Individual differences in learning from worked examples by senior secondary mathematics students

The primary purpose of this research was to examine individual differences in learning from worked examples. By integrating cognitive style theory and cognitive load theory, it was hypothesised that an interaction existed between individual cognitive style and the structure and presentation of worked examples in their effect upon subsequent student problem solving. In particular, it was hypothesised that Analytic-Verbalisers, Analytic-Imagers, and Wholist-lmagers would perform better on a posttest after learning from structured-pictorial worked examples than after learning from unstructured worked examples. For Analytic-Verbalisers it was reasoned that the cognitive effort required to impose structure on unstructured worked examples would hinder learning. Alternatively, it was expected that Wholist-Verbalisers would display superior performances after learning from unstructured worked examples than after learning from structured-pictorial worked examples. The images of the structured-pictorial format, incongruent with the Wholist-Verbaliser style, would be expected to split attention between the text and the diagrams. The information contained in the images would also be a source of redundancy and not easily ignored in the integrated structured-pictorial format. Despite a number of authors having emphasised the need to include individual differences as a fundamental component of problem solving within domainspecific subjects such as mathematics, few studies have attempted to investigate a relationship between mathematical or science instructional method, cognitive style, and problem solving. Cognitive style theory proposes that the structure and presentation of learning material is likely to affect each of the four cognitive styles differently. No study could be found which has used Riding's (1997) model of cognitive style as a framework for examining the interaction between the structural presentation of worked examples and an individual's cognitive style. 269 Year 12 Mathematics B students from five urban and rural secondary schools in Queensland, Australia participated in the main study. A factorial (three treatments by four cognitive styles) between-subjects multivariate analysis of variance indicated a statistically significant interaction. As the difficulty of the posttest components increased, the empirical evidence supporting the research hypotheses became more pronounced. The rigour of the study's theoretical framework was further tested by the construction of a measure of instructional efficiency, based on an index of cognitive load, and the construction of a measure of problem-solving efficiency, based on problem-solving time. The consistent empirical evidence within this study that learning from worked examples is affected by an interaction of cognitive style and the structure and presentation of the worked examples emphasises the need to consider individual differences among senior secondary mathematics students to enhance educational opportunities. Implications for teaching and learning are discussed and recommendations for further research are outlined.

Learning power and language expressiveness

The topic of the present work is to study the relationship between the power of the learning algorithms on the one hand, and the expressive power of the logical language which is used to represent the problems to be learned on the other hand. The central question is whether enriching the language results in more learning power. In order to make the question relevant and nontrivial, it is required that both texts (sequences of data) and hypotheses (guesses) be translatable from the “rich” language into the “poor” one. The issue is considered for several logical languages suitable to describe structures whose domain is the set of natural numbers. It is shown that enriching the language does not give any advantage for those languages which define a monadic second-order language being decidable in the following sense: there is a fixed interpretation in the structure of natural numbers such that the set of sentences of this extended language true in that structure is decidable. But enriching the original language even by only one constant gives an advantage if this language contains a binary function symbol (which will be interpreted as addition). Furthermore, it is shown that behaviourally correct learning has exactly the same power as learning in the limit for those languages which define a monadic second-order language with the property given above, but has more power in case of languages containing a binary function symbol. Adding the natural requirement that the set of all structures to be learned is recursively enumerable, it is shown that it pays o6 to enrich the language of arithmetics for both finite learning and learning in the limit, but it does not pay off to enrich the language for behaviourally correct learning.

