This study aimed to model mathematics growth of students from Primary 3 to Secondary 3 from two approaches, namely, growth in content domains, and in cognitive domains. The sample consisted of 866 Hong Kong students who were followed longitudinally from Primary 3 to Secondary 3. The data were originally collected by the Education Bureau of Hong Kong. Plausible values of achievements at Primary 3, Primary 6, and Secondary 3 in three cognitive domains (Knowing, Applying, and Reasoning) were obtained using between-item multidimensional Rasch partial credit modelling. A modified autoregressive cross-lagged design was used to predict later achievement in the cognitive domains by prior achievements in these domains. Analysis was repeated for growth in content domains (Number, Shape and Space, Measures, Data Handling, and Algebra). Analysis showed that students' later mathematics achievement was strongly predicted by their previous achievement in the Knowing and the Number domains.
[Copyright © 2014 Education Bureau, HKSARG.]

In educational settings, action research can be used in a variety of areas such as (1) teaching methods; (2) learning strategies; (3) evaluative procedures; (4) attitudes and values; (5) continuing professional development of teachers and; (6) administration (Cohen, Manion & Morrison, 2000). Due to various reasons, there are few action research in schools and in higher education in Hong Kong (Li, Yu, Lam & Fok, 1999; Kember & Gow, 1992). Even in other place of the world, action research with empirical data is not much in teacher education (Ross & Bondy, 1996). This study is an investigation in using the KWL method to support teacher educators in conducting action research for enhancing learning of student-teachers as well as in continuing professional development of teacher educators in improving teaching skills, increasing powers of analysis, and heightening self-awareness of one's teaching. Participants comprised 32 student-teachers who were currently enrolled in a three year teacher certificate teacher education programme at the Hong Kong Institute of Education. The KWL method can record "what they know (K) and what they want (W) before lesson" as well as "what they learn (L) after lesson". Records of their prior knowledge (K), their expectation (W), their learning (L) can be analyzed to explore the structure of their learning and its changes. All these information together with the data collected in the action research cycle (plan, act, observe and reflect) will give much hints and insights to the teacher educators to reflect on their own teaching.

Data collected for accountability purposes often involve nested or hierarchical data structure. For instance, in the development of a value-added indicator system, achievement data are collected at the student-level but inferences are to be made at the school and system levels. Here, students are nested within classes, classes are nested within schools, and schools within regions. Since the late 1980s multilevel modelling has been used as a standard approach to handle such nested data structure. Research has shown that failure to apply multilevel models to nested data structure leads to wrong statistical inferences. Furthermore, much valuable information may be lost if the nested data structure is not modelled explicitly. In the last twenty years, the application of multilevel modelling has been extended to areas other than the handling of nested data structure. Multilevel modelling can now be applied for effective analysis of complicated data structures, including longitudinal data (e.g. growth trajectory), multivariate data (e.g. achievement in the four skills in the learning of English), discrete outcome data (e.g. students’ choice of entry to universities versus work), multiple membership data (e.g. the modelling of students’ mobility across schools in the estimation of the value added by schools to academic achievement), and cross-classified data structure (e.g. secondary schools taking students from a number of ‘feeder’ primary schools). The presentation will provide a non-technical introduction to multilevel modelling. Examples will be drawn from the value-added indicator system of the Hong Kong Special Administrative Region, and research on self-directed learning using the latest version of the MlwiN software package (Goldstein, 2003). Strengths and weaknesses of multilevel modelling will be discussed in the analyses of these real data.

The use of Rasch measurement in the high-stakes testing of educational achievement increases at an outstanding rate. It provides the psychometric background for system-wide examinations in Hong Kong, Australian national beachmarking testing and many educational systems in the US. Its use in Computer Adaptive Testing is fundamental to the in-school assessment systems provided by NWEA in the US and the CEM Centre in the UK. More important for APERA delegates is the growing use of Rasch measurement for small and large scale educational research projects conducted in schools and universities by academic researchers. The development of sample independent invariant measures for educational research allows researchers to address problems that remained intractable under previous analytical methods. Presenters in this symposium will provide an international perspective on the use of Rasch scales in projects including student feedback about teaching, gifted students, mathematics education, self-efficacy, dyslexia in Chinese language and readiness for early school learning.