrong (시비지심). 6 Seven emotions are joy (희), anger (노), sadness (애), fear (구), love (애), hate (오) and desire (욕). 7 Ye, the manifestation of li and ki, is one of the osang (오상: five constants), including humanity/benevolence (인), righteousness (의), wisdom (지), and faithfulness (신). 8 During Joseon dynasty, Koreans were classified into six categories: yangban (양 반), jung-in (중인), sangmin (상민), cheonmin (천민), baekjeong (백정) and nobi (노 비), in which the distinctions between every individual were recognized and understood. The caste system was abolished in early twentieth centuries after Japanese invasion. 5

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teacher, that person needs to choose a honorific form of speech jondaenmal (존댓말) to show great respect. Gyeong (경) meaning to respect is “a method of concentrating on study while always maintaining a focused body and mind through a reverent attitude” (Kim, 2018 p. 29). It is the pivot of or key to all methods of study. For instance, sohak (소학: The Elementary Learning) relies on gyeong to begin and dehak (대학: The Great Learning) relies on gyeong to proceed with the investigation of things (격물) and the extension of knowledge (치지) (Kim, 2018). In contrast, if one is speaking to a classmate, they may use banmal (반말: Informal, blunt speech form). This speech level is only used when the speaker addresses someone of the same age/ status. Otherwise, this is considered as an insult/humiliation or an act of rudeness. It is not permissible to address teachers by their names. The only form that students have even used for teacher is seonsaengnim (선생님: Respected teacher). “The hierarchical Confucianism value system meant that the ties formed between students and teachers constituted a stifling restraint on individual initiative and freedom of action” (Eckert, Lee, Lew, Robinson, & Wagner, 1990, p. 143). Thus, a level of respect and sociopsychological distance exist between teacher-student relationships in all classroom settings. Joseon Korean tried to achieve social unity through NeoConfucianism philosophy by creating a country united enough to be seen as one extended family (Kim, 2014). Based on sayu9-paldeok10 (사유팔덕), Koreans feel a strong connection to those within their in-group. Virtues such as loyalty chung (충), fraternity je (제) and faithfulness/trustworthiness sin (신) are crucial in maintaining harmony in the bureaucratic society so that each member would assume their reciprocal responsibilities, and they are noticeable in the communication and interactive patterns. For instance, Korean use the first-person plural pronoun woori (우리) extensively and obligatorily, which reflects unity and collectivistic value in the society. Woori literally translated as ‘we’, ‘us’ or ‘our’ is commonly used to replace ‘my’ to ‘our’, and in this logic, ‘my family’ becomes ‘our family’, ‘my wife’ becomes ‘our wife’. Stressing one’s ownership is considered selfish, uncooperative behaviour, and boasting about one’s own intelligence and ability is a serious transgression against traditional morality of sadan-chiljeong. Research by Hofstede (2010) suggests that the idea of collectivism is established in children’s early childhood and is further developed and strengthened during their school years, as he explains, in the collectivist classroom, the virtues of harmony and maintaining face reign supreme. Confrontations and conflicts should be avoided or at least should be formulated so as not to hurt anyone; students should not lose face if this can be avoided. Shaming (that is, invoking the group’s honour) is an effective way of correcting offenders: they will be set straight by their ingroup members. At all times, the teacher is dealing with the student as part of an in-group, never as an isolated individual (p. 118). Suohjusim (수오지심) of sadan is the beginning of righteousness (의), and saving chemyon is to avoid being embarrassed by one’s own mistakes. The perception of others that a person fails to meet the social expectation becomes less desirable is grounds for deep shame (치). Based on the theory of propriety, students try to avoid

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making mistakes and maintain a humble attitude sayangjisim (사양 지심) by concealing their knowledge/accomplishments out of consideration for the feelings of others. De Mente (2012) argues that Koreans have been conditioned for generations to be especially sensitive about shaming anyone or themselves being shamed e something that can result from the wrong level of speech being used, from not using the proper form of address or title, from criticism, from weaknesses being revealed, and so on (p. 246). Although Korean attitudes toward Neo-Confucian values have altered through democratisation, modernisation and globalisation, their respect for traditional values and the code of social ethics is systematically encoded in the form of utterances that had been transmitted through early Korean dynasties and remains unchanged in the contemporary society. Therefore, we asked ourselves: How do we analyse the mathematical discourse given the complexity of the honorific language system? 3. Mathematical discourse analysis 3.1. Classroom talk The crucial role of classroom talk plays in students’ mathematical development has been well documented (e.g. Brown & Hirst, 2007; Mercer & Sams, 2006). Methods for analysing talk have their roots in social linguistics that examine the relationship between the forms and structures of English language and the uses in social context (Mercer, 2010). The fundamental discourse structure between teacher and students is usually characterised by InitiationResponse-Feedback (Sinclair & Coulthard, 1975) or InitiationResponse-Evaluate (Mehan, 1979). In other words, the teacher initiates an interaction, the student responds, then the teacher provides feedback to evaluate student’s response. Influenced by the sociocultural theory (Vygotsky, 1978), recent research has shifted the focus on discourse structure of IRF/E to classroom interactions. It is through these interactions and social processes that students develop their mathematical knowledge and skills in class. Not only students learn from interacting with teacher, but collective thinking and understanding can also be created through the interactions amongst students. Mathematical discourse consists of questioning and explaining of mathematical ideas, and is useful to describe and understand classroom teaching and learning (Hufferd-Ackles, Fuson, & Sherin, 2004). As described by Moschkovich (2003, p. 326), “participating in mathematical discourse practices can be understood in general as talking and acting in the ways that mathematically competent people talk and act when talking about mathematics”. Mathematical discourse includes not only the mathematical vocabularies and definitions, but also the meanings, styles and modes of arguments that belong to the language of mathematics. It is the language that teachers and students use to communicate and interact in the classroom as part of teaching/learning the conceptual and procedural understanding of the mathematics itself. From this perspective, classroom talk becomes a resource for understanding the sociocultural practice of mathematics classroom. 3.2. Teacher revoicing

9 Sayu (사유: Four cords/anchors) are propriety (예), righteousness (의), integrity (염), shame (치). 10 Paldeok (팔덕: Eight virtues) are humanity/benevolence (인), righteousness (의), propriety (예), wisdom (지), loyalty/allegiance (충), faithfulness/trustworthiness (신), filial piety (효), fraternity (제).

