Relationship between pre-service mathematics teachers’ knowledge, beliefs and instructional practices in China

In this paper we examine the relationship between teachers’ knowledge, beliefs and instructional practices based on a study with 495 Chinese pre-service mathematics teachers. The results indicate that Chinese pre-service mathematics teachers tend to hold mixed beliefs about the nature of mathematics, and a constructivist view about mathematics teaching and learning, and that they are inclined to report that their teaching is inquiry-oriented. Mathematical content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) were found not to correlate with the teachers’ self-reported instructional practice, in contrast to pre-service mathematics teachers’ beliefs, which showed a stronger association with their self-reported inquiry-oriented instructional practice. Moreover, pre-service teachers’ dynamic beliefs about the nature of mathematics, and constructivist beliefs about mathematics teaching and learning, acted as mediators between pre-service mathematics teachers’ MCK, MPCK and instructional practice respectively.

Introduction
The high mathematics achievement of Eastern, currently especially Chinese, students identified in large-scale international studies (see the most recent results of the PISA study; OECD 2019) has attracted considerable attention in researchers and policy makers all over the world for several years. Many researchers have proposed possible influencing factors for these high achievements, such as culture, language or mathematics curriculum, which may contribute to the high quality of East Asian, and currently especially Chinese students' mathematics learning outcomes (see Leung 2017 for details). Other researchers, however, compared mathematics instruction in China with that from Western countries (e.g., USA and Australia) under the assumption that mathematics instruction influences students' mathematics learning more directly (e.g., Schleppenbach et al. 2007;Xu andClarke 2013, 2019). In these cross-national comparative studies, it was identified that Chinese mathematics teachers tend to structure lessons, respond to students' errors and interact with students differently. In other words, it seems that mathematics teachers in China teach mathematics in a quite different way.
However, simply identifying what teachers do differently in the classroom is not enough for a full understanding of teachers' mathematics instructional practice (Artzt and Armour-Thomas 1999). Teachers' thoughts behind the behavior should be investigated specifically and simultaneously, in order to understand why and how teachers do what they do in the classroom. Two factors, namely teacher knowledge and beliefs, have been widely accepted as being more closely and directly related to teachers' instructional practices (Ernest 1989;Philipp 2007;Schoenfeld, 1998). Empirical findings-identified in previous studies-were not always consistent (Francis et al. 2014), especially as the relationship between teachers' beliefs and instructional practice has been described as rather complex (Lloyd 1999). The same holds for the relationship between teacher knowledge and instructional practice.
Moreover, in previous studies in the field, teacher knowledge and teacher beliefs were quite often examined either in parallel or separated, that is, the theoretical foundation of these studies emphasized solely the role of one factor and totally ignored the other (Charalambous 2015). Therefore, it is still not clear how teachers' knowledge and beliefs interact to inform teachers' instructional practice (Lui and Bonner 2016). Furthermore, most of the previous studies in the field are mainly qualitative in nature, involving case studies of a single or a few mathematics teachers (e.g., Adler et al. 2005;Charalambous 2015;Wilkins 2008;Zhang and Wong 2015). This specificity constrains the understanding of the complex relationship among these three aspects from a more general viewpoint. Therefore, it is necessary to develop more sophisticated models of the relationship among these factors (Adler et al. 2005).
In addition to these concerns, most previous studies in the field took place in Western countries such as those in Europe, or in the USA. Little quantitative empirical evidence is available to date from non-Western countries, for example from China as an influential East Asian country with a quite unique mathematics education culture. However, both teacher knowledge and teacher beliefs have been clearly argued as socially and culturally shaped mental constructs (Felbrich et al. 2012;Schoenfeld 1998). Correspondingly, mathematics teaching can be described fundamentally as a cultural activity (Stigler and Hiebert 1999).
Therefore, from a social and cultural point of view, findings identified in previous studies conducted in Western contexts may not necessarily, or at least not fully, reflect the actual relationship of Chinese mathematics teacher knowledge, beliefs and instructional practices. In view of this gap in the literature, using the theoretical framework developed in the Teacher Education and Development Study in Mathematics (TEDS-M) and the involvement of a large number of pre-service mathematics teachers at secondary school level in China, the aim of the present study is to investigate the relationship between their knowledge, beliefs and practice. Findings will thus provide empirical quantitative evidence for the understanding of how teacher knowledge and teacher beliefs interact to guide instructional practice in the social and cultural context of China.

Mathematics teachers knowledge
Teacher knowledge has been modelled as a multi-faceted construct (Ball et al., 2008;Blömeke and Delaney 2012;Shulman 1987). Various frameworks have been proposed to classify the components of teacher knowledge based on the seminal work of Shulman (1986Shulman ( , 1987; amongst others, these frameworks include the widely cited classification by the project Mathematical Knowledge for Teaching (MKT, Ball et al. 2008). In this framework, teacher knowledge is mainly described as subject matter knowledge (SMK) and pedagogical content knowledge (PCK). More recently, in the first international teacher education study conducted under the auspices of the IEA, the Teacher Education and Development Study in Mathematics (TEDS-M), teacher knowledge was the core component of professional competence of pre-service mathematics teachers at the end of their education. In the framework of TEDS-M, teacher knowledge was differentiated mainly according to mathematics content knowledge (MCK), mathematics pedagogical content knowledge (MPCK), and general pedagogical knowledge (GPK) Tatto et al. 2008). In the relevant research, these three components of teacher knowledge have been considered as important factors for effective mathematics instruction and students' mathematical learning (Baumert et al. 2010;König et al. 2014). In the present study, the framework developed in TEDS-M was adopted to describe and classify pre-service mathematics teacher knowledge in China.
Content knowledge is one of the core components of teacher knowledge in every framework mentioned above, which mainly refers to the knowledge of the subject matter and its organizing structure (Shulman 1986). Teachers' understanding of the subject matter includes the awareness of important structures of the subject and goes beyond factual knowledge (Petrou and Goulding 2011). Similarly, content knowledge in mathematics includes both the basic factual knowledge of various branches of mathematics such as algebra, geometry, number and data-included in the framework of TEDS-M-and the conceptual knowledge of structuring and organizing principles of mathematics as a discipline (Blömeke and Delaney 2012). Furthermore, as part of their content knowledge, teachers need to understand both "that something is so" and "why it is so" (Shulman 1986, p. 9). Although a deep understanding of mathematical content is needed in order to successfully accomplish their professional activities (Döhrmann et al. 2012), it needs to be taken into account that MCK differs from advanced academic mathematics knowledge offered at institutes of higher education, as well as from everyday mathematical knowledge (Kleickmann et al. 2013).
PCK refers to subject-specific knowledge for teaching, to make subject matter accessible to students (Shulman, 1986). Ever since the work of Shulman (1986Shulman ( , 1987, PCK has been regarded as an important topic in research on teaching and teacher education. Shulman (1986) identified two components that are central to PCK, namely, knowledge of instructional strategies and representations, and knowledge of students' (mis)conceptions, which was later extended. For example, in the field of mathematics education, Krauss et al. (2008) proposed within the COACTIV study that mathematics teachers' PCK should include knowledge of mathematical tasks, knowledge of students' existing conceptions and prior knowledge, and knowledge of mathematic-specific instructional strategies.
Similarly, in the TEDS-M project, the following two subdomains of PCK were differentiated: (a) curricular knowledge and knowledge of planning for mathematics teaching and learning; (b) knowledge of how to enact mathematics for teaching and learning (Tatto et al. 2008). The first subdomain mainly refers to knowledge at the pre-active stage, such as establishing appropriate learning goals, seeing connections within the curriculum, planning and selecting appropriate activities and methods, predicting typical student responses and misconceptions, and planning appropriate instructional methods. The second sub-domain refers to knowledge at the interactive stage, including knowledge of how to analyze and evaluate students' mathematical solutions and arguments, provide appropriate feedback, and analyze and diagnose students' questions (Döhrmann et al. 2012;Tatto et al. 2008).

