Constructivism and constitutionalism: Some implications for the first mathematics education

There is a dualistic assumption underlying constructivism: thinking takes place in an inner subjective world, divorced from the outer objective reality and knowledge is constructed there by the individual through material and mental acts. In a phenomenological framework the fundamental unity between human beings and the world in which they live is assumed. Knowledge represents ways of seeing, experiencing, thinking about the world and it is constituted through the internal relation between the knower (subject) and the know (object). It is shown that these two kinds of ontological and epistemological assumption have radically different implications for how the development of arithmetic skills is seen and conceptualized

The early language gap between first- and second-language learners: acquisition of Chinese characters among preschoolers

For culturally and linguistically diverse children, early second language (L2) development is important for school achievement and social inclusion. These children face challenges in acquiring L2, especially in Hong Kong, where the dominant Chinese language contrasts strongly with their home languages. Studies that compared the language abilities of first language (L1) and L2 students in English-speaking contexts have reported young L2 learners’ disadvantage in using the dominant language in oral language and comprehension at school entry. The findings raise the question of whether L2 learners who fall behind their L1 peers in language abilities will be further disadvantaged, showing a weaker development gradient. This study used the Chinese Character Acquisition Assessment (CCAA) to compare character acquisition of 491 L2 children aged from 3 to 6 years against that of 240 of their L1 peers from Hong Kong kindergartens. The CCAA is comprised of six subtests and assesses children’s abilities to make associations among character written form (orthography), sound, and meaning. Results showed that L2 learners had greater development in meaning and sound associations across class levels, implying that they may first develop oral language related abilities. In addition, results indicate that diverging gaps between L1 and L2 learners’ Chinese character acquisition existed across class levels for the associations involving written character form, but not in regard to associations between character meaning and sound. This study highlights the Chinese learning needs of L2 preschoolers and provides understanding of their abilities in mapping among character written forms, sounds, and meanings. The findings suggest the importance of supporting L2 children’s oral language at earlier stages of Chinese learning, and the need to provide instructional support to compensate for their relative weakness in literacy at school entry

The university of learning: beyond quality and competence

This book looks at the theory and practice of learning and how universities can improve their quality and competence. It tackles the past failure of the quality and competence movements and advocates a move towards 'Universities of Learning'. The authors advocate an integration of elements that are often dealt with separately--theory and practice, teaching and research, and the levels of institution and individual--and handle these dimensions of integration in conjunction with each other

Learning in and out of university : Aboriginal and Torres Strait Islander students’ conceptions and strategies used to learn

Research suggests that students’ approaches to learning and learning outcomes are closely related to their conceptions of learning. This paper describes a phenomenographically inspired investigation into conceptions of formal learning held by 22 Aboriginal and Torres Strait Islander students from three Australian universities in Queensland; experiences of informal learning, reasons for studying and strategies used to learn were also investigated. The attrition rate for these students in tertiary education is higher than that of any other group of students. It was hoped that information gained may delineate factors that contribute to high attrition rates and therefore inform courses of action that may lead to improved teaching and learning practices for these students. Additionally, success in tertiary education for Aboriginal and Torres Strait Islander students may increase their involvement in mainstream society. Results showed that they view and approach university learning in much the same way as other university students. It was also apparent that, generally, the strategies these students used did not match the conceptions of learning they held. An interesting result was the difference between the conceptions of formal learning and explanations of informal learnin

What is made possible to learn when using the variation theory of learning in teaching mathematics?

The variation theory of learning emphasizes variation as a necessary condition for learners to be able to discern new aspects of an object of learning. In a substantial number of studies, the theory has been used to analyze teaching and students’ learning in classrooms. In mathematics education, variation theory has also been used to explore variation in sets of instructional examples. For example, it has been reported how teachers, by using variation and invariance within and between examples, can help learners to engage with mathematical structure. In this paper, we describe the variation theory of learning, its underlying principles, and how it might be appropriated by teachers. We illustrate this by an analysis of one teacher’s teaching before and after he participated in three lesson studies based on variation theory. Both the theory and the empirical illustration focus on ‘what is made possible to learn’ in different learning situations. We show that in the two analyzed lessons, different things were made possible to learn