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.

Mind change complexity of learning logic programs

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

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.

Revisiting 'how we learn' in academia : practice-based learning exchanges in three Australian universities

Ideas of 'how we learn' in formal academic settings have changed markedly in recent decades. The primary position that universities once held on shaping what constitutes learning has come into question from a range of experience-led and situated learning models. Drawing on findings from a study conducted across three Australian universities, the article focuses on the multifarious learning experiences indicative of practice-based learning exchanges such as student placements. Building on both experiential and situated learning theories, the authors found that students can experience transformative and emotional elucidations of learning, that can challenge tacit assumptions and transform the ways they understand the world. It was found that all participants (hosts, students, academics) both teach and learn in these educative scenarios and that, contrary to common (mis)perceptions that academics live in 'ivory towers', they play a crucial role in contributing to learning that takes place in the so-called 'real world'.

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.

Beyond discovery : a case study of teacher interaction, young children and computer tasks

The integration of computer technologies into everyday classroom life continues to provide pedagogical challenges for school systems, teachers and administrators. Data from an exploratory case study of one teacher and a multiage class of children in the first years of schooling in Australia show that when young children are using computers for set tasks in small groups, they require ongoing support from teachers, and to engage in peer interactions that are meaningful and productive. Classroom organization and the nature of teacher-child talk are key factors in engaging children in set tasks and producing desirable learning and teaching outcomes.