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A Comparison of Mathematics Assessment in Australian and Chinese Primary Schools:Different or Similar?

Dacheng Zhao

(SUCCESS, Australia)
Abstract: According to international comparative studies, it appears that there are recognised differences in mathematics achievement between Australian and Chinese students. This achievement gap is generally explained in terms of differences in teaching practice and cultural attitudes to education. This paper reports a comparative study of mathematics assessment between Australian and Chinese primary schools to investigate assessment factors accounting for this gap. Using qualitative case study approach, classroom assessment practices were observed. How teachers and parents viewed assessment were obtained through semi-structured interviews. Documents related to government policies, samples of the students’ work sheets as well as past examination papers were analyzed. The findings of the investigation showed clearly that despite considerable differences in assessment including the standards of assessment and the place mathematics assessment results have in the education structure of the country, however many similarities were found. A gap existed between the intended and implemented assessment both in Australian and Chinese primary schools. In order to bridge the gap between intended and implemented assessment, it is argued that explicit professional training in mathematics assessment is essential for both pre-service and in-service teachers in both countries.
Key words: Australia, China, comparative study, mathematics achievement, assessment

International comparison of mathematics achievement has become one of the ‘hot topics’ for mathematics educators around the world (Leung, Graf & Lopez-Real, 2006; Mullis, Martin & Foy, 2008; OECD, 2000; 2013). This paper reports the results of a comparative study of mathematics assessment in Australian and Chinese primary schools and discuss what we can learn from this comparative study. The paper formulates a plan to bridge the gaps in every school, where it was discovered that there were gaps between intended and implemented assessment in schools. Background to the study, including the relationship between achievement and assessment is introduced in Part one. This is followed by the brief description of research framework underpinning the whole project, and research methods utilized. Main findings of the study are then presented and discussed.
Introduction: mathematics achievement and assessment
In order to keep up with developments in ‘the knowledge economy’, students all over the world have to deepen their understanding of mathematics and uplift their level of competency. Linking students’ achievement in mathematics to a nation’s economic competitiveness and projecting this to the future, is widely acknowledged (OECD, 2001; United Nations Children’s Fund, 2000).  Mathematics educators around the world are interested in knowing about the status of their mathematics education and how that education compares with those in other countries. The focus of international education has therefore been placed on international comparisons of mathematics achievement and exploring any factors which may account for differences in those achievements (Mullis, Martin & Foy, 2008; OECD, 2000; Zhao & Singh, 2011).
International comparison of mathematics achievement
A considerable number of studies comparing mathematics achievement among students from many countries, and on a large scale, conducted over more than more than four decades have persistently observed that students from China including from Mainland China, from Hong Kong, and from Taiwan, consistently outperformed those from their Western counterparts including those hailing from Australia (Lapointe, Mead & Askew, 1992; Lokan Ford & Greenwood, 1997; Mullis et al., 2008). For example, in 1990-91, the Centre for the Assessment of Educational Progress surveyed mathematics and science performance of 13-year-old students (Second International Assessment of Educational Progress) from twenty education systems. Mainland China outperformed all other education systems in the study in terms of mathematics achievement (Lapointe et al., 1992). TIMSS 2007 (Mullis et al., 2008) provides a most recent and compelling achievement data. At the fourth grade, Hong Kong students had the highest average mathematics achievement comparing all other 36 countries. At the eighth grade, the students from Chinese Taipei had the highest average mathematics achievement among students from 49 countries.
To explain the mathematics achievement gap, researchers have described considerable differences that might contribute to the gap between China and their Western counterparts. These include differences in cultural attitudes to education (Leung, et al., 2006), mathematics teaching practices (Stevenson & Stigler, 1992), teachers’ mathematics pedagogy knowledge (Ma, 1999), content and standards of mathematics curricula (Lindquist, 2001) and out-of-school curricula (Lin, 2001).
The relationship between mathematics achievement and assessment
Recognizing the limitation in mathematics assessment, some researchers believed that the superior performance of Chinese students might be limited to specific form and content of tests used by large-scale comparative studies. For example, by using both process-constrained and process-opened problems to test Chinese and American students, Cai (2000) indicated that in comparison with American students, Chinese students’ superiority was limited to certain aspects of mathematics achievement, including basic skills of computation and solving routine problems. American students performed better than their Chinese counterparts in aspects such as using visual and graphical representations and solving open-ended problems.
