scholarly journals New Thermodynamics: Inelastic Collisions, Blackbody Radiation, Entropy and Light

2020 ◽  
Vol 2 (6) ◽  
Author(s):  
Kent W. Mayhew
Keyword(s):  
Mathematical Modelling ◽  
Real World ◽  
Blackbody Radiation ◽  
Inelastic Collisions ◽  
Elastic Collisions ◽  
The Real ◽  
Radiation Entropy

Most collisions that we witness are inelastic. Irrationally, the sciences have evolved around elastic collisions, which allows for simpler mathematical modelling. Since a result of inelastic collisions are photons, we examine the feasibility of an ensemble of inelastic collisions producing a blackbody spectrum. This will lead to reconsideration of how the light that governs our lives is produced, i.e., light from both the stars and incandescent lightbulbs. A brief discussion of entropy being a mathematical contrivance based upon elastic collisions is included. A consequence of collisions being inelastic becomes, entropy can only be an approximation when applied to the real world. And this fits well with “New Thermodynamics”.

scholarly journals New Thermodynamics: Inelastic Collisions and Cosmology

2020 ◽  
Vol 2 (6) ◽  
Author(s):  
Kent W. Mayhew
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Mathematical Modelling ◽  
Real World ◽  
Inelastic Collisions ◽  
Elastic Collisions ◽  
The Real ◽  
The Creation

The sciences have evolved around elastic collisions although most collisions are inelastic. Elastic collisions allow for simpler mathematical modelling, that may not be particularly suitable for cosmology. Inelastic collisions create photons. This has led to consideration of an ensemble of inelastic collisions producing CMB. This will further lead to brief discussions concerning the nature of dark matter, and dark energy. This will then be followed by a simpler analogy concerning the creation of Hawking’s radiation. A consequence of collisions being inelastic is that as a mathematical contrivance, entropy may only be an approximation when applied to the real world. And this fits well with this author’s “New Thermodynamics”.

scholarly journals The role of reading comprehension in mathematical modelling: improving the construction of a real-world model and interest in Germany and Taiwan

2021 ◽  
Author(s):  
Janina Krawitz ◽  
Yu-Ping Chang ◽  
Kai-Lin Yang ◽  
Stanislaw Schukajlow
Keyword(s):  
Reading Comprehension ◽  
Mathematical Modelling ◽  
Real World ◽  
Situational Interest ◽  
Problem Solver ◽  
Learning Material ◽  
World Model ◽  
The Real ◽  
Real World Situation ◽  
Modelling Problems

AbstractTo solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving modelling problems, and fostering reading comprehension might lead to better modelling competence. Further, ease of comprehension and involvement have been found to increase interest in the learning material, and thus, improving reading comprehension might also increase interest in modelling. The aims of this study were to (a) determine whether providing students with reading comprehension prompts would improve the modelling sub-competencies needed to construct a model of the real-world situation and their interest in modelling and (b) analyze the hypothesized effects in two different educational environments (Germany and Taiwan). We conducted an experimental study of 495 ninth graders (201 German and 294 Taiwanese students). The results unexpectedly revealed that providing reading comprehension prompts did not affect the construction of a real-world model. Further, providing reading comprehension prompts improved students’ situational interest. The effects of providing reading comprehension prompts on the construction of a real-world model were similar in Germany and Taiwan. Students’ interest in modelling improved more in Germany. An in-depth quantitative analysis of students’ responses to reading prompts, their solutions, and their interest in the experimental group confirmed the positive relation between reading comprehension and modelling and indicated that the reading comprehension prompts were not sufficient for improving reading comprehension. Implications for future research are discussed.

scholarly journals Teaching mathematical modelling: a framework to support teachers’ choice of resources

2019 ◽  
Vol 39 (2) ◽  
pp. 127-144
Author(s):  
Peter K Dunn ◽  
Margaret F Marshman
Keyword(s):  
Mathematical Modelling ◽  
Mathematical Models ◽  
Mathematics Teachers ◽  
Real World ◽  
Real Data ◽  
Model Structure ◽  
The Real ◽  
Using Data ◽  
Do So ◽  
Poor Practice

AbstractMathematics teachers are often keen to find ways of connecting mathematics with the real world. One way to do so is to teach mathematical modelling using real data. Mathematical models have two components: a model structure and parameters within that structure. Real data can be used in one of two ways for each component: (a) to validate what theory or context suggests or (b) to estimate from the data. It is crucial to understand the following: the implications of using data in these different ways, the differences between them, the implications for teaching and how this can influence students’ perceptions of the real-world relevance of mathematics. Inappropriately validating or estimating with data may unintentionally promote poor practice and (paradoxically) reinforce in students the incorrect idea that mathematics has no relevance to the real world. We recommend that teachers approach mathematical modelling through mathematizing the context. We suggest a framework to support teachers’ choice of modelling activities and demonstrate these using examples.

scholarly journals When will I ever use that? Giving students opportunity to see the direct application of modelling techniques in the real world.