Mathematics teachers' beliefs
Teachers' beliefs have been one of the most broadly investigated topics in the field of mathematics teacher education. However, so far, no agreed definition of beliefs has been developed (Leder 2019). One common trend is to define teacher beliefs as "psychologically held understandings, premises, or propositions about the world that are thought to be true" (Philipp 2007, p. 259). Similarly to the construct of teacher knowledge, teacher beliefs have been regarded to be a multifaceted construct (Cross, 2009;Ernest, 1989). In terms of mathematics teacher's beliefs, the critical components include beliefs about the nature of mathematics, and beliefs about mathematics teaching and learning (Ernest 1989;Speer 2005;Thompson 1992).
Teachers' beliefs about the nature of mathematics refer to teachers' "conscious or subconscious beliefs, concepts, meanings, rules, mental images, and preference concerning the discipline of mathematics" (Thompson 1992, p. 132). In the TEDS-M study, the framework proposed by Grigutsch et al. (1998) was employed to conceptualize the nature of mathematics from the following four views: formalismrelated view, scheme-related view, process-related view, and application-related view. Fundamentally, the first two views, namely, the formalism-related view and schemerelated view, mainly describe mathematics as being static, consisting of accurate results and infallible procedures, or as a procedure-driven body of facts and formulas Thompson 1992). In contrast, the latter two views, namely the process-related view and applicationrelated view, conceptualize mathematics as a dynamic and continually expanding domain of knowledge based on sensemaking and pattern-seeking (Felbrich et al. 2012;Thompson 1992).
Teachers' beliefs about mathematics teaching and learning refer to teachers' views on their preferred ways of teaching mathematics, and views on how it is learned, for example, their conceptions of ideal classroom teaching activities, what behaviors and mental activities are involved in mathematics learning, and what constitutes appropriate and prototypical mathematics learning activities (Chan and Elliott 2004;Ernest 1989;Thompson 1992). In the TEDS-M framework, teachers' beliefs about mathematics teaching and learning were mainly differentiated between two views on mathematics teaching and learning: (1) a knowledge transmission (or "traditional") view, in which mathematics teaching is seen as a process of knowledge transmission and students receive knowledge from teachers passively, and (2) a constructivist view, in which mathematics teaching is seen as facilitating students' knowledge construction Tatto et al. 2008).

Instructional practice
Instructional practice refers to what happens in a teacher's classroom (Depaepe and König 2018). In literature, various ways have been used by researchers to classify instructional practice, such as teacher-centered (or traditional instruction) and student-centered (or constructivist instruction) (Hogan et al. 2013). In mathematics education, after the implementation of mathematics curriculum reform globally at around the year 2000, student-centered instruction or inquiry-based instruction has been widely advocated in many countries (Cai and Howson 2013). In such an approach to mathematics instruction, students are supposed to engage actively in meaningful and real life related mathematical problems or activities so that they can make conjectures and investigations, collect and analyze data, and communicate and collaborate with their peers. In this approach, the teacher works mainly as a facilitator guiding students' activities (Wilkins 2008).
Mathematics instruction has also been accepted as a multidimensional construct (Kelcey et al. 2019). While investigating teachers' instructional practice, cognitive activation and providing student learning support have been specifically emphasized by researchers (e.g., Baumert et al. 2010;Depaepe and König 2018). In mathematics instruction, the aspect of cognitive activation refers to how cognitively challenging teachers' instructional strategies and selected tasks are for students . Student support refers to the teacher's well-judged support for students' learning process, when they meet difficulties during working on the cognitively challenging tasks (Depaepe and König 2018;Kunter et al. 2013).
Many methods have been used in previous studies in order to study teachers' instructional practices, such as classroom observation conducted by external observers (mainly via video-recording), and student ratings and selfreported survey by teachers (mainly via questionnaire survey) (Depaepe and König 2018). However, either method has its own advantages and disadvantages. The self-reported way has been widely employed by researchers. With a main aim of involving a relatively large group of participants. Teachers are aware of strengths and weaknesses of their instructional practices, which should be reflected in their ratings of questionnaire items. They are able to relate the content of such items to a relatively long period of teaching time, whereas external observation usually accounts for a thin slice of teacher-student interaction in the classroom, which may limit generalization of observational data. Whereas student ratings of instructional practice are valid regarding classroom interaction visible to students, such as the prevalence of disruptive student behavior, teacher ratings are valid also concerning the evaluation of instructional concepts that are behind the visible teaching processes in the classroom (Wagner et al. 2013). However, since teacher ratings may be "biased by self-serving strategies or teaching ideals" (Kunter and Baumert, 2006, p. 231), empirical results should be interpreted with caution.

The relationship among teacher knowledge, beliefs and instructional practice
During the past decades, researchers explored already how teacher knowledge and teacher beliefs influence their teaching practice, especially in mathematics education. First, in terms of the relationship between MCK and teaching practice, it has been theoretically argued that teachers' MCK has a direct relationship with their instructional practices (e.g., Ernest 1989). Similarly, in the review conducted by Fennema and Franke (1992), they concluded that "when a teacher has a conceptual understanding of mathematics, it influences classroom instruction in a positive way'' (p. 151). However, the empirical findings are less clear. For example, Hill et al. (2008) reported that teachers with stronger Mathematics Knowledge for Teaching (MKT) (including common and specialized mathematics content knowledge) made fewer mathematical errors, responded more appropriately to students, and chose examples that helped students construct meaning. In contrast, Shechtman et al. (2010) found that teachers' MKT did not correlate with the three areas of instructional decision-making investigated in their study: decisions about topic coverage, choice of teaching goals, and use of technology. Such inconsistent findings suggest on the one hand that teachers' subject matter knowledge alone does not ensure effective teaching performance (Kahan et al. 2003). On the other hand, it may imply the existence of other types of knowledge, such as pedagogical content knowledge (PCK), which might be more closely related to teachers' instructional practices. Indeed, in empirical studies PCK has been recognized as a knowledge facet needed by teachers to provide high quality instruction. For example, Baumert et al. (2010) found that, compared with teachers' MCK, teachers' MPCK was more powerful in predicting instructional quality as conceptualized by the cognitive demand of tasks used during teaching. Similarly, Speer and Wagner (2009) found that due to the lack of MPCK, even teachers having extensive teaching experience and possessing strong content knowledge still faced challenges when trying to provide analytic scaffolding to move whole-class discussions toward a lesson's mathematical goals.
Besides the fact that teachers' knowledge shapes teachers' practices, teacher beliefs, including beliefs about the nature of mathematics and its learning and teaching, have long been argued as another critical factor, which may influence teachers' instructional practice. For some researchers, compared to teacher knowledge, teacher beliefs are an even stronger influential factor. For example, as Ernest (1989) pointed out, it is possible for two teachers with similar knowledge to teach mathematics in quite different ways due to their different beliefs about the nature of mathematics and its teaching and learning.
Due to the critical role played by teacher belief in teachers' practices, many studies have investigated the relationship between the two aspects. However, the relationship between teacher beliefs and instructional practices was found to be a "subject of controversy and is acknowledged to be both subtle and complex" (Beswick 2007, p. 96). In some studies, teacher beliefs were found to be consistent with teachers' teaching practices (e.g. Wilkins 2008) and in other studies, inconsistencies between teacher beliefs and teachers' practices were reported (e.g. Raymond 1997).
However, it has been generally accepted that for the implementation of a reformed mathematics curriculum, teachers need to be equipped with corresponding beliefs about mathematics and its teaching and learning (Lloyd 1999). If mathematics teachers' beliefs are not congruent with beliefs underpinning the reformed mathematics curriculum, then it will affect the degree of the implementation of the innovation ideas (Handal and Herrington 2003). Based on the global move towards group discussion, collaboration and inquiry ways of mathematics teaching (Paine et al. 2016), teachers' dynamic beliefs about the nature of mathematics and constructivist beliefs about mathematics teaching and learning seems to be more closely related to reform based styles of mathematics teaching.
In addition, researchers also argued that teacher knowledge and teacher beliefs interact to shape teachers' decisions and actions in classrooms (Charalambous 2015). How exactly this interaction works, however, has not been examined broadly. A few qualitative studies explored how teacher knowledge and teacher beliefs jointly influence instructional practice. For example, Zhang and Wong (2015) found that in-service mathematics teachers in China with similar professional knowledge interpreted students' mathematics learning differently due to differences in their beliefs about mathematics. Bray (2011) investigated how four American third-grade teachers' beliefs and knowledge influenced their error-handling capacity. The study found that teachers' ways of handling student errors during class discussion of mathematics were clearly linked to both teacher beliefs and teacher knowledge, with some aspects of teacher response being more strongly linked to knowledge and others being influenced more by beliefs. More recently, Charalambous (2015) also investigated how three American pre-service mathematics teachers' knowledge and beliefs interacted to influence their practices. His study found that teachers, who possessed only strong knowledge, could not ensure the creation of mathematically rich environments, and teachers with beliefs that are inconsistent with reform-based curriculum could impede teachers from performing in ways that their knowledge could otherwise have supported.
Such findings from previous qualitative studies may suggest that teacher beliefs will not only directly influence teachers' teaching practices but that they may also mediate the relationship between teacher knowledge and instructional practice (Charalambous 2015;Wilkins 2008). A few quantitative studies indeed verified the mediating role played by teacher beliefs. For example, Wilkins (2008) investigated the relationship between 481 in-service elementary teachers' MCK, their beliefs about the effectiveness of inquirybased instruction and their use of inquiry-based instruction. The study found that beliefs partially mediated the effects of content knowledge and instructional practice. Similarly, Campbell et al. (2014) investigated 266 upper-grade elementary teachers' MCK and MCPK, perceptions and students' achievement and found that teachers' beliefs regarding mathematical solutions and instruction to support incremental mastery of skills interacted with content and pedagogical content knowledge.

