Mathematical Modeling Skills Research Articles

Application of Fuzzy Relation Equations to Student Assessment

Mathematical modelling appears today as a dynamic tool for teaching/learning mathematics, because it connects mathematics with real world applications and therefore increases the student interest on the subject. Fuzzy relation equations, which are obtained by the composition of binary fuzzy relations, are used in this work as a tool for evaluating student mathematical modelling skills. A classroom application and other suitable examples are also presented illustrating our results.

Психолого-педагогічні аспекти формування умінь математичного моделювання в учнів старшої школи

Психолого-педагогічні аспекти формування умінь математичного моделювання в учнів старшої школи

A unique large-scale undergraduate research experience in molecular systems biology for non-mathematics majors.

Systems biology is frequently taught with an emphasis on mathematical modeling approaches. This focus effectively excludes most biology, biochemistry, and molecular biology students, who are not mathematics majors. The mathematical focus can also present a misleading picture of systems biology, which is a multi-disciplinary pursuit requiring collaboration between biochemists, bioinformaticians, and mathematicians. This article describes an authentic large-scale undergraduate research experience (ALURE) in systems biology that incorporates proteomics, bacterial genomics, and bioinformatics in the one exercise. This project is designed to engage students who have a basic grounding in protein chemistry and metabolism and no mathematical modeling skills. The pedagogy around the research experience is designed to help students attack complex datasets and use their emergent metabolic knowledge to make meaning from large amounts of raw data. On completing the ALURE, participants reported a significant increase in their confidence around analyzing large datasets, while the majority of the cohort reported good or great gains in a variety of skills including "analysing data for patterns" and "conducting database or internet searches." An environmental scan shows that this ALURE is the only undergraduate-level system-biology research project offered on a large-scale in Australia; this speaks to the perceived difficulty of implementing such an opportunity for students. We argue however, that based on the student feedback, allowing undergraduate students to complete a systems-biology project is both feasible and desirable, even if the students are not maths and computing majors. © 2016 by The International Union of Biochemistry and Molecular Biology, 45(3):235-248, 2017.

Subject design and factors affecting achievement in mathematics for biomedical science

ABSTRACTReports such as Bio2010 emphasize the importance of integrating mathematical modelling skills into undergraduate biology and life science programmes, to ensure students have the skills and knowledge needed for biological research in the twenty-first century. One way to do this is by developing a dedicated mathematics subject to teach modelling and mathematical concepts in biological contexts. We describe such a subject at a research-intensive Australian university, and discuss the considerations informing its design. We also present an investigation into the effect of mathematical and biological background, prior mathematical achievement, and gender, on student achievement in the subject. The investigation shows that several factors known to predict performance in standard calculus subjects apply also to specialized discipline-specific mathematics subjects, and give some insight into the relative importance of mathematical versus biological background for a biology-focused mathematics subject.

ICT mediated collaborative work in system dynamics learning

Although mathematical modeling is a general engineering skill, problem analysis and solution design conventional tools in systems engineering, such as use case diagrams, class diagrams and relational diagrams among others, are often not supported by a mathematical model or this is not made explicit during learning. This may affect the ability of the systems engineer for interdisciplinary work, whose participation in the requirements determination phase of the software development process can be reduced to be notified of the needs identified by the other actors, without a critical contribution of its party. This paper presents results of research that show the favorable effect of collaborative work mediated by information and communication technology ICT on System Dynamics mathematical modeling skills developing by Systems Engineering students.

Investigating and developing engineering students’ mathematical modelling and problem-solving skills

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.

A Trapezoidal Fuzzy Method for Assessing Students’ Mathematical Modeling Skills

Fuzzy logic due to its nature of characterizing each case with multiple values offers a rich field of resources covering the assessment of situations characterized by a degree of vagueness and/or uncertainty. In this paper, we apply a new trapezoidal fuzzy assessment model (TRFAM) for measuring students’ mathematical modeling (MM) skills. TRFAM is actually a variation of the commonly used in fuzzy logic centre of gravity (COG) defuzzification technique, which we have properly adapted and utilized in earlier papers as an assessment model. Our COG and TRFAM models focus on students’ quality performance by assigning greater coefficients to the higher scores. A classroom experiment is also presented, illustrating our results in practice. Through this experiment the above two models are compared to each other and also with two traditional assessment methods based on principles of bivalent logic (the calculation of means and of the GPA index) and some useful conclusions are drawn.

Rationale and resources for teaching the mathematical modeling of athletic training and performance

A number of professions rely on exercise prescription to improve health or athletic performance, including coaching, fitness/personal training, rehabilitation, and exercise physiology. It is therefore advisable that the professionals involved learn the various tools available for designing effective training programs. Mathematical modeling of athletic training and performance, which we henceforth call "performance modeling," is one such tool. Two models, the critical power (CP) model and the Banister impulse-response (IR) model, offer complementary information. The CP model describes the relationship between work rates and the durations for which an individual can sustain them during constant-work-rate or intermittent exercise. The IR model describes the dynamics by which an individual's performance capacity changes over time as a function of training. Both models elegantly abstract the underlying physiology, and both can accurately fit performance data, such that educating exercise practitioners in the science of performance modeling offers both pedagogical and practical benefits. In addition, performance modeling offers an avenue for introducing mathematical modeling skills to exercise physiology researchers. A principal limitation to the adoption of performance modeling is a lack of education. The goal of this report is therefore to encourage educators of exercise physiology practitioners and researchers to incorporate the science of performance modeling in their curricula and to serve as a resource to support this effort. The resources include a comprehensive review of the concepts associated with the development and use of the models, software to enable hands-on computer exercises, and strategies for teaching the models to different audiences.

Assessing student teams developing mathematical models applied to business and industrial mathematics

Using case studies and group work, this project attempted to provide students with experience of business and industrial working practices and also to address the issue of how to solve practical mathematical problems. Students were organised into teams and tasked with solving a problem presented in the form of a real world industrial case study. Each group was assessed on their problem solving abilities, mathematical modelling skills and also on their team work and contribution to the group. Industrial partners were also invited to judge the final solutions presented by the group and feedback was offered, based on the ‘real world’ situation presented by the case studies.

Hector Hugo García: promoting research on cysticercosis in Peru

Hector Hugo García: promoting research on cysticercosis in Peru

Developing mathematical modelling skills: The role of CAS

Mathematical modelling as one component of problem solving is an important part of the mathematics curriculum and problem solving skills are often the most quoted generic skills that should be developed as an outcome of a programme of mathematics in school, college and university. Often there is a tension between mathematics seen at all levels as ‘a body of knowledge’ to be delivered at all costs and mathematics seen as a set of critical thinking and questioning skills. In this era of powerful software on hand-held and computer technologies there is an opportunity to review the procedures and rules that form the ‘body of knowledge’ that have been the central focus of the mathematics curriculum for over one hundred years. With technology we can spend less time on the traditional skills and create time for problem solving skills. We propose that mathematics software in general and CAS in particular provides opportunities for students to focus on the formulation and interpretation phases of the mathematical modelling process. Exploring the effect of parameters in a mathematical model is an important skill in mathematics and students often have difficulties in identifying the different role of variables and parameters This is an important part of validating a mathematical model formulated to describe, a real world situation. We illustrate how learning these skills can be enhanced by presenting and analysing the solution of two optimisation problems.