Co-constructing decimal number knowledge

This mathematics education research provides significant insights for the teaching of decimals to children. It is well known that decimals is one of the most difficult topics to learn and teach. Annette’s research is unique in that it focuses not only on the cognitive, but also on the affective and conative aspects of learning and teaching of decimals. The study is innovative as it includes the students as co-constructors and co-researchers. The findings open new ways of thinking for educators about how students cognitively process decimal knowledge, as well as how students might develop a sense of self as a learner, teacher and researcher in mathematics.

David L. Rosenhan (1929–2012)

Presents an obituary for David L. Rosenhan (1929–2012). A distinguished psychologist and professor emeritus at Stanford University, Rosenhan died February 6, 2012, at the age of 82, after a long illness. Born in Jersey City, New Jersey, on November 22, 1929, he received a bachelor’s degree in mathematics (1951) from Yeshiva College and a master’s degree in economics (1953) and a doctorate in psychology (1958) from Columbia University. A professor of law and of psychology at Stanford University from 1971 until his retirement in 1998, Rosenhan was a pioneer in applying psychological methods to the practice of law, including the examination of expert witnesses, jury selection, and jury deliberation. A former president of the American Psychology–Law Society and of the American Board of Forensic Psychology, Rosenhan was a fellow of the American Association for the Advancement of Science, of the American Psychological Association, and of the American Psychological Society. Before joining the Stanford Law School faculty, he was a member of the faculties of Swarthmore College, Princeton University, Haverford College, and the University of Pennsylvania. He also served as a research psychologist at the Educational Testing Service. As generations of Stanford students can attest, David Rosenhan was a spellbinding lecturer who managed to convey the sense that he was speaking to each individual, no matter how large the group. To his graduate students, he was consistently encouraging and optimistic, always ready to share a joke or story, and gently encouraging of their creativity and progressive independence as researchers. The lessons he cared most about offering, in the classroom as in his research, were about human dignity and the need to confront abuse of power and human frailties.

A sequential Monte Carlo framework for adaptive Bayesian model discrimination designs using mutual information

In this paper we present a unified sequential Monte Carlo (SMC) framework for performing sequential experimental design for discriminating between a set of models. The model discrimination utility that we advocate is fully Bayesian and based upon the mutual information. SMC provides a convenient way to estimate the mutual information. Our experience suggests that the approach works well on either a set of discrete or continuous models and outperforms other model discrimination approaches.

Co-thought gestures : supporting students to successfully navigate map tasks

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged 10–12 years) over a 3-year period as they solved map tasks that required spatial reasoning. The map tasks were representative of those typically found in mathematics classrooms for this age group and required route finding and coordinate knowledge. The results indicated that co-thought gestures were used to navigate the problem space and monitor movements within the spatial challenges of the respective map tasks. Gesturing was most influential when students encountered unfamiliar tasks or when they found the tasks spatially demanding. From a teaching and learning perspective, explicit co-thought gesturing highlights cognitive challenges students are experiencing since students tended to not use gesturing in tasks where the spatial demands were low.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

New constructions of anonymous membership broadcasting schemes

An anonymous membership broadcast scheme is a method in which a sender broadcasts the secret identity of one out of a set of n receivers, in such a way that only the right receiver knows that he is the intended receiver, while the others can not determine any information about this identity (except that they know that they are not the intended ones). In a w-anonymous membership broadcast scheme no coalition of up to w receivers, not containing the selected receiver, is able to determine any information about the identity of the selected receiver. We present two new constructions of w-anonymous membership broadcast schemes. The first construction is based on error-correcting codes and we show that there exist schemes that allow a flexible choice of w while keeping the complexities for broadcast communication, user storage and required randomness polynomial in log n,. The second construction is based on the concept of collision-free arrays, which is introduced in this paper. The construction results in more flexible schemes, allowing trade-offs between different complexities.

Mathematical Models of Tumor-Immune System Dynamics

"This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences."--Publisher website

The aerospace engineering challenge

Integrating Science, Technology, and Engineering in Mathematics authors share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms. This article describes an activity that introduced fourth-grade students to the work of aerospace engineers and to the science, technology, and mathematics principles associated with flight.

Multiliteracies pedagogy : creating claymations with adolescent, post-beginner English language learners

In addressing literacy in high school education, it is important to foreground the particular issues faced by growing numbers of English Language Learners (ELLs). In our increasingly culturally and linguistically diverse classrooms, this is a matter for all literacy teachers, as well as ELL specialists. In Australia, teachers of ELLs are experimenting with Multiliteracies pedagogy which provides rich opportunities to explore language learning experiences and outcomes that stretch beyond exercises in reproduction in written and oral modes only. This paper documents the practice of a high school teacher who uses a claymation project, producing a movie by stop-motion filming of clay figures, with a class of low-level English literacy learners. Drawing on observations of three particular students, the paper outlines a number of possibilities of this approach for English language learners. These include increased individual agency; enhanced engagement through collaboration; and the opportunity to explore various elements of multimodal text design.

