Teacher Capacity As A Key Element Of National Curriculum Reform In Mathematics:a Comparative Study Between China And Australia

From the plenary report of17th CPC National Congress to "Medium and Longterm Planning Outline for China's Educational Reform and Development (2010-2020)", China shows its value on improving teachers'quality and enhancing construction of the ranks of teachers at the national level in various aspects.Ministry of Education of China published the revised "Mathematics Curriculum Standard for Compulsory Education" in2011. Australian Curriculum, Assessment, and Reporting Authority (ACARA) shaped the Australian Curriculum in Mathematics being used across all states and territories in Australia for the first time in2010. In both Chinese and Australian national mathematics curricula,"number and algebra"'and "statistics and probability" are two single out of four (three) content strands. The two curricula in both countries have the same intentions and requirements on these two contents. For "number and algebra", it is more focused on bridging the learning of arithmetic and development of early algebraic thinking, and it is emphasized that the learning of number should be prepared for the leaning of algebra in later years whilst value on necessarily proficient and quick arithmetic calculation still remains. In the content of "statistics and probability", in contrast to traditional approaches to teaching focus on computations of theoretical probability, new emphases on data and development of statistical thinking and literacy are characterized.The intentions and requirements are clear on the two content strands in both countries. However mathematics teacher is the key element in the curriculum reform and implementation in both China and Australia. To introduce the national mathematics curriculum, several important questions need to be considered such as "whether the teachers have corresponding capacity" and "how to improve teachers'relevant capacity".As a result, this thesis aimed to look at mathematics teachers' responses and performance when facing the national curriculum reform in China and Australia which have completely different contexts, and to explore the similarities and differences between Chinese and Australian mathematics teachers and the causes. And then to evaluate the important influence to national curriculum reform from teacher as a key element and to think of some big issues on national curriculum reform and implementation. Based on these considerations, the main focus of this research is on teacher capacity of Chinese and Australian teachers under the background of national curriculum reform. That is teachers' judgement and disposition to act based on professional knowledge and experience. In this thesis, it means mathematics teachers' professional ability, when facing the national curriculum reform, to focus on specific mathematical contents ("number and algebra" and "statistics and probability", considering the same intentions on these two contents in both countries-connecting the learning of arithmetic and algebra and developing statistical thinking-,"relational thinking" and "statistical thinking" were respectively used in this thesis), to deeply interpret the intentions and big ideas of mathematics curriculum and to understanding students' mathematical learning and thinking, then to design specific teaching scenario and examples in mathematics classroom. The following questions were intended to be explored:1. What theoretical framework with what criteria can be used to both qualitatively and quantitatively analyze and classify the capacity between Chinese and Australian teachers?2. How is the capacity for Chinese and Australian teachers on the two contents of "relational thinking" and "statistical thinking"? What are the similarities and differences?3. What are the relationships between the different criteria of teacher capacity in mathematics?4. What criterion (criteria) can best describe teacher capacity in mathematics and can be seen as the critical criterion (criteria) and key element(s)?Pedagogical Content Knowledge (PCK) initialed by Shulman and Mathematical Knowledge for Teaching (MKT) developed by Ball et al. underpinned the theoretical position of this research. On the basis of PCK and MKT, combined with the research of Teacher Capacity that how teachers face and respond educational system reform and school change, considering contexts of national curriculum reform in both China and Australia, theoretical framework of this research was developed by considering teacher capacity in mathematics from four criteria:Criterion A, Knowledge of Mathematics; Criterion B, Interpretation of Intentions of the Official Mathematics Curriculum; Criterion C, Understanding of Students'Learning and Criterion D, Design of Teaching. For research, selected Chinese and Australian mathematics teachers in upper primary or secondary years were given research questionnaires.120(60Chinese and60Australian) and82(41Chinese and41Australian) were respectively collected for "relational thinking" and "statistical thinking" from the valid research questionnaires, the ratio between secondary teachers and that of primary schools were completely the same in China and Australia sample. Based on the four indicators in each of the four criteria, the collected questionnaires were firstly analyzed qualitatively. After that, all the questionnaires were double-coded according to teachers'responses and quantitative analysis was conducted with SPSS19English version. After the analyses on questionnaires,10teachers (five on "relational thinking" and five on "statistical thinking") from each country-20in total-were selected for the later stage in-depth interview considering their responses to the questionnaire. Several conclusions were found in as following:1. Teacher Capacity of Chinese and Australian teachers show evidently similar normal distributions on both "relational thinking" and "statistical thinking". The proportion between the numbers of High, Medium and Low Capacity teachers was approximately20%,60%and20%in both contents. However, Chinese and Australian teachers performed differently in the two contents, in "relational thinking", Chinese teachers scored higher on Criterion A (Knowledge of