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.

Learning to win process-control games watching game-masters

The present paper focuses on some interesting classes of process-control games, where winning essentially means successfully controlling the process. A master for one of these games is an agent who plays a winning strategy. In this paper we investigate situations in which even a complete model (given by a program) of a particular game does not provide enough information to synthesize—even incrementally—a winning strategy. However, if in addition to getting a program, a machine may also watch masters play winning strategies, then the machine is able to incrementally learn a winning strategy for the given game. Studied are successful learning from arbitrary masters and from pedagogically useful selected masters. It is shown that selected masters are strictly more helpful for learning than are arbitrary masters. Both for learning from arbitrary masters and for learning from selected masters, though, there are cases where one can learn programs for winning strategies from masters but not if one is required to learn a program for the master's strategy itself. Both for learning from arbitrary masters and for learning from selected masters, one can learn strictly more by watching m+1 masters than one can learn by watching only m. Last, a simulation result is presented where the presence of a selected master reduces the complexity from infinitely many semantic mind changes to finitely many syntactic ones.

Contextualising the teaching and learning of measurement within Torres Strait Islander schools

A one year mathematics project that focused on measurement was conducted with six Torres Strait Islander schools and communities. Its key focus was to contextualise the teaching and learning of measurement within the students’ culture, communities and home languages. There were six teachers and two teacher aides who participated in the project. This paper reports on the findings from the teachers’ and teacher aides’ survey questionnaire used in the first Professional Development session to identify: a) teachers’ experience of teaching in Torres Strait Islands, b) teachers’ beliefs about effective ways to teach Torres Strait Islander students, and c) contexualising measurement within Torres Strait Islander culture, Communities and home languages. A wide range of differing levels of knowledge and understanding about how to contextualise measurement to support student learning were identified and analysed. For example, an Indigenous teacher claimed that mathematics and the environment are relational, that is, they are not discrete and in isolation from one another, rather they interconnect with mathematical ideas emerging from the environment of the Torres Strait Communities.

Changing pedagogic codes in a class of landscape architects learning 'ecologically sustainable development'

Professional discourse in education has been the focus of research conducted mostly with teachers and professional practitioners but the work of students in the built environment has largely been ignored. This article presents an analysis of students’ visual discourse in the final professional year of a landscape architecture course in Brisbane, Australia. The study has a multi-method design and includes drawings, interviews and documentary materials, but focuses on the drawings in this paper. Using the theory of Bernstein, the analysis considers student representations as interrelations between professional identity and discretionary space for legitimate knowledge formation in landscape planning. It shows a shift in how students persuade the teacher of their expanding views of this field. The discussion of this shift centres on the professional knowledge that students choose rather than need to learn. It points to the differences within a class that a teacher must address in curriculum design in a contemporary professional course.

Promoting student understanding through complex learning

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by “continuing education as usual” (The National Academies, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualization. These technologies have led to significant changes in the forms of mathematical thinking that are required beyond the classroom. This paper argues for the need to incorporate future-oriented understandings and competencies within the mathematics curriculum, through intellectually stimulating activities that draw upon multidisciplinary content and contexts. The paper also argues for greater recognition of children’s learning potential, as increasingly complex learners capable of dealing with cognitively demanding tasks.

