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.

The nonconceptual gateway to early word learning

My research investigates why nouns are learned disproportionately more frequently than other kinds of words during early language acquisition (Gentner, 1982; Gleitman, et al., 2004). This question must be considered in the context of cognitive development in general. Infants have two major streams of environmental information to make meaningful: perceptual and linguistic. Perceptual information flows in from the senses and is processed into symbolic representations by the primitive language of thought (Fodor, 1975). These symbolic representations are then linked to linguistic input to enable language comprehension and ultimately production. Yet, how exactly does perceptual information become conceptualized? Although this question is difficult, there has been progress. One way that children might have an easier job is if they have structures that simplify the data. Thus, if particular sorts of perceptual information could be separated from the mass of input, then it would be easier for children to refer to those specific things when learning words (Spelke, 1990; Pylyshyn, 2003). It would be easier still, if linguistic input was segmented in predictable ways (Gentner, 1982; Gleitman, et al., 2004) Unfortunately the frequency of patterns in lexical or grammatical input cannot explain the cross-cultural and cross-linguistic tendency to favor nouns over verbs and predicates. There are three examples of this failure: 1) a wide variety of nouns are uttered less frequently than a smaller number of verbs and yet are learnt far more easily (Gentner, 1982); 2) word order and morphological transparency offer no insight when you contrast the sentence structures and word inflections of different languages (Slobin, 1973) and 3) particular language teaching behaviors (e.g. pointing at objects and repeating names for them) have little impact on children's tendency to prefer concrete nouns in their first fifty words (Newport, et al., 1977). Although the linguistic solution appears problematic, there has been increasing evidence that the early visual system does indeed segment perceptual information in specific ways before the conscious mind begins to intervene (Pylyshyn, 2003). I argue that nouns are easier to learn because their referents directly connect with innate features of the perceptual faculty. This hypothesis stems from work done on visual indexes by Zenon Pylyshyn (2001, 2003). Pylyshyn argues that the early visual system (the architecture of the "vision module") segments perceptual data into pre-conceptual proto-objects called FINSTs. FINSTs typically correspond to physical things such as Spelke objects (Spelke, 1990). Hence, before conceptualization, visual objects are picked out by the perceptual system demonstratively, like a finger pointing indicating ‘this’ or ‘that’. I suggest that this primitive system of demonstration elaborates on Gareth Evan's (1982) theory of nonconceptual content. Nouns are learnt first because their referents attract demonstrative visual indexes. This theory also explains why infants less often name stationary objects such as plate or table, but do name things that attract the focal attention of the early visual system, i.e., small objects that move, such as ‘dog’ or ‘ball’. This view leaves open the question how blind children learn words for visible objects and why children learn category nouns (e.g. 'dog'), rather than proper nouns (e.g. 'Fido') or higher taxonomic distinctions (e.g. 'animal').

Web searching interaction model based on user cognitive styles

As more and more information is available on the Web finding quality and reliable information is becoming harder. To help solve this problem, Web search models need to incorporate users’ cognitive styles. This paper reports the preliminary results from a user study exploring the relationships between Web users’ searching behavior and their cognitive style. The data was collected using a questionnaire, Web search logs and think-aloud strategy. The preliminary findings reveal a number of cognitive factors, such as information searching processes, results evaluations and cognitive style, having an influence on users’ Web searching behavior. Among these factors, the cognitive style of the user was observed to have a greater impact. Based on the key findings, a conceptual model of Web searching and cognitive styles is presented.

Assessing cognitive development in early childhood : a comparison of the Bayley-III and the Stanford-Binet fifth edition

The Bayley Scales of Infant Development, Third Edition (Bayley-III) and Stanford-Binet Intelligence Scale, Fifth Edition (SB5) were administered in a sample of 26 typically developing children (12 males and 14 females) aged 24 – 42 months. Children completed the assessments in two separate sessions, counterbalanced for order of administration. Scores on the two instruments were not significantly related, with the exception of the SB5 Knowledge score, which was moderately correlated with the Language score on the Bayley-III (r = .41, p = 0.04). Despite no other significant correlations, for 22 of the 26 children, scores were very consistent across the two instruments. Implications for test selection are discussed.

Cognitive processes and strategies employed by children to learn spatial representations

Children often have difficulties in learning spatial representations. This study investigated the effect of four different instructional formats on learning outcomes and strategies used when dealing with spatial tasks such as assembly procedures. It was hypothesised that instructional material that imposed least extraneous cognitive load would facilitate enhanced learning. Forty secondary students were presented with four types of instruction; orthographic drawing, isometric drawing, physical model and, isometric and physical model together. The findings provide evidence to suggest that working from physical models caused least extraneous cognitive load compared to the isometric and orthographic groups. The model group took less time, had more correctly completed models, required fewer extra looks, spent less time studying the instruction and made fewer errors. Problem decomposition, forward working and attending to information in the foreground of the graphical representation strategies were analysed.

