Mathematics and complex learning

There is unprecedented worldwide demand for mathematical solutions to complex problems. That demand has generated a further call to update mathematics education in a way that develops students’ abilities to deal with complex systems.

Professional growth through working together : a study of reciprocal benefits for teacher and education advisor through classroom based professional development

Teacher professional development provided by education advisors as one-off, centrally offered sessions does not always result in change in teacher knowledge, beliefs, attitudes or practice in the classroom. As the mathematics education advisor in this study, I set out to investigate a particular method of professional development so as to influence change in a practising classroom teacher’s knowledge and practices. The particular method of professional development utilised in this study was based on several principles of effective teacher professional development and saw me working regularly in a classroom with the classroom teacher as well as providing ongoing support for her for a full school year. The intention was to document the effects of this particular method of professional development in terms of the classroom teacher’s and my professional growth to provide insights for others working as education advisors. The professional development for the classroom teacher consisted of two components. The first was the co-operative development and implementation of a mental computation instructional program for the Year 3 class. The second component was the provision of ongoing support for the classroom teacher by the education advisor. The design of the professional development and the mental computation instructional program were progressively refined throughout the year. The education advisor fulfilled multiple roles in the study as teacher in the classroom, teacher educator working with the classroom teacher and researcher. Examples of the professional growth of the classroom teacher and the education advisor which occurred as sequences of changes (growth networks, Hollingsworth, 1999) in the domains of the professional world of the classroom teacher and education advisor were drawn from the large body of data collected through regular face-to-face and email communications between the classroom teacher and the education advisor as well as from transcripts of a structured interview. The Interconnected Model of Professional Growth (Clarke & Hollingsworth, 2002; Hollingsworth, 1999) was used to summarise and represent each example of the classroom teacher’s professional growth. A modified version of this model was used to summarise and represent the professional growth of the education advisor. This study confirmed that the method of professional development utilised could lead to significant teacher professional growth related directly to her work in the classroom. Using the Interconnected Model of Professional Growth to summarise and represent the classroom teacher’s professional growth and the modified version for my professional growth assisted with the recognition of examples of how we both changed. This model has potential to be used more widely by education advisors when preparing, implementing, evaluating and following-up on planned teacher professional development activities. The mental computation instructional program developed and trialled in the study was shown to be a successful way of sequencing and managing the teaching of mental computation strategies and related number sense understandings to Year 3 students. This study was conducted in one classroom, with one teacher in one school. The strength of this study was the depth of teacher support provided made possible by the particular method of the professional development, and the depth of analysis of the process. In another school, or with another teacher, this might not have been as successful. While I set out to change my practice as an education advisor I did not expect the depth of learning I experienced in terms of my knowledge, beliefs, attitudes and practices as an educator of teachers. This study has changed the way in which I plan to work as an education advisor in the future.

Les littératies multiples et le devenir plurilingue (Keynote)

Cette présentation met en avant la Théorie des Littératies Multiples (TLM) et l’importance de lire, lire le monde et se lire, dans le but de se transformer en contexte plurilingue. La première partie de cette communication sera consacrée à la présentation des principes fondamentaux de la TLM. Il est vrai que la littératie valorisée par l’école est souvent celle qui est la plus prisée dans la recherche et l’enseignement. La TLM enlève la littératie scolaire de sa place privilégiée et l’insère dans un agencement de littératies au foyer, à l’école et dans la communauté. Les littératies, en tant que construit renvoient aux mots, aux gestes, aux attitudes, ou plus exactement, aux façons de parler, de lire, d’écrire et de valoriser les réalités de la vie. Elles sont une façon de devenir avec le monde. Les littératies constituent des textes au sens large (comme par exemple, la musique, l’art, la physique et les athématiques) qui peuvent être visuels,oraux, écrits, tactiles,olfactifs ou numériques. Elles se fusionnent aux contextes sociopolitiques, culturels, économiques, genrés et racialisés, qui de par leur caractère mobile et fluide transforment les littératies génératrices de locuteurs, de scripteurs, d’artistes, d’ava tars et de communautés. Les littératies prennent leur sens en contexte, dans le temps et l’espace où on se trouve De ce fait, leur actualisation n’est pas prédéterminée et est imprévisible. La TLM s’intéresse aux rôles joués par les littératies. Lire, lire le monde et se lire a pour fonction importante entre autres de transformer une vie, une communauté et une société. La deuxième partie de cette communication sera consacrée à un projet de recherche ayant pour objectif d’explorer la façon dont des enfants acquièrent simultanément deux ou plusieurs systèmes d’écriture. Des enfants âgés de 5 à 8 ans ont participé à des activités filmées en salle de classe, au foyer et dans leur quartier. Puis des entretiens ont été menés avec les enfants, leurs parents et leurs enseignants. Ce projet nous permet de mieux saisir ce que signifient en contexte plurilingue les littératies en tant que processus. Le projet s’intéresse à ce qu’implique lire, lire le monde et se lire à l’école, au foyer et dans la communauté. Dans une société pluraliste, nous sommes plus que jamais ensibilisés aux contextes particuliers dans lesquels lire, lire le monde et se lire s’actualisent, qu’il s’agisse d’un nouvel arrivant ou d’une personne vivant en milieu minoritaire.