Using poster presentations as assessment of work integrated learning

Background / context: The ALTC WIL Scoping Study identified a need to develop innovative assessment methods for work integrated learning (WIL) that encourage reflection and integration of theory and practice within the constraints that result from the level of engagement of workplace supervisors and the ability of academic supervisors to become involved in the workplace. Aims: The aim of this paper is to examine how poster presentations can be used to authentically assess student learning during WIL. Method / Approach: The paper uses a case study approach to evaluate the use of poster presentations for assessment in two internship units at the Queensland University of Technology. The first is a unit in the Faculty of Business where students majoring in advertising, marketing and public relations are placed in a variety of organisations. The second unit is a law unit where students complete placements in government legal offices. Results / Discussion: While poster presentations are commonly used for assessment in the sciences, they are an innovative approach to assessment in the humanities. This paper argues that posters are one way that universities can overcome the substantial challenges of assessing work integrated learning. The two units involved in the case study adopt different approaches to the poster assessment; the Business unit is non-graded and the poster assessment task requires students to reflect on their learning during the internship. The Law unit is graded and requires students to present on a research topic that relates to their internship. In both units the posters were presented during a poster showcase which was attended by students, workplace supervisors and members of faculty. The paper evaluates the benefits of poster presentations for students, workplace supervisors and faculty and proposes some criteria for poster assessment in WIL. Conclusions / Implications: The paper concludes that posters can effectively and authentically assess various learning outcomes in WIL in different disciplines while at the same time offering a means to engage workplace supervisors with academic staff and other students and supervisors participating in the unit. Posters have the ability to demonstrate reflection in learning and are an excellent demonstration of experiential learning and assessing authentically. Keywords: Work integrated learning, assessment, poster presentations, industry engagement.

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').

Loneliness and classroom participation in adolescents with learning disabilities : a social cognitive view

Students with learning disabilities (LD) often experience significant feelings of loneliness. There is some evidence to suggest that these feelings of loneliness may be related to social difficulties that are linked to their learning disability. Adolescents experience more loneliness than any other age group, primarily because this is a time of identity formation and self-evaluation. Therefore, adolescents with learning disabilities are highly likely to experience the negative feelings of loneliness. Many areas of educational research have highlighted the impact of negative feelings on learning. This begs the question, =are adolescents with learning disabilities doubly disadvantaged in regard to their learning?‘ That is, if their learning experience is already problematic, does loneliness exacerbate these learning difficulties? This thesis reveals the findings of a doctoral project which examined this complicated relationship between loneliness and classroom participation using a social cognitive framework. In this multiple case-study design, narratives were constructed using classroom observations and interviews which were conducted with 4 adolescent students (2 girls and 2 boys, from years 9-12) who were identified as likely to be experiencing learning disabilities. Discussion is provided on the method used to identify students with learning disabilities and the related controversy of using disability labels. A key aspect of the design was that it allowed the students to relate their school experiences and have their stories told. The design included an ethnographic element in its focus on the interactions of the students within the school as a culture and elements of narrative inquiry were used, particularly in reporting the results. The narratives revealed all participants experienced problematic social networks. Further, an alarmingly high level of bullying was discovered. Participants reported that when they were feeling rejected or were missing a valued other they had little cognitive energy for learning and did not want to be in school. Absenteeism amongst the group was high, but this was also true for the rest of the school population. A number of relationships emerged from the narratives using social cognitive theory. These relationships highlighted the impact of cognitive, behavioural and environmental factors in the school experience of lonely students with learning disabilities. This approach reflects the social model of disability that frames the research.

Levels of awareness of professional ethics used as a sensitizing method in project-based learning

There is a need for educational frameworks for computer ethics education. This discussion paper presents an approach to developing students’ moral sensitivity, an awareness of morally relevant issues, in project-based learning (PjBL). The proposed approach is based on a study of IT professionals’ levels of awareness of ethics. These levels are labelled My world, The corporate world, A shared world, The client’s world and The wider world. We give recommendations for how instructors may stimulate students’ thinking with the levels and how the levels may be taken into account in managing a project course and in an IS department. Limitations of the recommendations are assessed and issues for discussion are raised.