Sequential development of algebra knowledge : a cognitive analysis

Learning to operate algebraically is a complex process that is dependent upon extending arithmetic knowledge to the more complex concepts of algebra. Current research has shown a gap between arithmetic and algebraic knowledge and suggests a pre-algebraic level as a step between the two knowledge types. This paper examines arithmetic and algebraic knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Results of a longitudinal study designed to investigate students' readiness for algebra are presented. Thirty-three students in Grades 7, 8, and 9 participated. A model for the transition from arithmetic to pre-algebra to algebra is proposed and students' understanding of relevant knowledge is discussed.

Personalizing the design of computer-based instruction to enhance learning

This paper reports two studies designed to investigate the effect on learning outcomes of matching individuals' preferred cognitive styles to computer-based instructional (CBI) material. Study 1 considered the styles individually as Verbalizer, Imager, Wholist and Analytic. Study 2 considered the bi-dimensional nature of cognitive styles in order to assess the full ramification of cognitive styles on learning: Analytic/Imager, Analytic/ Verbalizer, Wholist/Imager and the Wholist/Verbalizer. The mix of images and text, the nature of the text material, use of advance organizers and proximity of information to facilitate meaningful connections between various pieces of information were some of the considerations in the design of the CBI material. In a quasi-experimental format, students' cognitive styles were analysed by Cognitive Style Analysis (CSA) software. On the basis of the CSA result, the system defaulted students to either matched or mismatched CBI material by alternating between the two formats. The instructional material had a learning and a test phase. Learning outcome was tested on recall, labelling, explanation and problem-solving tasks. Comparison of the matched and mismatched instruction did not indicate significant difference between the groups, but the consistently better performance by the matched group suggests potential for further investigations where the limitations cited in this paper are eliminated. The result did indicate a significant difference between the four cognitive styles with the Wholist/Verbalizer group performing better then all other cognitive styles. Analysing the difference between cognitive styles on individual test tasks indicated significant difference on recall, labelling and explanation, suggesting that certain test tasks may suit certain cognitive styles.

Cognitive skills required in contemporary workplaces

This paper discusses some of the changes occurring in contemporary workplace practices, and the implications these have for the types of knowledge and skills required to work in such environments. Increasingly, workers need to be multi-skilled to function effectively in contemporary work environments. The nature of multi-skilling is explained in terms of cross-skilling, up-skilling and higher-order thinking skills, and the relevance of multi-skilling in today's workplaces is examined. Finally, the paper explores some factors affecting the acquisition of these desired skills in light of current work practices.

Wellness education : an integrated theoretical framework for fostering transformative learning