The ascendancy of oracy in university courses: Implications for teachers and second language users

This chapter reports on a study of oracy in a first-year university Business course, with particular interest in the oracy demands for second language-using international students. The research is relevant at a time when Higher Education is characterised by the confluence of increased international enrolments, more dialogic teaching and learning, and imperatives for teamwork and collaboration. Data sources for the study included videotaped lectures and tutorials, course documents, student surveys, and an interview with the lecturer. The findings pointed to a complex, oracy-laden environment where interactive talk fulfilled high-stakes functions related to social inclusion, the co-construction of knowledge, and the accomplishment of assessment tasks. The salience of talk posed significant challenges for students negotiating these core functions in their second language. The study highlights the oracy demands in university courses and foregrounds the need for university teachers, curriculum writers and speaking test developers to recognise these demands and explicate them for the benefit of all students.

Get Into Vocational Education (GIVE) Gladstone Pilot Project : Final Report to Rio Tinto Alcan Community Fund

This report describes the Get Into Vocational Education (GIVE) pilot project run at Gladstone Central State School from September to December 2010. The report describes the aims, budget, and timeline of the project and its findings in relation to each of the three major objectives of the project, namely (a) build awareness of, interest in, and familiarity with trades as a future vocation and opportunity for advancement; (b) enhance literacy, numeracy and science knowledge and performance; and (c) provide motivation and engagement to stay on at school and build towards a productive future. The clear findings of the GIVE Gladstone Year 4 pilot project are that, for students at risk in terms of school attendance, engagement and learning: (1) awareness of trades, literacy, mathematics and science knowledge, and motivation and engagement all improve and, in most cases, dramatically improve, in the GIVE structure; (2) this improvement involves transfer to situations and concepts not directly addressed in the project; and (3) the crucial factor in the GIVE structure that gives the improvement is the integration of classroom work with trades experiences and not the classroom and trades experiences themselves (although it is better if these are good).

Get Into Vocational Education (GIVE) Rockhampton Region Pilot Project : Final Report to The John Villiers Trust

This report describes the Get Into Vocational Education (GIVE) pilot project run in the Rockhampton Region at two schools in 2011. The report includes a description of the project, including its aims, budget, and timeline; and the findings in relation to each of the three major objectives of the project, namely (a) build awareness of, interest in, and familiarity with, trades as a future vocation and opportunity for advancement; (b) enhance literacy, numeracy and science knowledge and performance; and (c) provide motivation and engagement to stay on at school and build towards a productive future. The clear findings of the GIVE Rockhampton Region pilot project are that, for students at risk in terms of school attendance, engagement and learning: (1) awareness of trade practices in horticulture, hospitality, retail, and design and engineering, literacy, mathematics and science knowledge, and motivation and engagement all improve and, in most cases, dramatically improve, in the GIVE structure; and (2) the crucial factor in the GIVE structure that gives the improvement is the integration of classroom work with trades experiences and not the classroom and trades experiences themselves (although it is better if these are good).

The relationship between listening and other language skills in International English Language Testing System

Listening comprehension is the primary channel of learning a language. Yet of the four dominant macro-skills (listening, speaking, reading and writing), it is often difficult and inaccessible for second and foreign language learners due to its implicit process. The secondary skill, speaking, proceeds listening cognitively. Aural/oral skills precede the graphic skills, such as reading and writing, as they form the circle of language learning process. However, despite the significant relationship with other language skills, listening comprehension is treated lightly in the applied linguistics research. Half of our daily conversation and three quarters of classroom interaction are virtually devoted to listening comprehension. To examine the relationship of listening skill with other language skills, the outcome of 1800 Iranian participants undertaking International English Language Testing System (IELTS) in Tehran indicates the close correlation between listening comprehension and the overall language proficiency.

A framework for mathematics graphical tasks : The influence of the graphic element on student sense making

Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students’ mathematics understandings. Through an iterative design, the investigation described the sense making of 11–12-year-olds as they decoded mathematics tasks which contained a graphic. An ongoing analysis of two phases of data collection was undertaken as we analysed the extent to which various elements of text, graphics, and symbols influenced student sense making. Specifically, the study outlined the changed behaviour (and performance) of the participants as they solved graphical tasks that had been modified with respect to these elements. We propose a theoretical framework for understanding the composition of a graphical task and identify three specific elements which are dependently and independently related to each other, namely: the graphic; the text; and the symbols. Results indicated that although changes to the graphical tasks were minimal, a change in student success and understanding was most evident when the graphic element was modified. Implications include the need for test designers to carefully consider the graphics embedded within mathematics tasks since the elements within graphical tasks greatly influence student understanding.