2016 ◽  
Vol 14 (3) ◽  
pp. 45
Author(s):  
Ros Porter ◽  
Hannah Bartholomew
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Real World ◽  
Direct Application ◽  
First Year ◽  
Thought Processes ◽  
The Real ◽  
Modelling Techniques

Mathematical modelling is unfamiliar to many young mathematicians and can be a source of anxiety for many. Although many first year mathematics undergraduates will have used mathematical models throughout GCSE and A Level most are unaware of this. Very few understand what a mathematical model is, fewer still the concept of building a model. In our experience students are reluctant to try and build their own models and fail to see the value of modelling skills in the real world. We invited 3 speakers to attend a first year modelling lecture to talk about the models they use in their jobs with the intention that this would help students see that modelling skills and analytical thought processes are valuable tools for a maths graduate. The speakers had different employment backgrounds being from banking, research (chemistry) and transport engineering. Each spoke for approximately 10 mins. giving an outline of their field. The lecture was followed by tutorials in which students were asked to reflect on what the speakers had said and how this related to their own learning. Two of the speakers also attended the tutorials and were able to have more informal conversations with the students.

scholarly journals Can mathematical modelling work as a creativity-demanding activity? An empirical study in China

ZDM ◽  
2021 ◽  
Author(s):  
Xiaoli Lu ◽  
Gabriele Kaiser
Keyword(s):  
Mathematical Modelling ◽  
Mathematics Teachers ◽  
Real World ◽  
Core Competencies ◽  
Mathematical Problem ◽  
Significant Negative Correlation ◽  
School Students ◽  
Economic Changes ◽  
The Real ◽  
Real World Problems

AbstractCreativity has been identified as a key characteristic that allows students to adapt smoothly to rapid societal and economic changes in the real world. However, Chinese students appear to perform less well in mathematical problem-solving and problem-posing abilities, which are strongly connected to mathematical creativity. Mathematical modelling has recently been introduced as one of the six core competencies in the Chinese mathematical curriculum and is built on students’ ability to solve real-world problems using mathematical means. As mathematical modelling is characterised by openness regarding the understanding of complex real-world problems and the complex relationship between the real world and mathematics, for the strengthening of creativity, mathematical modelling activities seem to be adequate to accomplish this purpose. In this paper, we describe a study with 71 upper secondary school students, 50 pre-service mathematics teachers, and 66 in-service mathematics teachers, based on an extended didactical framework regarding mathematical modelling as a creativity-demanding activity. The results of the study indicate a significant correlation between modelling competencies and creativity aspects. Especially significant correlations between the adequacy of the modelling approaches and the two creativity aspects of usefulness and fluency could be identified, as well as a significant negative correlation between usefulness and originality. The results of the correlational analysis of relationships among the four criteria were not always consistent in the three participant groups. Overall, the results have implications for the promotion of creativity for various expertise groups and demonstrate the dependency of the modelling activities on the mathematical knowledge of the participants and the mathematical topic with which they are dealing.

scholarly journals GetReal in mathematical modelling: a review of studies predicting drug effectiveness in the real world

2016 ◽  
Vol 7 (3) ◽  
pp. 264-277 ◽  
Author(s):  
Klea Panayidou ◽  
Sandro Gsteiger ◽  
Matthias Egger ◽  
Gablu Kilcher ◽  
Máximo Carreras ◽  
...  
Keyword(s):  
Mathematical Modelling ◽  
Real World ◽  
The Real ◽  
Drug Effectiveness

Current Issues: Evidence-Based Practice for the Real World: Thoughts on Clinical Education in Communication Disorders

2010 ◽  
Vol 20 (3) ◽  
pp. 100-105 ◽  
Author(s):  
Anne K. Bothe
Keyword(s):  
Clinical Education ◽  
Real World ◽  
Evidence Based Practice ◽  
Communication Disorders ◽  
University Faculty ◽  
Evidence Based ◽  
Speech Language Pathology ◽  
Basic Principles ◽  
The Real ◽  
Language Pathology

This article presents some streamlined and intentionally oversimplified ideas about educating future communication disorders professionals to use some of the most basic principles of evidence-based practice. Working from a popular five-step approach, modifications are suggested that may make the ideas more accessible, and therefore more useful, for university faculty, other supervisors, and future professionals in speech-language pathology, audiology, and related fields.

The Real-World Fellowship

2006 ◽  
Vol 40 (7) ◽  
pp. 47
Author(s):  
LEE SAVIO BEERS
Keyword(s):  
Real World ◽  
The Real
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