Theories of learning mathematics

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies – or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. So, for healthy theories on development to occur, four Darwinian functions should function: (a) variation – avoid orthodoxy and encourage divergent thinking, (b) selection – submit all assumptions and innovations to rigorous testing, (c) diffusion – encourage the shareability of new and/or viable ways of thinking, and (d) accumulation – encourage the reuseability of viable aspects of productive innovations.

Evaluation of the "reconceptualising early mathematics learning" project

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure enables mathematical thinking and simple forms of generalisation from an early age. The project aims to promote a strong foundation for mathematical development by focusing on critical, underlying features of mathematics learning. This paper provides an overview of key aspects of the assessment and intervention, and analyses of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in the evaluation throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ assessment and a Pattern and Structure Assessment (PASA) interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a relatively short period of time.

An English-translated parallel corpus for the CJK Wikipedia collections

In this paper, we describe a machine-translated parallel English corpus for the NTCIR Chinese, Japanese and Korean (CJK) Wikipedia collections. This document collection is named CJK2E Wikipedia XML corpus. The corpus could be used by the information retrieval research community and knowledge sharing in Wikipedia in many ways; for example, this corpus could be used for experimentations in cross-lingual information retrieval, cross-lingual link discovery, or omni-lingual information retrieval research. Furthermore, the translated CJK articles could be used to further expand the current coverage of the English Wikipedia.

Cross-Lingual knowledge discovery : Chinese-to-English article linking in Wikipedia

In this paper we examine automated Chinese to English link discovery in Wikipedia and the effects of Chinese segmentation and Chinese to English translation on the hyperlink recommendation. Our experimental results show that the implemented link discovery framework can effectively recommend Chinese-to-English cross-lingual links. The techniques described here can assist bi-lingual users where a particular topic is not covered in Chinese, is not equally covered in both languages, or is biased in one language; as well as for language learning.

SnowSports interactive a global start-up's challenges

A case study based on the experiences of (at the time of writing) Brisbane-based start-up SnowSports Interactive and their plans for global expansion. This case study questions whether SnowSports interactive is ready for global expansion, and if so which country should be its primary target? Once a country has been chosen, how should SnowSports approach and enter the market? This case study prompts business (in particular international business students) to consider a company's readiness in entering a global market, utlising evaluating tools in a wide range of discipline - product, human resources, capital, busines strategy. Furthermore students are asked to match SnowSports' unique characteristics with a country and an entry strategy. Ability to answer questions posed in this case study will demonstrate high level understanding in entrepreneurship and innovation, international business strategy, and cultural awareness; and demonstrate ability in theoretical and framework application

Urban renewal, migration and memories : the affordances of place-based pedagogies for developing immigrant students’ literate repertoires

This paper reports on the new literacy demands in the middle years of schooling project in which the affordances of placed-based pedagogy are being explored through teacher inquiries and classroom-based design experiments. The school is located within a large-scale urban renewal project in which houses are being demolished and families relocated. The original school buildings have recently been demolished and replaced by a large ‘superschool’ which serves a bigger student population from a wider area. Drawing on both quantitative and qualitative data, the teachers reported that the language literacy learning of students (including a majority of students learning English as a second language) involved in the project exceeded their expectations. The project provided the motivation for them to develop their oral language repertoires, by involving them in processes such as conducting interviews with adults for their oral histories, through questioning the project manager in regular meetings, and through reporting to their peers and the wider community at school assemblies. At the same time students’ written and multimodal documentation of changes in the neighbourhood and the school grounds extended their literate and semiotic repertoires as they produced books, reports, films, powerpoints, visual designs and models of structures.

Widening participation in university learning

This paper reports how one Australian university and the Queensland Department of Education and Training (DET) are working together to increase the number of school students from low socio-economic backgrounds enrolling in undergraduate university degrees. This innovative program involves university lecturers and school teachers working together in the delivery and assessment of four Bachelor of Education units (or subjects) to a cohort of Year eleven and twelve students at a secondary school. Focus group interviews collected data from 26 students, 7 parents, 4 school and 3 university staff to assess the effectiveness of the program. All stakeholders viewed the program as a highly valuable opportunity to experience university learning with 31 high school graduating students being made offers to enter full-time university in the 2010 and 2011. This positive result has particular significance in the current drive in Australia and elsewhere to increase the participation in higher education of young people from under-represented groups.