A brief description of mathematics education context in Mainland China
Due to the cultural, historical and political differences, the history of the development of mathematics education at both primary and secondary school level in Mainland China is quite different from the history of mathematics education in most Western countries. Therefore, the modern mathematics movement did not exert any influence on the development of mathematics education in Mainland China. Basic mathematics skills and traditional mathematics topics such as Euclidean geometry have kept their relevance until now (Zhang et al. 2016). Right after the establishment of The People's Republic of China in 1949, mathematics textbooks used in Mainland China were adopted directly from the former Soviet Union. Mathematics education in the former Soviet Union emphasized the rules and regulations of basic knowledge and the rigor of proof, including the training of logical reasoning (Zhang et al. 2004). Such features were not only reflected in the textbooks published in 1952 and in the subsequent revised textbooks, but also significantly influenced the ways mathematics teaching and learning were conducted in Mainland China (Xu 2013). Against this background, even though the mathematics curriculum at primary and secondary school level in Mainland China later experienced several periods of change, a unique feature of Chinese mathematics education practice was gradually shaped, that is, 'two basics', namely, basic mathematics concepts and basic mathematics skills (Ni et al. 2014;Zhang et al. 2004). A main characteristic of this culture is the emphasis on the acquisition of foundational mathematics knowledge (e.g., mathematical definitions and principles), and problem solving skills other than the development of students' creative thinking (Leung 2001(Leung , 2017. Mathematics teaching is "predominantly content orientated and exam driven. Instruction is very much teacher dominated and student involvement minimal" (Leung 2001, p. 35). In addition, students have few opportunities for group work or activities but do routine exercises individually and repeatedly in order to solve problems quickly later (Leung 2001;Ni et al. 2014).
The emphasis on accurate and abstract mathematics in mathematics classrooms and the development of students' problem solving skills under the 'two basics' mathematics education culture on the one hand equipped Chinese students with a solid foundation in mathematics, which helped them perform quite well in international comparative studies. On the other hand, limitations of this culture, such as neglecting the processes of constructing and advancing mathematics knowledge, the connections between different forms of knowledge, and especially the connections between mathematics and students' real lives and its application in these contexts, and students' active role in the learning of mathematics, have been recognized and criticized (Ni et al. 2014). Due to limitations of this sort, in 2001, the Chinese government started a new round of mathematics curriculum reform. Constructivism was "borrowed" from the West "as a dominant theory" (Tan 2017, p. 241), which underpins this round of mathematics curriculum reform.
Therefore, under the influence of constructivism, fundamental changes were made to the selection and inclusion of mathematics content, mathematics teaching and learning methods and assessment systems (Ni et al. 2014). Significant changes were also made to the description of mathematics itself in the reformed mathematics curriculum standards and its revised version. Instead of the excessive emphasis on the abstract and rigorous nature of mathematics, mathematics was further described as a tool, a foundation for science and technology, which is able to be applied in all the aspects of social production and daily life, and a kind of human culture as well (Ministry of Education 2001, 2011. In terms of mathematics teaching and learning methods, fundamentally, teachers were strongly encouraged to use inquiry-based mathematics instruction, which can facilitate the processes of knowledge construction and the application of knowledge. In addition, students were encouraged to use various ways of learning mathematics such as self-exploration and cooperation with their peers, rather than receiving information entirely from their teachers (Ministry of Education 2001, 2011. In other words, a significant change in mathematics instruction is encouragement for the traditional teachercentered approach to be replaced by a student-centered approach (Tan 2017).

Research questions and hypotheses
This study investigates the relationship between Chinese pre-service teachers' knowledge, beliefs and self-reported instructional practices, namely: MCK, MPCK, beliefs about the nature of mathematics, beliefs about mathematics teaching and learning, and instructional practices. We hypothesize the following: -a direct effect of MCK and MPCK on instructional practice; -a direct effect of beliefs about the nature of mathematics and beliefs about mathematics teaching and learning on teachers' instructional practice; -a mediation role played by beliefs between MCK, MPCK and instructional practice.

Participants of the study
A convenience sample of 495 pre-service mathematics teachers (369 females) participated in the study. 134 of them completed their teaching practicum in junior secondary schools and the other 359 completed their teaching practicum in senior secondary schools. Overall, all had some kind of teaching experience and all of them were trained to teach secondary school mathematics after their graduation. In China, pre-service teachers are trained in specific teacher training institutions (Normal universities or colleges) with a heavy focus on subject matter. Those 495 pre-service mathematics teachers were all in their fourth year of study and therefore close to completing their degree. They were from four Normal universities at different levels located in the western, central and coastal part of China. Currently, in China teacher education universities generally provide 4-year bachelor's programs for pre-service teachers. Because of the influence of the national centralized curriculum system for pre-service teacher training, the curriculum in different institutions is quite similar all over China. The curriculum during pre-service mathematics teacher education includes general courses (e.g., English, general pedagogy and general psychology), mathematics subject related courses, mathematics education related courses and fieldwork or internships in schools for a semester. Around 60% of the total pre-service teacher curriculum hours are devoted to mathematics subject courses such as advanced algebra, analytical geometry, function analysis, abstract algebra, and topology (Paine et al. 2003;Li et al. 2008).

MCK and MPCK paper-pencil test
The Chinese version of the instruments developed in TEDS-M to test pre-service mathematics teachers' MCK and MPCK used in Taiwan were directly used with slight modifications in the present study (mainly referring to the traditional writing used in Taiwan). In TEDS-M, the MCK and MPCK instruments were designed in a paper-and-pencil test style. Participants were given 60 min to complete the tests for MCK and MPCK. The lower-secondary assessment consisted of three booklets with 103 items in total: there were 76 MCK related items and 27 MPCK related items. The 103 items were distributed in the three booklets following a balanced-incomplete-block design with the aim of capturing the desired breadth and depth of teacher knowledge.
The 76 MCK related items covered number, algebra and geometry as the main content areas of school mathematics, and, with a few items, the area of data. The 27 MPCK items covered the following two aspects: (1) curricular and planning knowledge; and (2) knowledge about how to teach mathematics. These two sets of items were given approximately equal weight. The majority of items in the MCK and MPCK instruments were complex multiplechoice items with a few open response items. The MCK and MPCK instruments were already validated in a Chinese context as they had been used in Taiwan and Singapore (in English) within the TEDS-M study, and the context of the present study was similar to this investigation. Furthermore, the released MCK and MPCK items were already validated with in-service mathematics teachers in Chongqing, a city in Mainland China (Yang et al. 2018).

Mathematics-related beliefs questionnaire
The original Chinese versions of the questionnaires designed in TEDS-M to investigate pre-service mathematics teachers' beliefs about the nature of mathematics and beliefs about learning mathematics were used in the present study. The part concerning beliefs about the nature of mathematics included 12 items in total, which were distributed into two dimensions, namely, mathematics as a process of inquiry (6 items, with items like the following sample item: "In mathematics many things can be discovered and tried out by oneself") and mathematics as a set of rules and procedures (6 items, with items like the following sample item: "Fundamental to mathematics is its logical rigor and precision"). These two dimensions represent two different major perspectives on the nature of mathematics, namely, dynamic and static perspectives.
Questions concerning beliefs about the learning of mathematics also covered two dimensions: learning mathematics through following teacher direction (labeled as the traditional view, with 6 items like the following sample item: "Pupils need to be taught exact procedures for solving mathematical problems"), and learning mathematics through active involvement (labeled as constructivist beliefs, with 6 items like the following sample item: "In addition to getting the right answer, it is important to understand why the answer is correct"). Pre-service teachers rated the beliefs statements on a five-point Likert scale (1 = "strongly disagree" and 5 = "strongly agree").
To validate the two questionnaires for the purpose of the present study, the sample of pre-service mathematics teachers was randomly distributed into two groups for exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). For the beliefs about the nature of mathematics, two factors were identified in the EFA that accounted for 44.98% of the variance. One item from the scale reflecting a static view and one item from the dynamic scale with a crossfactor loading were deleted. A following CFA demonstrated a satisfactory model fit of the resulting two-factor model including 9 items (X 2 = 57.75, X 2 /df = 3.03, GFI = .933, TLI = .901, RMSEA = .064).
Concerning the beliefs about mathematics learning and teaching, two factors were also identified during EFA that accounted for 40.52% of total variance. During EFA, factor loadings of two items from the traditional beliefs scale were below 0.40 and these were deleted along with one item from the constructivist beliefs scale with cross-loading. The CFA showed that the two-factor model with 9 items had a good fit (X 2 = 65.36, X 2 /df = 2.51, GFI = .941, TLI = .918, RMSEA = .055).