Enabling 21st century learning spaces : practical interpretations of the MCEETYA Learning Spaces Framework at Bounty Boulevard State School, Queensland, Australia

While the Queensland and Australian Governments have recognised the importance of new spaces for teaching and learning, particularly with the Rudd Government's Building the Education Revolution, the practical implementation of new spaces is largely left to schools and even individual teachers. This article proposes a theory for the consideration of 21st century learning spaces in relation to the learner, desired knowledge and understanding, digital technology and digital pedagogy. New and emerging learning spaces at Bounty Boulevard State School are analysed and critiqued through an analysis of the guiding principles offered by the 'Learning in an Online World: Learning Spaces Framework' (MCEETYA, 2008) publication, including flexibility, inclusivity, collaboration, creativity and efficiency. The argument put forward in this article is that 21st century learning spaces can be enabled while acknowledging barriers of resourcing and current ICT infrastructure.

The applicability of Bowen's family theory to the Malay population

The changes of economic status in Malaysia have lead to many psychosocial problems especially among the young people. Counselling and psychotherapy have been seen as one of the solutions that are practiced in Western Culture. Most counselling theorists believe that their theory is universal however there is limited research to prove it. This paper will describe an ongoing study conducted in Malaysia about the applicability of one Western counselling Theory, Bowen’s family theory the Differentiation of self levels in the family allow a person to both leave the family’s boundaries in search of uniqueness and continually return to the family in order to further establish a sense of belonging. In addition Bowen believed that this comprised of four measures: Differentiation of Self (DSI), Family Inventory of Live Event (ILE), Depression Anxiety and Stress Scale (DASS) and Connor-Davidson Resilience Scale (CD-RISC). Preliminary findings are discussed and the implication in enhancing the quality of teaching family counselling in universities explored.

Incorporating authentic assessment into different university learning scenarios

There is a current requirement for universities to prepare graduates who are skilled in practical as well as theoretical knowledge of the workplace. It is argued in this paper that assessment, as integral to the teaching/learning process, should also relate to the real world context of the workplace, in that students are able to transform, use and apply the knowledge that they learn into these contexts. While assessment authentic for students in a university setting is often a difficult task for lecturers. This paper discusses three different learning contexts that involved different assessment experiences linked in some way to real world learning and application of the theory. The results of the trial indicated that as contexts became close to a real world experience, the sustainability of the assessment became more problematic. While acknowledging the difficulty of these practices, it is suggested that there is a need for a continuous cycle of evaluation amid some creative and innovative approaches to assessment practice.

Working together for Toby : early childhood student teachers engaging in collaborative problem-based learning around child abuse and neglect

Early childhood teacher education programs have a responsibility, amongst many, to prepare teachers for decision-making on real world issues, such as child abuse and neglect. Their repertoire of skills can be enhanced by engaging with others, either face-to-face or online, in authentic problem-based learning. This paper draws on a study of early childhood student teachers who engaged in an authentic learning experience, which was to consider and to suggest how they would act upon a real-life case of child abuse encountered in an early childhood classroom in Queensland. This was the case of Toby (a pseudonym), who was suspected of being physically abused at home. Students drew upon relevant legislation, policy and resource materials to tackle Toby’s case. The paper provides evidence of students grappling with the complexity of a child abuse case and establishing, through collaboration with others, a proactive course of action. The paper has a dual focus. First, it discusses the pedagogical context in which early childhood student teachers deal with issues of child abuse and neglect in the course of their teacher education program. Second, it examines evidence of students engaging in collaborative problem-solving around issues of child abuse and neglect and teachers’ responsibilities, both legal and professional, to the children and families they work with. Early childhood policy-makers, practitioners and teacher educators are challenged to consider how early childhood teachers are best equipped to deal with child protection and early intervention.

Expression and connection : the integration of the reflective learning process and the writing process into social network sites

A number of instructors have recently adopted social network sites (SNSs) for learning. However, the learning design of SNSs often remains at a preliminary level similar to a personal log book because it does not properly include reflective learning elements such as individual reflection and collaboration. This article looks at the reflective learning process and the public writing process as a way of improving the quality of reflective learning on SNSs. It proposes a reflective learning model on SNSs based on two key pedagogical concepts for social networking: individual expression and collaborative connection. It is expected that the model would be helpful for instructors in designing a reflective learning process on SNSs in an effective and flexible way.