2006 POSTGRADUATE CONFERENCE Assessing Chinese Students’ Understandings in matics and Science: Ensuring Valid and Reliable based largely upon the quantification of students’ understandings, which iffer to entify what students ‘know’ and ‘can do'. To explore alternative modes of assessing the conceptual translations from Chinese to English, the need to provide Chinese stu importance of the researcher being present for the collect was consid main study to ensure improved validity. W th ot only for assessing student understanding but in helping to identify a learning trajectory for mathematics and science e of the major challenges for teachers has been the need to embed assessment into e teaching and learning process so that it is used to provide constructive feedback to students and teachers 2002; Wilson & Sloane 2000). In this new climate, teachers consider both the purpose and Mathe Data within International Contexts Chunxia Wang, Dr Debra Panizzon & Professor John Pegg Abstract Assessment practices in China are are measured using multiple-choice tests based upon rote-learning and memorisation. These methods d from global trends in education where there is a move towards assessment approaches that attempt id understanding of Chinese students, a study was designed based upon the Structure of the Observed Learning Outcome (SOLO) model as the theoretical framework. While the model has been used extensively in many Western countries including Australia, United States and the United Kingdom, this was the first study to be undertaken with Year 5 students in China. This paper describes the research issues that emerged from the pilot study including problems in ensuring the accuracy of dents with the opportunity to provide their ‘best possible’ explanations, and the ion of data. Once identified, each of these issues ered carefully in the design and implementation of the ith is achieved, emerging patterns demonstrate the applicability of the SOLO model n concepts for these Chinese students. In the last few years there has been a global trend towards outcomes-based education. This change in focus requires a move from assessment as a way of measuring and quantifying student achievement, to one that gauges the depth and quality of students’ understandings (Bell & Cowie 2001; Black & William 1998; Treagust et al. 2001). On th (Black & Harrison types of assessment used in their classrooms and how these tasks provide information on the ‘level’ of student’s understanding. The implications of teachers having this information is that it can lead to more focused teaching that enhances student learning in discipline areas (Biggs 1996). While this has been a difficult transition for educational systems in western countries (Pegg & Panizzon 2006), it represents major challenges in countries where there is a strong tradition towards examinations. 388 UNIVERSITY OF NEW ENGLAND China presents just such a context. From the beginning of civil service examinations (A.D. 581-617) to the a larger study to investigate implications ssociated with assessing Chinese students’ understandings of science and mathematics concepts using the e educational context of the study including an overview of the SOLO model. The purpose and design of the pilot are then detailed followed by a summary of the research findings. nd emphasis of assessment in the urrent Chinese education system, it is necessary to provide an historical glimpse of the complex relationship ories and the long history of the civil examination system. xaminations in China occurred during the Sui Dynasty (A.D. 581-617) and tes for these examinations were expected to memorise the five classics and four books, then produce the writings. The emphasis was on memorising huge amounts of material from the classics so as st talented individuals in the country for the service of the State (Tsang 1968). During this long period, Confucian learning, imperial power, and year they were abandoned in 1905, examination success and civil service careers were inextricably linked. Together, they provided access to wealth and membership of the ‘upper’ class in China (Pepper 1996). Even today, this examination-performance-driven meritocracy can still be seen as an important motivating force for learning and career achievement irrespective of social class in China (Delors 1996). In this paper we discuss the pilot study undertaken as part of a SOLO model. Initially, we outline th Finally, we discuss the research issues that emerged, and how these were considered in the main study to ensure the validity of the results. Chinese Educational Context China has always valued education highly recognising it as a means of ensuring the success of individuals and society as a ‘whole'. In order to understand the struggle, experience, a c between traditional Confucian educational the The importance of education in Chinese culture is derived from the teaching of Confucius. In theory, the end- product of Confucian education was the cultivation of a person in the ethical sense. In practice, however, it was concerned more with the preparation and selection of a ruling elite (Pepper 1996). The classic text underpinning education was the Confucian