Professor Chris Matthews is from the Quandamooka people of Minjerribah (Stradbroke Island) in Queensland Australia. Chris received a PhD in applied mathematics from Griffith University and was a Senior Lecturer in applied mathematics at the Griffith School of Environment, Griffith University. Over the last ten years, Chris developed a deeper interest in mathematics education for Aboriginal and Torres Strait Islander learners and exploring the connections between mathematics and Aboriginal and Torres Strait Islander knowledges. Chris is currently the Chair of the Aboriginal and Torres Strait Islander Mathematics Alliance (ATSIMA) that aims to transform mathematics education for Aboriginal and Torres Strait Islander learners. He is also a senior curriculum advisor for Australian Curriculum, Asessment and Reporting Authority (ACARA) for the National Mathematics Curriculum working to including Aboriginal and Torres Strait Islander perspectives in the curriculum. Chris has recently been appointed the Associate Dean (Indigenous Leadership and Engagement) in the Science Faculty at University Technology of Sydney (UTS). As part of this role, Chris will be leading a team of academics to transform the Science curriculum to meet the Indigenous Graduate Attribute and develop a Community of Indigenous STEM professionals at UTS.
Howlett, C, Ferreira, JA, Seini, M & Matthews, C 2013, 'Indigenising the Griffith school of environment curriculum: Where to from here?', Australian Journal of Indigenous Education, vol. 42, no. 1, pp. 68-74.View/Download from: Publisher's site
This article presents a discussion on a study undertaken by academics within the Griffith School of Environment, Brisbane, Australia that sought to explore the potential of an Indigenised curriculum to attract and retain Indigenous students, and thereby facilitate greater participation of Indigenous students in science. The article highlights the need for staff to be both reflective and reflexive about the limitations their particular knowledge systems may impose on Indigenous ways of knowing and knowledge systems. The article also acknowledges the need for professional development opportunities for staff prior to any attempts towards Indigenisation of the curriculum. Copyright © The Authors 2013.
Kendall, E, Sunderland, N, Barnett, L, Nalder, G & Matthews, C 2011, 'Beyond the rhetoric of participatory research in Indigenous communities: Advances in Australia over the last decade', Qualitative Health Research, vol. 21, no. 12, pp. 1719-1728.View/Download from: Publisher's site
Evidence-based approaches to health care have been difficult to achieve in Indigenous populations across the world, a situation which has contributed to the significant health disparities found in this group. One reason for the inadequacy of evidence-based health interventions is that empirical knowledge tends to be organized around professional disciplines that are grounded in Western ways of knowing. In this article we describe events that have led to more appropriate research methods in Australia, and the resulting changes in the research community. The principles that have guided Australian research policy development might not yet be fully matured, but the improvements we have experienced over the last several decades have gone a long way toward acknowledging the significant disparities that affect Indigenous people and the role of researchers in addressing this issue. © SAGE Publications 2011.
Ewing, B, Cooper, TJ, Baturo, AR, Matthews, C & Sun, H 2010, 'Contextualising the Teaching and Learning of Measurement within Torres Strait Islander Schools', Australian Journal of Indigenous Education, vol. 39, no. 1, pp. 11-23.View/Download from: Publisher's site
A one-year mathematics project that focused on measurement was conducted with six Torres Strait Islander schools and communities. Its key focus was to contextualise the teaching and learning of measurement within the students' culture, communities and home languages. Six teachers and two teacher aides participated in the project. This paper reports on the findings from the teachers' and teacher aides' survey questionnaire used in the first Professional Development session to identify: a) teachers' experience of teaching in the Torres Strait Islands, b) teachers' beliefs about effective ways to teach Torres Strait Islander students, and c) contexualising measurement within Torres Strait Islander culture, communities and home languages. A wide range of differing levels of knowledge and understanding about how to contextualise measurement to support student learning were identified and analysed. For example, an Indigenous teacher claimed that mathematics and the environment are relational, that is, they are not discrete and in isolation from one another, rather they interconnect with mathematical ideas emerging from the environment of the Torres Strait communities. © 2010, Cambridge University Press. All rights reserved.
