Ngai-Ying Wong

Student Engagement in Mathematics: Development of Instrument and Validation of Construct (1)

Universal education has aggravated the problems of students’ disengagement in learning, highlighting in particular, a greater range of motivations to learn and wider diversification in students’ interests. Students’ engagement with curriculum has become a crucial element in classroom learning. How we cultivate their involvement in the curriculum may be seen as being far more important than the epistemological consideration in the design of the school curriculum. Though aspects of behavioural, affective and cognitive engagements have been revealed in literature, we are still in need of a validated instrument that measures student engagement for further research. In the present study, an instrument of student engagement in the subject area of mathematics was developed through grounded research. Its validity was established by statistical methods

Cross-Cultural Validation of Models of Approaches to Learning: An Application of Confirmatory Factor Analysis.

Abstract Six structural equation models were tested by analysing responses to the Learning Process Questionnaire of 10 samples of primary and secondary school students from Nigeria, Zimbabwe, Malaysia, Beijing, Hong Kong and Canada. Confirmatory factor analyses provided general support for the cross‐cultural within‐construct validity of the questionnaire. As predicted, the dimensions of deep and surface approaches to learning received cross‐cultural support, but the positioning of the achieving dimension varied across cultures. This is in line with the notion that students who adopt an achieving approach will adopt different strategies which will be likely to maximise their achievement according to particular course and teacher characteristics.

The lived space of mathematics learning

Abstract Students’ conceptions of mathematics and mathematics learning are important research issues in mathematics education, as they bear significant relationship to student’s mathematics performance. In this paper, as an attempt to reconceptualise students’ conceptions of mathematics, the notion of “the lived space of mathematics learning” is introduced, referring to the space experienced by learners and spanned by all the dimensions in which problems in mathematics vary from each other, and from non-mathematical problems. This “lived space” constrains what the learners will regard as mathematics and as mathematics learning, and constrains therefore their conceptions of mathematics and mathematics learning. Based on this understanding, the present study is aimed at investigating the relationship between students’ conceptions of mathematics and how they actually tackle mathematical problems. By using a variety of open-ended non-routine mathematical problems, the extent of variations in students’ conceptions of mathematics and in their lived space of mathematics learning were explored. Non-routine mathematics problems as tasks could bring about a sharp contrast with the usual problems in their classroom learning. Students were interviewed after they were asked to attempt several mathematical problems, some being routine and some open-ended. Through a detailed analysis of students’ interview protocols, characteristic features of their conceptions of mathematics and mathematics learning have been revealed. These were discussed in terms of the existing classroom teaching and examination culture. It is argued that the present notion of the lived space can also point to ways to broaden students’ current narrow conceptions of mathematics.

A Longitudinal Study of the Psychosocial Environmental and Learning Approaches in the Hong Kong Classroom

Abstract Structural equation models linking cognitive and affective factors, approach to learning, and perceptions of the actual and preferred mathematics classroom environments were tested in a longitudinal study involving 356 secondary school students in Hong Kong. Models of acceptable fit that clarified the effects of classroom environment on how students learn and the outcomes they achieve were obtained. Numerous significant paths from prior learning experience to environmental variables were identified; the most salient path from classroom environment to learning outcomes was that between an enjoyable classroom environment and cognitive achievement. An enjoyable classroom environment mediated the causal relationship between a deep approach and high-level achievement. However, classroom environment did not seem to influence changes in approach to learning.

The Relationship among Mathematics Achievement, Affective Variables and Home Background.

One thousand seven hundred and sixty six secondary school students in Hong Kong participated in the present study, in which the relationship among mathematics achievement, affective variables and home background was investigated. It was found that mathematics achievement was most closely related with self-concept, academic self-concept and attitudes towards mathematics. Self- and parental expectations were the most influential factors to these affective variables. It was also found that Hong Kong students spent, on the average, over 33% of homework time on mathematics homework. The time spend on homework, however, did not exhibit significant correlation with mathematics achievement.

The Influence of Technology on the Mathematics Curriculum

There had been repeated calls for the use of information and communication technologies in education in general and in mathematics teaching in particular, to meet the challenges of the information age. Inclusion of calculators and computers into the mathematics curriculum is found in many systems around the world. By investigating the curriculum documents of six ‘Western’ countries (the United States, the United Kingdom, Australia, New Zealand, France, and the Netherlands) and eight ‘Far Eastern’ systems (Mainland China, Taiwan, Hong Kong, Macau, Japan, South Korea, Singapore, and Malaysia), we can visualise what impact technology on mathematics education is bringing about. By investigating the need for repositioning the mathematics curriculum in the last section, the author initiates a discussion on what is meant by ‘mathematics’ and by ‘mathematics education’.

Comparing Primary and Secondary Mathematics Teachers’ Beliefs about Mathematics, Mathematics Learning and Mathematics Teaching in Hong Kong and Australia

This study has demonstrated a number of important aspects about the need for the consideration of teachers’ beliefs about mathematics, mathematics learning and mathematics teaching. Foremost among these is that, as measured on the beliefs instrument used here, teachers in Hong Kong, at both primary and secondary levels, espouse significantly different beliefs from those espoused by their NSW counterparts. If we believe that teachers’ beliefs affect their teaching and that teaching affects student outcomes, then it is possible that the differences in beliefs which are highlighted by this study could help explain some of the differences in student achievement which have been reported in international studies.

Developing an Instrument for Identifying Secondary Teachers’ Beliefs About Education for Sustainable Development in China

Education for Sustainable Development (ESD) has been recently recognized as an important area in the new Chinese educational reform. As teachers play a pivotal role, knowing and developing an effective and easy-to-use instrument for tapping teachers’ beliefs is essential. This article reports an attempt to develop an instrument with mixed methods. The finalized instruments comprise two subscales with satisfactory reliability indices obtained. Sustainability values (VSD) consists of four dimensions: respect and care for the community of life; ecological integrity; social and economic justice; and democracy, nonviolence, and peace. Teaching beliefs of ESD (TESD) consists of three dimensions: relevance to daily life; students’ need in the future; and integrated teaching. With these validated instruments, future research and potential problems will be less strenuous.

Effects of Self-Monitoring and Perceived Approval on Delinquent Behavior Among Hong Kong Adolescents

It has been established that perceived approval from relevant others is related to delinquent behavior. The aim of the present study was to investigate how this relationship was mediated by self- monitoring. Eight hundred twenty-eight students from Grade 7 to Grade 9 were asked to respond to a questionnaire that measured their self-monitoring, the frequency they committed delinquent acts, and the perceived approval of committing these acts from their parents, teachers, and friends. Regression analyses indicated that self- monitoring wax an interacting factor between perceived approval and delinquency. On further path analyses, it was found that self- monitoring acted as a mediating factor, and that the relationship between delinquent behavior and perceived approval was more apparent among high self- monitoring individuals.

Mathematics education in Hong Kong under colonial rule

Mathematics education in Hong Kong went through various stages of development under the period of British colonial rule for more than a century. Though modern ideas from the West were influential, they were blended with Chinese tradition and local pragmatism, and a localized mathematics curriculum was then eventually consolidated. This was a result of a careful striking of balance between laissez-faire and direct control. Looking back on such historical developments, one may gain insights into the issues induced by the current trend of managerialism and performativity.