However, considerable differences existed in Cai’s study and other comparative studies. For example, according to Stevenson and Stigler (1992) in their Michigan Studies, they used both typical mathematics problems (routine questions) and novel problems (open-ended questions) to assess students. They found that for nearly every item the mean score of the American students was lower than that of Chinese students. They claimed that Chinese students’ superiority was not restricted to a narrow range of well-rehearsed, automatic computational skills, but was manifest across all the tasks including open-ended tasks (Stevenson & Stigler, 1992, pp. 39-41).
These contradictory findings related to assessment raise an interesting question about the assessment used in assessing students’ achievement in comparative studies. As Eckstein and Noah (1992) noted, the study of assessment practices seems to have been a largely neglected aspect of comparative education. Clearly, there is a lack of in-depth research that investigates assessment factors contributing to apparent differences in student achievement. Especially there is lack of comparative studies incorporating descriptive knowledge of assessment practices and examining similarities and differences in ‘authentic’ settings (Zhao, Mulligan & Mitchelmore, 2006).
In order to raise education standards, assessment practices have played an increasingly important role in education both in China and Australia (Zhao, 2000; 1999; Zhao et al, 2006). It is widely acknowledged that student’s mathematics achievement is affected not only by officially prescribed mathematics standards, but also by the mathematics teaching and assessment (Black & Wiliam, 1998; Clarke, 2000).
Clarke (1996) claims that contemporary mathematics assessment reflects an international consensus regarding to the nature of mathematics learning. He argues that assessment should be recognized, not as a neutral element in the mathematics curriculum, but as a powerful mechanism for the social construction of mathematics competence.
In contrast, Leung et al., (2006) suggests that ‘there have been different views and approaches to assessment of students’ achievement in Mathematics’ (p. 17). They argue that the East Asian education systems including Mainland China, Hong Kong and Taiwan are characterized by highly competitive examinations. Teachers and parents attach great importance to education, and there is high expectation for their students and children to succeed. Academic achievement has been considered a means of bringing honor to one’s family. This high expectation on students to succeed as provides another important source of motivation for students to learn. In addition, the differences in social and economic status between the academically high qualified and low qualified is much greater in East Asia than that in the West. This sends a message to students about the importance of academic achievement, and constitutes another source of extrinsic motivation for students’ learning. Similarly, it is argued that influence by the traditional ‘examination culture’, assessment has been regarded as the ‘baton’ directing teaching and learning in China (Zhao, 1999).
Assessment has been assumed an increasingly important role in mathematics education across nations, which educators need to realize and exploit the significant role of assessment plays on mathematics teaching and learning (Clarke & Stephens, 1996; Zhao, 2000). Leder and Forgasz (1992) indicate that the link between student learning of mathematics, the teaching methods adopted in the mathematics classroom, and the assessment procedures used to determine and measure student knowledge are addressed by the research community and closely related to the nature of assessment. They argue that by limiting the domain of mathematics sampled, assessment has often been a restrictive influence. Broadening the areas and skills evaluated, and reinterpreting assessment as a way of communicating students’ current understandings to teachers, can lead to positive rather than destructive reinterpretations of mathematics learning.
A number of researchers (e.g. Black & Wiliam, 1998; Bright & Joyner, 1998) report that developing pedagogical knowledge through assessment of students’ mathematical learning has a substantial impact on teachers’ instruction and hence on students’ learning. Black and Wiliam (1998) argue that the standards of learning can be elevated by improving the formative assessment process in the classroom. They argue that formative assessment can be an essential component of classroom work and that its development can raise standards of achievement. Little and Wolf (1996) address the relationship between assessment and teaching and learning. They argue that the emphasis on assessment is now evident worldwide, both in developing and developed countries. It has been commonly accepted that reform in assessment is a necessary condition for any reform of the mathematics curriculum.
In summary, the current literature reviewed indicates that mathematics assessment has a strong influence on mathematics teaching, learning and students’ mathematics achievement. A focus of this investigation was to explore Therefore, to understand the mathematics achievement gap between China and Australia, the influence of assessment on achievement should be a focus of investigation (Zhao, et al., 2006).
Research framework and methodology notes
The major purpose of this comparative study is to investigate similarities and differences in mathematics assessment practices both in China and Australia at primary school level, and identify factors that may account for these similarities and differences.