Matthews, C 2009, 'Geothermal energy prospectivity of the Torrens Hinge Zone: evidence from new heat flow data', Exploration Geophysics, vol. 40, no. 3, pp. 288-300.View/Download from: Publisher's site
Hauser, V, Howlett, C & Matthews, C 2009, 'The Place of Indigenous Knowledge in Tertiary Science Education: A Case Study of Canadian Practices in Indigenising the Curriculum', Australian Journal of Indigenous Education, vol. 38, no. S1, pp. 46-58.View/Download from: Publisher's site
In Australia, Indigenising the curriculum is increasingly acknowledged as a possible avenue for addressing Indigenous under-representation in tertiary science education in a culturally appropriate and relevant manner. While no Australian university has implemented such a program, there is much to be learnt about the inherent complexities of Indigenising curriculum before it is pursued. In Canada, however, innovative university programs have been implemented that imbed Indigenous knowledge into the curriculum. This paper details key findings from research that sought to learn from Canadian practices in Indigenising tertiary science curriculum, by exploring the practices and experiences of two Canadian programs: Trent University's Indigenous Environmental Studies program, and Cape Breton University's Integrative Science program. © 2009, Cambridge University Press. All rights reserved.
Howlett, C, Seini, M, Matthews, C, Dillon, B & Hauser, V 2008, 'Retaining Indigenous Students in Tertiary Education: Lessons from the Griffith School of Environment', Australian Journal of Indigenous Education, vol. 37, no. 1, pp. 18-27.View/Download from: Publisher's site
Low retention of Indigenous peoples in all Australian universities has been identified as a problematic issue by the Australian Federal government. Griffith University (GU), Queensland, Australia, provided funding to examine the factors affecting Indigenous retention in higher education, with the aim of developing innovative participation and retention strategies specifically for Indigenous students. This paper focuses on research conducted within the Griffith School of Environment that questioned the possible links between the provision of information to commencing Indigenous students and their retention. It essentially examines to what extent current university structures support Indigenous enrolments and retention, via the information they receive upon enrolling. From interviews conducted in an informal discussion format with currently enrolled Indigenous students in the Griffith School of Environment, critical deficiencies were identified in the information Indigenous students receive during the early transition phase of university entrance. A key finding of this study, and which is the subject of current research, was the support amongst the students for the development of an Indigenised curriculum in science as a strategy for improving the attraction and retention of Indigenous students. This paper details the research project and its findings. © 2008, Cambridge University Press. All rights reserved.
Matthews, CJ, Newton, DB, Braddock, RD & Yu, B 2007, 'Analysing the sensitivity behaviour of two hydrology models', Environmental Modeling and Assessment, vol. 12, no. 1, pp. 27-41.View/Download from: Publisher's site
Recently, the New Morris Method has been presented as an effective sensitivity analysis tool for mathematical models. The New Morris Method estimates the sensitivity of an output parameter to a given set of input parameters (first-order effects) and the extent these parameters interact with each other (second-order effects). This method requires the specification of two parameters (runs and resolution) that control the sampling of the output parameter to determine its sensitivity to various inputs. The criteria for these parameters have been set on the analysis of a well-behaved analytical function (see Cropp and Braddock, Reliab. Eng. Syst. Saf. 78:77-83, 2002), which may not be applicable to other physical models that describe complex processes. This paper will investigate the appropriateness of the criteria from (Cropp and Braddock, 2002) and hence the effectiveness of the New Morris Method to determine the sensitivity behaviour of two hydrologic models: the Soil Erosion and Deposition System and Griffith University Representation of Urban Hydrology. In the first case, this paper will separately analyse the sensitivity of an output parameter on a set of input parameters (first- and second-order effects) for each model and discuss the physical meaning of these sensitivities. This will be followed by an investigation into the sampling criteria by exploring the convergence of the sensitivity behaviour for each model as the sampling of the parameter space is increased. By comparing these trends to the convergence behaviour from Cropp and Braddock (2002), we will determine how well the New Morris Method estimates the sensitivity for each model and whether the sampling criteria are appropriate for these models. It will be shown that the New Morris Method can provide additional insight into the functioning of these models, and that, under a different metric, the sensitivity behaviour of these models does converge confirming the sampling criteria set by Cropp and Brad...
Lee, HS, Matthews, CJ, Braddock, RD, Sander, GC & Gandola, F 2005, 'Erratum: A MATLAB method of lines template for transport equations (Environmental Modelling & Software (2004) 19 (603-614) PII: S1364-8152(03)00211-1 and DOI: 10.1016/j.envsoft.2003.08.017', Environmental Modelling and Software, vol. 20, no. 3, p. 377.View/Download from: Publisher's site
Matthews, CJ, Cook, FJ, Knight, JH & Braddock, RD 2005, 'Handling the water content discontinuity at the interface between layered soils within a numerical scheme', Australian Journal of Soil Research, vol. 43, no. 8, pp. 945-955.View/Download from: Publisher's site
In general, the water content (θ) form of Richards' equation is not used when modeling water flow through layered soil since θ is discontinuous across soil layers. Within the literature, there have been some examples of models developed for layered soils using the θ-form of Richards' equation. However, these models usually rely on an approximation of the discontinuity at the soil layer interface. For the first time, we will develop an iterative scheme based on Newton's method, to explicitly solve for θ at the interface between 2 soils within a numerical scheme. The numerical scheme used here is the Method of Lines (MoL); however, the principles of the iterative solution could be used in other numerical techniques. It will be shown that the iterative scheme is highly effective, converging within 1 to 2 iterations. To ensure the convergence behaviour holds, the numerical scheme will be tested on a fine-over-coarse and a coarse-over-fine soil with highly contrasting soil properties. For each case, the contrast between the soil types will be controlled artificially to extend and decrease the extent of the θ discontinuity. In addition, the numerical solution will be compared against a steady-state analytical solution and a numerical solution from the literature. © CSIRO 2005.
