Interesting.

Borrowing from Arcavi (https://www.researchgate.net/publication/225216743_The_role_of_visual_representations_in_the_learning_of_mathematics_Educational_Studies_in_Mathematics_523_215-241), seeing the thing itself, with the aid of technology which overcomes the limitation of our sight, provides not only a fulfillment of our desire to “see” and the subsequent enjoyment, but it may also sharpen our understanding, or serve as a springboard for questions which we were not able to formulate before.

Thank you, Prof. Anton Vrdoljak, I did not know this reference, and I will read it carefully.

The topic does deserve attention, now that as eTeachers, we have to increase our ability to teach in virtual environments and to make students understand better our teachings.

I ask you to allow me to reference it later on, as a part of the discussion in the thread.

You're welcome Pedro L. Contreras E. and thanks for recommendation! Next, I strongly agree regarding the importance of this topic.

The real skill is the ability to present research results in a graphic form.

Tku & I agree, Prof. Anton Vrdoljak

I write for all here, the references to the short NANO MOOC, I took:

• Bills, C. (2002) ‘Mental mathematics’ in Haggarty, L. (ed.), Aspects of Teaching Secondary Mathematics: Perspectives on Practice, London, Routledge.
• Mason, J. (1988) ‘Imagery, imagination, and mathematics classrooms’ in Pimm, D. (ed.), Mathematics, Teachers and Children, Sevenoaks, Hodder, and Stoughton.
• The Open University (1988) ME234 Using Mathematical Thinking, Block 1 Investigating Mathematics, Unit 2 Working Mathematically, Milton Keynes, The Open University.

Shortly, I will be sharing with RG community a short preprint story about a very complicated physics problem, which some collaborators and I, managed to convert into a z = x + i y visual effect, after 11 years.

Best Regards.

I do agree partially with you, Dear Waldemar Łasica thank you (tku) so much, the skill in sciences visualization is a plus here.

However, what about this statement of mine:

"Why we do always try to repeat visualizing, what others have visualized previously, without questioning ourselves, if that is what it is really needed to be visualized for teaching or even research?"

Best Regards.

Pedro L. Contreras E., What do you mean when you write about visualization in mathematics. In math, chalk and blackboard and correct comment are irreplaceable. When it comes to complex numbers, as we know, they can be presented in three ways. It is also known that by playing with blocks it is easy to present the basics of functional analysis in an understandable way, not at the University but at the kindergarten.

Thank You for your post, Prof. Mirosław Grzesik

You probably answer yourself with your phrase, I unquote you "...playing with blocks it is easy to present the basics of functional analysis in an understandable way, not at the university but at the kindergarten..."

I am not a mathematician, my understanding of functional analysis was only a short rigorous introduction in analysis III in the former USSR, that I poorly understood.

This is the statement, that the authors of the MOOC course I took, and I regard as important, I unquote them (Ronnie Goldstein & Alan Bloomfield, 2012, Using visualization in maths teaching, the Open University free course)

"As teachers, we need to ensure that we are very aware of all the processes of mathematics and so we must always attempt to know what our students are visualizing."

Pedro L. Contreras E., Well, for me, visualization is really a presentation of a lecture using what I call "pictures". However, a lecture on mathematics presented in its entirety with the use of, for example, power point, that is with "pictures", is unacceptable to me.

Thank you, Prof. Mirosław Grzesik

I see your point. Here my question is different, it doesn't have to be with PowerPoint to teach lectures & visualize lectures.

It is the power of visualization itself. I worked years in the oil industry and in the 90s I used a silicon station to visualize complex wavefronts. Now 20 years later, I see how this science has evolved in the teaching and popularization of science.

You can check and enjoy if you wish the following YouTube channel for example and post here your comments:

https://www.youtube.com/watch?v=fbhrRz7AXyo

I also have been recently enjoyed with young generations that use python visualization libraries, and I am amazed.

Best Regards.

I accept your personal point of view, Prof. Vadim S. Gorshkov

But if teachers improve visualization skills is good for all. I guess is not an imposition, it is a style and a necessity during CoV's new era.

Best Regards.

Thank you so much for recommending this thread, Prof. Omar H. Abdalla

Take Care & Best Regards.

Pedro L. Contreras E., What are we currently discussing, because I do not know whether it is about visualizing the course of an industrial process, or about teaching, or about popularizing science, or finally about the python programming language? There are many so-called simulators, or software combining numerical calculations with graphics. Their names could be mentioned for a long time. I still remember analog machines, Simula or MathCad programs. Of course, the first versions of these programs.

Please read the thread first, Prof. Mirosław Grzesik, thank you.

We are from the same old USSR school, Prof. Vadim S. Gorshkov

However, I see many advantages of visualization for teaching and learning at different times and grades, and I spent time learning some quite difficult packages to do it, which is true. So why not use it?

Do you remember when catastrophe theory started to be popular many years ago in the USSR? I cannot remember the equations but I remember well the plots.