Link discovery for Chinese/English cross-language web information retrieval

Nowadays people heavily rely on the Internet for information and knowledge. Wikipedia is an online multilingual encyclopaedia that contains a very large number of detailed articles covering most written languages. It is often considered to be a treasury of human knowledge. It includes extensive hypertext links between documents of the same language for easy navigation. However, the pages in different languages are rarely cross-linked except for direct equivalent pages on the same subject in different languages. This could pose serious difficulties to users seeking information or knowledge from different lingual sources, or where there is no equivalent page in one language or another. In this thesis, a new information retrieval task—cross-lingual link discovery (CLLD) is proposed to tackle the problem of the lack of cross-lingual anchored links in a knowledge base such as Wikipedia. In contrast to traditional information retrieval tasks, cross language link discovery algorithms actively recommend a set of meaningful anchors in a source document and establish links to documents in an alternative language. In other words, cross-lingual link discovery is a way of automatically finding hypertext links between documents in different languages, which is particularly helpful for knowledge discovery in different language domains. This study is specifically focused on Chinese / English link discovery (C/ELD). Chinese / English link discovery is a special case of cross-lingual link discovery task. It involves tasks including natural language processing (NLP), cross-lingual information retrieval (CLIR) and cross-lingual link discovery. To justify the effectiveness of CLLD, a standard evaluation framework is also proposed. The evaluation framework includes topics, document collections, a gold standard dataset, evaluation metrics, and toolkits for run pooling, link assessment and system evaluation. With the evaluation framework, performance of CLLD approaches and systems can be quantified. This thesis contributes to the research on natural language processing and cross-lingual information retrieval in CLLD: 1) a new simple, but effective Chinese segmentation method, n-gram mutual information, is presented for determining the boundaries of Chinese text; 2) a voting mechanism of name entity translation is demonstrated for achieving a high precision of English / Chinese machine translation; 3) a link mining approach that mines the existing link structure for anchor probabilities achieves encouraging results in suggesting cross-lingual Chinese / English links in Wikipedia. This approach was examined in the experiments for better, automatic generation of cross-lingual links that were carried out as part of the study. The overall major contribution of this thesis is the provision of a standard evaluation framework for cross-lingual link discovery research. It is important in CLLD evaluation to have this framework which helps in benchmarking the performance of various CLLD systems and in identifying good CLLD realisation approaches. The evaluation methods and the evaluation framework described in this thesis have been utilised to quantify the system performance in the NTCIR-9 Crosslink task which is the first information retrieval track of this kind.

Principles of motor learning in ecological dynamics : a comment on functions of learning and the acquisition of motor skills (with reference to sport)

This paper provides a commentary on the contribution by Dr Chow who questioned whether the functions of learning are general across all categories of tasks or whether there are some task-particular aspects to the functions of learning in relation to task type. Specifically, they queried whether principles and practice for the acquisition of sport skills are different than what they are for musical, industrial, military and human factors skills. In this commentary we argue that ecological dynamics contains general principles of motor learning that can be instantiated in specific performance contexts to underpin learning design. In this proposal, we highlight the importance of conducting skill acquisition research in sport, rather than relying on empirical outcomes of research from a variety of different performance contexts. Here we discuss how task constraints of different performance contexts (sport, industry, military, music) provide different specific information sources that individuals use to couple their actions when performing and acquiring skills. We conclude by suggesting that his relationship between performance task constraints and learning processes might help explain the traditional emphasis on performance curves and performance outcomes to infer motor learning.

Basic cognitive experiences and definitions in the Longman Dictionary of Contemporary English

This study applies theories of cognitive linguistics to the compilation of English learners’ dictionaries. Specifically, it employs the concepts of basic level categories and image schemas, two basic cognitive experiences, to examine the ‘definition proper’ of English dictionaries for foreign learners. In the study, the definition proper refers to the constituent part of a reference work that provides an explanation of the meanings of a word, phrase or term. This rationalization mainly consists of defining vocabulary, sense division and arrangement, as well as the means of defining (i.e. paraphrase, true definition, functional definition, and pictorial illustration). The aim of the study is to suggest ways of aligning the consultation and learning of definitions with dictionary users’ cognitive experiences. For this purpose, an analysis of the definition proper of the fourth edition of the Longman Dictionary of Contemporary English (LDOCE4) from the perspective of basic cognitive experiences has been undertaken. The study found that, generally, the lexicographic practices of LDOCE4 are consistent with theories of cognitive linguistics. However, there exist shortcomings that result from disregarding basic cognitive experiences.