Teacher revoicing provides opportunities for scaffolding students during classroom discussion, which can be viewed as a Vygotskian theoretical construct in analysing social interaction. Moschkovich (2015, p.1070) argues that revoicing “provides an example of a teacher move that can serve to manage the tension

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between providing appropriate calibrated support while also providing opportunities beyond the learners’ current proficiency, but not through direct instruction”. This discourse strategy has been adopted to analyse and describe the orchestration of mathematical discussion in many studies conducted in the Anglophone countries (Herbel-Eisenmann, Drake, & Cirillo, 2009). For instance, Forman et al. (1998) use revoicing to analyse the socialization of argumentation in the lesson on area measurement, setting an example for other studies. Besides, monolingual classrooms, Moschkovich (2015) illustrates how revoicing can facilitate students’ participation in a bilingual classroom, and argues that “revoicing can build student’s everyday language while providing exposure to formal academic language” (p. 1076). Teacher revoicing reinforces and enhances student’s mathematical comprehension while simultaneously demonstrating precise mathematical language. It provides the language scaffold in a multilingual mathematics classroom (Enyedy et al., 2008), and supports Englishlanguage learners in mathematical discussion (Banse, Palacios, Merritt, & Rimm-Kaufman, 2017). Although revoicing has been examined in monolingual and multilingual classrooms in Englishspeaking countries, it has not been used to analyse the mathematical processes in the Confucian classroom and we aim to fill this research gap. 4. Data collection Korean education system is highly regulated in providing “the same content and quality of education to every elementary student regardless of his or her residential area” (Kim & Albert, 2015, p. 53). The scope and sequence of the curriculum, as well as the pacing of the topic are driven by the textbook and teacher’s guide, designed and developed by the Ministry of Education. Lesson structure, instructional strategies, problem set and manipulatives used are standardized. Hence, students in the same grade level learn the same curriculum content in almost the same way based on the same set of values across the country. A lot of effort goes into maintaining the quality of teachers, and for every curriculum revision, teacher education programmes are provided in making sure that everyone understands the new curriculum initiatives and the ways of teaching. Teacher distribution is controlled by the government, and teachers are required to change schools every five years (Seoul Metropolitan Office of Education [SOME], 2019). Given this backdrop, Korean teachers are considered to have similar pedagogical practices, and the data collected should reflect the reality of classroom situation across the country. And, a case study approach allowed us to comprehend the larger phenomenon through focusing on the detailed examination of the specific case (Rossman & Rallis, 2003). 4.1. Participants This paper draws on an analysis of classroom video-data in our larger study situated at a demographically diverse elementary government school. It is an average local school affiliated with one of the universities in Seoul, the capital city of South Korea. We spent a total of 6 weeks at this school, where second-grade teachers participated voluntarily in the study: Ms. Tae-ri and Ms. Do-yeon11, who had eight years and nineteen years of teaching experiences at the time of the study respectively. Ms. Do-yeon is a co-author of the mathematics textbooks. She was highly regarded in the school for her knowledge and experiences in mathematics teaching; and respected by students and parents (the observation was based on

the interactions during an open class12). As mentioned, Korean society is heavily based on jangyuyuseo, where one’s speech manner should reflect his/her age and social status/ranking in relation to the listener (Kim & Choi, 2015). Students are humble and show greater respect to teachers with higher ranks. As compared with other classes in school, the egalitarian atmosphere is much less in Ms. Do-Yeon’s class.13 Also, given her high social status in school and the community, a wider socio-psychological distance between teacher-student relationships could be expected. Therefore, her class was chosen as the focus of analysis to illustrate how revoicing support students’ development of the mathematical processes in Confucian classroom settings. 4.2. Settings The curriculum focus was on multiplication. This topic was selected because our earlier findings have shown special linguistic features in the learning of multiplication (Sum & Kwon, 2018), which provided us with a rich set of data in understanding classroom talk. Six lessons (based on the teachers’ guide) were videotaped for each teacher, and revoicing strategy was evident in their teaching practice. The data corpus included video recordings of classroom observation using three cameras (teacher camera, student camera and whole class camera), teachers’ interviews, students’ work and other instructional materials. Field notes were maintained to record the organization/structure of the class and the types of changes in the instructional activity. 4.3. Transcription & translation All utterances of teacher and students in video data were transcribed and represented by S: Single student; SN: Single student different from the last speaker; Ss: Multiple students, but not the entire class. E: Entire class.//double backslashes to indicate overlapping speech. In order to avoid content being lost in translation, the transcribed talk in Korean remains throughout the analysis. Some of the original transcripts are shown along with the English translation to illustrate the subtle nuance of the Korean language. There are two number systems in Korea that are used interchangeably: Native numerals and Sino-Korean numerals with Chinese origin. The use of system depends on the mathematical context. For instance, native numerals are used for counting and Sino-Korean numerals are used for calculation (Sum & Kwon, 2018). In order to distinguish them in written format, Sino-Korean numerals and native numerals are represented in Arabic numbers and written English format respectively. For example, the Sino-Korean numerals il (일), i (이), sam (삼), sa (사), o (오) and yuk (육) are represeted by 1, 2, 3, 4, 5 and 6; and the native numerals hana (하 나), dul (둘), set (셋), net (넷), daseot (다섯), and yeoseot (여섯) are represented by one, two, three, four, five and six. 5. Data analysis In this lesson, Ms. Do-yeon went through some word problems on the digital display. These questions were similar in terms of structure/type and the level of difficulties. Our focus is on a microanalysis of the mathematical discourses of one particular task, which reflects Confucius’ teaching, “if after showing students one corner they do not come back to me with the other three, I will not repeat myself” (the Analects, 7:8). It also includes other