Canon comprising a collection of important writings that have been studied and examined over the past 2,000 years. These texts provided the context of Confucian teaching and learning, and are usually referred to as the five classics (Wu Jing) and four books (Si Shu). The beginning of civil service e lasted for 1300 years. These examinations were abandoned in 1905. To pass the different levels of examinations from the Sub-Prefect, Prefect and Ju Ren (Master’s degree) (Purcell 1936), the selection procedures required strict assessment standards supported by a stringent method of implementation. Candida re to write highly structured essays. All knowledge resided in classical writings, called the ‘eight-legs’ (Ba Gu Wen), a kind of full-dress formal essay. Essentially, the education system was about selecting the mo 389 2006 POSTGRADUATE CONFERENCE bureaucratic authority were bound together. Taken in total, these aspects extorted significant influence over Chinese life and society (Pepper 1996). Western learning ideas and teaching methods did not emerge in China until the western intrusion into China at the end of the 19th century (Pepper 1996). As a consequence of this ‘melding of minds’, China began considering changes in education at the beginning of the 20th century. During the 1920s, the content and objectives of examinations were extended, a change influenced directly by the United States and European educational systems (Han & Yang 2001). During this period, Professor Liao Shicheng and Chen Heqin collaborated on a book titled Methods of Intelligence Testing (Liao & Chen 1921). This was the first time Western psychometrics was introduced into China by Chinese academics. Although the imperial examination system was abolished almost 100 years ago, its impact is still evident in China today with examinations considered the most important component of education in China. The examination focus has influenced the purpose and curriculum content of Chinese education and has resulted in particula particular, memorisation and rote-learning strategies function of education, overshadowing the plementation of creative thinking and problem-solving approaches. As a consequence, there are high recent years, the examination-driven educational focus has aroused debate and controversy among Chinese educators with a view that China must embrace the move towards an outcomes-based approach to education. However, this is difficult given the historical traditions and the need to change the ‘culture’ in terms of the purp akers to school teachers, there is a call to reform the cu l assessment practices from focusing on how uch students know to how well it is understood and can be transferred to other learning situations. In at teachers should be encouraging students to provide learly, educational reform is underway to improve the quality of learning and teaching so as to ensure a r teaching methods and learning strategies in the classroom (Lee 1985). In underpin the im parental and societal expectations, exerting great pressure on Chinese youth to excel in examinations. In ose and importance of education generally (Yang 2002). From educational decision-m rrent educationa m keeping with this view, Xian (2005) suggested th greater explanations and opinions, along with opportunities to demonstrate analysis, reasoning, and discussion skills. This view contrasts greatly to the traditional rote-learning and fact-listing strategies required to achieve success in current examinations. C positive future for Chinese students. This reform is aimed at fostering innovative capabilities and improving the practical competence of all students (Jiang 2002; Yang 2002). Central to this idea of change in education is assessment. In particular, assessment should be organised so that it provides information to the teacher and student about the quality of understanding and where teaching might most profitably be directed. 390 UNIVERSITY OF NEW ENGLAND Ass The work of Biggs and Collis (1982 quality of le appears to be a consistent sequen variety of school-based tasks (Biggs & Collis 1989). Underlying the model is the assumption that cognitive understanding does not characterist Collis tions, history, geography, poetry, language learning, science and SOLO carried out in Australia, USA, Hong Kong, UK and many other countries. hile these levels occur within each mode, the specific nature of these levels is dependent on the particular mode targeted by the stimulus item. The fi • ical environment. For the very young child it is the with • at the ent objects and events. For the adult, this mode of functioning assists in the appreciation of art and music and leads to a form of knowledge referred to • Formal where a person is able to consider concepts that are abstract. Students are no longer able to work with ‘principles’ and ‘theories.’ In its more essing the Quality of Students’ Understandings , 1991) has provided a powerful model to assist the evaluation of the arning outcomes. The SOLO model as a framework offers a systematic way of observing what ce or pattern of learning (learning cycle) displayed by learners within a equate to a stable cognitive construct as with Piaget (1954), but involves individual ics that are content and context dependent. Over the past 20 years, the SOLO model (Biggs & 1982, 1991) has been used in a variety of subject and topic areas, including number and opera history (Pegg 2003). The research and practice of has been Incorporated in the SOLO model are two important features. The first concerns the nature or abstractness of the response and is referred to as the mode of thinking. It refers to the type of intellectual functioning required to address adequately a particular stimulus, e.g. mathematics question. The second feature depends on an individual’s ability to handle, with increased sophistication, relevant cues. This feature is referred to as levels of response, which are seen to reside within cycles of learning that provide a hierarchical description of the nature of the structure of a response. W ve modes of thinking are: Sensorimotor where a person reacts to the phys mode in which motor skills are acquired. In adult life, the mode is utilised as skills associated various sports develop and evolve. Ikonic when a person is able to internalise actions in the form of images. It is in this mode th young child develops words and images that repres as intuitive. • Concrete-symbolic when a person thinks by the use of a symbol system such as written language and number systems. Thinking in this mode is reliant on a ‘real-world’ referent. This is the most common mode addressed in learning in the upper primary and secondary school. restricted to a real-world referent and are advanced form it involves the development of disciplines. 391 2006 POSTGRADUATE CONFERENCE • Post Formal when a person is able to question or challenge the fundamental structure of theories or W t ired mode (say, concrete-symbolic) do n understanding (such as ikonic or sensorimotor). This is referred to as s Gardner’s • Unistructural (U): where the individual focuses on the domain/problem, but uses only one piece of al (R): where all data are now available, with each piece woven into an overall mosaic of relationships culminating in a logical endpoint. The whole has become a coherent structure lacking Ikonic disciplines (Panizzon 2003). hile he five modes of thinking are distinct, the functioning in a later acqu es ot preclude the use of an earlier acquired mode to support multi-modal functioning and supports other theories, such a Multiple Intelligences (Gardner & Hatch 1989). The important consideration here is that once a mode has been accessed, then all earlier acquired modes are available and continue to develop throughout life in response to experiential, social, cultural, educational, or genetic factors (Collis et al. 1998). In terms of the second feature of the model, three levels of responses comprise a cycle of learning within a particular mode. These are referred to as: relevant data so the response may be inconsistent. • Multistructural (M): where two or more pieces of data are identified as independent units. No integration is demonstrated between the data with inconsistencies often evident in the response. • Relation inconsistencies within the given context. The modes of thinking and levels of responses within these modes are summarised in Figure 1. Modes Post formal Formal Concrete symbolic Sensori motor Age in years (Not to scale) knowledge Forms of Theoretical Theoretical R U M R U M R Declarative IntuitiveU M Tacit 0 1.5 6 16 20 U M R Figure 1: Modes and levels in SOLO Model (Adapted from Biggs & Collis 1991) 392 UNIVERSITY OF NEW ENGLAND While the U, M, and R levels identify a cycle of learning in a mode, research studies over the few years have indicated that a single cycle is restrictive and does not explain fully the development of a concept (Campbell t al. 1992; Collis et al. 1998; Levins & Pegg 1993; Panizzon 2003; Panizzon et al. 2005; Pegg 1992, 2003; = e Watson et al. 1995). Subsequently, two unistructural – multistructural – relational cycles (i.e., U1-M1-R1 and U2-M2-R2) have been incorporated into the model for the concrete-symbolic and formal modes (see Figure 2). new mode R R M M U U1 2 1 1 2 2 = new cycle previous mode Figure 2: Two learning cycles in the concrete-symbolic mode In Figure 2 the ‘previous mode’ refers to the ikonic mode and the six levels represent two cycles of learning in the concrete-symbolic mode. The diagram illustrates the general development pattern expected moving from U1 to M1 to R1 etc. The equal sign on the pathway from R1 to U2 indicates diagrammatically that for many students this development is more about mental chunking of the ideas as opposed to the addition of ecessarily new content. The ‘new cycle’ represents potentially a further cycle of development in the concrete-symbolic mode and the ‘new mode’ in this example refers to the formal mode. Research Method The overall aim of the study discussed in this paper is to identify developmental pathways in students’ conceptions of six different concepts (three in mathematics and three in science). In addition, interest was directed at exploring the differences and similarities in student’s cognitive growth both within and across science and mathematics. Information of this type would provide a basis for teachers and other educators in assessing students’ understandings and in selecting particular teaching strategies to enhance students’ learning. However, given that the SOLO model had not been used in China previously, the purpose of the pilot study was to investigate the appropriateness of the SOLO model (Biggs & Collis 1982, 1991) as a framework and identify aspects of the research design necessary to provide valid results. n 393 2006 POSTGRADUATE CONFERENCE Curriculum Context subjects are compulsory for students in Years 1-9. Both subjects in Year 5 use the clude term tests, academic year tests and entrance tests for a higher grade. Local education departments a assessment in schools in China. 