UTS site search

Dr Layna Groen


Layna undertook undergraduate studies at the University of Sydney, majoring in Pure Mathematics, with submajors in Physics, Geology and Applied Mathematics. She then undertook a Diploma of Education at the then Sydney Teachers College.

After teaching high school maths and science for three years, she commenced the Graduate Diploma in Operations Research, followed by a Masters of Applied Science in the same area at the University of Technology, Sydney.

Her interest in financial modeling then lead her to the University of New South Wales, where she completed a Masters of Commerce (Honours) in Finance.

She returned to the University of Technology, Sydney to complete her Doctor of Philosophy (2002), again in the area of financial modeling. For some years Layna was the Course Director/Program Leader for the Bachelor of Mathematics and Finance program, and at various times held the positions of Exemptions Coordinator and Elective Coordinator for the School of Mathematical Sciences.  She is current the Academic Liaison Officer for her School and the Honours Coordinator.

She has held the position of Assistant Student Ombud, and later the Student Ombud, positions she held from 2004 to 2010. She was a Science Faculty Representative on Academic Board 2008-2012, and was a member of the Academic Administration Committee from 2008 to 2012.  During this time she chaired working groups on Assessment Policy and Procedures and Admissions Policy and Procedures, and continues to work in the area of Rules review. She returned to the Academic Administration Committee in 2015 as the Deputy Chair.


For many years, Layna has been involved with the Sydney Chapter of the Australian Society for Operations Research, and has held positions as Treasurer and Chair at various times. She was a member of the International Ombudsman Association during her time as a Student Ombud.

Image of Layna Groen
Senior Lecturer, School of Mathematical and Physical Sciences
DipEd (Syd), BSc (Syd), GradDip OR (NSWIT), M Comm(Hons) (UNSW), M App Sc (UTS), PhD (UTS)
Member, Australian Society for Operations Research
+61 2 9514 2266

Research Interests

Dr Groen has undertaken a small number of consulting projects in queueing theory and simulation, while her research interests focus on static and dynamic optimisation, including optimal control, and mathematical modeling.

She has worked on the optimal location of tsunami warning buoys in the Indian Ocean and the Mediterranean Sea.  With her final year Operations Research class, she has constructed a multiple-objective goal programming model for water allocation in the Murrumbidgee catchment.

Layna is a Senior Lecturer with 25 years experience in the teaching of Operations Research at the undergraduate and postgraduate levels, and in the supervision of honours and postgraduate students. 

She has taught the undergraduate subjects 35140 Introduction to Quantitative Management, 35241 Optimisation in Quantitative Management, and 35340 Quantitative Management Practice in the Faculty of Science as well as a number of postgraduate and honours level Operations Research subjects. This includes subjects in optimal control, stochastic programming and large scale mathematical programming.  She has also lectured and tutored first year mathematics subjects for Engineering and Science students.  One of her current research interests is first year preparedness for mathematics for STEM students.  She has a long time interest in learning design and innovation in mathematics assessment.

She has also taught the postgraduate subject 21742 Quantitative Management for the Faculty of Business and continues to teach the current equivalent subject.  She also teaches Project Management for postgraduate Science students.


