Australian learning and teaching council projects in the mathematical sciences : a retrospective

Since 2004, the Australian Learning and Teaching Council (ALTC) and its predecessor, the Carrick Institute for Learning and Teaching in Higher Education, have funded numerous teaching and educational research-based projects in the Mathematical Sciences. In light of the Commonwealth Government’s decision to close the ALTC in 2011, it is appropriate to take account of the ALTCs input into the Mathe- matical Sciences in higher education. Here we present an overview of ALTC projects in the Mathematical Sciences, as well as report on the contributions they have made to the Discipline.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

A Summative Evaluation of the Stronger Smarter Learning Communities Project : Vol 1 and Vol 2

This is a summative evaluation of the Stronger Smarter Learning Communities (SSLC) project that examines whether and how the SSLC project had an impact on Australian state schools which adopted its models and approaches. Drawing from qualitative and quantitative data sets, it also presents the largest scale and most comprehensive analysis of Indigenous education practices and outcomes to date. It includes empirical findings on: success in changing school ethos and community engagement; challenges in progress at closure of the 'gap' in conventionally measured achievement and performance; schools' and principals' choices in curriculum and instruction; profiles of teachers' and principals' training and views on teacher education; and a strong emphasis on community and school Indigenoous voices and views on Indigenous education.

Learning with FIRST LEGO League

Robotics is a valuable tool for engaging students in the hands-on application of science, technology, engineering, and mathematics (STEM) concepts. Robotics competitions such as FIRST LEGO League (FLL) can increase students’ interest in the STEM subjects and can foster their problem solving and teamwork skills. This paper reports on a study investigating students’ perceptions on the influence of participating in a FLL competition on their learning. The students completed questionnaires regarding their perceptions of their learning during the FLL challenge and were also interviewed to gain a deeper understanding of their questionnaire responses. The results show that the students were engaged with the FLL challenge and held positive views regarding their experience. The results also suggest that students involved with the FLL challenge improved their learning about real-world applications, problem solving, engagement, communication, and the application of the technology/engineering cycle.

Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Outcomes of the Chemistry Discipline Network Mapping Exercises: Are the Threshold Learning Outcomes met?

The Chemistry Discipline Network has recently completed two distinct mapping exercises. The first is a snapshot of chemistry taught at 12 institutions around Australia in 2011. There were many similarities but also important differences in the content taught and assessed at different institutions. There were also significant differences in delivery, particularly laboratory contact hours, as well as forms and weightings of assessment. The second mapping exercise mapped the chemistry degrees at three institutions to the Threshold Learning Outcomes for chemistry. Importantly, some of the TLOs were addressed by multiple units at all institutions, while others were not met, or were met at an introductory level only. The exercise also exposed some challenges in using the TLOs as currently written.

Learning without boundaries

Discipline boundaries of science and technology education are inevitable. Often, such barriers are an obstacle to industry-based learning leading to preventable complexities. Industry-based learning is a complex scenario, rather than conventional learning, leading to the study of liquid learning, which is a timely concept to investigate learning without boundaries. Liquid learning consists of accountability, expectations and driven by outcomes with different learning choices. Liquid learning is a significant phenomenon requiring awareness in the science and technology education. This paper aims to discuss some practical issues when designing industry-based learning without boundaries. A case study approach is reviewed and presented.

A matrix for appropriate assessment of workplace learning in stem disciplines

With increasing interest shown by Universities in workplace learning, especially in STEM disciplines, an issue has arisen amongst educators and industry partners regarding authentic assessment tasks for work integrated learning (WIL) subjects. This paper describes the use of a matrix, which is also available as a decision-tree, based on the features of the WIL experience, in order to facilitate the selection of appropriate assessment strategies. The matrix divides the WIL experiences into seven categories, based on such factors as: the extent to which the experience is compulsory, required for membership of a professional body or elective; whether the student is undertaking a project, or embedding in a professional culture; and other key aspects of the WIL experience. One important variable is linked to the fundamental purpose of the assessment. This question revolves around the focus of the assessment: whether on the person (student development); the process (professional conduct/language); or the product (project, assignment, literature review, report, software). The matrix has been trialed at QUT in the Faculty of Science and Technology, and also at the University of Surrey, UK, and has proven to have good applicability in both universities.