Research framework
A conceptual framework of this comparative study is the theory of three levels of curriculum, adopted from the International Association for the Evaluation of Education Achievement (IEA) for their international comparative studies (Robitaille, 1980; Robitaille & Garden, 1989):
• the intended curriculum and assessment: the requirements of curriculum and assessment as specified at national or system level in terms of standards and syllabus
• the implemented curriculum and assessment: the practices of curriculum and assessment as interpreted and delivered by classroom teachers
• the attained curriculum: the curriculum which is learned by students, as demonstrated by their attitudes and achievements
By using the above framework, the IEA studies (Husen, 1967a, b; Mullis et al., 1997, 2000; Robitaille & Garden, 1989) have explored some intended and implemented curriculum factors that contribute to students’ achievement in mathematics. Unlike IEA studies, this study intended to investigate factors of intended and implemented assessment that contributed to mathematics achievement. The major research questions guiding this comparative study are: what are the key differences and similarities in mathematics assessment policies and practices between Australian and Chinese primary schools, and what factors can account for these?
Methodology notes
To answer the research questions, case study is regarded as the most appropriate research approach (Merriam, 1998; Yin, 1994). As Stevenson and Nerison-Low (2002) indicated, interpretation of data in a large-scale quantitative study is difficult, because it is difficult to measure precisely by using questionnaires, especially since much of the information is retrospective. They recommend the use of case study as a supplement to large-scale studies in international comparison of mathematics achievement, so as to interact with the respondents, to probe details, and to elaborate answers.
In this comparative study, three primary schools (two from Australia and one from China) were selected for this case study. Two Australian schools were chosen from the Sydney metropolitan region and the Chinese school was chosen from the Guangzhou metropolitan region. The selection of these schools involved purposive sampling (Bogden & Biklen, 1998), and the three schools were chosen to illuminate particular differences and similarities between educational settings relevant for investigation of mathematics assessment policies and practices in Australian and Chinese schools (Maxwell, 1998; Merriam, 1998).
In order to collect authentic, valid data of the mathematics assessment policies and practices in the three schools, observation of classroom practices, analysis of policy documents, student work samples and examination papers, and interviews with teachers and parents were employed. In accordance with Ball (1993), classroom observation can offer a firsthand account of teaching and assessment practices in the mathematics classroom and, when combined with interviews and document analyses, allows for a holistic interpretation of the phenomenon being investigated.
The purpose of classroom observation in this study was to investigate the pattern of mathematics assessment at the three schools, and to describe the general approach to assessment adopted in the schools. The majority of observation indicators on the Classroom Observation Record were adopted from mathematics classroom observation protocols used by Stigler and Hiebert (1999) for their TIMSS video studies, but the items relevant to assessment practice were designed by the researcher. The mathematics classroom observation focused on teacher and student behavior and their interactions through the process of teaching and learning in sequence from the beginning to the end of the lesson. The key information sought from observation was focused on activities related to assessment, such as teacher’s analysis of students’ responses and adjustment of the lesson according to students’ responses. In each school, five mathematics lessons of each teacher were observed.
After the observation of classes, a post-observation interview was progressed, teachers were asked to explain the rationale underlying their classroom assessment practices. Six mathematics teachers (one teacher per grade) were recommended from each school by the principal to be interviewees. The teacher interviews consisted of twelve open-ended questions including interviewees’ teaching experience, knowledge related to mathematics assessment, and perspectives on mathematics assessment. The key information sought from teachers was related to ‘what’, ‘how’ and ‘why’ mathematics was assessed.
The analysis of government educational policy documents enabled the researcher to gain more insights into the intended assessment at system level (Merriam, 1998). Other documents including the school websites and newsletters, policy statements, mathematics programs and resources, students’ mathematics work samples, examination papers, homework and students’ portfolios or school reports were also analysed. The analysis of work samples or examination papers was based on the intended assessment standards drawn from government policy documents. During the study, the processes of data collection and analysis were simultaneous. Content analysis (Denzin & Lincoln, 2003) started from the first transcript of the interview, first classroom observation sheet and the review of the first document. Emerging insights, categories and themes were formed over the data collection period for each case. When all the tapes were transcribed and the classroom observation sheets and documents were collected together, a more holistic approach to data analysis based on the three levels of curriculum and the assessment was used to undercover emerging themes. In the last stage, cross-case analysis was used to analyse the key differences and similarities of assessment policies and practices between the two countries.
Main findings of the study: Differences and similarities in mathematics assessment
Based on the data analysis, the findings are summarized in terms of differences and similarities in mathematics assessment. The differences are presented in the first part of this section in terms of classroom assessment practices, formal assessment and purpose of assessment. This is followed by the presentation of similarities in terms of the intended assessment and implemented assessment.