Instructional practice
The questionnaire designed in a study by Depaepe and König (2018) was adapted and validated to assess preservice mathematics teachers' self-reported instructional practices. The original items were designed to investigate general instructional practices. Therefore, all items of the two dimensions, cognitive activation and providing learning support to students, were especially modified according to the mathematics teaching context concerning the mathematics education reality in China and inquiry-oriented mathematics teaching as emphasized in the recent mathematics curriculum standard in China. Sub-dimensions included in the scale were as follows: (1) for cognitive activation, which includes two sub-dimensions: ① the use of cognitively demanding tasks (4 items). One item, "I gave students mathematical challenging tasks" was added to the sub-dimension, which originally had three items. In addition, the original item "I asked the students questions that they had really to think about" was modified as "I asked students mathematics questions they had to really think about"; and ② stimulating students' cognitive independence (5 items). Two items, like "In mathematics teaching, I encouraged students to find solutions from different perspectives" were added to the original three items in this sub-dimension; (2) student support, which includes two sub-dimensions: ① encouraging students (4 items); all the four original items, such as "I supported students additionally when they needed help", were directly used since all of them met the mathematics education situation in China; and ② dealing with student heterogeneity (4 items); mathematics education related information was added to the original four items in the sub-dimension. Items were rated on a four-point Likert scale (1 = "strongly disagree" and 4 = "strongly agree").
The content of the 17 items was validated by two experienced secondary school mathematics teachers and modifications were made according to their comments. In addition, EFA and CFA were performed for construct validation of the modified questionnaire. During EFA, the four sub-dimensions were identified that accounted for 59.93% of the total variance. The sub-dimension, encouraging students and dealing with student heterogeneity, had one cross-factor loading item and this item was deleted. The CFA confirmed that the two-factor model with the 16 remaining items had a good fit with the latent constructs (X 2 = 309.57, X 2 /df = 2.69, GFI = .938, TLI = .927, RMSEA = .058).
For data collection, participants from each of the four universities were distributed into two lecture rooms and completed the knowledge test and beliefs survey individually at the same time. All the participants were given 60 min for the knowledge test and 20 min for the beliefs survey and the questionnaire on self-reported instruction, with a 10-min break between them.

Data analysis
Besides the validation analysis for the instruments as mentioned above, the data analysis was comprised of the following steps. First, the open response items were coded following the TEDS-M coding rubrics. For each of the booklets, 20% of the open response items were coded by two independent trained raters. Cohen's Kappa indicated high agreement (k > 0.89 and K average = 0.92). With respect to the multiple-choice and complex multiple-choice items, items with no response or an incorrect response were coded as 0, and each correct answer was coded as 1. After the completion of coding, item response theory (IRT) scaling methods were used to estimate scale scores for MCK and MPCK. One-dimensional Rasch model (1 parameter model) was used to analyze test data, and the internal consistency of the overall MCK and MPCK was examined using Expected a Posteriori estimation (EAP). Reliability coefficients of MCK and MPCK were 0.82 and 0.79 respectively. The second step of the data analysis was descriptive analysis. Means and standard deviations for all scales were computed.
The third step of data analysis was to examine the relationship between teacher knowledge, beliefs and instructional practice. Manifest correlations were estimated between pre-service mathematics teachers' MCK, MPCK, their mathematics-related beliefs and their self-reported instructional practices. Subsequently, path analysis was conducted to examine the interactive function of knowledge and belief to instructional practice. Mplus was used for the path analyses.

Descriptive results
As shown in Table 1, in terms of the beliefs about the nature of mathematics, relatively speaking, the item mean score of dynamic beliefs is greater than the item mean score of static beliefs, which illustrates that pre-service mathematics teachers' dynamic beliefs about mathematics are stronger than their static beliefs. However, the mean score of the static beliefs is also greater than 3, which indicates that the participants in this study tend to hold mixed beliefs about the nature of mathematics.
Regarding the beliefs about mathematics teaching and learning, the item mean score of traditional teaching is quite close to 2 and the item mean score of constructivist teaching is greater than 4. Such results suggest that our sample of Chinese pre-service mathematics teachers reject traditional beliefs about mathematics teaching and learning; instead they hold constructivist beliefs about mathematics teaching and learning.
With respect to pre-service mathematics teachers' selfreported instructional practice, mean scores of three of the aspects, namely the use of cognitively demanding tasks, stimulating students' cognitive independence, and encouraging students, are quite close to 3.5 (maximum is 4), and the mean score of the final aspect is 3.30, which suggest that the participants evaluated their teaching as inquiry-oriented.

Correlational analysis results
In terms of the correlation between two tested knowledge variables (MCK and MPCK) and beliefs and self-reported practices, as shown in Table 2, both MCK and MPCK were found to be positively and significantly correlated with pre-service teachers' dynamic beliefs about the nature of mathematics and constructivist beliefs about mathematics teaching and learning. Weak negative associations were observed between the two knowledge variables, MCK and MPCK, and traditional teaching and learning beliefs, while no systematic relation existed comparing these to static beliefs about the nature of mathematics. However, except for one weak positive association between MPCK and one subaspect of self-reported instructional practice, the use of cognitively demanding tasks, all the associations between the two knowledge variables and other sub-aspects of instructional practice were found to be positive but insignificant.
As to the correlation between beliefs about the nature of mathematics and the other constructs, moderate and positive significant associations were identified between static beliefs about the nature of mathematics and traditional beliefs about mathematics teaching and learning, as well as between dynamic beliefs about the nature of mathematics and constructivist beliefs about mathematics teaching and learning. No associations were identified between static beliefs about the nature of mathematics and the four sub-aspects of selfreported instructional practice. However, relatively stronger significant and positive associations were identified between dynamic beliefs about the nature of mathematics and the four sub-aspects of instructional practice.
Similar patterns were also identified between pre-service mathematics teachers' beliefs about mathematics teaching and learning and self-reported instructional practices. As shown in Table 2, negative but only weak associations (r is between − 0.07 and − 0.02) were observed between traditional beliefs about mathematics teaching and learning and the four sub-aspects of self-reported instructional practice. However, relatively stronger positively significant associations (r is between 0.25 and 0.33) were observed between constructivist beliefs about mathematics teaching and learning and the four sub-dimensions of instructional practice.

Path analysis results
Basing on the results of association analysis, a path analysis was performed to examine the relationship between pre-service mathematics teachers' MCK, MPCK, dynamic beliefs about mathematics, constructivist beliefs about mathematics teaching and learning, and instructional practice. The final path model fits the data well, X 2 = 339.11, X 2 /df = 2.35, GFI = .928, TLI = .925, CFI = .936, RMSEA = .052. The path coefficients for the final model are presented in Fig. 1.
Firstly, as shown in Fig. 1, both dynamic beliefs about the nature of mathematics and constructivist beliefs about mathematics teaching and learning positively and significantly predicted pre-service mathematics teachers' self-reported instructional practices (β = 0.31 and 0.22 respectively). Secondly, it was found that MPCK was positively associated with pre-service mathematics teachers' dynamic beliefs about the nature of mathematics (β = 0.10) and constructivist