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Open classes are classroom observations cater for parents in South Korea. The class consisted of 27 students, 14 boys and 13 girls, age varied from seven to eight. 13

11

The names of the teachers and students are pseudonyms.

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distinctive elements of the Korean language, which provides readers a better idea of sociocultural background. We used revoicing as an analytical framework to examine the speech activities associated with reasoning and problem-solving in a form of language socialization. We examined the transcripts of the video recordings to identify the discourse strategies employed and to trace students’ responses over time of the particular discourse move. Classroom talk consisted of teacher’s direct instruction with choral response (CR) by the entire class/multiple students, as well as some individual and group presentations. Revoicing involves the reuttering of students’ utterances through repeating, expanding, rephrasing and reporting by the teacher (Forman et al., 1998). This serves to reformulate and coordinate students’ responses, and to create alignments and oppositions for intellectual classroom discussion (O’Connor & Michaels, 1996). The excerpts of teacher’s discourse moves were identified based on the characteristics of revoicing defined by O’connor and Michaels (1993, 1996) and Herbel-Eisenmann et al. (2009). Furthermore, the linguistic features and communication patterns in the Korean language were taken into consideration. These include students’ names and first person pronouns (e.g. ‘you’ and ‘woori’) that allow the teacher to relate a student’s utterance to the ongoing academic content/discussion, as well as, laminating verb such us ‘think/ thought (생가샜다)’ to connect the subject participant with another proposition, and to animate students as sources of a proposition. Likewise, discourse marker ‘so (그러니까/그래서)’ is often used to link an utterance to an earlier utterance, and to make an inference about what was spoken previously. Another characteristic is the content proposition that allows students to clarify the academic content of what he/she has spoken of, and the position of him/her with respect to the content. This also allows the teacher to align the student with others who previously contributed in the discussion. The sociolinguistic approach provides a framework for analysing the orchestration of classroom talk, yet the concept of forms and structures of talk does not allow us to understand students’ mathematical development. Therefore, we also adopted Toulmin’s framework, which has been used by researchers as an analytical tool for analysing argumentation structure of revoicing Forman et al. (1998). Toulmin, Rieke, & Janik, 1984, p. 14) refer argumentation as “a whole activity of making claims, challenging them, backing them up by producing reasons, criticizing those reasons, rebutting those criticisms and so on”. There are four elements in any argument: Claims, grounds, warrants and backings. Claims “contain the implications that there are underlying reasons that could show them to be well founded and therefore entitled to be generally accepted” (Toulmin, Rieke, & Janik, 1984, p. 29). They are supported by grounds, which are facts that have already been accepted. Warrants are statements which connected the claims and the grounds. Backings are required to demonstrate such warrants provided are sound and relevant. This framework allows us to focus on the propositional content of the teachers and the argumentations of the students. It helps to frame the development and progression of students’ reasoning and knowledge construction, which goes beyond the analysis of the educational function of revoicing. To provide a more comprehensive view on revoicing as an instructional strategy, Kwon and her colleagues (2008) identify the roles revoicing plays in facilitating the construction of mathematics. They include revoicing (1) as a ‘binder’ that connects/ combines diverse perspectives to generate comprehensive mathematics; (2) as a ‘springboard’ that provides scaffolding for students to clarify, elaborate, and extend their mathematical positions through reflection; (3) as a form of socialization, the cultural way of doing mathematics; and finally (4) for ownership, in which mathematics is constructed by the students themselves instead of being given by the teacher. This study looks at revoicing functions as a

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discourse strategy for conveying sociocultural knowledge into ways of reasoning and thinking.

6. Findings In this word problem, the strawberries are arranged as a form of a 3 by 8 rectangular array (Fig. 1). Students were asked to consider different strategies in finding the total number of strawberries and to write down the multiplication number sentences in their notebooks. Na-yeon used humble-form of the first person single pronoun je (제: I) in turn 3 to show respect and she is accountable for the mathematical content that followed. From the Korean’s collectivistic perspective, students normally restrict the mention of an individual to a minimum, only in the case where they need to focus on themselves or contrast themselves with another individual. This opening line in turn 3 can also be observed in later episodes whenever a single student presents to the class. The entire class then uttered the student’s full name in choral mode to give support. This shows the explicit attribution to student authorship/ownership, aiming to facilitate students’ autonomy initiated in the student-centred curriculum. Na-yeon was soft-spoken and many students could not hear her voice. Therefore, some students rebroadcasted “4 times 614” to amplify her claim. Ms. Do-yeon asked “Why is it 4 times 6?” to encourage Na-yeon and the class to think about the underlying reasons. She pressed Na-yeon to elaborate the claim, while also accepting it as a base for warrant. In turn 8, Ms. Do-yeon used basic counting concept to guide students to produce reasons, She counted the number of strawberries in one group “one, two, three, four gae 15”. Notice that she added a bound noun gae (개) next to the numeral, which is a general classifier used for inanimate objects to show the number of pieces. In English, numerals are freely used in conjuction with nouns alone to indicate the number or amount of entities being spoken of, and in this case four strawberries. But in Korean, one must say ne gae (네 개, four-piece) and gae must be used to express what is being counted. Nouns must always co-exist with an appropriate classifier for the purpose of counting. She then counted the number of groups, “one, two, three, four, five, six. Ah … so, 4 times 6”. This sequence of the number sentence is the same as the way Korean read Gugudan, the ancient Korean multiplication tables. Ms. Do-yeon made a warranted inference “geureonikka (그러니 까: So)” that linked her utterance to that of the originator, Na-yeon. As mentioned, in a collectivist classroom, the teacher is constantly dealing with the entire class, rarely as an isolated individual. Her turn structure shows not only she was accepting Na-yeon’s claim as a basis for the warranted inference, but also allowing other students to participate in the discussion, as seen in students’ choral response. In this episode, Ms. Do-yeon asked Jea-sung to provide a warrant and elaborate on the modes of reasoning in making such claim. She asked about the number of strawberries in one jul (줄: A line, represents both row and column). The array model is one of the learning objectives in the teaching of multiplication concept, in which the two numbers multiplied play equivalent roles and are not distinguishable as multiplicand and multiplier. Her prompts encouraged students to think about the backing in the form of a rectangular array. Some students produced the warrant “eight gae”