English as identity formation

Literate practices and identities matter, those of both students and their teachers. There is considerable research exploring the discursive construction of students’ literacy practices and identities and the discursively mediated identities of literacy and English teachers. As Moje and Luke (2009) note, how identity is viewed influences and is influenced by the way literacy is viewed. Teachers’ literate identities and conceptualisations of literacy shape what counts as literacy in their classrooms, but also frame, shape and often limit students’ identities, both as readers and as writers (Hall, 2012).

First Literacies: Art, Creativity, Play, Constructive Meaning-Making

In this chapter art and play are considered children’s ‘first languages’, and therefore are placed at the centre of a curriculum for young children. Through art and play, children represent thought and action, which underpins their later understanding of the ‘second languages’ of reading, writing and numbering. Key issues such as image-making, graphic action, imagination, narrative, empathetic engagement and internalised thought are analysed as evidence of children’s construction of knowledge through art and play. Symbol making is the essence of being human. In children’s art and play, their symbol use captures their sensory modes in emotional and embodied ways, as children know their worlds and their place. The chapter addresses how children’s creation, manipulation and meaning making through engaged interaction with art materials are precursors to learning to read and write and, as first languages, should not be discarded nor replaced. The notion of creativity is explored in relation to pedagogical approaches. In a climate of testing regimes that emphasise ‘academic’ achievements, teachers are encouraged to not lose sight of imagination, pretence, constructive meaning making, holistic teaching and being a co-player and co-artist.

Personas of students accessing a peer-facilitated support for learning program

STIMulate is a support for learning program at the Queensland University of Technology in Brisbane, Australia. The program provides assistance in mathematics, science and information technology for undergraduate students. This paper develops personas - archetypal users - that represent the attitudes and motivations of students that utilise STIMulate (in particular, the IT stream). Seven different personas were developed based on interviews gathered from Peer Learning Facilitators (PLF) who are experienced students that have excelled in relevant subject areas. The personas were then validated by a PLF focus group. Developing the personas enabled us to better understand the characteristics and needs of the students using the STIMulate program, enabling a more critical analysis of the quality of the service provided.

Motivation and behavioural patterns of students accessing a peer-facilitated support for learning program

This paper describes the development and use of personas, a Human Computer Interaction (HCI) research methodology, within the STIMulate peer learning program, in order to better understand student behaviour patterns and motivations. STIMulate is a support for learning program at the Queensland University of Technology (QUT) in Brisbane, Australia. The program provides assistance in mathematics, science and information technology (IT) for course work students. A STIMulate space is provided for students to study and obtain one-on-one assistance from Peer Learning Facilitators (PLFs), who are experienced students that have excelled in relevant subject areas. This paper describes personas – archetypal users - that represent the motivations and behavioural patterns of students that utilise STIMulate (particularly the IT stream). The personas were developed based on interviews with PLFs, and subsequently validated by a PLF focus group. Seven different personas were developed. The personas enable us to better understand the characteristics of the students utilising the STIMulate program. The research provides a clearer picture of visiting student motivations and behavioural patterns. This has helped us identify gaps in the services provided, and be more aware of our assumptions about students. The personas have been deployed in PLF training programs, to help PLFs provide a better service to the students. The research findings suggest further study on the resonances between some students and PLFs, which we would like to better elicit.

A case study of teaching English and multimodality with ICTs: Constraints and possibilities

Current Australian policies and curricular frameworks demand that teachers and students use technology creatively and meaningfully in classrooms to develop students into 21C technological citizens. English teachers and students also have to learn new metalanguage around visual grammar since multimodal tasks often combine creative with critical General Capabilities (GC) with that of the of ICTs and literacy in the Australian Curriculum: English (AC:E). Both teachers and learners come to these tasks with varying degrees of techno-literacy, skills and access to technologies. This paper reports on case-study research following a technology based collaborative professional development (PD) program between a university Lecturer facilitator and English Teachers in a secondary Catholic school. The study found that the possibilities for creative and critical engagement are rich, but there are real grounded constraints such as lack of time, impeding teachers’ ability to master and teach new technologies in classrooms. Furthermore, pedagogical approaches are affected by technical skill levels and school infrastructure concerns which can militate against effective use of ICTs in school settings. The research project was funded by the Brisbane Catholic Education Office and focused on how teachers can be supported in these endeavours in educational contexts as they prepare students of English to be creative global citizens who use technology creatively.

A new load distribution strategy for linear network with communication delays

In this paper, we propose a new load distribution strategy called `send-and-receive' for scheduling divisible loads, in a linear network of processors with communication delay. This strategy is designed to optimally utilize the network resources and thereby minimizes the processing time of entire processing load. A closed-form expression for optimal size of load fractions and processing time are derived when the processing load originates at processor located in boundary and interior of the network. A condition on processor and link speed is also derived to ensure that the processors are continuously engaged in load distributions. This paper also presents a parallel implementation of `digital watermarking problem' on a personal computer-based Pentium Linear Network (PLN) topology. Experiments are carried out to study the performance of the proposed strategy and results are compared with other strategies found in literature.