Discussion
Based on the adaptation of the instruments developed in the TEDS-M study and related studies, in the present study we investigated 495 pre-service mathematics teachers' knowledge, mathematics beliefs, self-reported instructional practice and the relationship between the three variables.
As reported above, in terms of pre-service teachers' beliefs about the nature of mathematics, the surveyed teachers were found to agree on both the static and dynamic aspect of mathematics. This result suggests that the pre-service teachers tend to hold mixed beliefs about the nature of mathematics as was reported in previous studies for pre-service teachers at the end of teacher education (e.g., Felbrich et al. 2012;Tang and Hsieh 2014). For teachers' beliefs about mathematics teaching and learning, the study reports a strong tendency to hold a constructivist rather than a traditional view. Overall, it seems that pre-service mathematics teachers' dynamic beliefs about the nature of mathematics and constructivist beliefs about mathematics teaching and learning display a certain degree of psychological strength, and therefore, these two aspects may be considered as "core beliefs" (Cross 2009, p. 327). Moreover, the surveyed Chinese pre-service mathematics teachers were found to tend to believe that their teaching is inquiry-oriented. Chinese pre-service mathematics teachers' constructivist views of mathematics teaching and learning and selfreported inquiry-oriented instructional practices, together with their views of the nature of mathematics, are all not consistent with findings identified in previous studies related to Chinese teachers. It was found in previous comparative studies that teachers from Eastern countries and regions (e.g., Mainland China and Hong Kong) tend to hold a more rigid view of mathematics, or they mainly focus on the internal and logical structure of mathematics (Bryan et al. 2007;Leung 1995). For their pedagogical beliefs, in-service mathematics teachers from Mainland China and Hong Kong were also found to place more emphasis on abstract reasoning and verbal engagement over physical engagement, and with fewer in-class group activities (Bryan et al., 2007;Cai and Wang 2010).
Such inconsistencies may imply, first, that pre-service mathematics teachers are already equipped with ideas emphasized in the reformed mathematics curriculum in China as described above. Since the latest national reformed mathematics curriculum was started in 2000, a dynamic view of mathematics and a learner-centered view about mathematics learning and teaching have been promulgated in China since then. Therefore, pre-service mathematics teachers have not only experienced the reformed mathematics curriculum when they were students in schools. In addition, these reformed views have been integrated into preservice teacher training curricula and emphasized during the pre-service training period (Ni et al. 2014). Therefore, such schooling and pre-service training experience apparently allowed them to gradually accept the reformed ideas in terms of the nature of mathematics and the ways mathematics teaching and learning should take place.
In addition, the correlation analysis and path analysis results reported above first suggest that both of the two knowledge variables, MCK and MPCK, did not significantly correlate with pre-service mathematics teachers' selfreported instructional practices. The insignificant association between MCK and instructional practice is consistent with findings identified in previous studies (e.g., Baumert et al. 2010). For example, Wilkins (2008) found that the increase of teachers' content knowledge did not predict teachers' increased use of inquiry-based instructional practice, in contrast, content knowledge was found to have a negative effect on teachers' use of inquiry-based instructional practice. Similar findings were also reported in studies by Hill et al. (2008) and Shechtman et al. (2010).
However, it is quite interesting that pre-service mathematics teachers' MPCK did not significantly correlate with their self-reported inquiry-oriented instructional practices, as MPCK has been widely accepted in literature as the predominant knowledge that is needed for teachers' effective teaching practice. As mentioned above, in empirical studies conducted in Western contexts, for example, in Germany, MPCK was found to be even more powerful in predicting teachers' instructional quality. However, considering the policy and practice of initial teacher education in China and especially curricular requirements for pre-service mathematics teachers, it may not be that difficult to understand the insignificant association. In China, during the pre-service training period, more than 60% of the courses are subjectrelated theoretical courses, and only a limited number of courses are related to pedagogy, including mathematics education methods, and teaching skills practice (Paine et al. 2003). Such a tradition may provide pre-service mathematics teachers with quite limited opportunities to improve their MPCK and relate it to practical situations of instructional quality. Therefore, during their teaching practicum period, with the help of their mentors and their own observations in schools, most of them may acquire inquiry-based teaching skills, but this acquisition will not necessarily guarantee a significant association between MPCK and their selfreported instructional practices.
A second clear pattern, which could be identified from correlation analysis and path analysis is that pre-service mathematics teachers' dynamic beliefs about the nature of mathematics and constructivist beliefs about mathematics teaching and learning are relatively strongly and significantly associated with their self-reported instructional practices. Such findings are consistent with theoretical assumptions related to the effective implementation of the inquiry-based mathematics curriculum. It has been widely accepted for decades in the literature that "the quality of teaching and learning will improve if teachers hold beliefs that are supportive of constructivist-based, student-centered practices" (Francis et al. 2014, p. 340). Similar empirical findings indeed have been identified in previous studies (e.g., Handal and Herrington 2003;Lloyd 1999). Such findings further imply that pre-service mathematics related beliefs about dynamic aspects of mathematics and constructivist aspects of mathematics teaching and learning indeed are aligned with their teaching practices.
Moreover, relatively speaking, pre-service mathematics teachers' dynamic beliefs about mathematics and constructivist pedagogical beliefs showed a stronger association with, or have stronger power in, predicting their selfreported inquiry-oriented instructional practices than their knowledge. This finding is also consistent with results from previous studies in terms of the relationship between teacher knowledge and their practices and the relationship between teacher beliefs and their practices (e.g., Cooney 2001;Ernest 1989). Similarly, Wilkins (2008) also found that teachers' beliefs had the strongest overall effect on teachers' use of inquiry-based instructional practices. However, this finding is not consistent with findings identified in more recent studies. For example, Lui and Bonner (2016) identified a significant positive relationship between teachers' conceptual mathematics knowledge and instructional plans, but no relationship between teachers' constructivist beliefs about mathematics teaching and learning. Such mixed consistency or inconsistency suggest that more studies are needed in this field for a fuller understanding of the complex relationships among these three aspects.
Furthermore, the present study indicated that pre-service teachers' dynamic beliefs about the nature of mathematics and constructivist beliefs about mathematics teaching and learning acted as mediators between pre-service mathematics teachers' MCK, MPCK and instructional practice respectively. Such findings on the one hand support the results of previous studies, and the results of the present study are also in agreement that teachers' knowledge will indirectly influence teachers' instructional practices through the mediation of teachers' beliefs (Ernest 1989;Wilkins 2008). Beliefs may be regarded as a 'filter' through which pre-service teachers evaluate their teaching behavior in the classroom (Ernest 1989;Philipp 2007), which in turn influences their self-reported instructional practices. That means that teacher knowledge and teacher beliefs will to a certain degree interact together to shape teachers' teaching practices (Charalambous, 2015). However, on the other hand, these findings suggest that only certain types of beliefs, or core beliefs with certain psychological strength, may play the mediator role, especially the beliefs that tend to be aligned with teachers' instructional practices. Of course, as pointed out in previous studies (e.g., Charalambous 2015; Wilkins 2008), more studies, especially quantitative studies, are needed before a concrete conclusion can be developed.

Conclusion and implication
As reported above, findings of our study show that both of the two knowledge variables, MCK and MPCK, did not correlate with teachers' self-reported instructional practices. Pre-service mathematics teachers' beliefs showed a stronger association with their self-reported inquiry-orientated instructional practices. However, only pre-service teachers' core beliefs, namely dynamic beliefs about the nature of mathematics and constructivist beliefs about mathematics teaching and learning, were found to act as main mediator between pre-service mathematics teachers' MCK, MPCK and instructional practice respectively.
Overall, the study also has several limitations, which should also be discussed. Firstly, concerning the data collection methods, one large limitation is the usage of a selfreport questionnaire survey to collect data on pre-service teachers' instructional practices. Therefore, it might be possible that in reality, these teachers taught in a different way. In addition, a paper-and-pencil test was used to assess preservice mathematics teachers' MCK and MPCK, however, teacher beliefs and instructional practice were measured through self-reports. The differences in data collections methods may also have led to the relatively strong association between teacher beliefs and instructional practice, and the insignificant association between teacher knowledge and instructional practice. Therefore, as suggested in previous similar studies (e.g., Depaepe and König 2018), future studies should consider combining other data sampling methods with the questionnaire survey, for example, classroom observation or video recording methods, to analyze teachers' instructional practice, in order to avoid measurement errors.
Secondly, the study tested and required the pre-service teachers to answer the questionnaires only once. It might be possible that after the pre-service mathematics teachers actually worked in schools, especially after a couple of years, not only their knowledge, their beliefs and even the ways they used to teach mathematics would be changed significantly. Therefore, a longitudinal design of a study might be helpful not only to fully understand the relationships between the three variables, but also the change of relationships of the three variables when teachers are in different professional development stages.
Based on the involvement of a relatively large number of pre-service mathematics teachers in China, the central goal of the present study was to explore the relationship between teacher knowledge, teacher beliefs, and their self-reported inquiry-oriented instructional practices. So far, this study is one of the very few quantitative studies in the field of mathematics teacher education to explore the interactive effect of teacher knowledge and teacher beliefs on teachers' instructional practice in a non-Western context. Therefore, the findings identified in the present study can provide empirical evidence for the understanding of the relation between the three factors.