14 Read as sa kop-haki yuk. Korean students are taught and insisted upon to write the multiplicand before the multiplier in the number sentences. 15 Note that, native numerals “hana, dul, set, net gae” instead of Sino-Korean numerals “il, i, sam, sa” should be used in counting. Therefore, written English format is represented to distinguish the differences in speaking.

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Fig. 1. A 3 by 8 rectangular array.

Episode 1 1 Ms. Doyeon 2 Ms. Doyeon 3 Na-yeon 4 E 5 Na-yeon 6 Ms. Doyeon 7 Ss 8 Ms. Doyeon

9 Ss 10 Ms. Doyeon

How many strawberries are there? We can represent as a multiplication sentence. Try to think of as many ways as possible. Na-yeon, can you present? 제가 발표하겠습니다

I am going to present. Na-yeon Kim. 4 times 6 is 24. How many?

사 곱하기 육은 이십사입니다

4 times 6. Why is it 4 times 6, Na-yeon? One, two, three, four gae in one muk keum (a group). How many muk keum are there? One, two, three, four, five, six. Ah … so, 4 times 6 is … 24. 24. This is how you found out. [The teacher writes on the board 4  6 ¼ 24]

하나 둘 셋 네개가 한 묶이야 이게 몇 묶음 있어요? 하나 둘 셋 넷 다섯 여섯 아 그러니까 사 곱하기 육 은

이십사 이십사 이렇게 발견했대

Episode 2 11 Ms. Doyeon 12 Jea-sung 13 E 14 Jea-sung 15 Ms. Doyeon 16 Ss 17 Ms. Doyeon 18 Ss 19 Ms. Doyeon

Any other thoughts? [Jea-sung raises his hand.] Yes, Jea-sung. I am going to present. Jea-sung Lee. 8 times 3 is 24. Why 8 times 3? How many gae in one jul? Eight gae. Eight gae. How many jul of eight gae? Three gae//Three jul. Three jul. Three muk keum. So, that’s Jea-sung’s 8 times 3 is 24. This is what you thought. [The teacher writes on the board 8  3 ¼ 24]

in one jul to support Jea-sung’s argument. The teacher then repeated and extended by questioning the number of jul. Some students said three gae and others said three jul. Ms. Do-yeon did not tell them directly that gae was an incorrect answer. This is different from IRF/IRE triadic pattern; she has reserved the right to give direct feedback or evaluate students’ responses. As a result, students did not feel embarrassed by giving an ‘incorrect/imperfect’ answer. Their chemyon were saved by teacher repeating “three jul” and rephrasing/expanding to “three muk keum”. Her discourse move changed students’ warrants from gae to jul and muk keum, in

팔 곱하기삼은 이십사 입니다. 한 줄이 몇 개있어? 여덟개 여덟개. 여덟개가 몇줄있어? 세개//세줄 세줄 세묶음 그러니까 재성은 팔 곱하기 삼은 이십사 이렇게 생각 했대

which the mathematics position had been identified. Revoicing layered jul and muk keum into the statement, reinforcing and expanding students’ mathematical vocabulary. The discourse move in turn 19 aligned the warrant to Jea-sung’s claim, thereby indicating her own alignment with the way the argument was framed. Ms. Do-yeon provided a series of questions in such a way that allowed students to unpack their ideas, to produce reasons for their claims, and to formulate supporting arguments. Once again, she concluded with the discourse marker “geureonikka (그러니까: So)” which cast Jea-sung as the subject of

E.S.W. Sum, O.N. Kwon / Teaching and Teacher Education 88 (2020) 102964

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Episode 3 20

Ms. Do-yeon

21 22 23 24 25 26 27 28

Yea-jun E Yea-jun Ms. Do-yeon SN Ms. Do-yeon SN Ms. Do-yeon

Anyone else? Woori Yea-jun is going to present. I am going to present. Yea-jun Kim. 6 4. Why 6 4? 6 … Ah, can I speak? How do you group them? Three gae each. 6, three gae. If we have three gae in here, then there are six gae. Then, how many groups of six gae in here? One, two, three, four. So, how can we represent this in a multiplication sentence? Four groups of six gae. 6 4 24. [The teacher writes on the board 6  4 ¼ 24]

