Accelerating junior-secondary mathematics

Unfortunately, in Australia there is a prevalence of mathematically underperforming junior-secondary students in low-socioeconomic status schools. This requires targeted intervention to develop the affected students’ requisite understanding in preparation for post-compulsory study and employment and, ultimately, to increase their life chances. To address this, the ongoing action research project presented in this paper is developing a curriculum of accelerated learning, informed by a lineage of cognitivist-based structural sequence theory building activity (e.g., Cooper & Warren, 2011). The project’s conceptual framework features three pillars: the vertically structured sequencing of concepts; pedagogy grounded in students’ reality and culture; and professional learning to support teachers’ implementation of the curriculum (Cooper, Nutchey, & Grant, 2013). Quantitative and qualitative data informs the ongoing refinement of the theory, the curriculum, and the teacher support.

Structuring representations of continuous data through investigations in grade 1

The study of data modelling with elementary students involves the analysis of a developmental process beginning with children’s investigations of meaningful contexts: visualising, structuring, and representing data and displaying data in simple graphs (English, 2012; Lehrer & Schauble, 2005; Makar, Bakker, & Ben-Zvi, 2011). A 3-year longitudinal study investigated young children’s data modelling, integrating mathematical and scientific investigations. One aspect of this study involved a researcher-led teaching experiment with 21 mathematically able Grade 1 students. The study aimed to describe explicit developmental features of students’ representations of continuous data...

On the symbiosis of law and truth in Christian theology: Reconciling universal and particular through the Pauline law of love

This article argues that the secular liberal and positivist foundations of the modern Western legal system render it violent. In particular, the liberal exclusion of faith and subjectivity in favour of abstract and universal reason in conjunction with its privileging of individual autonomy at the expense of the community leads to alienation of the individual from the community. Similarly, the positivist exclusion of faith and theology from law, with its enforced conformity to the posited law, also results in this violence of alienation. In response, this article proposes a new foundation for law, a natural law based in the truth of Trinitarian theology articulated by John Milbank. In the Trinity, the members exist as a perfect unity in diversity, providing a model for the reconciliation of the legal individual and community: the law of love. Through the law of love as the basic norm, individuals love their neighbours as themselves, reconciling the particular and the universal, and providing a community of peace rather than violence.

Affordances of ICTs: an environmental study of a French language unit offered at university level

This project investigates the integration of Information Communication Technologies (ICTs) into educational settings by closely looking at the uptake of the perceived affordances offered by ICTs by students enrolled in a French language course at Queensland University of Technology. This cross-disciplinary research uses the theoretical concepts of: Ecological Psychology (Gibson, 1979; Good, 2007; Reed, 1996); Ecological Linguistics (Greeno, 1994; Leather & van Dam, 2003; van Lier 2000, 2003, 2004a, 2004b); Design (Norman, 1988, 1999); Software Design/ Human-Computer Interaction (Hartson, 2003; McGrenere & Ho, 2000); Learning Design (Conole & Dyke, 2004a, 2004b; Laurillard et al. 2000;); Education (Kirschner, 2002; Salomon, 1993; Wijekumar et al., 2006) and Educational Psychology (Greeno, 1994). In order to investigate this subject, the following research questions, rooted in the theoretical foundations of the thesis, were formulated: (1) What are the learners’ attitudes towards the ICT tools used in the project?; (2) What are the affordances offered by ICTs used in a specific French language course at university level from the perspective of the teacher and from the perspective of language learners?; (3) What affordances offered by ICT tools used by the teacher within the specific teaching and learning environment have been taken up by learners?; and (4) What factors influence the uptake by learners of the affordances created by ICT tools used by the teacher within the specific teaching and learning environment? The teaching phase of this project, conducted between 2006 and 2008, used Action Research procedures (Hopkins, 2002; McNiff & Whitehead, 2002; van Lier 1994) as a research framework. The data were collected using the following combination of qualitative and quantitative methods: (1) questionnaires administered to students (Hopkins, 2002; McNiff & Whitehead, 2002) using Likert-scale questions, open questions, yes/no questions; (2) partnership classroom observations of research participants conducted by Research Participant Advocates (Hopkins, 2002; McNiff & Whitehead, 2002); and (3) a focus group with volunteering students who participated in the unit (semi-structured interview) (Hopkins, 2002; McNiff & Whitehead, 2002). The data analysis confirms the importance of a careful examination of the teaching and learning environment and reveals differences in the ways in which the opportunities for an action offered by the ICTs were perceived by teacher and students, which impacted on the uptake of affordances. The author applied the model of affordance, as described by Good (2007), to explain these differences and to investigate their consequences. In conclusion, the teacher-researcher considers that the discrepancies in perceiving the affordances result from the disparities between the frames of reference and the functional contexts of the teacher-researcher and students. Based on the results of the data analysis, a series of recommendations is formulated supporting calls for careful analysis of frames of reference and the functional contexts of all participants in the learning and teaching process. The author also suggests a modified model of affordance, outlining the important characteristics of its constituents.