Lee, HS, Matthews, CJ, Braddock, RD, Sander, GC & Gandola, F 2004, 'A MATLAB method of lines template for transport equations', Environmental Modelling and Software, vol. 19, no. 6, pp. 603-614.View/Download from: Publisher's site
Many environmental problems involve diffusion and convection processes, which can be described by partial differential equations (PDEs). This paper will describe the development of a MATLAB template that generates a numerical solution to PDEs using the method of lines. The template will be applied to various unsaturated flow problems within soil physics to demonstrate the versatility of the method. In particular, the template will generate solutions for three cases (1) one-dimensional Richards' equation for vertical infiltration; (2) coupled one-dimensional Richards' equation and solute transport equation for horizontal water and contaminant flow; and (3) two-dimensional Richard's equation for unsaturated flow over a complex geometry. Where possible, the results from the template will be compared against analytical solutions to determine the accuracy of the numerical solution. In addition, the paper will provide a discussion on possible extensions to the template and future directions. © 2003 Elsevier Ltd. All rights reserved.
Matthews, CJ, Braddock, RD & Sander, GC 2004, 'Modeling flow through a one-dimensional multi-layered soil profile using the Method of Lines', Environmental Modeling and Assessment, vol. 9, no. 2, pp. 103-113.View/Download from: Publisher's site
The vertical flow of water through horizontal layers of soil is considered using the Method of Lines. Continuity of mass principles are used to develop the interface boundary conditions, by introducing fictitious points at the interface, and the boundary conditions are handled using explicit and iterative approximations. Both the pressure based, and the water content based forms of Richards' equation are solved using the Method of Lines. The solutions obtained are compared with some particular analytic solutions obtained from the literature, and the results show that good accuracy can be achieved. It is also shown that the water content model can handle a large discontinuity at the interface when compared against the analytical solution. This result is also confirmed against a numerical example from the literature, and was effective for relatively dry initial conditions.
Weeks, SW, Sander, GC, Braddock, RD & Matthews, CJ 2004, 'Saturated and unsaturated water flow in inclined porous media', Environmental Modeling and Assessment, vol. 9, no. 2, pp. 91-102.View/Download from: Publisher's site
This paper considers the two-dimensional saturated and unsaturated flow of water through inclined porous media, namely a waste dump or hill slope. Since the partial differential equation governing this water flow transforms from being parabolic to elliptic as the water flow varies from unsaturated to saturated, an iterative, finite differencing scheme is used to develop a numerical solution. The model can be used to investigate the effects that hill slope angle, depth of soil cover and hilltop width have on water accumulation in the dump and the time required for saturation to occur at different areas in the dump domain. The accuracy and reliability of the computer based solution is tested for two different boundary conditions - (1) no flow on all boundaries (i.e., the internal redistribution of soil moisture to steady state) and (2) a constant rainfall flux on the dump surface. Numerical studies then show the effects of changing the hill slope angle, depth of layer, and dump geometry on the flow characteristics in the dump.
Mousley, JA & Matthews, C 2018, 'Australia: Mathematics and its teaching in Australia' in Mathematics and its teaching in the Asia-pacific region, pp. 113-155.
Heinson*, G, Carter, S, Krieger, L, Boren, G & Matthews, C 2015, 'Magnetotelluric Monitoring of a Hydraulic Fracturing in Moomba, South Australia', International Conference and Exhibition, Melbourne, Australia 13-16 September 2015, International Conference and Exhibition, Melbourne, Australia 13-16 September 2015, Society of Exploration Geophysicists and American Association of Petroleum Geologists.View/Download from: Publisher's site
Matthews, CJ, Cook, FJ, Braddock, RD & Knight, JH 2005, 'Comparing two new transformations for the water content form of richards' equation', Proceedings of the 14th IASTED International Conference on Applied Simulation and Modelling, pp. 186-191.