Introduction to Nature of Minangkabau Culture With the Philosophy of Learning from the Nature Through Scientific Approach

Beside language as part of culture, children needs to know the culture and philosophy of the society. The Minangkabau people call their homeland the name of the nature of Minangkabau, with the philosophy, “learn from the nature” (Alam takambang jadi guru). The nature, is interpreted as a source of knowledge and even takes knowledge, skills and attitudes and normative behaviors that guides the people's lives. Making nature as a source of knowledge is in line with scientific approaches. The purpose of this study is to describe the introduction of the Minangkabau culture with the philosophical learn from the nature to become a professional teacher in early childhood learning through a scientific approach. The method used in this research was the R & D method. The research sample were the kindergarten in Bukittinggi Municipality. The instrument in collecting data were learning programs including semester programs, RPPM and RPPH, which were integrated to the introduction of the culture of the Minangkabau with the philosophy. Observation was done during the teacher carrying out learning approach. The results showed that from the 3 selected themes, the results of the introduction of the Minangkabau natural culture with the philosophical learn from the nature so the teacher could be introduced by applying a scientific approach.

INTRODUCTION
Besides learning language as part of culture, young learner needs to know the culture of the society. In West Sumatra with its Minangkabau culture, the children are provided with the introduction of the Minangkabau natural culture in early childhood learning is in line with the 2013 PAUD curriculum which aims to provide a broad learning experience for children to have the foundation to master the competencies needed for life in the present and the future, and develop their abilities as heirs to the nation's creative culture and care about the problems of society and the nation.
The natural culture of Minangkabau with the philosophical learn from the nature or Alam Takambang jadi Guru literally means "nature become the teacher" being a teacher in early childhood learning has not been integrated in 16 Kindergartens in the city of Bukittinggi that was observed in 2019. Survey results, documentation and interviews show that there is no kindergarten that introduces the philosophy of learn from the nature in early childhood learning. So it is deemed necessary to design a learning curriculum based on local Minangkabau culture with the philosophical learn from the nature in early childhood learning through a scientific approach.
Philosophical learn from the nature So the Teacher is generally interpreted as a wisdom of life to provide a holistic view of life based on reflections on life experience and scientific experience. Philosophy means doing contemplation to find solid foundations as a platform for everything that attracts human attention in pure proportions. (Sayuti, 2012: 182). A deep contemplation will give rise to a feeling of freedom, give birth to people who understand the basic themes of religiosity, outlook on life, and create humans who are able to build their own thoughts.
Humans who are able to develop their own thoughts, are human beings who are independent, religious, have a outlook on life and character. All the potential is not created by itself, but is obtained through education. Early childhood education / PAUD with a learning process that is carried out in a structured and planned manner, which is contained in a curriculum. The 2013 PAUD curriculum is designed with characteristics to optimize children's overall development which includes six aspects of development (religious and moral values, physical-motor, cognitive, language, social emotional, and art) which are reflected in the balance of attitudes, knowledge and skills, by using thematic learning and scientific approaches in providing educational stimulation.
Scientific comes from the word science which means knowledge. Seefeldt and Barbour (Dadan: 2018) mentioned that the ability of science in early childhood processes includes: the ability to observe, classify, draw conclusions, communicate, and apply them based on the scientific experience gained. Science invites children to think critically, with science children learn to find and prove the truth of something or reject something. It can be concluded that the scientific approach is a learning approach that gives children the opportunity to learn from real experiences, observe, try, find and infer what they see and observe.
The 2013 PAUD curriculum is philosophically aimed at developing children's abilities as heirs to a nation's culture that is creative and cares for the problems of society and the nation. Children as heirs of the nation's culture must know the local culture before knowing Indonesia as a whole. The Minangkabau natural culture with the philosophical learn from the nature is carried out through a scientific approach as a contextual experience for children to get to know Minangkabau culture early on.
Based on the description above, the problem that the researcher will adopt in this study is the Introduction to the Natural Philosophy of the Minangkabau learn from the nature in Early Childhood Learning with a Scientific Approach in Kindergarten Bukittinggi. This research was conducted in 16 kindergartens in the ABTB sub-district of Bukittinggi city with a population of 16 kindergarten heads and 87 group A and group B kindergarten teachers in 2019/2020. This study aims to describe the development of early childhood learning curriculum based on Minangkabau natural culture with the philosophical learn from the nature through a scientific approach in kindergarten.

The Philosophy "Learn from the Nature"
The Minangkabau traditional philosophy adheres to inductive logic in understanding something, where everything is based on observations of what is happening in the environment. Then it was thought according to the truth standards adopted by the Minangkabau community, namely based on alua (plot), proper (propriety), and maybe, so that the natural philosophy of the nature emerged as a teacher (Yulika, 2012: 181). For the Minangkabau, the natural the nature being a teacher is proof of the existence of God that is certain and unshakable. God the Creator of all that exists. Therefore, the Minangkabau believe in the Koran as a guide and guide to their lives as popular adage. Adat Basandi Syarak, Syari Basandi Kitabullah Maintaining the Integrity of the Specifications.
The Minangkabau people see Nature with all its elements always consisting of four elements called nan ampek (the four). Just as there is sun, there is moon, there is earth, and there is star, there is day, there is night, there is morning and evening, there is east, there is west, there is north and there is south, there is fire, there is water, there is land, and there is wind, (Navis, 1984: 59). Each of these elements live with their existence in one harmony, which is dynamic with the dialectics of nature called Bakarano Bakajadian (having a cause and effect). Four according to the philosophical nature of Minangkabau namely the nature of the stem (plants), animal nature, the natural mind, and the supernatural, (Yulika, 2012: 182). The scientific approach is believed to be the golden bridge of the development and development of the attitudes, skills and knowledge of students, by promoting inductive reasoning. Inductive reasoning views specific phenomena or situations to then draw conclusions as a whole. Inductive reasoning puts specific evidence in a wider relation of ideas. (Suryana: 2017) Inductive methods of nature emerge become teachers in early childhood learning in animal nature, which is observed in ant life. The ants go hand in hand and are organized so that it is revealed in the saying "seperti samuik bairiang" (like ants hand in hand). Ants are always shaking hands, if they meet, as the phrase "tagak sapo manyapo, sit tagua managua" (standing up greeting each other, sitting reprimanding each other). The other nature of the ants is the values in looking for food, "how can you get samo balabo, missing samo marugi" (if you can be as lucky, if you lose as losers). Ants can also be observed from how to settle and rest, and make defense in layers. All of the symptoms that ants for the Minangkabau people are natural are not teachers, which are interpreted inductively from natural phenomena (animals). Children are naturally attracted to animals from a young age (DeLoache et al., 2011 in Strous, Nyhout and Ganea: 2018) and animals are widely displayed in books or learning media designed for young children.
Natural inductive method of stems (herbs), observed in the life of a cassava. Cassava that still lives and grows everywhere and various conditions. Either planted, thrown into a pond, sanded, piled up with rubbish, in a ditch, and others cassava remains alive and thriving. The nature of cassava is often expressed "hiduiklah tuba cassava in the middle of the tacampak nyo tumbuah juo" (living like a cassava stem that lives anywhere) regardless of where it is located.
The method of the proof of the supernatural, namely in life that always has two dimensions "good and bad". Human life always faces these two realities that lead to the concepts of heaven and hell. Falsaat Minangkabau explains the good and bad meanings of life inductively through the analogy to the life of the trunk and animal realms above The inductive method of thinking, when Minangkabau people think and understand every thought result. What is expressed in the proverbial Minang "pikia palito hati" (the mind of the lamp), means between raso jo pareso, meaning between mind and belief that must be in line. Raso is in the heart (soul, belief), and a sense of being under the realm of the mind (logic. Minangkabau people think and draw learning from the provisions of nature. So it is not uncommon for the proverbial and petitih that Advances in Social Science, Education and Humanities Research, volume 463 guide their customs sourced from events that occur in nature. In fact children can be introduced to cultures that are appropriate to the context of the environment, to develop the ability to think and conceptualize social problems in accordance with their background, which aims to gain insight into life that occurs in the surrounding culture and also experience others, (Eliza: 2017). Early childhood education is a very important education for children in the next life. The quality of experience gained by children at an early age will make it more meaningful to achieve their future. (Eliza: 2013). The results of Joseph S. Agbenyegaa's research, Tamakloeb and Klibthongc, 2017) stated that children need to develop their views of the reality in their cultural community, they need to develop the ability to think, imagine and conceptualize social problems and gain insight about their personal lives and also the experiences of others.
The introduction of Minangkabau culture with the philosophical nature of takambang becomes a teacher through a scientific approach aimed at providing an understanding of children about the way the Minangkabau community views nature as a source of learning observed through the environment around the child with a scientific approach that is observed by the child continuously, (Eliza; 2017). All of them are summarized in two main points, namely culture and ideology. How to convey the teachings of noble advice through traditional expressions expressed using parable language and comparisons whose meanings are conveyed in terms of class (indirect).
Parables and comparisons can be made by referring to the nature and characteristics of plants (flora), animals (fauna), or to human behavior, (Hasanuddin;2016). The closeness of the Minangkabau people to the natural environment of their lives and at the same time making the natural environment as a learning vehicle that can be understood as a formulation of local wisdom of the Minangkabau community that human life is very dependent on the natural environment and therefore humans must always maintain harmony with the natural environment.