5 ilot Study Design heme 1: Identify developmental pathways in students’ understanding in mathematics and science. ience, one in mathematics) were selected. Both these s. Subsequently, it was possible to explore the similarities and differences that emerged round shape birthday cakes between sixteen (16) people so ii. Describe it as much detail as possible why we get day and night on the Earth? (science) hese questions were written in Chinese and posted to the Year 5 teachers in the school. Teachers then uestions in Chinese while the teachers were present. The students were encouraged to provide as much ere posted back to Australia where they were translated into English by the researcher, and then analysed Mathematics and science National Standard Curriculum of China. Summative assessment tasks are conducted in both courses and in develop these tests. In addition, schools implement other assessments, such as tests before the delivery of new topic, at the completion of a topic, and after an extended period time. Clearly, formal testing is a major orm off ample S Contact was made with a Chinese school located in Wu Han, the capital city of Hu Bei Province that had een visited previously by the researcher. With approval received from the principal, approximately 50 Year b students were invited to complete two questions providing their responses in Chinese. The sample consisted f an even distribution of female and male students. o P Guiding the study were: T Theme 2: Explore underlying thinking traits in Year 5 students undertaking mathematics and science. To identify relevant topic areas for the Chinese students, relevant curriculum materials were accessed and explored. From these documents two items (one in sc items had been used with Australian primary students in Years 5 and 6 thereby supporting the construct validity of the item between the two groups of students. The two questions were: i. Explain how you would divide nine (9) that each person receives the same amount? (mathematics) T wrote the questions on the board during a lesson allocated to the task. All the participants answered the q detail in their explanations as they could while addressing each question. Once completed, the responses w using the SOLO model. 394 UNIVERSITY OF NEW ENGLAND Data analysis ereby enabling two experienced researchers with SOLO to verify the accuracy of the coding. The English rsity of New England checked each translated script for accuracy nd met with the researcher to cross-check the procedure. el) sorted ng being demonstrated. The reliability of the 7; Wiersma 1991). and the comparison of the responses was not a part of the pilot study, the responses provided by e age. So, despite the rst of the nature of the question relating to notation and the students started dealing with the problem in such a way that most responses were each person to receive the same mount of cake by the division. the second learning cycle of the concrete-symbolic mode (U2, M2, R2), students attempted to use fraction notation and operations in their solutions. The best responses had the students expressing fractions in terms The first critical task was to translate student responses from Chinese into English for coding purposes th translation was a critical component of the research and had to be undertaken sensitively and rigorously to ensure the reliability of translation (De Vijver & Leung 1997; Twinn 1997). Therefore, a native Chinese speaker who was an academic at the Unive a With translation completed, the researcher and co-researchers (experts with the SOLO mod responses into ‘like’ categories. Once established, each category was considered in light of the SOLO model identifying the mode of thinking and level of understandi categorisation of responses was checked using independent rankings from the two colleagues with an overall agreement percentage calculated (i.e. 93-96%). This was undertaken for the two questions by comparing the odings between two researchers (Denzin 199c Findings from Pilot Study The initial findings are presented in relation to the research themes explored in the pilot study important aspects about research design that emerged from the process. The analysis of students’ responses provided two cycles of learning in the concrete-symbolic mode in both mathematics and science subjects. lthough a detailed A the students were similar in structure to those of Australian students of the sam differences in culture and language, the scripts from two different