Differences in mathematics assessment 
First, from classroom observations, it was found that Australian teachers preferred using individual assessment. Teachers usually checked students’ classroom assignments individually during classroom time. Since portfolios were used as the major approach to assessment and reporting mathematics achievement at two Australian schools, teachers paid close attention to collecting students’ work samples regularly. In contrast, teachers at the Chinese school preferred group assessment. They checked students’ classroom assignments collectively at the end of the class. They used written examinations distributed by the local pedagogical office more often than their Australian counterparts. It appeared that due to the large size of the classes (around 50 students) at the Chinese School, students had few opportunities to answer questions, to demonstrate their work, and receive immediate teacher feedback during their mathematics classes compared to the students at the two Australian schools, where the average class size was less than 30 students. However, it seemed that Chinese students were better prepared for their classes (most of them were able to follow teacher’s instructions and did their seat-work very well) than the Australian students.
Second, from the analysis of formal assessment documents, it was found that there were considerable differences in the representation of the problems and content standards of assessment between Australian and Chinese schools. Most test items from Australian schools were presented as pictures or drawings, while most test items included in the examination papers of the Chinese school were presented in words or mathematical symbols, even in Years 1 and 2. Test items included in the Chinese school’s examination papers contained more items testing students’ memory of basic mathematics facts and computing skills. Its content was more advanced and contained more abstract items testing students’ understanding of advance mathematics concepts and relationships between different mathematics concepts.  
Third, the interviews with the teachers indicated that considerable differences existed in teachers’ views on the purpose of assessment. Most teachers at the two Australian schools indicated that the major purpose of their assessment was to gather information about students’ learning and use it for improving their teaching. Although most teachers interviewed at the Chinese school recognised the importance of assessment for their teaching, they believed that major purpose of assessment was to inspect students’ mathematics learning to stimulate students’ motivation to improve achievement levels. Two teachers explained that according to Chinese tradition, teachers attributed students’ achievement (or lack thereof), to their motivation, and parents deeply respected and supported the teachers. Therefore, the focus of assessment was on improving teaching practices in two Australian schools, but it was more focused on ‘pushing students’ to achieve at the Chinese schools.
Last but not the least, the interviews with parents showed the large differences between Chinese parents (whether living in China or in Australia) and Australian parents (native English speakers) in terms of parents’ beliefs on mathematics assessment and attitudes towards mathematics achievement. Chinese parents attached high value to their children’s mathematics achievement, since it is one of the key subjects tested by the National College Entrance Examination. All the Chinese parents had high expectations of their children’s mathematics achievement and they all encouraged their children to work hard in mathematics learning to enable entry to key schools (selective schools). They also paid great attention to their children’s mathematics learning and had contacted with mathematics teacher regularly to check their children’s mathematics test results. They adopted a similar approach to their children’s after-school time, either sending children to coaching schools or coaching their children by themselves through checking their children’s mathematics homework daily. They reported the average after-school time their children spent on mathematics learning was about four hours per week. In contrast, the Australian parents interviewed attached higher value to English than mathematics and indicated that they did not push their children to study hard to get better mathematics achievement. They had similar views on after-schools’ tutoring and thought children’s after-school time should be play time. Australian parents reported that they did not send their children to coaching schools and their children only spent half an hour per week on after-school mathematics learning, which is strikingly different from the Chinese parents’ views.
Similarities in mathematics assessment   
Despite considerable differences in mathematics assessment between Australian and Chinese schools, many similarities were found from policy documents, classroom practices, students’ examination papers and teachers’ interviews.
First, from curriculum policy documents indicated that the intended mathematics curriculum and assessment in both systems shared the similar views on the nature and purpose of assessment. Both systems recommended that the major purpose of assessment should be the improvement of students’ learning by integrating assessment with teaching and learning, and supporting curriculum rather than driving curriculum (Chinese Ministry of Education, 2000; DETYA, 2000).  Mathematics curricula in both systems also suggested similar strategies for assessing students’ mathematics. Both systems recommended a variety of strategies for mathematics assessment. For example, Australian Education Council (1990) recommended strategies for mathematics assessment including teacher-observation and questioning; structured interviews with students; paper-and-pencil tests; oral tests; practical skills tests; work- or project-based assessment; collected samples of students’ independent work; individual homework assignment; group reports; anecdotal records; self-assessment and peer assessment (p. 22). Similarly Chinese Ministry of Education (2000) addressed that the methods of assessment need to have varied approaches such as paper-and-pencil examination, thematic activities, writing essays, group activities, self assessment and daily observations by the teachers which can be synthesized to form a scientific and reasoned method of assessment (pp. 5-6).