This study will present two new transformations that are applied to the water content (θ) form of Richard's Equation: 1) a reference soil transformation and 2) a constant "relative gradient ratio" transformation. The reference soil transformation enables a model to simulate water flow in a given soil in terms of θ for a reference soil. The main advantage of this transformation is that it provides a continuous 6 profile across soil layers. However, the choice of a reference soil could also provide some numerical advantages by, for example, minimising the effect of sharp wetting fronts. An analytical expression will be derived that approximates the effect a transformation has on the gradients within a system. This approximation is based on the notion of relative gradients and will assist in analysing, which reference soils are appropriate for the problem. In addition, the analytical approximation can be used to derive general transformations for partial differential equations (PDEs). For this study, we will derive a constant "relative gradient ratio" transformation that will decrease relative gradients within the system by a constant factor (ε). Using the Method of lines (MOL), numerical solutions will be generated for a test case from the literature for both transformed and non-transformed equations. By comparing these solutions, this paper will analyse whether the new transformations improve the efficiency and/or accuracy of the numerical solution for the test case problem.
Matthews, CJ, Knight, JH, Cook, FJ & Braddock, RD 2005, 'The effect of heat on the diversion length of capillary barriers', MODSIM05 - International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, Proceedings, pp. 1772-1778.
Within the literature, capillary barriers have been suggested as an alternative hydraulic barrier in cover liners for waste dumps. When a waste dump reaches its full capacity, cover liners are usually constructed over the waste mound to seal the waste from the surrounding environment. One main function of a cover liner is to prevent substantial amounts of water infiltrating into the waste material thereby preventing leaching and potentially contamination of the ground water system. A capillary barrier consists of a fine soil overlying a coarse soil, which can impeded infiltrating water at the soil layer interface by capillary forces. Breakthrough into the coarse soil will only occur once enough water has accumulated at the interface to overcome the water-entry pressure of the coarse soil. If a capillary barrier is inclined, water will flow laterally downslope (or upslope) until breakthrough is reached. The length of this lateral flow, parallel to the slope, is known as the diversion length. Additionally, sealed waste can produce a substantial amount of heat due to the decomposing waste material. Therefore, it is important to explore the effect of heat on the performance of capillary barriers. This paper will explore the effect of heat on the diversion length of a capillary barriers by using a numerical model based on the Method of Lines. The model will be used to simulate one-dimensional coupled heat and water flow through a capillary barrier consisting of a Glendale clay loam over Berino fine sand. The domain will be rotated by a given angle and will represent flow through an elongated slope where the edge effects can be ignored. It will be assumed that the underlying waste will generate a constant heat source while the soil surface experiences a constant water flux. Under these conditions, the heat generated by the waste will result in heat and water fluxes moving up the soil profile towards the soil surface opposing the infiltrating water flux. To estimate the...
Matthews, CJ, Knight, JH, Cook, FJ & Braddock, RD 2005, 'Using analytical solutions for homogenous soils to assess numerical solutions for layered soils', MODSIM05 - International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, Proceedings, pp. 1279-1285.
Analytical solutions for non-steady flow are an important aspect of mathematical modeling in all fields of computational science. An analytical solution provides an exact solution for a specific (simplified) test case, which then can be used to test and verify numerical solutions. Within soil physics, there has been a multitude of analytical solutions that model transient flow through one-dimensional homogenous soil profiles under various flow conditions. For homogenous soils, analytical solutions exist for realistic soil types (i.e. non-linear hydraulic functions) and for coupled solute and water transport. However, for layered soils, there has only been one analytical solution for non-steady flow. Even though this solution has been useful for testing numerical schemes, the disadvantages of the solution are 1) it is lengthy, complex and difficult to program; 2) is only valid for a particular form of the hydraulic functions with a constant hydraulic diffusivity (D); and 3) one of the key soil parameters is constant across soil layers. To overcome these limitations, we will use a transformation technique to transform an analytical solution for water flow in a homogenous soil to obtain an analytical solution for an idealized layered soil profile. The idealized analytical solution arises from only transforming part of the solution over a selected segment of the spatial domain. For this study, we examine 1) a linear transformation of the solution variable (θ) and the spatial coordinate system (z) and 2) a non-linear transformation of the solution variable (θ). As a starting point, we will use a simple analytical solution developed by Clothier et al. (1981), which models constant flux infiltration into a field soil: Bungendore fine sand. This soil is a special case since experimentally, it was shown that D is near constant and K is approximately quadratic. Under these properties (1) reduces to the well-known Burgers' equation. Note that under the non-linear transforma...