countries suggest that students demonstrate a consistent hierarchical pathway in learning these concepts. Students’ understandings of fractions The responses displayed an increasing degree of complexity. Student responses that were coded in the fi learning cycle of the concrete-symbolic mode (U1, M1, R1) used diagrams and written cues to address the question. They did not demonstrate an understanding the operations involved. Hence, there was no attempt to solve the problem using mathematical notation. In other words, most of focused on the action of dividing nine cakes rather than the effect of the action. Therefore, the most common difficulty to emerge for students working in this cycle was how to allow a In 395 2006 POSTGRADUATE CONFERENCE of common denominators and completing a simple addition. This was coded as M2 in the concrete-symbolic he following chart provides an overview for the type of responses provided for the development of understanding about the concept of a fraction. The responses within the first cycle of the concrete-symbolic ctions and consequences (see Figure 3). mode. T mode describe the a Figure 3: Examples of student responses for the first learning cycle in the concrete- symbolic mode The responses within the second cycle use fraction notation to describe the effect of their actions (see Figure ). 4 396 UNIVERSITY OF NEW ENGLAND Figure 4: Examples of student responses for the second learning cycle in the concrete- symbolic mode o cycles of learning within the concrete-symbolic mode were entifiable. 1) indicated that students were aware that the change of day and night had something to do with the position or movement of the Earth and the Moon in relation to the Sun. When the Earth moves Students’ understandings of day and night The coding of all the responses for the concept of day and night demonstrated that the majority of Chinese students in Year 5 were capable of expressing and reasoning a scientific concept within the concrete- symbolic mode. As with the fractions question, tw id Responses within the first cycle (U1, M1, R While students recognised that daylight meant that one side of the Earth received day and the other side night, their explanations of how and why this occurred were limited. Interestingly, a number of alternative conceptions emerged in relation to ‘the Sun rising and falling’ and ideas about the ‘moon only being visible at night’: towards the Moon, night is coming, because the Moon is dark. When the Earth moves towards the Sun, the day is coming (U1 with focus on movement of the Earth). The side of the Earth facing the Sun is day, otherwise it is night. The Earth is round, it moves around the Sun. The light from the Sun reflects on the Earth, that is how we get day and night (M1 with focus on movement of the Earth, the position of the Earth and the Sun, and descriptions about the behaviour of these bodies). 397 2006 POSTGRADUATE CONFERENCE How does the Earth get day and night? I think it is because the Earth spins all the time. The Sun doesn’t move at all. It takes 24 hours for the Earth to spin one cycle. The Earth gets day is because one side of the Earth is facing the Sun, and the other side is opposite the Sun, so it e then able to use this information to explain that the length of aylight and night varied depending on where one was positioned on the Earth. Therefore, explanations in gets night (R1 with the interrelationships between factors identified and a logical endpoint attained). In the second cycle of the concrete-symbolic mode (U2, M2, R2), explanations focused on the spinning of the Earth on its axis. There was recognition that it was this spinning that caused light on one side of the Earth and darkness on the other. Some students wer d this cycle demonstrated a scientific description of one or more factors involved in the phenomena and how these factors interrelate to each other: The Earth is moving, and the Moon and the Sun are moving too. The Sun is the centre of the Solar system. The Earth spins on the axis, if it doesn’t meet the Moon at the same spot, the Earth gets day. Otherwise, the Moon will shadow the Earth, so the Earth gets night (U2 with realisation that the axis is critical to day and night). The Earth spins on its axis from West to East while it orbits around the Sun from west to east. tThe Earth is spinning causes the change of the day and nigh , its orbiting around the Sun brings important, but also direction of spin similar to those identified for Year 5 and 6 students in Australia. This adds further support to he applicability of the SOLO model for Chinese students. onsiderations Emerging • Need to ensure a degree of consistency in how the data were collected. the change of the four seasons (M with the axis identified as 2 although an alternative conception in this example). Clearly, there is a difference in thinking of students between the first and second cycles of the concrete- symbolic mode. In the case of the first cycle, students described planetary movement generally while those in the second cycle demonstrated some degree of explaining the process behind day and night. Again, these results were suggesting t Methodological C A number of operational