Scientific Approach
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Learning is carried out through a scientific approach in the play process. The scientific approach in the 2013 PAUD curriculum is a learning process that is designed so that students actively build attitudes, knowledge, and skills competencies through the stages of observing, asking questions, gathering information, reasoning, and communicating. The process of organizing learning is endeavored to be able to build ideas to express freedom, imagination and creativity so as to develop religious and moral values, motor skills, cognitive, language, social emotional and arts in accordance with the principles of child development. The scientific approach to questioning, is a dialogical approach between teacher and child on a predetermined theme, asking that children do can develop children's thinking skills. (Suryana; 2017).
Scientific learning in early childhood is very important for many aspects of child development. the researchers recommend that scientific learning be introduced before children enter school, even children from birth. Children in their development and growth or early years experience several important things, so it is necessary to develop their views about the reality around and local culture, they need to develop the ability to think, imagine and conceptualize themselves in their environment and personal life. and the experiences of others around them, (Joseph S. Agbenyegaa, Tamakloeb and Klibthongc, 2017).

RESEARCH METHOD
This type of research used in this research is Research and Development (R & D), because it is in accordance with the objectives to be achieved. Research and development is the research and development of education is the process used to develop and validate educational production, (Borg and Gall 1983)..
Description of the study findings study the curriculum, learning programs in kindergarten, introduction of Miangkabau natural culture by integrating the philosophical nature of takambang to become a teacher into the learning program, including determining themes, making RPPM and RPPH. Next apply in the form of learning activities. Observing the effectiveness of learning activities, and at the same time discussing with the school principal again: Preliminary research • Literature study and field observations to gather theories and data relating to the philosophical nature of the Takambang become a Minangkabau teacher • Study of needs analysis and teachers. The broad trial phase, by choosing kindergartens with a large number of classes, is based on consideration of the number of teachers and kindergarten environments that are very adequate. This research develops the learning model so the success criteria can be seen through: Indicators or applicability criteria of the model can be seen from (1) indicators of teaching materials (2) benefits of teaching materials.

Implementing the philosophical
Literature and field study results that researchers collected for the introduction of the old culture of Minangkabau with the philosophical nature of Takambang became a teacher through a scientific approach to several RPPM / RPPH learning programs with learning plans on learning themes such as themes 1) animals for stems, 2) plants for the trunk realm, 3) for the supernatural and the thought world integrated almost on all themes. Program by lifting learning material that is suitable with the learning objectives. Data is collected from the RPPM / RPPH of teachers in several kindergartens by integrating natural material into a teacher.
The design of Minangkabau natural culture learning with philosophical nature of Takambang becomes a teacher through a scientific approach.
The concept of the model to be designed refers to the development model design According to Dick and Carry, (1996)

Scientific Approach
The introduction of the Minangkabau natural culture with the philosophical nature of Takambang became a teacher through a scientific approach. Designing learning, through a variety of materials and learning methods in introducing philosophical nature to the teacher.
Learning by integrating the natural culture of Minangkabau with the philosophical nature of Takambang becomes a teacher through a scientific approach to the material, methods and techniques of early childhood learning.
The learning plan is designed with special procedures carried out in learning activities. Learning plans are prepared starting from semester programs, weekly learning plans and daily learning plans and assessment of the learning process. The learning theme chosen is adapted to nature which will be explained to children. Selection of themes with appropriate learning materials and methods.

CONCLUSION
This research is about discussing the introduction of the natural culture of Minangkabau with the philosophical nature of Takambang being a teacher through a scientific approach. The results showed that a learning program was arranged by integrating the Minangkabau natural philosophical nature of Takambang into a teacher. the preparation of a learning program that teaches children about God's created nature can be a source of learning, can be used as a guide in acting and behaving. The preparation of this learning program experienced several obstacles, especially regarding the delivery of natural material from the Takambang to become a teacher who had been mistaken in the perception of the teacher in interpreting the philosophy, so that presenters were needed who really understood the natural culture of Minangkabau with the natural philosophy of Takambang being a teacher.


Application of 3D Laser Scan Technology in the Surveying and Mapping of Ancient Buildings

Taking Wang’s ancestral temple in Yongshan Town, Leping City, Jiangxi Province as the research object, through the teaching practice of surveying and mapping of ancient buildings, this paper summarizes the advantages and disadvantages of 3D laser scan technology in surveying and mapping of ancient buildings and discusses the Methods and approaches of combining industry-university-research cooperation mode in local colleges and universities under the background of cultural relics protection.

Introduction
As of December 2018, China has selected five batches of traditional villages. There are a large number of historical buildings and immovable relics in these villages, which need to be surveyed, studied and sorted out. In the guidance document for the evaluation of the professional education of higher education issued by the Ministry of Housing and Urban-Rural Development in 2017, the quality of education was clearly stated to be "familiar with the importance and basic principles of historical and cultural heritage protection and the use of existing buildings, and to be able to conduct architectural survey, mapping and preliminary conservation or renovation design". At present, there are 298 colleges and universities with architecture in China, and the number of graduates reaches about 18,000 each year. This is an important force involved in the mapping and protection of ancient buildings. At the same time, it should be noted that traditional surveying and mapping requires a large amount of investment in human resources and time costs. Due to the serious shortage of architectural heritage protection professionals, it is difficult to effectively complete the corresponding basic work such as obtaining surveying and mapping data and drawings, and establishing records, which brings inconvenience to the protection and research work [1]. With the increasingly severe situation of cultural relics protection, it is necessary for local colleges and universities to carry out surveying and mapping teaching with new technology, new ideas and new methods.
This time we surveyed and mapped the historical buildings through the combination of the 3D laser scanning technology and the traditional manual mapping, and then analyzed the problems.

The Process and Problems of Traditional Manual Measurement
Surveying and mapping of ancient buildings is the only way to study, protect, maintain and build Chinese ancient buildings. Accurate and reliable data and correct information expression are the goals of surveying and mapping of ancient buildings. The earliest surveying and mapping event recorded in level, right rule". "Zhun", "sheng", "gui" and "ju" are measuring tools commonly used since ancient times. [2] since then, ancient China has made continuous innovations in measuring tools, and some fields even reached the advanced level of the world at that time. However, the history of China's real use of Western surveying and mapping technology began in the 16th century when the western missionary Matteo Ricci came to China for exchange. Later, the Qing government set up more than ten schools, including Beiyang School of Surveying and Mapping, Baoding School of Surveying and Mapping, Beijing Army School of Surveying and Mapping and some local schools. Surveying and mapping gradually developed into an independent discipline. After the development of this period, the technical level in the late Qing Dynasty gradually changed from traditional surveying and mapping to modern surveying and mapping [3]. These surveying and mapping fields cover engineering, railway, mineral, water and other aspects, while for ancient architectural surveying and mapping, we have to mention the Chinese Construction Society established in the early 20th century. In the 16 years since its establishment, "many precious ancient architectural examples have been discovered and recorded, and thousands of surveying and mapping results have been completed, which laid a solid foundation for the framework of Chinese architectural history and became a brilliant starting point for the research and protection of Chinese architectural heritage" [3].
With the development of technology, the era of surveying and mapping based on manual surveying has quietly changed. Since the 1980s, total station measurement technology, close-range photogrammetry technology and 3D laser scanning technology have gradually occupied the main market of surveying and mapping, but the most promising technology is the 3D laser scanning technology at present. In short, no matter which kind of mapping technology it is, all are guided by the accurate and readable drawing and mapping results.