the verb of the speech/cognition as mentioned in O’Connor and Michaels (1996, pp. 79-80), indirect speech/report speech is a key part of the revoicing utterance. The use of such verbs depicts or animates the students as the originator of the intellectual content of the revoiced utterance, even though the teacher may have reformulated it. Furthermore, the type of sequences that has been observed in previous revoicing studies usually involves “one student in alignment with one point” (O’Connor & Michaels, 1993, p. 327); and what makes a good classroom discussion is “no one is talking while someone else is. Take turns” (Krusi, 2009, p. 121). These appeared to be the social norms in the Western classrooms. In contrast, choral response is a typical discursive act in Korea and seems to be determined by the code of social ethics, faithfulness between friends in samgang-oryun. In order to maintain the harmonious relationship in the classroom, a claim made by an individual student belongs to the whole class, even though the teacher may cast them as the subject for his/her claim. The transcripts here exemplify how a teacher scaffolds students’ discussion to develop reasoning and problem-solving skills within an ongoing social interaction. Mathematics is co-constructed by the students themselves instead of being given by the teacher nor an individual student. In this Confucian context, revoicing creates a sense of coownership, and this is more explicit in the following episode. Ms. Do-yeon addressed the student, by saying woori Yea-jun, which reflects the collectivist elements in the hierarchical classroom. This first person plural pronoun is grammatically incorrect in English, and also confusing for non-Korean listeners. Yet, it is often used to “reinforce the togetherness and closeness of the members of a group, drawing a clear line between us and them” (Kim & Choi, 2015, p. 157). By making use of woori, the teacher reconnected Yeajun with the rest of the class. Instead of the typical CR as seen in the previous episodes, in-group members felt obliged to assist and cooperate based on the virtues of sayu-paldeok. From this we can appreciate the collective need for mutual support and obligation in the Korean classroom. One student interrupted and asked if he could speak (turn 25), while another student provided a warrant for Yea-jun to support his claim in banmal (in turn 27, and this will be further discussed in Episode 5). Ms. Do-yeon repeated Yea-jun’s claim by asking “Why 6 416? 6 …”, and hoping for a backing of such an ambiguous argument of the two numbers. She signalled how the claim could be articulated by repeating Yea-jun’s utterance “6 …“, which indicated the number of strawberries in each group. She then questioned the student to

16

6 4 read as yuk sa, the Sino-Korean numbers mean 6 times 4 in Gugudan.

우리 예준이 발표해보자

육 사 입니다 아 내가 말하려고 했는데 어떻게 묶은거지? 세 개씩 육이 세 개. 요기 세 개하면 여섯 개 이니까. 여섯개가 네 묶음 이니까. 육사 이십사.

support the claim using the concept of equal groups to make the warrant more sound and relevant. Students start to develop the idea of using equal groups to solidify their reasoning for multiplication e six gae each. Revoicing, as a springboard, clarifies and elaborates students’ mathematical position. It also reorganizes students’ prior knowledge while putting the scripts of Gugudan to convey specific and precise mathematical meaning as a form of socialization. It bridges students’ cultural knowledge acquired outside of school to the mathematical task in the classroom. This allows students to connect number relations and meaning into the context of multiplication situations. Revoicing constructs students’ mathematical knowledge and understanding, simultaneously scaffolding the formal academic language in the discussion. Instead of direct instruction, the multiplication concept of equal groups was highlighted by the teacher through questioning and revoicing, which shapes students’ multiplicative thinking and reasoning as the lesson progressed. In this episode, So-hun’s utterance reflected his reasoning and thinking skills developed through earlier episodes. He was able to extend his claim to give a more complete warrant of his mathematical position. Revoicing highlights critical concepts and ideas under discussions so that students can adapt those concepts and ideas to formulate their own arguments. Unlike the previous episodes, So-hun took the initiative to provide a warrant in supporting his claim. He considered this multiplication situation as equal groups, each consisting of three strawberries. Even though he may not be ready to use mathematical language accurately, his multiplicative reasoning has been developed. As seen in turn 35, Ms. Do-yeon revoiced by reuttering So-hun’s warrant “Ah … 3 each” and rephrasing it to “Three gae each. How many muk keum?” She did not point out the problems of the answer, including the misuse of number word sam (삼) instead of se (세), and the absence of the numerical classifier, gae. Once again, So-hun’s chemyon was saved in front of his fellow classmates. She rephrased the Sino-Korean to native numerals and included the classifier gae. This also demonstrates the sociocultural way of speaking mathematically in the Korean language, which builds students’ everyday language while developing the formal language. The number naming system is an essential aspect of mathematics learning that students need to acquire at an early stage, and may not be taught easily through direct instruction. Ms. Do-yeon asked So-hun the number of groups and he expanded his warrant by saying “eight groups”. Notice that he was aware of his previous misuse of the number word and was able to self-correct in the next turn (36), by using the right number word yeodeol (여덟: Eight). Finally, the salient discourse maker “geuraeseo (그래서: So)” marks a warranted inference, and she repeated his utterance to give an assent. This episode indicates that students are able to formulate and produce warrants to connect grounds to their clams with