Automatic spoken language identification utilizing acoustic and phonetic speech information

Automatic spoken Language Identi¯cation (LID) is the process of identifying the language spoken within an utterance. The challenge that this task presents is that no prior information is available indicating the content of the utterance or the identity of the speaker. The trend of globalization and the pervasive popularity of the Internet will amplify the need for the capabilities spoken language identi¯ca- tion systems provide. A prominent application arises in call centers dealing with speakers speaking di®erent languages. Another important application is to index or search huge speech data archives and corpora that contain multiple languages. The aim of this research is to develop techniques targeted at producing a fast and more accurate automatic spoken LID system compared to the previous National Institute of Standards and Technology (NIST) Language Recognition Evaluation. Acoustic and phonetic speech information are targeted as the most suitable fea- tures for representing the characteristics of a language. To model the acoustic speech features a Gaussian Mixture Model based approach is employed. Pho- netic speech information is extracted using existing speech recognition technol- ogy. Various techniques to improve LID accuracy are also studied. One approach examined is the employment of Vocal Tract Length Normalization to reduce the speech variation caused by di®erent speakers. A linear data fusion technique is adopted to combine the various aspects of information extracted from speech. As a result of this research, a LID system was implemented and presented for evaluation in the 2003 Language Recognition Evaluation conducted by the NIST.

A programming language for software components

Component software has many benefits, most notably increased software re-use; however, the component software process places heavy burdens on programming language technology, which modern object-oriented programming languages do not address. In particular, software components require specifications that are both sufficiently expressive and sufficiently abstract, and, where possible, these specifications should be checked formally by the programming language. This dissertation presents a programming language called Mentok that provides two novel programming language features enabling improved specification of stateful component roles. Negotiable interfaces are interface types extended with protocols, and allow specification of changing method availability, including some patterns of out-calls and re-entrance. Type layers are extensions to module signatures that allow specification of abstract control flow constraints through the interfaces of a component-based application. Development of Mentok's unique language features included creation of MentokC, the Mentok compiler, and formalization of key properties of Mentok in mini-languages called MentokP and MentokL.

Developing speaking assessment tasks to reflect the 'social turn' in language testing

Interactional competence has emerged as a focal point for language testing researchers in recent years. In spoken communication involving two or more interlocutors, the co-construction of discourse is central to successful interaction. The acknowledgement of co-construction has led to concern over the impact of the interlocutor and the separability of performances in speaking tests involving interaction. The purpose of this article is to review recent studies of direct relevance to the construct of interactional competence and its operationalisation by raters in the context of second language speaking tests. The review begins by tracing the emergence of interaction as a criterion in speaking tests from a theoretical perspective, and then focuses on research salient to interactional effectiveness that has been carried out in the context of language testing interviews and group and paired speaking tests.

Generalised self-efficacy in relation to the life transitions of adult learners in a university setting : towards a narrative constructivist model of self-regulation

This paper demonstrates a model of self-regulation based on a qualitative research project with adult learners undertaking an undergraduate degree. The narrative about the participant’s life transitions, co-constructed with the researcher, yielded data about their generalised self-efficacy and resulted in a unique self-efficacy narrative for each participant. A model of self-regulation is proposed with potential applications for coaching, counselling and psychotherapy. A narrative method was employed to construct narratives about an individual’s self-efficacy in relation to their experience of learning and life transitions. The method involved a cyclical and iterative process using qualitative interviews to collect life history data from participants. In addition, research participants completed reflective homework tasks, and this data was included in the participant’s narratives. A highly collaborative method entailed narratives being co-constructed by researcher and research participants as the participants were guided in reflecting on their experience in relation to learning and life transitions; the reflection focused on behaviour, cognitions and emotions that constitute a sense of self-efficacy. The analytic process used was narrative analysis, in which life is viewed as constructed and experienced through the telling and retelling of stories and hence the analysis is the creation of a coherent and resonant story. The method of constructing self-efficacy narratives was applied to a sample of mature aged students starting an undergraduate degree. The research outcomes confirmed a three-factor model of self-efficacy, comprising three interrelated stages: initiating action, applying effort, and persistence in overcoming difficulties. Evaluation of the research process by participants suggested that they had gained an enhanced understanding of self-efficacy from their participation in the research process, and would be able to apply this understanding to their studies and other endeavours in the future. A model of self-regulation is proposed as a means for coaches, counsellors and psychotherapists working from a narrative constructivist perspective to assist clients facing life transitions by helping them generate selfefficacious cognitions, emotions and behaviour.