The History and Present Situation of 3D Laser Scanning Measurement
Since its entry into China in 2000, 3D laser scanning technology has been widely used in the fields of architectural heritage protection, virtual reality, deformation monitoring, medical and industrial measurement, and emergency services [4]. It continues to play an important role in ancient building surveying, cultural relics protection and recording.
In 2004, the Palace Museum and Beijing University of Civil Engineering and Architecture applied 3D laser scanning technology to the digital mapping of the ancient buildings of the Forbidden City, summarized and studied the methods and theories for processing 3D data. Finally, the relevant technical requirements for the collection standard, mapping content and expression form of 3D data of ancient buildings were put forward, and the specific implementation schemes of technical process design, data acquisition and processing were summarized [5].
In 2007, Tianjin University also used Tianbao 3D laser scanner to scan the Fengguo Temple Hall in Liaoningand the Summer Palace, etc., obtained the original data and carried out subsequent data processing research. To some extent, it summarized the status quo of ancient building surveying and mapping in China and proposed relevant solutions [6].
In 2014, Ding Yanhui from Beijing University of Civil Engineering and Architecture started with 3D laser scanning data, combined with manual mapping, discussed the application research of ancient building mapping and information management based on 3D laser scanning data, comprehensively elaborated how to apply 3D laser scanning technology to analyze the deformation of ancient building structure, wood structure modeling and data display, color record of ancient building and process records, etc. At last, he put forward a research model of ancient building survey and information management based on 3D laser scanning technology [7].
The above researches have elaborated and analyzed the 3D laser scanning technology in the ancient building mapping technical level, including how to establish the 3D information management system of the ancient buildings, the creation of the ancient building triangle network model, and the detailed process of the ancient building 3D scanning. Some articles also involve the superiority and inferiority of traditional mapping, as well as the superiority and the insufficiency of the 3D laser scanning technology. However, it is the first time for Jiangxi ancient ancestral hall to use 3D laser scanning technology for surveying and mapping, and there is no discussion on the advantages and disadvantages of the combination of traditional manual surveying and 3D laser scanning from the perspective of teaching practice and drawing.

Introduction to Wang's Ancestral Hall
Wang's ancestral hall, also known as wangzongwuci or zhaomutang, is located in Yongshan village, Leping City, Jiangxi Province (figure 1). There are more than 70 traditional buildings in the village, mainly in the architectural style of Gan school in Ming and Qing Dynasties. Wang's ancestral hall, which is in the middle of the old street, is the physical witness of Yongshan's history. The ancestral hall was built in Chongzhen period of Ming Dynasty. It has been renovated many times in modern times and is now used for important activities of clans. Wang's ancestral hall is the only stage relic of the Ming Dynasty in Leping. Its wood, brick and stone carvings are lifelike, with high cultural and historical value.

3D Laser Scanning Operation
Wang's ancestral hall is the object of this survey. The survey tools used include tape, steel ruler, plumb, hand-held laser rangefinder and 3D laser scanner. Auxiliary tools include vertical ladder, flashlight, card camera and UAV. Both methods of surveying and mapping are used. Among them, there are seven steps from 3D laser scanning point cloud data to CAD drawing.
• Understand the basic information of ancient buildings.
• Determine the location and number of mapping targets.
• Splicing point cloud data, optimize point cloud data, Import CAD.
• Combine with survey drawing, Conclusion analysis and comparison.

Intervention of Traditional Manual Measurement
Draw the plan, elevation and section with proper scale. The next step is to measure and to dimension the previously drawn sketch. For some ancient building components with special-shaped outline, it is too cumbersome to draw directly, so the author takes photos and videos of them. Sort out and check the mapping data, and use CAD to draw when the depth of the drawing is required.

Combination of 3D Laser Scanning and Manual Measurement
After the RISCAN PRO software completes the point cloud splicing, the point cloud model is presented in the view in the scale of 1:1 in CAD. Its spatial coordinates are repositioned, and the outlines of each facade, plane and other drawings are drawn by using the method of curving. The section can be roughly drawn. Because this model is composed of many points, only many points in dense arrangement can be seen when zooming, so its boundary is difficult to determine. And the point clouds between different components overlap each other, so only the general outline can be described.

Mapping Results and Modeling
The results of 3D scanning and mapping, as well as the 3D scanning auxiliary drawing are shown in figure 2 and figure 3.       The advantages of manual mapping are as follows: (1) The measuring instrument is cheap and the tool cost is low.
(2) It has greatly trained the patience, basic skills and understanding of the mapping personnel.
(3) Surveying and mapping tools are portable, easy to get started and fast to use.

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The disadvantages of manual mapping mainly include the following four points. (1) The surveyors directly contact with the ancient buildings, which is easy to cause secondary damage to the old buildings in disrepair. If the surveyors climb the mezzanine or roof of ancient buildings, it will cause some safety risks to them.
(2) The surveying and mapping time of complex ancient buildings is long and the mapping task is large. If the teaching time of surveying and mapping is limited, then the accuracy is difficult to be guaranteed. In addition, the internal joint mode of some mortise and tenon structures cannot be observed directly, which will bring difficulties to the sectional and detail drawing.
(3) To observe the ancient building components from the perspective of human will produce certain perspective effect, and all drawings are projection drawings, which will bring certain errors to the drawing.
(4) The angle of 3D direction cannot be accurately measured by ordinary instruments.

Advantages and Disadvantages of 3D Laser Scanning
Mapping. The point cloud model obtained by 3D laser scanning technology is of great significance for ancient building surveying and mapping. Compared with traditional surveying and mapping methods, it has some advantages and disadvantages. Its advantages are mainly reflected in the following aspects: • The first paragraph after a section or subsection heading should not be indented; subsequent paragraphs should be indented by 5 mm.
• Time is shortened and it can be reused in complex buildings. 3D laser scanning technology can collect point cloud data of the measured buildings in a short time, which greatly reduces the workload of surveying and mapping.
• Restore 3D information exactly. For the ancient buildings that are not easy to climb or the cultural relics that need to be protected, the data needed cannot be measured, only the possible structure can be figured out with the structure of similar ancient buildings, but the two-dimensional figure can be accurately drawn in the obtained model. And the drawing has no perspective error, and the shape and scale also maintain the effect of the building itself to the maximum extent.
• It is convenient to get accurate angle data. The wall of the front courtyard of Wang's ancestral hall is not rectangular, but an irregular polygon. Therefore, to accurately measure the angle, the manual method has a great error, which is easy to cause the difficulty of alignment between the walls in the later drawing. 3D scanning can be directly linked in CAD, which eliminates the difficulty of measuring angle and is very convenient.
Although 3D laser scanning technology can greatly reduce the workload of surveying and mapping ancient buildings, there are still many problems to be solved, and its disadvantages are mainly as follows.
• There is still room for optimization for the restoration of building details. At present, the accuracy of 3D scanning can meet the requirements of large components drawing. This problem also needs to rely on traditional mapping methods to solve. And this method is safe enough to carry out. Climbing is needed only when the details need to photographed, but one does not need to climb when measuring the elevation and profile data.
• The roof beam column structure of the building cannot be measured through the ceiling. The three-dimensional laser emits visible light and has no penetrability, so the occluded part cannot be scanned and the interior of the staggered component cannot be displayed. The three-dimensional laser instrument receives the reflection pulse of laser, and the data of specular reflection and material beyond the critical incidence angle cannot be collected [10]. In the actual surveying and mapping, the beam column structure above the floor can only be observed with the help of ladder climbing, which may cause damage to the floor of ancient buildings, and the surveyors also have certain safety risks.
• The color information of the object cannot be obtained. 3D laser scanner is mainly used to obtain the 3D spatial information of the size, shape and location of cultural relics, but it cannot acquire its color pattern and texture information. In order to obtain the color and texture, the camera is used, but the information is lack of integrity and clarity [11].
• The accuracy is affected by natural conditions such as temperature. According to the general equation of laser transmission distance in the atmosphere, the laser echo signal power is related to the atmospheric transmittance from laser source to target, the transmission attenuation coefficient of laser beam in the atmosphere, the reflectivity of target and other variables [12]. Traditional surveying and mapping can be carried out except for extremely bad weather.
• Point cloud data stitching of multi measurement base points is easy to cause point cloud coincidence. It is difficult to fit the point cloud completely in the process of splicing because of the angle deviation of multiple measurements. In this operation, there are multiple roofs and multi-layer beam sections, and even the thickness of point cloud varies due to the characteristics that laser can penetrate some materials.

Conclusion
At present, the application of 3D laser scanning technology in Jiangxi cultural relics is still in infancy. There are 11 colleges and universities in Jiangxi Province to open architecture, which is enough to form a surveying and mapping team. From the perspective of cultural relics and buildings protection, Jiangxi needs a lasting, efficient and professional team to map cultural relics and buildings. In view of the above problems, the author believes that the discipline advantage colleges and universities should strengthen cooperation with local colleges and universities, in line with the principle of mutual benefit, while improving the level of surveying and mapping, and promoting the protection of local cultural relics and buildings. Secondly, it is suggested that the Department of Cultural Relics should set up special funds to support the renewal of surveying and mapping tools in colleges and universities. Finally, the Digital Library of Cultural Relics should be established to avoid the dilemma that the ancient buildings are damaged by natural disasters and man-made disasters and cannot be repaired.