Acquiring search expertise : learning experiences and threshold concepts

Expert searchers engage with information as information brokers, researchers, reference librarians, information architects, faculty who teach advanced search, and in a variety of other information-intensive professions. Their experiences are characterized by a profound understanding of information concepts and skills and they have an agile ability to apply this knowledge to interacting with and having an impact on the information environment. This study explored the learning experiences of searchers to understand the acquisition of search expertise. The research question was: What can be learned about becoming an expert searcher from the learning experiences of proficient novice searchers and highly experienced searchers? The key objectives were: (1) to explore the existence of threshold concepts in search expertise; (2) to improve our understanding of how search expertise is acquired and how novice searchers, intent on becoming experts, can learn to search in more expertlike ways. The participant sample drew from two population groups: (1) highly experienced searchers with a minimum of 20 years of relevant professional experience, including LIS faculty who teach advanced search, information brokers, and search engine developers (11 subjects); and (2) MLIS students who had completed coursework in information retrieval and online searching and demonstrated exceptional ability (9 subjects). Using these two groups allowed a nuanced understanding of the experience of learning to search in expertlike ways, with data from those who search at a very high level as well as those who may be actively developing expertise. The study used semi-structured interviews, search tasks with think-aloud narratives, and talk-after protocols. Searches were screen-captured with simultaneous audio-recording of the think-aloud narrative. Data were coded and analyzed using NVivo9 and manually. Grounded theory allowed categories and themes to emerge from the data. Categories represented conceptual knowledge and attributes of expert searchers. In accord with grounded theory method, once theoretical saturation was achieved, during the final stage of analysis the data were viewed through lenses of existing theoretical frameworks. For this study, threshold concept theory (Meyer & Land, 2003) was used to explore which concepts might be threshold concepts. Threshold concepts have been used to explore transformative learning portals in subjects ranging from economics to mathematics. A threshold concept has five defining characteristics: transformative (causing a shift in perception), irreversible (unlikely to be forgotten), integrative (unifying separate concepts), troublesome (initially counter-intuitive), and may be bounded. Themes that emerged provided evidence of four concepts which had the characteristics of threshold concepts. These were: information environment: the total information environment is perceived and understood; information structures: content, index structures, and retrieval algorithms are understood; information vocabularies: fluency in search behaviors related to language, including natural language, controlled vocabulary, and finesse using proximity, truncation, and other language-based tools. The fourth threshold concept was concept fusion, the integration of the other three threshold concepts and further defined by three properties: visioning (anticipating next moves), being light on one's 'search feet' (dancing property), and profound ontological shift (identity as searcher). In addition to the threshold concepts, findings were reported that were not concept-based, including praxes and traits of expert searchers. A model of search expertise is proposed with the four threshold concepts at its core that also integrates the traits and praxes elicited from the study, attributes which are likewise long recognized in LIS research as present in professional searchers. The research provides a deeper understanding of the transformative learning experiences involved in the acquisition of search expertise. It adds to our understanding of search expertise in the context of today's information environment and has implications for teaching advanced search, for research more broadly within library and information science, and for methodologies used to explore threshold concepts.

Scaffolding techniques : a teacher training for cooperative learning in Thailand primary education

Using cooperative learning in classrooms promotes academic achievement, communication skills, problem-solving, social skills and student motivation. Yet it is reported that cooperative learning as a Western educational concept may be ineffective in Asian cultural contexts. The study aims to investigate the utilisation of scaffolding techniques for cooperative learning in Thailand primary mathematics classes. A teacher training program was designed to foster Thai primary school teachers’ cooperative learning implementation. Two teachers participated in this experimental program for one and a half weeks and then implemented cooperative learning strategies in their mathematics classes for six weeks. The data collected from teacher interviews and classroom observations indicates that the difficulty or failure of implementing cooperative learning in Thailand education may not be directly derived from cultural differences. Instead, it does indicate that Thai culture can be constructively merged with cooperative learning through a teacher training program and practices of scaffolding techniques.

Modelling as a vehicle for philosophical inquiry in the mathematics curriculum

Philosophical inquiry in the teaching and learning of mathematics has received continued, albeit limited, attention over many years (e.g., Daniel, 2000; English, 1994; Lafortune, Daniel, Fallascio, & Schleider, 2000; Kennedy, 2012a). The rich contributions these communities can offer school mathematics, however, have not received the deserved recognition, especially from the mathematics education community. This is a perplexing situation given the close relationship between the two disciplines and their shared values for empowering students to solve a range of challenging problems, often unanticipated, and often requiring broadened reasoning. In this article, I first present my understanding of philosophical inquiry as it pertains to the mathematics classroom, taking into consideration the significant work that has been undertaken on socio-political contexts in mathematics education (e.g., Skovsmose & Greer, 2012). I then consider one approach to advancing philosophical inquiry in the mathematics classroom, namely, through modelling activities that require interpretation, questioning, and multiple approaches to solution. The design of these problem activities, set within life-based contexts, provides an ideal vehicle for stimulating philosophical inquiry.