Optimum Wellness involves the development, refinement and practice of lifestyle choices which resonate with personally meaningful frames of reference. Personal transformations are the means by which our frames of reference are refined across the lifespan. It is through critical reflection, supportive relationships and meaning making of our experiences that we construct and reconstruct our life paths. When individuals are able to be what they are destined to be or reach their higher purpose, then they are able to contribute to the world in positive and meaningful ways. Transformative education facilitates the changes in perspective that enable one to contemplate and travel a path in life that leads to self-actualisation. This thesis argues for an integrated theoretical framework for optimum Wellness Education. It establishes a learner centred approach to Wellness education in the form of an integrated instructional design framework derived from both Wellness and Transformative education constructs. Students’ approaches to learning and their study strategies in a Wellness education context serve to highlight convergences in the manner in which students can experience perspective transformation. As they learn to critically reflect, pursue relationships and adapt their frames of reference to sustain their pursuit of both learning and Wellness goals, strengthening the nexus between instrumental and transformative learning is a strategically important goal for educators. The aim of this exploratory research study was to examine those facets that serve to optimise the learning experiences of students in a Wellness course. This was accomplished through three research issues: 1) What are the relationships between Wellness, approaches to learning and academic success? 2) How are students approaching learning in an undergraduate Wellness subject? Why are students approaching their learning in the ways they do? 3) What sorts of transformations are students experiencing in their Wellness? How can transformative education be formulated in the context of an undergraduate Wellness subject? Subsequent to a thorough review of the literature pertaining to Wellness education, a mixed method embedded case study design was formulated to explore the research issues. This thesis examines the interrelationships between student, content and context in a one semester university undergraduate unit (a coherent set of learning activities which is assigned a unit code and a credit point value). The experiences of a cohort of 285 undergraduate students in a Wellness course formed the unit of study and seven individual students from a total of sixteen volunteers whose profiles could be constructed from complete data sets were selected for analysis as embedded cases. The introductory level course required participants to engage in a personal project involving a behaviour modification plan for a self-selected, single dimension of Wellness. Students were given access to the Standard Edition Testwell Survey to assess and report their Wellness as a part of their personal projects. To identify relationships among the constructs of Self-Regulated Learning (SRL), Wellness and Student Approaches to Learning (SAL) a blend of quantitative and qualitative methods to collect and analyse data was formulated. Surveys were the primary instruments for acquiring quantitative data. Sources included the Wellness data from Testwell surveys, SAL data from R-SPQ surveys, SRL data from MSLQ surveys and student self-evaluation data from an end of semester survey. Students’ final grades and GPA scores were used as indicators of academic performance. The sources of qualitative data included subject documentation, structured interview transcripts and open-ended responses to survey items. Subsequent to a pilot study in which survey reliability and validity were tested in context, amendments to processes for and instruments of data collection were made. Students who adopted meaning oriented (deep/achieving) approaches tended to assess their Wellness at a higher level, seek effective learning strategies and perform better in formal study. Posttest data in the main study revealed that there were significant positive statistical relationships between academic performance and total wellness scores (rs=.297, n=205, p<.01). Deep (rs=.343, n=137, p<.01) and achieving (rs=.286, n=123, p<.01) approaches to learning also significantly correlated with Wellness whilst surface approaches had negative correlations that were not significant. SRL strategies including metacognitive selfregulation, effort, help-seeking and critical thinking were increasingly correlated with Wellness. Qualitative findings suggest that while all students adopt similar patterns of day to day activities for example attending classes, taking notes, working on assignments the level of care with which these activities is undertaken varies considerably. The dominant motivational trigger for students in this cohort was the personal relevance and associated benefits of the material being learned and practiced. Students were inclined to set goals that had a positive impact on affect and used “sense of happiness” to evaluate their achievement status. Students who had a higher drive to succeed and/or understand tended to have or seek a wider range of strategies. Their goal orientations were generally learning rather than performance based and barriers presented a challenge which could be overcome as opposed to a blockage which prevented progress. Findings from an empirical analysis of the Testwell data suggest that a single third order Wellness construct exists. A revision of the instrument is necessary in order to juxtapose it with the chosen six dimensional Wellness model that forms the foundation construct in the course. Further, redevelopment should be sensitive to the Australian context and culture including choice of language, examples and scenarios used in item construction. This study concludes with an heuristic for use in Wellness education. Guided by principles of Transformative education theory and behaviour change theory, and informed by this representative case study the “CARING” heuristic is proposed as an instructional design tool for Wellness educators seeking to foster transformative learning. Based upon this study, recommendations were made for university educators to provide authentic and personal experiences in Wellness curricula. Emphasis must focus on involving students and teachers in a partnership for implementing Wellness programs both in the curriculum and co-curricularly. The implications of this research for practice are predicated on the willingness of academics to embrace transformative learning at a personal level and a professional one. To explore students’ profiles in detail is not practical however teaching students how to guide us in supporting them through the “pain” of learning is a skill which would benefit them and optimise the learning and teaching process. At a theoretical level, this research contributes to an ecological theory of Wellness education as transformational change. By signposting the wider contexts in which learning takes place, it seeks to encourage changing paradigms to ones which harness the energy of each successive contextual layer in which students live. Future research which amplifies the qualities of individuals and groups who are “Well” and seeks the refinement and development of instruments to measure Wellness constructs would be desirable for both theoretical and applied knowledge bases. Mixed method Wellness research derived and conducted by teams that incorporate expertise from multiple disciplines such as psychology, anthropology, education, and medicine would enable creative and multi-perspective programs of investigation to be designed and implemented. Congruences and inconsistencies in health promotion and education would provide valuable material for strengthening the nexus between transformational learning and behaviour change theories. Future development of and research on the effectiveness of the CARING heuristic would be valuable in advancing the understanding of pedagogies which advance rather than impede learning as a transformative process. Exploring pedagogical models that marry with transformative education may render solutions to the vexing challenge of teaching and learning in diverse contexts.

Learning the kernel matrix with semidefinite programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive semidefinite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space - classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -using the labeled part of the data one can learn an embedding also for the unlabeled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method for learning the 2-norm soft margin parameter in support vector machines, solving an important open problem.

Scaffolding techniques : a teacher training for cooperative learning in Thailand primary education

In general, the benefits of using cooperative learning include academic achievement, communication skills, problem-solving, social skills and student motivation. Yet cooperative learning as a Western educational concept may be ineffective in a different learning system. The study aims to investigate scaffolding techniques for cooperative learning in Thailand primary education. The program was designed to foster Thai primary school teachers’ cooperative learning implementation that includes the basic tenets of cooperative learning and socio-cognitive based learning. Two teachers were invited to participate in this experimental teacher training program for one and a half weeks. Then the teachers implemented a cooperative learning in their mathematics class for six weeks. The data from teacher interview and classroom observation indicated that the both teachers are able to utilise questions to scaffold their students’ engagement in cooperative learning. This initiative study showed that difficulty or failure of implementing cooperative learning in Thailand education may not be derived from cultural difference. The paper discussed the techniques the participant teachers applied with proactive scaffolding, reactive scaffolding and scaffolding questions that can be used to facilitate the implementation of cooperative learning in Thai school.