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appropriate scaffolding and language support using revoicing. As we can see from the argumentations in these episodes, students’ discourse under teacher’s guidance can become more advanced. Students were able to develop their mathematical reasoning gradually from counting procedures (in Episode 1) to a rectangular array (in Episode 2), and then equal groups (in Episodes 3 and 4). Our analysis also showed some linguistic features that are specific to the Korean language. Ms. Do-yeon started with solving a problem in context e strawberries arranged in an array format. Then through mathematical conventions and language scaffolding carefully structured by herself, students were able to mathematize the multiplicative problem, from strawberries to the focus on gae, a general classifier that can be used for other objects like, apple, oranges, balls, coins. The context became irrelevant and there was a shift in abstraction in the mental structuration of the situation. Hence, the multiplicative situation can be generalised for what is true in other cases. In this episode, Jin-hwan’s claim was a multiplication of a 2-digit number by a 1-digit number, which is beyond the learning objective in grade two. Ms. Do-yeon asked Jin-hwan for his reasoning (in turn 47) and put him in the role of defender of his claim. Some students responded by saying aniya (아니야: No), and two other students each provided a different warrant “2 times 12” (turn 48) and “Half each” (turn 49) in banmal. Once again, this shows the virtues of sayu-paldeok embedded in the classroom, where students feel a strong bonding in their fraternity and faithfulness within in-group. Although their responses in banmal were not intentionally addressed to Ms. Do-yeon, she intervened and revoiced their arguments. She provided the backing with a clearer explanation by indicating two groups of twelve on the digital display and asking for “verification or clarification” (Chapin, O’Connor, & Anderson, 2009, p. 183) if her extra information fitted the argument by saying “Half like this?” She tried to incorporate the two arguments, Jin-hwan with one position, and the other students with another position. Students attempted to explain their views that others could understand. They listen to and learn from one another. The mathematical thinking was made visible in the discussion so that any misinterpretation and misconception could be easily identified through elaboration and verification/clarification. Ms. Do-yeon used questioning and revoicing to gather information about students’ thinking and reasoning and to orchestrate the on-going mathematical discussion. There are several discourse moves that indicate the moral imperative of jangyuyuseo in the hierarchical classroom. Compared with the Korean language, English (or Chinese) has hardly any hierarchical honorific forms. Thus, it is not easy to have a direct translation. Jin-hwan used two different speech levels when answering the teacher (turn 41, sip-i kop-haki i imnida) and his

fellow classmate (turn 44, sip-i kop-haki i). The verbal sentence ending e imnida (입니다) is jondaenmal, which is “how students speak to their teachers” (Lee & Ramsey, 2000, p. 259). This formal speech form can be observed whenever a student speaks to the teacher. The addressee-related honorifics signal formality and the psychological distance between the speaker and the addressees reflects hierarchy in terms of age and/or social ranking. Students in class speak up only when invited. Yet in the episode, students were explicitly posing their contribution in contrast to the previous speaker. Teacher revoicing orchestrates different mathematical arguments without considering the addressees of these arguments. The teacher recasts upcoming student’s positions to highlight students’ trajectory and to reveal the mathematical connection behind their claims. Ms. Do-yeon’s discourse moves consolidated students’ arguments and generated a more comprehensive mathematics that highlighted the commutativity concept in multiplication, even to the extent of factor pairs of 24. Teacher revoicing connects diverse mathematical perspectives in honorifics and different speech styles/levels that function as a binder. It also serves the purpose of acknowledging and validating students’ contribution, while changing it slightly to make implied analogy more explicit.

7. Discussion The episodes in this article exemplify the effect of the curricular initiatives in the past ten years, which put an explicit emphasis on students’ mathematical processes by specifying reasoning, communication and problem-solving abilities as learning objectives beyond conceptual understanding (Hwang & Han, 2013). Pang (2012) highlights some significant changes in recent curriculum, and states that, in terms of mathematical discourse, a teacher is expected not to dominate classroom talk but to encourage students to develop and present their own ideas with open-ended questions and timely feedback. In the learning environment, a teacher is expected to employ small-group or individual activities beyond the prevalent whole-class organization and to establish a permissive learning atmosphere in which all students are actively engaged in classroom discussion (p. 138). As suggested in the mathematics curriculum, to make questioning meaningful, teachers should consider addressing students’ responses/reactions according to their cognitive development and experiences. Questions should be open-ended to allow students to solve them using a variety of methods/strategies, explaining and comparing methods/strategies wherever appropriate (Minstry of Education, Science, and Technology, 2009). In this particular mathematical task, Ms. Do-yeon purposefully employed

Episode 4 29

Ms. Do-yeon

30 31 32 33 34 35

So-hun E So-hun Ms. Do-yeon So-hun Ms. Do-yeon

36 37

So-hun Ms. Do-yeon

Any other methods? Let’s try. So-hun, can you present? I am going to present. So-hun Jang. 3 times 8. Why 3 times 8? 3 each. Ah … 3 each. Three gae each. How many muk keum? Eight muk keum. Eight muk keum. Ah, so, 3 times 8 is 24? 3 times 8 is 24. [The teacher writes on the board 3  8 ¼ 24]

삼 곱하기 팔 입니다 삼씩입니다 아 여기 삼씩 세 개씩 몇 묵음? 여덟묶음 여덟묶음 그래서 삼 곱하기 팔은 이십사 했구나?

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Episode 5 38 39 40 41 42 43 44 45 46 47 48 49 50

Ms. Do-yeon Jin-hwan E Jin-hwan Ms. Do-yeon SN (girl) Jin-hwan SN (girl) Ss Ms. Do-yeon SN SN Ms. Do-yeon

51 52 53 54 55

Ms. Do-yeon Seol-hwa E Seol-hwa Ms. Do-yeon

56 57 58

Gu-Jun. E Gu-Jun

Any other thoughts, Jin-hwan? I am going to present. Jin-hwan Jang. 12 times 2. Why 12 times 2? 2 times 12, no? 12 times 2. No. [she shakes her head.] No.//No. How do you group in 12? 2 times 12. Half each. Half like this? Half, twelve gae, twelve gae, two groups. Can we do this? Oh, yes. And then? Seol-hwa, can you present? I am going to present. Seol-hwa Jang. 2 times 12. 2 times 12 also works. Grouping two gae each. Twelve groups in total. 12 times 2. Any other thoughts? Yes Gu-Jun. I am going to present. Gu-Jun. One times twenty-four.

59

Ms. Do-yeon

This is the whole set. One times the whole. That’s one times twenty-four.