Groen, L., Chivers, B., Sidoti, A., Ma, J., Cheung, T.Y., Sow, D., Alharthy, A.A., Li, M., Cheng, Y., Wu, H. & Ding, L. 2013, 'A water resource allocation model for an area in the Murray-Darling Basin', Adapting to change: the multiple roles of modelling - Abstracts, 20th International Congress on Modelling and Simulation, The Modelling and Simulation Society of Australia and New Zealand, Adelaide, pp. 749-749.
Abstracts of the 20th International Congress on Modelling and Simulation (MODSIM2013). All papers were reviewed by at least two independent reviwers.
Groen, L. 2013, 'Steps toward mastery learning in a first year mathematics service subject', Australian Conference on Science and Mathematics Education 2013, Uniserve Science, The University of Sydney, Canberra, ACT, pp. 29-29.
Groen, L., Beames, S.Y., Coupland, M.P., Stanley, J. & Bush, S. 2013, 'Are science students ready for university mathematics?', Proceedings of the Australian Conference of Science and Mathematics Education (2013), ACSME 2013, University of Sydney, The Australian National University, Canberra.
Groen, L. 2011, 'Improving Tsunami Warning Times for Coastal Populations of the Mediterranean Sea', World OR: Global Economy and Sustainable Environment Program and Abstracts, 19th Triennial Conference of the International Federation of Operational Research Societies, International Federation of Operational Research Socities, Melbourne, pp. 101-101.
Program and abstracts for the conference.
Groen, L. 2011, 'Engaging mathematics students through undergraduate research', Proceedings of the Australian Conference on Science and Mathematics Education, Australian Conference on Science and Mathematics Education, Uniserve Science, Melbourne, pp. 44-48.
Conference abstracts and papers.
Groen, L. & Selvadurai, N. 2009, 'Strategic Positioning of Tsunami Detection Buoys in the Caribbean', National Conference of the Australian Society for Operations Research - Proceedings of Abstracts and Papers, The 20th National Conference of the Australian Society for Operations Research, Australian Society for Operations Research, Surfers Paradise, Gold Coast, Queensland Australia, pp. 45-46.
Groen, L. & Blazek, K. 2007, 'Optimising the Location of Tsumani detection Buoys in the Indian Ocean', 19th National Conference of the Australian Society for Operations Research - Conference Proceedings, Operations Research for Today and Tomorrow, Australian Society for Operations Research (Melbourne Chapter), Melbourne.
Groen, L. 2007, 'Meeting expectations - a focus of professional practice in an final year undergraduate mathematics course', Symposium Proceedings: Science Teaching and Learning Research Using Threshold Concepts, cience Teaching and Learning Research Using Threshold Concepts, Uniserve, Sydney, Australia, pp. 34-39.
View/Download from: UTS OPUS
This paper argues that achievement of many of the attributes of graduates in professional practice in operations research, or quantitative management science, can be developed best trhoguh a learning design that reflects current professional knowledge, skills and values. this necessarily places gthe focus of the learning design squarely on the student, with technology and communication at the nexus of the subject learning activities, and assessment tasks tailored to reflect this. The first steps in examination of the effectiveness of this form of learning design are undrtaken for a final year capstone subject in the Quatitative Management Science major in a Bachelor of scienc program. This examination is undertaken from the perspectve of students and teaching staff through the nalaysis of discussions with students conducted at milestones throughout the semester. positive student outcomes can be identified.
Groen, L. 2006, 'Enhancing learning and measuring learning outcomes in mathematics using online assessment', Symposium Proceedings: Assessment in Science Teaching and Learning, Assessment in science Teaching & Learning, Uniserve Science, Sydney, Australia, pp. 56-61.
View/Download from: UTS OPUS
Groen, L. & Carmody Jones, G. 2005, 'Blended learning in a first year mathematics subject', Proceedings of the Blended Learning in Science Teaching and learning, Blended Learning in Science Teaching and Learning`, Uniserve Science, Sydney, Australia, pp. 50-55.
View/Download from: UTS OPUS
This paper argues that the achievement of learning objectives for a first year mathematics subject, Operations Research Modelling can be best fostered through a blended learning design.'Blended learning' can be used in a variety of contextx. In this paper, the definition used is that of the integration of 'traditional' learning activities - lectures, tutorials, Mathematica and optimisation laboratories and paper-based assessment tasks - with leanring activities and environments more usually associated with other disciplines - collaborative learning, online assessment, peer review, case studies, spreadsheet technology, and the information and communication technology, Blackboard. It is argued that a blended learning design includes learning activities that more closely mirror professional practice and is ore likely to encourage a deep approach to learning. Effectiveness of the blended learning design is examined from the perspective of students and teaching staff, trhough the analysis of responses to questionnaires and comments collected.