The association between motivation in school physical education and self-reported physical activity during Finnish junior high school : a self-determination theory approach

The main purpose of this longitudinal study was to investigate the role of motivational climates, perceived competence and motivational regulations as antecedents of self-reported physical activity during junior high school years. The participants included 237 Finnish students (101 girls, 136 boys) that were 13 years old at the first stage of the study. Students completed the motivational climate and perceived competence questionnaires at Grade 7, motivation towards physical education questionnaire at Grade 8, and self-reported physical activity questionnaire at Grade 9. A path analysis revealed a path from task-involving motivational climate via perceived competence and intrinsic motivation to self-reported physical activity. Perceived competence and intrinsic motivation were statistically significant mediators between task-involving motivational climate and self-reported physical activity. This finding supports the four-stage causal sequence model of motivation.

The enactment of formative assessment in English language classrooms in two Chinese universities : teacher and student responses

The College English Curriculum Requirements (CECR), announced by the Chinese Ministry of Education in 2007, recommended the inclusion of formative assessment into the existing summative assessment framework of College English. This policy had the potential to fundamentally change the nature of assessment and its role in the teaching and learning of English in Chinese universities. In order to document and analyse these changes, case studies involving English language teachers and learners were undertaken in two Chinese Universities: one a Key university in the national capital; the other a non-Key university in a western province. The case study design incorporated classroom observations and interviews with English language teachers and their students. The type and focus of feedback and the engagement of students in assessment were analysed in the two contexts. Fundamental to the analysis was the concept of enactment, with the focus of this study on the ways that policy ideas and principles were enacted in the practices of the Chinese university classroom. Understandings of formative assessment as applied in contexts other than the predominantly Western, Anglophone contexts from where many of its principles derive, are offered.

The OO files : providing online formative feedback on Contract Law learning in a narrative setting

Feedback, both formative and summative, enables students to reflect on their understandings and to restructure their thinking to develop their capabilities. It can also encourage positive motivation and help boost self-esteem. Online multiple choice questions can be an efficient and effective means of providing timely formative feedback. At the same time, locating learning in a narrative environment can facilitate engaging and effective learning experiences. Narratives can help learners to navigate through information and support cognitive and imaginative engagement. This article will discuss The 00 Files, an online suite of modules containing multiple choice questions situated in the narrative of a fictional law firm. It notes student responses to the program and discusses lessons that may be learnt from its development which may be of assistance to academics considering the development of similar programs for their courses.

Representative learning design in dynamic interceptive actions

The overarching aim of this thesis was to investigate how processes of perception and action emerge under changing informational constraints during performance of multi-articular interceptive actions. Interceptive actions provide unique opportunities to study processes of perception and action in dynamic performance environments. The movement model used to exemplify the functionally coupled relationship between perception and action, from an ecological dynamics perspective, was cricket batting. Ecological dynamics conceptualises the human body as a complex system composed of many interacting sub-systems, and perceptual and motor system degrees of freedom, which leads to the emergence of patterns of behaviour under changing task constraints during performance. The series of studies reported in the Chapters of this doctoral thesis contributed to understanding of human behaviour by providing evidence of key properties of complex systems in human movement systems including self-organisation under constraints and meta-stability. Specifically, the studies: i) demonstrated how movement organisation (action) and visual strategies (perception) of dynamic human behaviour are constrained by changing ecological (especially informational) task constraints; (ii) provided evidence for the importance of representative design in experiments on perception and action; and iii), provided a principled theoretical framework to guide learning design in acquisition of skill in interceptive actions like cricket batting.

Connecting across continents : collaborative learning in a Web 2.0 world

Purpose – The article aims to review a university course, offered to students in both Australia and Germany, to encourage them to learn about designing, implementing, marketing and evaluating information programs and services in order to build active and engaged communities. The concepts and processes of Web 2.0 technologies come together in the learning activities, with students establishing their own personal learning networks (PLNs). Design/methodology/approach – The case study examines the principles of learning and teaching that underpin the course and presents the students' own experiences of the challenges they faced as they explored the interactive, participative and collaborative dimensions of the web. Findings – The online format of the course and the philosophy of learning through play provided students with a safe and supportive environment for them to move outside of their comfort zones, to be creative, to experiment and to develop their professional personas. Reflection on learning was a key component that stressed the value of reflective practice in assisting library and information science (LIS) professionals to adapt confidently to the rapidly changing work environment. Originality/value – This study provides insights into the opportunities for LIS courses to work across geographical boundaries, to allow students to critically appraise library practice in different contexts and to become active participants in wider professional networks.