60

Ss

Ha ha ha …

questioning and revoicing strategy to develop students’ multiplicative reasoning and problem-solving skills. Through classroom talk, students learn the structure and rules of mathematical discourse that are new to them, and of course it could take some time for them to master. But this has contributed to the transformation of students’ mathematical practice, particularly in communicating mathematically that supports their socialization into the cultural organization of the mathematics community (Kwon et al., 2008). Revoicing creates an atmosphere in which students are comfortable to present and communicate their own mathematical ideas in a reasonable/logical manner, and thus, to draw conclusion. Students co-construct mathematical knowledge in a harmonise and respectful way based on Korean Neo-Confucianism philosophy of sadan-chiljeong and sayu-paldeok. Unlike the traditional discourse structure of IRF/IRE, teacher revoicing repeats and rephrases students’ utterance without giving directly response/ evaluation, which may cause embarrassment and ethnical emotional strain to students. Students are therefore not afraid to make mistakes for the fear of losing cheymon or being ashamed about failing to meet the social expectations of the teacher and their peers in the class. Confucius encourages multiple solutions to a question, where diverse perspectives are highly encouraged. Shim (2008) explains the role of teachers in similar context, Confucius directly communicates with his disciples through associated acts of evocation rather than through defined concepts. In other words, for Confucius, the role of teachers is not so much to explain or discuss what is good or right as to show it directly in their lives so that the learners can try to emulate it (p. 522). This educational philosophy is reflected in Ms. Do-yeon’s teaching practices. She assists students in knowledge construction and directs them through obstacles in the mathematical processes. She guides them in exploring a problem situation using various ways, putting the emphasis on strategies but not the

십이 곱하기 이 입니다 이곱하기 십이 아니야? 십이 곱하기 이 아니야 아니야 어 십이를 어떻게 묶어? 이곱하기 십이 반씩 아 이렇게 반씩?

이곱하기 십이입니다.

일곱하기 이십사 입니다 전체 일 곱하기 전체

solutions to the problems. Students are able to recognise the importance of mathematical processes in problem-solving and to respect different ideas and opinions. Diverse solution methods are valued in the classroom, and they are helpful for students in building the conceptual underpinnings of the academic content being taught, rather than just enhancing students’ procedural skills/ability per se. Moreover, students are able to extend their learning beyond their grade level. For example in Episode 5, they could deduce the factor of 24 by working through this mathematical task, even the term ‘factor pairs’ is never mentioned. Through whole-class discussion, significant mathematical communication happened in which students develop the “official mathematical language” (Herbel-Eisenmann, 2002) from their cultural knowledge and everyday language that empowered them to participate in the mathematical processes. As mentioned earlier, the most pronounced manifestation of Confucianism in contemporary Korea society is the emphasis on hierarchy. A study by Kim-Renaud (1988) argues that the Korean classroom environment is “hardly a friendly place for casual speech17 forms to appear” (p. 377). “A wrong term of address or disregard for honorifics toward a superior is invariably the cause of embarrassment and discomfort for the later” (Kim & Choi, 2015, p. 178). Despite the honorific-encoded utterances and the psychological distance in the classroom, revoicing orchestrates mathematical discourses of the whole class and between teacherstudent(s) and student(s)-student(s), in which ways of communication can be established for effective teaching and learning. Given this sociocultural background, we consider revoicing as an egalitarian discourse strategy in fostering classroom talk and mathematical discussion in a large-power-distance classroom. The revoicing strategy used in the Korean classroom is similar to that published in Anglophone research, involving a particular kind of reuttering of a student’s utterance by another participant (usually the teacher), and the use of linguistics concomitants such as

17 casual speech refers to those utterances that are observable in highly informal speech, regardless of the criteria of address, reference and politeness.

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indirect speech and the conjunctions. Yet, revoicing is different in Korea because 1) the teacher has to deal with the honorific system of the language, in which revoicing can be rephrased as the reuttering of a student’s utterance encoded with honorifics and different speech levels/styles; 2) in a collectivist classroom, a group-oriented worldview is evident in students’ CR, either as a group of students or the entire class. Hence, the teacher has to deal with a student as part of an in-group but not as an individual; 3) even the originator of the mathematics content is made explicit by the opening line “I am going to present”, a student who conceives of him/herself as part of a group remains chung to the group. Individual argumentation is co-owned by the group, and those who speak up do so in the name of their group under woori classroom; 4) western-style individualism is often seen as selfish behaviour in the Korean cultural context. Individual ideas are often subordinated to those of the group and people tend to feel more comfortable conforming to group ideas. Thus, mathematics knowledge is coconstructed by the group or the class. Having subgroups of three/ four students (instead of sitting in pairs) decreases students’ hesitation in speaking up and increases their participation in class. Students take increasing responsibility for making mathematical claims and provide warrant with backing. It also provides them with an encouraging and supportive learning atmosphere for intellectual exchange and constructive learning. 8. Conclusions This study exemplifies how teacher revoicing facilitates classroom talk in a rigid hierarchical atmosphere of Korean NeoConfucian classroom. This discourse strategy allows the teacher to orchestrate multiple voices of honorifics and different speech styles/levels in a classroom that is unique to Korea. Revoicing eliminates the honorific speech form tactfully for smooth flow of mathematical discussion. It provides support and opportunities in developing students’ higher-order reasoning and communication skills, by promoting classroom talk without the sociocultural framing that puts emphasis on jangyuyuseo and embodiment of ye. Hereafter, teachers can create a learning environment necessary for developing students’ mathematical processes. Our findings also illustrated a sharp contrast with typical Korean classrooms described in Learner’s Perspective Study, in which students rarely talked about mathematics beyond simple chorused responses (e.g. Clarke, Xu, & Wan, 2013a, 2013b). While labelled as ‘very traditional and old-fashioned’ in their approaches to teaching and learning, Koreans are adopting Western approaches for curriculum and instructional improvement. The linguistic inequality and hierarchical nature of Korean culture are not likely to change dramatically in the future, but teachers are taking actions to foster an egalitarian atmosphere in the classroom to support the new curriculum initiatives in the 21st century. We have shown that language is an important factor in understanding culture-specific classroom practice, and the analysis of mathematical discourse allows us to recognise the legacy of Confucian culture in a Korean elementary school. Earlier study on Confucian Heritage Culture (CHC) leaners (e.g. Biggs, 1996; Biggs & Watkins, 2001) were predominately conducted in Chinesespeaking classrooms, with limited research into the practices of classroom situated in non-Chinese speaking countries. Despite the fact that similarities particularly the set of values/concepts of Confucian pedagogy, exist, specific differences, such as instructional language, may be critically relevant to the understanding of the cultural practices among CHC classrooms. Whorf (1956) linguistic relatively hypothesis argues that the structure of a language can affect the thought process of the speakers of that language. This suggests that students in different CHC countries, whom speak