and technical issues emerged during the pilot study that required careful consideration in developing the design for the main study. These included the: • Use of questions that were contextually relevant to the students • Importance of accuracy in the translation process • Need for a larger student sample to obtain a variety of responses • Opportunity for students to provide their ‘best possible’ responses 398 UNIVERSITY OF NEW ENGLAND First, in relation to the questions used with students, the fraction item raised concerns because some of the students did not understand ‘a cake’ as this was not a commonly used term in Chinese culture. Although the ear 5 teacher (in China) had checked the question prior to its use, students raised questions that suggested data was the process used to ensure the ccuracy of translation. As the process used for the pilot appeared successful, it was adopted for the main vels of the SOLO model. To address this issue, the entire ohort of Year 5 students was invited to complete the questionnaires in the main study. This resulted in 150 ould collect the data in China. Most importantly, her presence ould ensure consistency in the information provided to students and the questionnaire process. that minimised the impact of potential ‘threats’ to the study. In addition, it ensured that the researcher was Y that the concept was ambiguous. While cakes of various shapes and sizes were relevant for the majority of students, this was clearly not the case across the board and suggested that an alternative object should be used in further research. Subsequently, this question was altered for the main study. Second, the fundamental aspect underpinning the validity of the a study. Initially, the researcher translated all written responses to each question. During a meeting with a Chinese-speaking senior academic from UNE, all of the responses for each of the questions were checked for accuracy. Third, the pilot study identified that selection of students from one or two classes in Year 5 did not provide a range of responses representative of the various le c participants answering the questions. Fourth, additional probing of students about particular statements made in their explanations would improve the quality of the data obtained. Consequently, interviews became a feature of the main study as they provided an opportunity to explore students’ understandings at a deeper level, clarify student explanations, and also allow any changes in thinking to be identified. Therefore, approximately 25% of students in the school Year 5 cohort were interviewed using purposive sampling. Finally, it was decided that the researcher sh w Furthermore, it would allow her to conduct the interviews in person, hence improve the depth of data obtained. The other major advantage was that it allowed the researcher to gain a greater awareness of the educational context while allowing observations of classrooms and interviewing of teachers about their views of teaching and learning to be undertaken. Although not incorporated into the final study, these insights provided an important background in interpreting the results at a broader level. Overall, these findings demonstrate clearly the necessity of undertaking a pilot study as a means of trialling and fine-tuning research techniques thereby ensuring the potential for greater reliability and validity of the data. In planning for the main study, each of these issues was addressed resulting in a well-structured design 399 2006 POSTGRADUATE CONFERENCE suitably confident in knowing what needed to be undertaken and how this should be achieved in an ethical manner. Conclusion The study outlined in this paper and the findings generated demonstrate the applicability of the SOLO model in the Chinese educational context. As with the Australian students, two learning cycles were identifiable in the concrete-symbolic mode for both questions. However, equally important were the methodological issues that emerged as the researcher worked through the data set. Careful consideration of these factors at this stage ensured a sound and robust design for the main study thereby maximising the validity of the final results. Unexpectedly, however, the pilot study identified a number of logistical requirements that could have hampered the research if not considered carefully prior to commencing the main study in a foreign country. This is an important outcome given that many international students work away from their supervisors during e data collection phase with minimal contact available. A staged research design that is carefully planned th helps ensure that most of the major difficulties are dealt with prior to the researcher’s departure. 400 UNIVERSITY OF NEW ENGLAND REFERENCES Bell, B. & Cowie, B. 2001, 'The characteristics of formative assessment in science education', Science ciation for Research in Science Teaching, April in New Orleans. ck, P.& William, D. 1998, 'Assessment and classroom learning', Assessment in Education, vol.5, no.1, ry, Sage, Thousand & Leung, K. 1997, Methods and Data Analysis for Cross-Cultural Research, Sage ousand Oaks, California. 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