Productivity and time use during occupational therapy and nutrition/dietetics clinical education : a cohort study

Background: Currently in the Australian higher education sector higher productivity from allied health clinical education placements are a contested issue. This paper will report results of a study that investigated output changes associated with occupational therapy and nutrition/dietetics clinical education placements in Queensland, Australia. Supervisors’ and students’ time use during placements and how this changes for supervisors compared to when students are not present in the workplace is also presented. Methodology/Principal Findings: A cohort design was used with students from four Queensland universities, and their supervisors employed by Queensland Health. There was an increasing trend in the number of occasions of service delivered when the students were present, and a statistically significant increase in the daily mean length of occasions of service delivered during the placement compared to pre-placement levels. For project-based placements that were not directly involved in patient care, supervisors’ project activity time decreased during placements, with students undertaking considerably more time in project activities. Conclusions/Significance: A novel method for estimating productivity and time use changes during clinical education programs for allied health disciplines has been applied. During clinical education placements there was a net increase in outputs, suggesting supervisors engage in longer consultations with patients for the purpose of training students, while maintaining patient numbers. Other activities are reduced. This paper is the first time these data have been shown and form a good basis for future assessments of the economic impact of student placements for allied health disciplines.

Get Into Vocational Education (GIVE) : motivating underperforming students

This study explores the effects of a vocational education-based program on academic motivation and engagement of primary school aged children. The Get Into Vocational Education (GIVE) program integrated ‘construction’ and the mathematics, English and science lessons of a Year 4 primary classroom. This paper focuses on investigating the components of the GIVE program that led to student changes in mathematical academic motivation and engagement resulting in outstanding gains in NAPLAN Numeracy results. The components proposed to have contributed to effectiveness of the GIVE program are: teacher and trainer expectations, task mastery and classroom relationships. These findings may be useful to researchers and educators who are interested in enhancing students’ mathematical academic motivation.

Critical theory and literacy

This handbook chapter explores the relationship between critical theory and seminal studies of literacy which investigate inequities in education. It identifies new research questions to explore the connections between literacy and power, but go beyond promises of emancipation.

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.

Multiliteracies and a new metalanguage for the moving image

Globalised communication in society today is characterised by multimodal forms of meaning making in a context of increased cultural and linguistic diversity, calling for the teaching of multiliteracies. This transformation requires the development of a new metalanguage or language of description for the burgeoning and hybridised variety of text forms associated with information and multimedia technologies. To continue to teach to a narrow band of print-based genres, grammars, and skills is to ignore the reality of textual practices outside of schools. This paper draws from classroom research in a multiliteracies classroom to provide a multimodal analysis of a claymation movie. The significance of the paper is the synthesis of a multimodal metalanguage for teachers and students to describe the features of work in the kineikonic (moving image) mode.

Learner strategy instruction and student uptake of strategies in a Japanese as a foreign language context

The Japanese language is recognised as being more difficult than European languages, needing three times more tuition time to reach comparable levels of proficiency. Encouraging Japanese as a Foreign Language (JFL) students to become aware of, and effectively use, learner strategies is one way to assist them become more controlled, effective learners leading to enhanced language learning. This thesis investigates the development and implementation of a JFL curriculum implemented in a university course for students learning JFL. The curriculum was developed specifically to assist beginner university students with the development of learner strategies appropriate for a JFL reading context. The theoretical underpinning of the study was informed by Educational Criticism (Eisner, 1998), which aims to describe, interpret and evaluate the processes of interaction between the teacher, the learner and the curriculum and the students' learning processes in a tertiary JFL classroom. The study investigated the effect on student learning processes of a JFL reading program that incorporated explicit learner strategy instruction and identified factors that enhanced or impeded the development of learner strategy knowledge. The participants in the study were 29 students enrolled in the course, 10 of whom volunteered to undertake additional tasks, and the two teachers who implemented the curriculum. Data collection involved a number of different strategies to observe the students' participation in the classroom and learning experiences. Learning processes were investigated through TOL protocols, classroom observations, course evaluations, interviews, and learner strategy use measurement instruments (SILL, SILK and SORS) to document student uptake of learner strategies. The design of the study and its applied focus recognised my expertise as a JFL teacher, curriculum writer and researcher, an approach that aligns with the purpose of a Professional Doctorate. Four general thematics, or principles, were identified in this study: „h Explicit learner strategy instruction provides the context for students to develop awareness of learner strategies and take control of their learning; „h Collaborative learning and interaction with teachers offers students the opportunity for shared knowledge construction; „h Reflection offers teachers and students the opportunity to reflect on their own learning style and strategy knowledge, and raises awareness of other available strategies; and „h Diverse cultural and linguistic backgrounds have an impact on curriculum implementation and student uptake of learner strategies. The study¡¦s methodological contribution is that it is one of the first in Australia to use Educational Criticism (Eisner, 1998) as a research methodology. The findings contribute to theoretical knowledge in the fields of Applied Linguistics, Second Language Teaching and Learning, Second Language Acquisition and JFL Teaching and Learning by offering new knowledge on the importance of learner strategies in the beginner JFL classroom, the potential of explicit strategy instruction, the value of reflection for both teachers and students, and the important role of the teacher in the process of curriculum implementation. The general principles identified and the findings of this in-depth study of a JFL classroom can be drawn upon to inform other teaching practice situations, and invite practitioners from not just Japanese, but from other language areas and other disciplines, to examine and improve their own practices, and suggest further research questions to pursue this line of enquiry.