Understanding Of Mathematical Models Research Articles

Exploring the Influence of Adaptive E-Learning Technology on Learners’ Perceptions of Mathematical Modeling and Simulation in South African Schools

This study investigates the influence of adaptive e-learning technology on learners’ understanding of mathematical modeling and simulation. Through a comprehensive literature review, theoretical framework development, and empirical analysis, the study examines the relationship between learners’ qualifications, geolocation, and their perceptions of e-learning technology. It utilized a quantitative research approach with a sample size of 66 learners and administered structured questionnaires to urban and rural school learners and analyzed data at p < .05 using the factorial multivariate analysis of variance (FMANOVA). The findings reveal variations in opinions among learners at different qualification levels regarding the use of e-learning technology in mathematical concepts. Moreover, urban and rural learners show disparities in their association of e-learning technology with mathematical understanding. The study emphasizes the need for practical approaches to e-learning, addressing challenges related to access, reliability, and ease of use. Recommendations include integrating adaptive e-learning technology into school curricula and providing adequate training and support for teachers. Furthermore, suggestions for future research encompass exploring long-term impacts, individual differences, teacher roles, assessment and feedback, equity and accessibility, professional development, and comparative studies. Overall, this study contributes to understanding the role of adaptive e-learning technology in mathematics education, providing valuable insights for practitioners and policymakers to enhance teaching and learning experiences.

Improving high school students’ perceptions of mathematics through a mathematical modelling course

AbstractLiterature shows there is support for adding connection and relevancy in mathematics for students through the use of real-world context and data in mathematical modelling. A teaching unit on mathematical modelling was designed within the context of future affordable housing for the local surrounding area. The teaching unit was implemented, and data were collected to address the research question: ‘How does exposure to mathematical modelling influence students’ perceptions and understandings of mathematical modelling?’ Data were collected through pre- and post-teaching unit surveys and post-teaching unit student interviews. Pre- and post-surveys were used to establish any changes in students’ perception towards mathematics, understanding of mathematical modelling and perceived relevance of mathematical modelling use to their own lives. Student interviews gained further insight into the student experience and associated perception changes. Statistical analysis of the survey responses included both hypothesis and nonparametric testing. Interviews were analysed using a thematic qualitative approach. Our analysis showed that a greater understanding of mathematical modelling was achieved, with many students unfamiliar with the concept prior to the teaching unit. It was also found that through the real-world context of the mathematical modelling unit, students had a new-found interest in mathematics.

Problem Solving for Teachers – Action Research in a Cross-Listed Undergraduate and Graduate Course

This article describes a course-based research experience in a cross-listed mathematical problem solving course for middle school pre-service and in-service teachers. The course was conducted entirely online due to statewide and university restrictions during the coronavirus pandemic. This study examines 4 undergraduate and 5 graduate students’ understanding of mathematical modeling. Undergraduate and graduate students were paired in groups to develop open-ended model-eliciting activities for their classmates to solve, and groups conducted educational action research to analyze their classmates’ work on the activities. We present one group’s activities and their results as an example of how action research can be conducted in a virtual teaching environment.

Engaging Preservice Secondary Mathematics Teachers in Authentic Mathematical Modeling: Deriving Ampere's Law

Incorporating modeling activities into classroom instruction requires flexibility with pedagogical content knowledge and the ability to understand and interpret students' thinking, skills that teachers often develop through experience. One way to support preservice mathematics teachers' (PSMTs) proficiency with mathematical modeling is by incorporating modeling tasks into mathematics pedagogy courses, allowing PSMTs to engage with mathematical modeling as students and as future teachers. Eight PSMTs participated in a model-eliciting activity (MEA) in which they were asked to develop a model that describes the strength of the magnetic field generated by a solenoid. By engaging in mathematical modeling as students, these PSMTs became aware of their own proficiency with and understanding of mathematical modeling. By engaging in mathematical modeling as future teachers, these PSMTs were able to articulate the importance of incorporating MEAs into their own instruction.