Groen, L. 2005, 'Changes in product quality and consumer responses', Proceedings of the 18th National ASOR Conference & 11th Australian Optimisation Day, National Conference of the Australian Society for Operations Research, Western Australian Centre of Excellence in Industrial Optimisation, Perth, Australia, pp. 67-74.
View/Download from: UTS OPUS
This article examines the dynamic relationship between a firm's decision to vary the quality of a product, consumer responses to this variation, and the ffect this could have on the firm's profit and value. This is achieved through the construction and anlysis of a discrete-time optimal control model which incorporates consumer response. The consumer response model is based on sampling the product's market prior to the reduction in quality. The model is then solved numerically. The optimal time to reduce quality is shown to be affected by the ratio of price and cost differentials associated with differences in quality and the shareholder's required rate of return.
Groen, L. & Coupland, M. 2014, 'What is mastered in Mastery Learning?', Connections and Continuity - Mathematics from School to University, Canberra.
View/Download from: UTS OPUS
Though numbers are as yet not large, in the past two years at UTS of first-year students who studied General Mathematics, alarmingly high proportions of Science, Engineering and Mathematics students failed their first core undergraduate Mathematics subject. A similar observation holds for students with a background of General Mathematics in the subject Foundation Mathematics, a subject designed to address any gap in assumed knowledge and skills. This is deeply concerning especially as the number of students enrolling in STEM courses with backgrounds in General Mathematics is increasing. These observations are not unique to UTS – what is sometimes referred to as the mathematics problem has been reported worldwide for well over a decade. Given that some students were not bridging the gap between secondary and tertiary mathematics, Mastery Learning was introduced into a number of first year subjects. Pass rates, student satisfaction, attitudes towards learning and retention of content improved for many students. For some students, however, the outcomes were not as positive and they questioned what it was they thought they were learning. So, what is mastered in Mastery Learning?
Groen, L., Coupland, M., Memar, J. & Langtry, T.N. 2014, 'The past, present and future student of Mathematics – mastery learning to address the assumed mathematics knowledge gap, encourage learning and reflection, and future-proof academic performance', The Australia New Zealand Mathematics Convention, Melbourne, Australia.
First year students and academic staff in Science, Technology, Engineering and Mathematics (STEM) disciplines currently face many challenges. Failure rates at UTS are high in first year undergraduate Mathematics subjects for STEM programs. These high failure rates are particularly pronounced in students who studied General Mathematics this includes the subject Foundation Mathematics, a subject designed to address any gap in assumed knowledge and skills of first year students. Attrition is also a concern, with around 10% attrition after one semester and an additional 15% after two semesters. UTS is not alone in facing these challenges – under-preparedness for tertiary mathematics is a problem world-wide. When this problem first came to light more than a decade ago, UTS introduced the Readiness Survey (diagnostic test) to assess the extent to which the 'Assumed Knowledge' could indeed be assumed. This assessment of assumed knowledge and the associated pre-teaching could be effective but as the failure rates demonstrate, success has been mixed. A meeting of first year Mathematics academics in 2013 decided to trial a different and historically successful approach – Mastery Learning. Mastery Learning endorses the belief that aptitude relates to the amount of time it takes someone to learn, rather than necessarily capability to master content. The research literature indicates positive effects of Mastery Learning on students, especially in achievement, attitudes towards learning and retention of content. This paper describes the learning design and positives and negatives of implementing Mastery Learning in first year Mathematics subjects.