disparate valued-laded languages, have different thinking processes and worldview. Therefore, further study is needed to understand how CHC influences the teaching and learning in classrooms based on different instructional languages. We also hope this study provides international researchers with a better understanding of current mathematical practices in South Korea. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.tate.2019.102964. References Banse, H. W., Palacios, N. A., Merritt, E. G., & Rimm-Kaufman, S. E. (2017). Scaffolding English language learners’ mathematical talk in the context of calendar math. The Journal of Educational Research, 110(2), 199e208. Biggs, J. B. (1996). Western misperceptions of the Confucian-heritage learning culture. In D. Watkins, & J. B. Biggs (Eds.), The Chinese learner: Cultural, psychological and contextual influences (pp. 45e67). Hong Kong: The University of Hong Kong, Comparative Education Research Centre. Biggs, J. B., & Watkins, D. A. (2001). Teaching the Chinese learner: Psychological and pedagogical perspectives. Hong Kong: Comparative Education Research Centre. The University of Hong Kong. Brown, R., & Hirst, E. (2007). Developing an understanding of the mediating role of talk in the elementary mathematics classroom. Journal of Classroom Interaction, 41(2), 18e28. Chapin, S. H., O’Connor, M. C., & Anderson, N. C. (2009). In Classroom discussions: Using talk to help students learn, grades 1-6. Sausalito, CA: Scholastic, Inc. Cho, I. (2014). Confucianism and the art of the Joseon dynasty. In H. Woo (Ed.), Treasures from Korea (pp. 1e12). New Haven, USA: Yale University Press. Choi, S.-C., & Lee, S.-J. (2002). The two-component model of chemyon-oriented behaviours in Korea: Constructive and defensive chemyon. Journal of CrossCultural Psychology, 33(3), 332e345. Clarke, D., Keitel, C., & Shimizu, Y. (2006). Mathematics classrooms in twelve countries: The insider’s perspective. 1. Rotterdam, the Netherlands: Sense Publishers. Clarke, D., Xu, L. H., & Wan, M. E. V. (2013b). Students speaking mathematics: Practices and consequences for mathematics classroom in different countries. In B. Kaur, G. Anthony, M. Ohtani, & D. Clarke (Eds.), Student voice in mathematics classrooms around the world (pp. 33e52). Rotterdam, the Netherlands: Sense Publisher. Clarke, D., Xu, L. H., & Wan, M. E. V. (2013a). Spoken mathematics as an instructional strategy: The public discourse of mathematics classrooms in different countries. In B. Kaur, G. Anthony, M. Ohtani, & D. Clarke (Eds.), Student voice in mathematics classrooms around the world (pp. 13e32). Rotterdam, the Netherlands: Sense Publisher. De Mente, B. L. (2012). The Korean mind: Understanding contemporary Korean culture. Boston, United States: Tuttle Publishing. Deuchler, M. (2004). Neo-Confucianism in the early Joseon dynasty: Some reflections on the role of ye. In Korean National Commission for UNESCO (Ed.), Korean Philosophy: Its tradition and modern transformation (pp. 43e54). New Jersey, USA: Hollym. Eckert, C. J., Lee, K.-B., Lew, Y. I., Robinson, M., & Wagner, E. W. (1990). Korea old and new: A history. Cambridge, MA: Harvard University Press. n, V., Mukhopadhyay, S., Esmonde, I., & Secada, W. Enyedy, N., Rubel, L., Castello (2008). Revoicing in a multilingual classroom. Mathematical Thinking and Learning, 10(2), 134e162. Forman, E. A., Larreamendy-Joerns, J., Stein, M. K., & Brown, C. A. (1998). “You’re going to want to find out which and prove it”: Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527e548. Grow-Maienza, J., Hahn, D.-D., & Joo, C.-A. (2001). Mathematics instruction in Korean primary schools: Structures, processes, and a linguistics analysis of questioning. Journal of Educational Psychology, 93(2), 363e376. Herbel-Eisenmann, B. (2002). Using student contributions and multiple representations to develop mathematical language. Mathematics Teaching in the Middle School, 8, 100e105. Herbel-Eisenmann, B., Drake, C., & Cirillo, M. (2009). “Mudding the clear waters”: Teachers’ take-up of the linguistic idea of revoicing. Teaching and Teacher Education, 25, 268e277. Hofstede, G. (2010). Cultures and organizations: Software of the mind. New York: McGraw-Hill. Hufferd-Ackles, K., Fuson, K., & Sherin, M. (2004). Describing levels and components of a math talk learning community. Journal for Research in Mathematics Education, 35, 81e116.

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