Mathematics for biological sciences undergraduates: a needs assessment

ABSTRACTThe purpose of this study was to investigate the mathematical needs of biological sciences undergraduate students. Student needs were measured through a needs assessment methodology scheme that included a content analysis of peer-reviewed journals, a nationwide cross-sectional survey, and semi-structured interviews. The research question that guided the study was: what are the mathematical needs of biological sciences undergraduate students as perceived by certain stakeholder groups? The stakeholder groups represented the areas of ecology, evolution, and behaviour, and developmental biology to portray two extremes in the use of mathematics. Major findings included: (1) The use of mathematics to support experimental design is the most consistent need across disciplines. (2) An overall understanding of mathematical models is needed as a minimum for scientific literacy. (3) Evolution and animal behaviour students need descriptive and inferential statistics, stochastic processes, differential equations, and mathematical models in general. Developmental biology students, on the other hand, need only descriptive and inferential statistics, and mathematical models. These needs, however, strongly vary depending on students’ career tracks within their subdisciplines, suggesting the necessity of a flexible undergraduate curriculum.

Using the Scientific Method to Engage Mathematical Modeling: An Investigation of pi

The purpose of this paper is to explain how to use the scientific method as the framework to introduce mathematical model. Two interdisciplinary activities, targeted for student in grade 6 or grade 7, are explained to show the application of the scientific method while building a mathematical model to investigate the relationship between the circumferences and the diameter of circular objects. In the first activity, a research question is pursued as it relates to the stated hypothesis. In the second activity, the same research question is retained; however, the use of exploration helps to build the hypothesis. The activities serve as examples to show how middle school math teachers may use scientific inquiry to motive students’ understanding of mathematical models as well as engage in science beyond the science classroom. Students will be able to identify, describe, analyze, interpret, validate, and report relationships between variables.

Developing understanding of mathematical modeling in secondary teacher preparation

This study examines the evolution of 11 prospective teachers’ understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include modeling as part of the school curriculum under current state standards. The module consisted of readings, analysis of the Common Core State Standards, carefully designed modeling activities, individual and group work, discussion, presentations, and reflections. The results show that while most prospective teachers had misconceived definitions of mathematical modeling prior to the module, they developed the correct understanding of modeling as an iterative process involving making assumptions and validating conclusions connected to everyday situations. The study reveals how the prospective teachers translated the modeling cycle into practice in the context of a carefully designed open-ended problem and the strong connections between modeling activities and promoting mathematical practices.

Lack of quantitative training among early-career ecologists: a survey of the problem and potential solutions

Proficiency in mathematics and statistics is essential to modern ecological science, yet few studies have assessed the level of quantitative training received by ecologists. To do so, we conducted an online survey. The 937 respondents were mostly early-career scientists who studied biology as undergraduates. We found a clear self-perceived lack of quantitative training: 75% were not satisfied with their understanding of mathematical models; 75% felt that the level of mathematics was “too low” in their ecology classes; 90% wanted more mathematics classes for ecologists; and 95% more statistics classes. Respondents thought that 30% of classes in ecology-related degrees should be focused on quantitative disciplines, which is likely higher than for most existing programs. The main suggestion to improve quantitative training was to relate theoretical and statistical modeling to applied ecological problems. Improving quantitative training will require dedicated, quantitative classes for ecology-related degrees that contain good mathematical and statistical practice.

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

‘Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum’ (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students’ attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221–240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students’ coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling – utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

Mathematical modeling as a component of understanding ratio-as-measure: A study of prospective elementary teachers

The authors employed a whole-class teaching experiment in a mathematics class for prospective elementary teachers to study the development of the ability to identify a ratio as the appropriate measure of a given attribute (“ratio-as-measure”). Prior studies as well as pretest data for this study demonstrated that students often invoke additive comparisons when multiplicative comparisons are appropriate. Analysis of the difficulties which students encountered in considering a ratio as an appropriate measure of an attribute of a physical situation led to the hypothesis that an understanding of ratio-as-measure requires, in addition to an understanding of aspects of multiplicative relationships, an understanding of mathematical modeling.