Journal articles

Groen, L., Coupland, M., Langtry, T., Memar, J., Moore, B.J. & Stanley, J. 2015, 'The Mathematics Problem and Mastery Learning for First-Year, Undergraduate STEM Students', International Journal of Learning, Teaching and Educational Research, vol. 11, no. 1, pp. 141-160.
View/Download from: UTS OPUS
In the 2014 academic year Mastery Learning was implemented in four first-year mathematics subjects in an effort to address a lack of preparedness and poor outcomes of increasing numbers of undergraduate students in science, engineering and mathematics programs. This followed partial success in the use of diagnostic testing and pre-teaching, active learning, and a greater emphasis on problem solving in context - under-prepared students were still more likely to fail the pre-teaching subject and to struggle with subsequent mathematics subjects. Also, failure rates overall were higher than benchmarks required. This paper describes the learning design used, and the outcomes achieved, with implementing Mastery Learning – the positive: improved academic success, time management, and attitudes towards learning and Mathematics, an increased sense of independence, confidence and retention of content, and reduced stress and anxiety; and the negative: students having a sense of being taught how to pass a test rather than having a deeper understanding of the content. It will be seen that this negative is a consequence of a small but important difference in implementation.
Thornton, B., Thornton-Benko, E. & Groen, L. 2011, 'Interacting psycho-economics expectations ratios with equity/debt realities suggests a crisis warning method', International Journal Bioautomotion, vol. 15, no. 4, pp. 215-222.
View/Download from: UTS OPUS
The recent April 2011 meeting of the G20 countries considered possible development of a global early warning system to avoid any future financial crisis. Psycho-economic factors are strong drivers of greed, fear and non-rational behavior and experience shows that they should not be excluded from such a project. Rational, logical behavior for attitude and actions has been an assumption in most financial models prior to the advent of the 2008 crisis. In recent years there has been an increasing interest in relating financial activity to phenomena in physics, turbulence, neurology and recent fMRI experiments show that cortical interactions for decisions are affected by previous experience. We use an extension of two Lotka-Volterra (LV) interactive equations used in a model for the 2008 crisis but now with fluctuation theory from chemical physics to interact the two previously used heterogenous interacting agents, the psycho-economic ratio C E of investor expectations (favourable/unfavourable) and the reality ratio of equity/debt. The model provides a variable, M, for uncertainties in C E arising from the ability of the economy to affect the financial sector. A condition obtained for keeping rates of change in M small to avoid divergence of spontaneous fluctuations, provides a quantifiable time dependent entity which can act as a warning of impending crisis. The conditional expression appears to be related to an extension of Ohm's law as in a recently discovered "chip" and memory - the memristor. The possible role of subthreshold legacies in C E from the previous crisis appears to be possible and related to recent neurological findings.
Groen, L., Botten, L. & Blazek, K. 2010, 'Optimising the location of tsunami detection buoys and sea-level monitors in the Indian Ocean', International Journal of Operational Research, vol. 8, no. 2, pp. 174-188.
View/Download from: UTS OPUS or Publisher's site
In the wake of the 2004 Boxing Day tsunami disaster, a global response to implement a tsunami warning system in the Indian Ocean became imperative. Steps in this direction were initiated in 2005 with plans for the deployment of up to 24 tsunami detection buoys. The purpose of this paper is to investigate the optimal placement of tsunami detection buoys and sea-level monitors, in order to provide warning to the greatest population potentially affected. We adopt a mathematical programming approach to examine this problem. It is determined that 10 sites are essential in ensuring that the maximum population can be warned. This has implications for construction and maintenance of the tsunami warning system in the Indian Ocean. Copyright © 2010 Inderscience Enterprises Ltd.
Groen, L., Joseph, A., Black, E., Menictas, M., Tam, W. & Gabor, M. 2010, 'Optimal location of tsunami warning buoys and sea level monitoring stations in the mediterranean sea', Science of Tsunami Hazards, vol. 29, no. 2, pp. 78-95.
View/Download from: UTS OPUS
The present study determines the optimal location of detection components of a tsunami warning system in the Mediterranean region given the existing and planned infrastructure. Specifically, we examine the locations of existing tsunameters DART buoys and coastal sea-level monitoring stations to see if additional buoys and stations will improve the proportion of the coastal population that may receive a warning ensuring a timely response. A spreadsheet model is used to examine this issue. Based on the historical record of tsunamis and assuming international cooperation in tsunami detection, it is demonstrated that the existing network of sea level stations and tsunameters enable around ninety percent of the coastal population of the Mediterranean Sea to receive a 15 minute warning. Improvement in this result can be achieved through investment in additional real-time, coastal, sea level monitoring stations. This work was undertaken as a final year undergraduate research project.
Groen, L. & Selvadurai, J.N. 2010, 'Strategic positioning of Tsunami detection buoys in the Caribbean Sea', Australian Society for Operations Research (ASOR) Bulletin, vol. 29, no. 2, pp. 15-26.
View/Download from: UTS OPUS
The December 2004 Indian Ocean tsunami increased global awareness to the destructive nature of tsunamis. International effort in constructing a tsunami warning system (TWS) in the Indian Ocean followed. The issue of constructing a cost- and performance-effective TWS is still on the agenda in a number of areas world-wide. This includes the countries bordering the Caribbean Sea. The purpose of this paper is to examine the effectiveness of the current Caribbean tsunami warning system and, where required, to suggest how its performance can be improved. It is found that relatively few additional detectors are required to improve performance.
Groen, L. 2006, 'Mathematics for Business Decisions', Australian Mathematics Teacher, vol. 1.
Groen, L. 2006, 'Essentials of Mathematics', The Australian Mathematics Teacher, vol. 62, no. 1.
Groen, L. 2006, 'Mathematics as a Constructive Activity', Australian Mathematics Teacher, vol. 62, no. 1.
Selected Peer-Assessed Projects