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.
Groen, L, Coupland, M, Memar, J & Langtry, T 2015, 'Mastery Learning to Address the Assumed Mathematics Knowledge Gap, Encourage Learning and Reflection, and Future-proof Academic Performance', International Journal of Innovation in Science and Mathematics Education, vol. 23, no. 2, pp. 65-79.View/Download from: UTS OPUS
UTS Science, Engineering and Mathematics students who have studied General Mathematics at high school are far more likely to fail their first undergraduate mathematics subject compared to their counterparts who meet the non-compulsory 'Assumed Knowledge' of 2 unit Mathematics. This problem has been growing in recent years as an increasing number of students seek to improve their tertiary entrance score by taking the no-calculus General Mathematics at the Higher School Certificate. This problem is not unique to the University of Technology, Sydney - mathematical under-preparedness is a problem world-wide, with a decade, or more, long history. For some years, UTS has used diagnostic testing and pre-teaching to assist under-prepared students. Unfortunately, students who studied General Mathematics are also more likely to fail the pre-teaching subject. This suggested something more was required. Mastery Learning was chosen as a potential solution. Results to date have been promising with improvements in academic success for under-prepared students. Students have also reported increased satisfaction, confidence and retention of content. However, some students felt all Mastery Learning taught them was how to pass the Mastery Tests. Differences in student experience appear to be due to differences in how Mastery Learning was implemented.
Zinder, Y, Memar, J & Singh, G 2013, 'Discrete Optimization With Polynomially Detectable Boundaries And Restricted Level Sets', Combinatorial Optimization and Applications, vol. 25, no. 2, pp. 308-325.View/Download from: UTS OPUS or Publisher's site
The paper describes an optimization procedure for a class of discrete optimization problems which is defined by certain properties of the boundary of the feasible region and level sets of the objective function. It is shown that these properties are possessed, for example, by various scheduling problems, including a number of well known NP-hard problems which play an important role in scheduling theory. For one of these problems the presented optimization procedure is compared with a version of the branch-and-bound algorithm by means of computational experiments
Gu, H, Memar, J & Zinder, Y 2018, 'Scheduling batch processing in flexible flowshop with job dependent buffer requirements: Lagrangian relaxation approach', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 119-131.View/Download from: Publisher's site
© Springer International Publishing AG, part of Springer Nature 2018. The paper presents a Lagrangian relaxation based algorithm for scheduling jobs in the two-stage flowshop where the first stage is comprised of several parallel identical machines and the second stage consists of a single machine processing jobs in the predefined batches. Motivated by applications where unloading and loading occur when the means of transportation are changed, the processing of the jobs, constituting a batch, can commence only if this batch has been allocated a portion of a limited buffer associated with the flowshop. This portion varies from batch to batch and is released only after the completion of the batch processing on the second stage machine. Each batch has a due date and the objective is to minimise the total weighted tardiness. The effectiveness of the proposed algorithm is demonstrated by computational experiments.
Gu, H, Memar, J & Zinder, Y 2018, 'Efficient lagrangian heuristics for the two-stage flow shop with job dependent buffer requirements', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 312-324.View/Download from: Publisher's site
© Springer International Publishing AG, part of Springer Nature 2018. The paper is concerned with minimisation of total weighted completion time for the two-stage flow shop with a buffer. In contrast to the vast literature on this topic, the buffer requirement varies from job to job and a job occupies the buffer continuously from the start of its first operation till the completion of its second operation rather than only between operations. Such problems arise in supply chains requiring unloading and loading of minerals and in some multimedia systems. The problem is NP-hard and the straightforward integer programming approach is impossible even for modest problem sizes. The paper presents a Lagrangian relaxation based decomposition approach that allows to use for each problem, obtained by this decomposition, a very fast algorithm. Several Lagrangian heuristics are evaluated by means of computational experiments.
Gu, H, Memar, J & Zinder, Y 2016, 'Search Strategies for Problems with Detectable Boundaries and Restricted Level Sets', DATA AND DECISION SCIENCES IN ACTION, 24th Australian-Society-for-Operations-Research (ASOR) Conference, SPRINGER INTERNATIONAL PUBLISHING AG, Univ New S Wales, Canberra Campus, Kensington, AUSTRALIA, pp. 149-162.View/Download from: Publisher's site
Memar, J, Zinder, Y & Kononov, AV 2018, 'Worst-case analysis of a modification of the brucker-garey-johnson algorithm', Communications in Computer and Information Science, pp. 78-92.View/Download from: Publisher's site
© Springer International Publishing AG, part of Springer Nature 2018. The paper presents the worst-case analysis of a polynomial-time approximation algorithm for the maximum lateness scheduling problem with parallel identical machines, arbitrary processing times and arbitrary precedence constraints. The algorithm is a modification of the Brucker-Garey-Johnson algorithm originally developed as an exact algorithm for the case of the problem with unit execution time tasks and precedence constraints represented by an in-tree. For the case when the largest processing time does not exceed the number of machines, we obtain a worst-case performance guarantee which is tight for arbitrary large instances of the considered maximum lateness problem. It is shown that, if the largest processing time is greater than the number of machines, then the worst-case performance guarantee for the list algorithm, obtained by Hall and Shmoys, is tight.
Memar, J, Singh, G & Zinder, Y 2013, 'Scheduling partially ordered UET tasks on dedicated machines', IFAC Proceedings Volumes (IFAC-PapersOnline), IFAC Conference on Manufacturing Modelling, Management, and Control, Elsevier, Saint Petersburg, Russia, pp. 1672-1677.View/Download from: UTS OPUS or Publisher's site
The paper is concerned with scheduling partially ordered unit execution time tasks on dedicated machines. The considered scheduling model is important in control of different systems, in particular computer systems. The presented algorithm is an alternative to the conventional branch-and-bound method. In contrast to the branch-and-bound method with its single search tree, corresponding to partitioning of the feasible region, the presented method involves a sequence of search trees each associated with a certain portion of the domain of the objective function. The branching is based on a generalisation of the Garey-Johnson due date modification. The performance of the presented algorithm is compared by means of computational experiments with a version of the branch-and-bound algorithm. © IFAC.
Zinder, Y, Memar, J & Singh, G 2010, 'Discrete optimisation with polynomially detectable boundaries and restricted level sets', Lecture Notes in computer Science Vol 6508: Combinatorial Optimization and Applications - 4th Annual International Conference on Combinatorial Optimization and Applications, international conference on Combinatorial optimization and applications, Kailua-Kona, USA, pp. 142-156.View/Download from: UTS OPUS or Publisher's site
The paper describes an optimization procedure for a class of discrete optimization problems which is defined by certain properties of the boundary of the feasible region and level sets of the objective function. It is shown that these properties are possessed, for example, by various scheduling problems, including a number of well-known NP-hard problems which play an important role in scheduling theory. For an important particular case the presented optimization procedure is compared with a version of the branch-and-bound algorithm by means of computational experiments
Groen, L, Coupland, M, Memar, J & Langtry, TN 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.