E-motion diaries : blogging emotional responses to online learning in higher education

Emotions are inherently social, and are central to learning, online interaction and literacy practices (Shen, Wang, & Shen, 2009). Demonstrating the dynamic sociality of literacy practice, we used e-motion diaries or web logs to explore the emotional states of pre-service high school teachers’ experiences of online learning activities. This is because the methods of communication used by university educators in online learning and writing environments play an important role in fulfilling students’ need for social interaction and inclusion (McInnerney & Roberts, 2004). Feelings of isolation and frustration are common emotions experienced by students in many online learning environments, and are associated with the success or failure of online interactions and learning (Su, et al., 2005). The purpose of the study was to answer the research question: What are the trajectories of pre-service teachers’ emotional states during online learning experiences? This is important because emotions are central to learning, and the current trend toward Massive Open Online Courses (MOOCs) needs research about students’ emotional connections in online learning environments (Kop, 2011). The project was conducted with a graduate class of 64 high school science pre-service teachers in Science Education Curriculum Studies in a large Australian university, including males and females from a variety of cultural backgrounds, aged 22-55 years. Online activities involved the students watching a series of streamed live lectures for the first 5 weeks providing a varied set of learning experiences, such as viewing science demonstrations (e.g., modeling the use of discrepant events). Each week, students provided feedback on learning by writing and posting an e-motion diary or web log about their emotional response. Students answered the question: What emotions did you experience during this learning experience? The descriptive data set included 284 online posts, with students contributing multiple entries. Linguistic appraisal theory, following Martin and White (2005), was used to regroup the 22 different discrete emotions reported by students into the six main affect groups – three positive and three negative: unhappiness/happiness, insecurity/security, and dissatisfaction/satisfaction. The findings demonstrated that the pre-service teachers’ emotional responses to the streamed lectures tended towards happiness, security, and satisfaction within the typology of affect groups – un/happiness, in/security, and dis/satisfaction. Fewer students reported that the streamed lectures triggered negative feelings of frustration, powerlessness, and inadequacy, and when this occurred, it often pertained to expectations of themselves in the forthcoming field experience in classrooms. Exceptions to this pattern of responses occurred in relation to the fifth streamed lecture presented in a non-interactive slideshow format that compressed a large amount of content. Many students responded to the content of the lecture rather than providing their emotional responses to this lecture, and one student felt “completely disengaged”. The social practice of online writing as blogs enabled the students to articulate their emotions. The findings primarily contribute new understanding about students' wide range of differing emotional states, both positive and negative, experienced in response to streamed live lectures and other learning activities in higher education external coursework. The is important because the majority of previous studies have focused on particular negative emotions, such as anxiety in test taking. The research also highlights the potentials of appraisal theory for studying human emotions in online learning and writing.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

Successful outcomes in vocational education and training courses and mathematics: how pedagogy and expectations influence achievement

This paper reports on a four year Australian Research Council funded Linkage Project titled Skilling Indigenous Queensland, conducted in regional areas of Queensland, Australia from 2009 to 2013. The project sought to investigate Vocational Education and Training (VET) and teaching, Indigenous learners’ needs, employer culture and expectations and community culture and expectations to identify best practice in numeracy teaching for Indigenous VET learners. Specifically it focused on ways to enhance the teaching and learning of courses and the associated mathematics in such courses to benefit learners and increase their future opportunities of employment. To date thirty - nine teachers/trainers/teacher aides and two hundred and thirty - one students consented to participate in the project. Nine VET courses offered in schools and Technical and Further Education Institutes (TAFE) were nominated to be the focus on the study. This paper focuses on student questionnaire responses and interview responses from teachers/trainers one high school principal and five students as a result of these processes, the findings indicated that VET course teachers work hard to adopt contextualising strategies to their teaching; however this process is not always straight forward because of the perceptions of how mathematics has been taught and learned by trainers and teachers. Further teachers, trainers and students have high expectations of one another with the view to successful outcomes from the courses.