Second, from classroom observation, similarities were found in that few teachers in the three schools assessed their students’ mathematics learning by using authentic assessment, in which mathematics was presented to students through real-life problems, including open-ended investigation or projects or integrated activities to explore within or after school. Teachers in three schools emphasised routine test tasks, which were drawn from textbooks. It was suggested that the intended assessment policy (e.g. using alternative assessment) recommended by Chinese and Australian policy-makers were not broadly implemented into the classrooms at the three schools, which indicated there was a mismatch between intended and implemented assessment both in Australian and Chinese primary schools. 
Third, from the analysis of examination papers or students’ work-samples, it was found that formal approach to assessment and reporting at the three schools were still dominated by paper-and-pen tests. Although portfolios were used at two Australian schools, they were really used as a collection of examination papers.
Last but not the least, teachers in the three schools shared some similar views on the mismatch between intended and implemented assessment. All teachers interviewed at two Australian schools indicated that to make portfolios representative of all aspects of students’ learning, there was a need to use a variety of assessment strategies. However, they indicated that lack of time and resources, inadequate professional training and lack of parental supports were the major factors hindering them from effective teaching and assessing in mathematics. Similarly, all the teachers interviewed at the Chinese school suggested that the mathematics achievement could not only be assessed by written examinations, they thought paper-and-pen examination was highly valued by parents and Chinese culture. They indicated that most information related to students’ mathematics learning was gleaned from their classroom observation, checking students’ seat work and homework. They also reported that large class sizes, constraints of the current examination system, traditional cultural views, and lack of resources and professional training were the major factors leading to the mismatch between intended and implemented assessment.
In summary, from the study reported here it is found that there existed a gap between the intended and implemented mathematics assessment both in Australian and Chinese primary schools. The interview data suggested that teachers in both countries did not have sufficient professional training in mathematics assessment, despite attending in-service training courses. It was also apparent that pedagogical knowledge alone did not ensure the teachers implemented intended assessment practices into their classroom routine.
Discussion the implication of the study
This study has extended our understanding of mathematics assessment practices in Australian and Chinese primary schools, and provided valuable insights into assessment factors contributing to Chinese students’ higher achievement in mathematics. It has provided an explanation for the gap between intended and implemented mathematics assessment in both countries. Several implications can be derived from the study that are relevant for future research, assessment practices in schools, professional development for teachers and educational policy-makers, which are discussed as follows.
In terms of implications for mathematics assessment and teaching, this study has made an attempt at linking assessment with teaching and learning, which is drawn from the literature on the integrating of assessment with teaching and learning. Classroom observation found that generally there was a mismatch between intended and implemented assessment both in Australian and Chinese primary schools. Case studies found that paper-and-pencil tests still dominated assessment practices across Australian and Chinese primary schools, although alternative assessment were advocated by the intended curriculum and assessment in both systems. Therefore, it is recommended that teachers should use assessment as a tool to diagnose students’ learning and include authentic items in their assessment, which mathematics is presented to students through real-life problems and assessment is focusing on the process of students’ thinking and the strategies students used and to guide their teaching activities.
In terms of implications for professional development of teachers, this study found that lack of professional training in assessment practices was one of the key reasons hindering teachers from using intended assessment strategies recommended at system level. The classroom observation and interview data suggested that both pre-service and in-service professional developments are needed. For pre-service training, it is recommended that a course related to assessment should be included in teacher education programs. This assessment course should contain specific content related to mathematics assessment for primary schools. For in-service training, it is recommended that teachers need more time and resources to improve their assessment practices and skills. They need time to communicate with their colleagues and reflect on their own mathematics teaching.
In terms of implications for future research, the findings of this study suggested that the assessment factors may contribute to a mathematics achievement gap between Chinese and Australian students. However, the findings from this study are based on a small sample of participants linked to just three particular schools and may not be generalizable to other assessment items or other settings. To test the findings of this study, there is more research needed to ascertain how cultural factors such as parents’ values and beliefs influence students’ mathematics achievement across East Asian and Western countries. Such studies might need to combine a large-scale quantitative study in conjunction with small-scale case studies, which may provide rich and thick background information for understanding achievement differences.
In conclusion, this paper has focused on comparing mathematics assessment in Australian and Chinese primary schools. Findings drawn from this comparative research provide insight into bridging the gap between intended and implemented assessment, and also contribute to the assessment factors accounting for the mathematics achievement gap between Chinese and Australian students. 
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