Mathematics) and Criterion D (Design of Teaching), and the global score as well; but in "statistical thinking", Australian teachers performed slightly better than their Chinese counterparts on all four criteria. However, the difference between China and Australia sample was not significant. This point supported the theoretical framework of this thesis which argued that Teacher Capacity should be demonstrated focusing on specific mathematical content, but not just a general description.2. The interrelations between the four criteria of Teacher Capacity had minor difference, but still showed the same trend. That is Criterion D (Design of Teaching) had statistically significant correlations with any of the other three criteria. However, when separated from Criterion D, the inter-relationships between the other three criteria will not be as strong as their relationship to Criterion D (design of Teaching).3. All four criteria were effective in classifying teachers, but Criterion D (Design of Teaching) was by far the most powerful criterion. First, Design of Teaching performed most effectively in discriminating between teachers as High, Medium and Low Capacity. Second, among all the four criteria, Design of Teaching has the closest relationships with the other three criteria, and the inter-relationships between the other three criteria are under the associations with Design of Teaching. Finally, in both "relational thinking" and "statistical thinking", teachers in both countries had biggest difficulties and performed most weakly on Design of Teaching, and this is the criterion the teachers need to pay most attention for improving their Teacher Capacity. As a result, Design of Teaching can be considered as the critical dimension and key element of Teacher Capacity.This thesis comprises of six chapters. Chapter One is Introduction which includes background of research, research questions, aims of research and significance of research. The second chapter is Literature Review, after defining the connotation of Teacher Capacity in this research, this chapter reviews the relevant research in China and in the west. In the review of the literatures, firstly it looks back to the developmental history of relevant research and different research thrusts on "mathematical knowledge for teaching" which has close connections with this research and point out the limitations of existed research. Then it explores how to develop the theoretical framework of Teacher Capacity in mathematics from previous research in this research. Chapter Three is Design and Methodology of Research, theoretical framework is firstly given. Then discuss the research design and process needed to put in effect and the issues of validity and reliability. Main research content and findings of this research are in Chapter Four and Chapter Five which apply the same structure-the new intentions and requirements of instruction for specific mathematical content (relational thinking or statistical thinking) are discussed in the beginning, after that, it introduces the research methodology and process in details, then the qualitative and quantitative analyses of the questionnaires followed by the in-depth interview with selected teachers, finally is the conclusion part of the research findings. The sixth chapter is Research Conclusions and Discussions, it is the summing up and reflections to the previous two chapters and some discussions of the limitations of this research and suggestions of ongoing research.What is innovative in this research is at first at the construction of the theoretical framework of Teacher Capacity in mathematics. Being different from existing research on mathematics teachers' knowledge, it is argued in this research that the research to mathematics teachers should be focused on specific mathematical contents and look at specific teaching design on particular contents. What is more, considering the background of national curriculum reform in both China and Australia, it takes Interpretation of Intentions of the Official Mathematics Curriculum as one important criterion.The second innovative point is that this is the first systemic comparative study between Chinese and Australian teachers in mathematics. Both China and Australia have recently published the new national curriculum in mathematics that is mandatory, but there is big difference between the social and cultural contexts and educational system in these two countries. Thus, this comparative study is able to offer valuable implications for deeply understanding the introduction and implementation of curriculum reform in mathematics.However, certain limitations still remain in this research.First of all, it is the attempt and innovation on theoretical development of this research to describe Teacher Capacity in mathematics focusing on specific mathematical contents, but meanwhile there exists limitations in this theoretical model. To have comparisons with the research on "Mathematical Knowledge for Teaching (MKT)", it is easier to give an overall classifications based on the teacher's MKT, and there will be difficulties in effectively describe a teacher's global Teacher Capacity using the theoretical model in this research. There were five teachers who were asked to anticipate both research studies on 'relational thinking" and "statistical thinking", some connections were found on one teacher's performance on different mathematical contents, but the conclusions were just implied and limited.Another limitation of this research was shown in the analysis of the research conclusions. Both qualitative and quantitative research were used in the thesis and the consistency of the qualitative and quantitative research was highly reached. And a serious of rigorous tests were conducted to check the validity and reliability of the analyses of questionnaire. However, the classification of high, medium and low levels for Teacher Capacity in mathematics were arbitrary to some extent.Furthermore, there was no classroom observation and recordings used in this research. Although the research questionnaires and interviews were robust enough to reflect anticipating teachers' capacity, no further explorations were conducted on the connection between teachers' teaching design and practical instructions.