Enhancing the teaching and learning of mathematical visual images

The literacy demands of mathematics are very different to those in other subjects (Gough, 2007; O'Halloran, 2005; Quinnell, 2011; Rubenstein, 2007) and much has been written on the challenges that literacy in mathematics poses to learners (Abedi and Lord, 2001; Lowrie and Diezmann, 2007, 2009; Rubenstein, 2007). In particular, a diverse selection of visuals typifies the field of mathematics (Carter, Hipwell and Quinnell, 2012), placing unique literacy demands on learners. Such visuals include varied tables, graphs, diagrams and other representations, all of which are used to communicate information.

Responding to black markets: Role of IT and network structures

This paper presents the unique black markets of asset pooling and leasing services, which exposes the nature and extent of industry-specific threats. We explore how firms providing such services together with their network structures that constitute the foundations of asset pooling and leasing respond to the threat of black markets. We encapsulate detecting and encountering the threat of black markets through the theoretical lens of agility, which encompasses the elements of sensing and responding (Overby et al. 2006; Roberts and Grover 2012). This novel concept of responding to threats using the agility lens has not been adequately addressed by past studies on enterprise agility. Through a case study of a global asset pooling and leasing company, we reveal the criticality of network structures, the impracticality of IT and inadequate tracking mechanisms that challenge firms in minimizing such threats.

Formal modelling and analysis of DNP3 secure authentication

Supervisory Control and Data Acquisition (SCADA) systems are one of the key foundations of smart grids. The Distributed Network Protocol version 3 (DNP3) is a standard SCADA protocol designed to facilitate communications in substations and smart grid nodes. The protocol is embedded with a security mechanism called Secure Authentication (DNP3-SA). This mechanism ensures that end-to-end communication security is provided in substations. This paper presents a formal model for the behavioural analysis of DNP3-SA using Coloured Petri Nets (CPN). Our DNP3-SA CPN model is capable of testing and verifying various attack scenarios: modification, replay and spoofing, combined complex attack and mitigation strategies. Using the model has revealed a previously unidentified flaw in the DNP3-SA protocol that can be exploited by an attacker that has access to the network interconnecting DNP3 devices. An attacker can launch a successful attack on an outstation without possessing the pre-shared keys by replaying a previously authenticated command with arbitrary parameters. We propose an update to the DNP3-SA protocol that removes the flaw and prevents such attacks. The update is validated and verified using our CPN model proving the effectiveness of the model and importance of the formal protocol analysis.

Anatomy of a trending topic : Methods for the visualisation of retweet chains [Anatomie eines Trending Topics: Methoden zur Visualisierung von Retweet-Ketten]

Twitter and other social networking sites play an ever more present role in the spread of current events. The dynamics of information dissemination through digital network structures are still relatively unexplored, however. At what time an issue is taken up by whom? Who forwards a message when to whom else? What role do individual communication participants, existing digital communities or the technical foundations of each network platform play in the spread of news? In this chapter we discuss, using the example of a video on a current sociopolitical issue in Australia that was shared on Twitter, a number of new methods for the dynamic visualisation and analysis of communication processes. Our method combines temporal and spatial analytical approaches and provides new insights into the spread of news in digital networks. [Social media dienen immer häufger als Disseminationsmechanismen für Medieninhalte. Auf Twitter ermöglicht besonders die Retweet-Funktion den schnellen und weitläufgen Transfer von Nachrichten. In diesem Beitrag etablieren neue methodische Ansätze zur Erfassung, Visualisierung und Analyse von Retweet-Ketten. Insbesondere heben wir hervor, wie bestehende Netzwerkanalysemethoden ergänzt werden können, um den Ablauf der Weiterleitung sowohl temporal als auch spatial zu erfassen. Unsere Fallstudie demonstriert die verbreitung des videoclips einer am 9. Oktober 2012 spontan gehaltenen Wutrede der australischen Premierministerin Julia Gillard, in der sie Oppositionsführer Tony Abbott als Frauenhasser brandmarkte. Durch die Erfassung von Hintergrunddaten zu den jeweiligen NutzerInnen, die sich an der Weiterleitung des Videoclips beteiligten, erstellen wir ein detailliertes Bild des Disseminationsablaufs im vorliegenden Fall. So lassen sich die wichtigsten AkteurInnen und der Ablauf der Weiterleitung darstellen und analysieren. Daraus entstehen Einblicke in die allgemeinen verbreitungsmuster von Nachrichten auf Twitter].

