Sense-making with the Mathematical Modelling Process: Developing a Framework for Faculty Practice

2020 ◽  
pp. 119-128
Author(s):  
Todd Abel ◽  
Mary Elizabeth Searcy ◽  
Tracie Mc Lemore Salinas
Keyword(s):  
Mathematical Modelling ◽  
Sense Making ◽  
Modelling Process

scholarly journals What Is Known about Secondary Grades Mathematical Modelling --A Review

2016 ◽  
Vol 8 (5) ◽  
pp. 12 ◽  
Author(s):  
Micah Stohlmann ◽  
Lina DeVaul ◽  
Charlie Allen ◽  
Amy Adkins ◽  
Taro Ito ◽  
...  
Keyword(s):  
Mathematical Modelling ◽  
Secondary Level ◽  
Future Research ◽  
Assessment Data ◽  
Unit Of Analysis ◽  
Knowledge And Skills ◽  
Construction Of Knowledge ◽  
Units Of Analysis ◽  
Secondary Grades ◽  
Modelling Process

<p><span lang="EN-US">Mathematical modelling is garnering more attention and focus at the secondary level in many different countries because of the knowledge and skills that students can develop from this approach. This paper serves to summarize what is it known about secondary mathematical modelling to guide future research. A targeted and general literature search was conducted and studies were summarized based on four categories: assessment data collected, unit of analysis studied, population, and effectiveness. It was found that there were five main units of analysis into which the studies could be categorized: modelling process/sub-activities, modelling competencies/ability, blockages/difficulties during the modelling process, students’ beliefs, and construction of knowledge. The main findings from each of these units of analysis is discussed along with future research that is needed. </span></p>

scholarly journals Mathematical modelling of electrical potential difference in a non-uniform electric field

2020 ◽  
pp. 64-72
Author(s):  
Mustafa Erol ◽  
İldahan Özdeyiş Çolak
Keyword(s):  
Electric Field ◽  
Mathematical Modelling ◽  
Electric Fields ◽  
Electrical Potential ◽  
Potential Difference ◽  
Uniform Electric Field ◽  
Electrical Potential Difference ◽  
Dc Power ◽  
Scalar Products ◽  
Modelling Process

This work offers an unproblematic teaching tool for the instruction of challeng-ing concept of electric potential difference in a non-uniform electric field. Specifically, mathematical modelling process is employed and managed to comprehend and teach exceedingly difficult concepts of uniform and non-uniform electric fields, electrical potential difference, scalar products of vectors and also concept of path integral. In order to accomplish those tasks, initially a basic conducting panel/sheet, that is simply a wet cardboard, is designed as a part of the apparatus, together with a dc power supply, a multi meter and connecting cables. The established method is interesting in the sense that the 3D wet cardboard is novel, very practical and minimal costing, hence the approach offers physics educators fresh teaching routes and opportunities to clarify the puzzling concept of electrical potential difference and further.

An Intelligent Mathematical Modelling Assistant for Analysis of Physical Systems

1992 ◽  
Author(s):  
D. P. Finn ◽  
J. B. Grimson ◽  
N. M. Harty
Keyword(s):  
Artificial Intelligence ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Case Based Reasoning ◽  
Physical Systems ◽  
Cad System ◽  
Engineering Problems ◽  
Transfer Problems ◽  
Modelling Process ◽  
Modelling Task

Abstract This paper describes work in progress aimed at developing an intelligent modelling assistant for the mathematical modelling task associated with engineering analysis. Mathematical modelling precedes detailed numerical analysis and involves formulating and evaluating engineering problems with the objective of proposing a candidate mathematical model that meets desired modelling requirements. The approach taken in this work is based on Chandrasekaran’s proposecritique-modify method which is adapted for modelling. The use of this paradigm is justified by viewing the mathematical modelling process as an activity of successive investigation and refinement of candidate mathematical models. The system architecture is based on exploiting a number of artificial intelligence techniques including model based reasoning, case based reasoning and rule based reasoning. A modelling options case base assists engineers in proposing candidate mathematical models. Engineering 1st principles and formulae are utilised within an artificial intelligence framework to provide a means of evaluating and critiquing the candidate mathematical models. The system is integrated with an existing interactive CAD system. The problem domain covered is application independent but will initially focus on the modelling and analysis of heat transfer problems.

scholarly journals Modelling in nutrition: An introduction

1999 ◽  
Vol 58 (1) ◽  
pp. 133-138 ◽  
Author(s):  
Peter D. G. Wilson ◽  
Jack R. Dainty
Keyword(s):  
Stable Isotope ◽  
Mathematical Modelling ◽  
Compartmental Modelling ◽  
Stable Isotope Tracers ◽  
Isotope Tracers ◽  
Hydrodynamic Analogy ◽  
Modelling Process

The purpose of the present paper is to provide an introduction to modelling, particularly mathematical modelling, for nutritional researchers with little or no experience of the modelling process. It aims to outline the function of modelling, and to give some guidance on factors to consider when designing protocols to generate data as part of the modelling process. It is not intended in any way to be a comprehensive guide to mathematical modelling. The paper discusses the uses of modelling, and presents a ‘hydrodynamic analogy’ to compartmental modelling, to explain the process to the non-mathematically-minded and to examine some of the pitfalls to be avoided when using stable-isotope tracers. Examples of the use of modelling in nutrition are presented, including methods for determining absorption, as well as a discussion of possible future avenues for nutritional modelling.

scholarly journals Understanding Early Mathematical Modelling: First Steps in the Process of Translation Between Real-world Contexts and Mathematics

2021 ◽  
Author(s):  
Ángel Alsina ◽  
María Salgado
Keyword(s):  
Mathematical Modelling ◽  
Important Data ◽  
Mathematical Objects ◽  
The Real ◽  
Childhood Education ◽  
Modelling Activity ◽  
Proposed Model ◽  
And Mathematics ◽  
Concrete Model ◽  
Modelling Process

Abstract The aim of this study is to provide data to better understand the processes of early mathematical modelling. According to this, an early mathematical modelling activity carried out by 21 Spanish schoolchildren aged 5–6 years is analysed, using the validated tool “Rubric for the Evaluation of Mathematical Modelling Processes” (REMMP). The results show that children link the content of the problem with their prior knowledge (understanding); identify the important data of the problem and simplify it (structuring); show some difficulties in substituting the elements of the real context for mathematical objects (mathematizing); use progressively mathematical objects and strategies in order to propose solutions for the problem (working mathematically); compare the solution with the initial problem (interpretation); justify the proposed model via valid arguments (validation); and also communicate the decisions taken throughout the modelling process and the concrete model obtained applied to the real context (presenting). We conclude that the description of this type of activities and the tools for their analysis could be used for grading and teaching tool in order to promote mathematic modelling in early childhood education.

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