Mathematical modeling is the process of a problem solving by the mathematical expression of real life event or a problem. This process enables learners to relate mathematics to real life and to learn it more meaningfully and permanently.

Realistic Mathematics Education – RME – is a domain-specific instruction theory for mathematics, which has been developed in the Netherlands. Characteristic of RME is that rich, “realistic” situations are given a prominent position in the learning process.

Mathematical Modelling Approach in Mathematics Education BY:Ayla Arseven

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Mathematical modeling can be defined as using mathematics to explain and define the events in real life, to test ideas and to make estimations about real life events. and is a domain-specific instruction theory for mathematic and a context in which students can in a later stage apply their mathematical knowledge “realistic” situations in the meaning of “real-world” situations are important in RME, “realistic” has a broader connotation here. It means students are offered problem situations which they can imagine

Mathematical modeling is the process of a problem solving by the mathematical expression of real life event or a problem. This process enables learners to relate mathematics to real life and to learn it more meaningfully and permanently.

Realistic Mathematics Education – RME – is a domain-specific instruction theory for mathematics, which has been developed in the Netherlands. Characteristic of RME is that rich, “realistic” situations are given a prominent position in the learning process.

Mathematical Modelling Approach in Mathematics Education BY:Ayla Arseven

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Five different perspectives on mathematical modeling in mathematics education By: Aline Abassian

https://www.tandfonline.com/doi/abs/10.1080/19477503.2019.1595360?af=R&journalCode=uiml20

Are we simply define that mathematical modeling is to solve the real life problems and in RME student can solve the problem with no specific domain , ?

Popular replies (1) Mathematical modeling is the process of a problem solving by the mathematical expression of real life event or a problem. ... Realistic Mathematics Education – RME – is a domain-specific instruction theory for mathematics, which has been developed in the Netherlands

Education defines mathematical modeling as a way of solving problems in the modern sciences, if, of course, modeling is carried out taking into account the real characteristics of the processes or systems that are being modeled.

The difference is that mathematical modeling can be part of RME. In other words, it is hardly possible to educate mathematical modeling by itself, since it is most often associated with an understanding of processes and systems studied in other sciences (physics & etc.).

Alexey Romanov is absolutely correct. We only have to look at the history of mathematics to see the interplay of "modeling" and mathematics. Quantum mechanics in physics needed a model - John von Neumann provided it and the spectral theory of unbounded operators ( the quantized Hamiltonian resulted) along with a rich mathematical theory. This is not new as Euler, Gauss, Poisson, etc. used the developed mathematics to address problems in the "real world." Mathematical modeling is not really a preview of mathematics whose responsibility is to develop to tools necessary to solve the problems in mathematics. If they happen to help those in the sciences - that's a positive benefit. But the sciences provide mathematicians with fodder to look deeper in the the mathematical structures that their work in the sciences promote.

Daniela Götze added an interesting answer. In the 1970's I was assigned to work with a psychologist, Julian Stanley who had established a program at Johns Hopkins on how to identify mathematically gifted children and to study how they learned, as a lowly grad student. Two of we lowly grad students were work with Stanley to develop courses that 10 to 12 year old kids who where identified as "gifted in mathematics" could comprehend without at their age level of mathematics background so naive mathematical ability could be measured. We settled on two topics for the courses, elementary number theory and projective geometry - even before they heard of Euclidean geometry. What I was amazed at was the ability of these kids to comprehend, visualize and develop and an intuition for the abstractions these subjects demanded with the basic rudimentary mathematics they had been exposed to.

https://en.wikipedia.org/wiki/Julian_Stanley

So my question - how does Stanley's pioneering work factor into what is going on the such models for teaching mathematics today and how do they handle the truly precocious in mathematics as not to bore them and turn them away from pursuing mathematics.

Daniela Götze,

Thank you for the information and answer. I examined the link and page you shared. I found really useful information. However, I could not find any examples of activities in elementary school. Are there any examples of elementary school-level classroom practices or activities for RME? (Especially at the first and second-grade level)

I assume you have traced down Stanley's work on line. Hopkins has long had a long history of research in education. The Center for the Social Organization of Schools was established in the late 1960's with the impieties of James Coleman.

http://web.jhu.edu/CSOS/about.html

https://en.wikipedia.org/wiki/James_Samuel_Coleman

In 1971 psychologist, Julian Stanley came to the math department with an idea. I was one of the two grad students assigned to work with Stanley. That introduced me the CSOS where which I also supported during my grad student days at Hopkins. Our goal with Stanley was to develop and teach courses to identified gifted youth that would test their ability to comprehend abstract mathematical concepts normally thought to be well beyond their age ability. Stanley went on to establish the Center for Talented Youth at Hopkins. Stanley's work started the long running study in education known as the "Study of Mathematically Precocious Youth."

https://en.wikipedia.org/wiki/Center_for_Talented_Youth

https://en.wikipedia.org/wiki/Study_of_Mathematically_Precocious_Youth

Through Stanley and a couple of the researches at CSOS who I also did some work for during my grad student days.

I actually have a published paper with Jim Richards and Nancy Karweit in "Educational and Psychological Measurement" which documented a Fortran simulation developed to test and analyze education growth.

I kept track of the programs after I received my degree at Hopkins and moved on in 1974. I lost track of most of what was happening in those programs in probably about 1985 or so.

I don't know how any of this applies to your interest, if so contacting the Hopkins School of Education of the researchers that that are continuing the SMPY study might be of some help.

Mathematical modeling in realistic mathematics education - IOPscience Article Mathematical modeling in realistic mathematics education