STEM: Challenges and opportunities for mathematics education

Climbing Mountains, Building Bridges is a rich theme for exploring some of the “challenges, obstacles, links, and connections” facing mathematics education within the current STEM climate (Science, Technology, Engineering and Mathematics). This paper first considers some of the issues and debates surrounding the nature of STEM education, including perspectives on its interdisciplinary nature. It is next argued that mathematics is in danger of being overshadowed, in particular by science, in the global urgency to advance STEM competencies in schools and the workforce. Some suggestions are offered for lifting the profile of mathematics education within an integrated STEM context, with examples drawn from modelling with data in the sixth grade.

Problem solving in a 21st century mathematics curriculum

Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

A continuum to characterise and support teacher interpretation of an innovative curriculum

A continuum for describing the degree to which teachers interpret the various features of a curriculum is presented. The continuum has been developed based upon the observation of classroom practices and discussions with a group of teachers who are using an innovative junior secondary mathematics curriculum. It is anticipated that the ongoing use of the continuum will lead to its improvement as well as the refinement of the curriculum, more focussed support for the teachers,improved student learning, and the building of explanatory theory regarding mathematics teaching and learning.

Mathematics, programming, and STEM

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10-week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

Written numeracy assessment in the early years: The challenges of pronouns and noun groups

We examine the challenges of pronouns and noun groups in the Australian Curriculum, Assessment and Reporting Authority’s (ACARA) Year 3 National Assessment Program - Literacy and Numeracy (NAPLAN) Numeracy Example Test (ACARA, 2015a). Framed by discourses of Literacy as a General Capability (ACARA, 2015b) in the Australian Curriculum: Mathematics (ACARA, 2015c), the pronouns and noun groups used in the Example Test are mapped onto the Australian Curriculum: English Content Descriptions (ACARA, 2015d). The findings are that some of the pronouns and noun groups used in the Example Test are more complex than what Year 3 children are expected to achieve in the Australian Curriculum: English. We thus stress the need for early years teachers of mathematics to account for the unique mathematical register of written mathematics problems so that young children are not only prepared for high-stakes written numeracy assessments, but are also enabled as a numerically literate citizen.

Regulation beyond government: Weber, Foucault and the liberal governance of media content

This paper steps back from the question of how regulation of digital media content occurs, and whether it can be effective, to consider the rationales that inform regulation, and the ethics and practices associated with content regulation. It will be argued that Max Weber's account of bureaucratic expertise remains relevant to such discussions, particularly insofar as it intersects with Michel Foucault's concept of governmentality, and contemporary applications of the notion of 'governing at a distance'. The nature of the challenges to media regulators presented by online environments, and by digital and social media, are considered in depth, but it is argued that the significance of regulatory innovations that respond to such challenges should not be underestimated, nor should the continuing national foundations of media regulation. It will also discuss the relevance of the concept of 'soft law' to contemporary regulatory practice.

Enterprise education: The frustration of a pure contest

Purpose This paper discusses the development of a strategy game for enterprise education. It is argued that requiring students to initially struggle with the game’s rules and strategies results in a worthwhile test of their persistence and ability to manage ambiguity. Further, that in the absence of uncertainty, students will not benefit from the game’s potential contribution to their overall learning. Approach The paper is constructed around the infusion of student narratives and the author’s self-reflective thoughts. The papers explores the process of developing a game that; - 1) provides the students with access to an enterprise reality, - 2) strengthens their engagement with the theoretical foundations of their studies, and; - 3) provides a process for serious self-reflection. Findings Despite the mixed views presented in this paper, the game’s development thus far has been very successful. Students do enjoy and benefit from enduring the frustration of a pure contest. Having to work through uncertainty is a good practice for students in Higher Education, especially those engaged in enterprise education. Practical Implications Whilst the use of games in experiential education is not uncommon, consideration of how and why they are developed is not always well understood. This paper suggests that enterprise educators have significant opportunities to develop games that genuinely provide student access to the entrepreneur’s way of life. Value of Paper This paper provides evidence of how a game can be constructed to add significant value to an existing curriculum. It also provides evidence of the inner thoughts of students frustrated by a challenge they refuse to give up on. As such, it provides a valuable window through which to contemplate the minds of tomorrow’s nascent entrepreneurs.