By answering the main question directly, yes. I see such a need. About 40 years ago I wrote a Pascal program to calculate the processes in various chemical reactors and illustrate the results in the form of graphs. I was also using Fortran to draw histograms back then. It was about the size distribution of the traces of droplets from the spray dryer. About 35 years ago, I also used Basic (numerical computing) with Grapher in my lectures. t was not the time of Windows, Linux or Aspen, but of DOS.

Yes, Prof. Vadim S. Gorshkov

In my case, images trigger my memory still at this age, I remember myself doing diagrams of questions in state examinations at MSU, I had a hard time remembering all the proofs.

Best Regards.

Yes, Prof. Vadim S. Gorshkov

Visualization is a very extensive subject, not easy to cover or to define some limits on it. I am learning all this & I find it interesting, for example in Moodle, scientists develop a particular plugin for visualization in teaching and learning asynchronously, and that is a Ph.D. thesis that well deserves attention.

Best Regards.

I wrote an article on the role of visualizations in mathematics for some years ago with a colleague of mine. It is published in Erkenntnis, a journal in philosophy: https://link.springer.com/article/10.1007%2Fs10670-008-9104-3

It could perhaps be of interest.

All the best,

Kajsa

Prof. Kajsa Bråting, good morning.

Thank you so much for sharing in this thread your paper

Article Visualizations in Mathematics

You reach very interesting conclusions on your work, for example, I unquote you (Bråting & Pejlare, 2008) "...Most of the students did not seem to be experienced enough to handle the tacitly understood ‘visual language‘ used in the mathematical community..."

I agree that students and even we as teachers sometimes do not know how to use proper visualization for teaching & learning, but it could be because we don't the know-how.

Best Regards.

Thank you and good look with your research!

Thank you so much, Prof. Kajsa Bråting

Best Wishes.

I think visualization in learning is a helpful tool. In Virtual Reality, you can create these images in a 3D space that promote student engagement and interaction. It is becoming more common in high school classes in the U.S.

Dr. Crystal Maraj, good morning.

Thank you for your post about the use of visualization in the US to teach in high schools.

Indeed "VR promotes students' engagement & interaction" as you point out.

Best Regards.

Visualization is the best form of conveying numerical results.

Dr. Waldemar Łasica , good morning.

Thank you for your post. Yes, as you state, I unquote you "Visualization is the best form of conveying numerical results"

I can remember 25 years back, me being a student and bringing to an instructor a data column, then the instructor looking at it for a while.

Best Regards.

Some time ago I wrote a piece about visualisation (and also spatial thinking), see: Chapter Spatial thinking and visualisation

Prof. Keith Jones,

Thank you so much for sharing in this thread your writing "Spatial thinking and visualisation"

We appreciate it. Best Regards.

In general, illustrativeness (but only correct!) Is highly desirable. But for each individual researcher, it depends on the individual characteristics of the functional balance of the cerebral hemispheres.

Prof. Alexey Orlovsky

Thank you so much for sharing in this thread your insights into this topic.

I agree with you that it strongly depends on the functional balance for each individual as you state.

Best Regards.

Alexey Orlovsky I think you are right about visualisation and this applies very much to the physical sciences. I was reading recently about the Solvay conference on Quantum Mechanics in 1927 and the fact that we lost the ability to visualise the atom and the electron. The statement "No-one understands quantum theory" is part of a similar problem that we have theories which are mathematically based which are difficult if not impossible to physically visualise.

This is one of the reasons that I think that visual presentations are superior to scientific papers when it comes to really understanding a theory. If we don't understand a theory then we are limited to the range of application that is dictated by the mathematical model.

Here is a visualisation example:

Data Prerecording of Conference Presentation on the Unification of Physics

Richard

Yes definitely.

I agree with your post, Prof Md Adnan Rahman

Best Regards.

Dear doctor Contreras

I appreciate his magnificent question that can help us so much to reflect on visualization in the Pure Sciences, one of the greatest problems that has plagued teaching for so long and continues to do so today.

The edges of the visualization are many, but today as yesterday and most of all, they require the passion of the teacher to demonstrate the usefulness of his science, I mean a teacher who not only repeats what is planned in the study program Rather, a teacher who sets out to find and bring to the classroom the visualized examples of the many problems his science can solve.

Creative teachers are needed to rescue their science from social antipathy and to demonstrate to their students and to society that, at any moment, the pure sciences can be loved, but at the same time, irremediably essential.

Chapter Quality of life and education in the knowledge society

A definite yes, but this requires a great deal of creativeness.

Prof. Reinaldo Requeiro, thank you so for your detailed post. Yes, as you indicated, it requires a lot of effort from teachers and lecturers. It is almost like learning a new language. The advantage is that new visualization tools are freely available for those with a good internet connection, but it requites time, patience and desire to improve.

Prof. Stephen I. Ternyik, thank you for your clarity on the issue. Yes, it requires almost an artistic spirit. It can take days to choose the right color palette for a plot, for example.

Best Regards.

Pedro L. Contreras E. It is worthwhile the effort to merge the scientific and artistic spirit; we can extend our research horizon with creative visualizations and exact computations as new tools of learning.

Pedro L. Contreras E.

https://www.researchgate.net/project/Presentation-of-the-standard-model-with-61-elementary-particles-in-a-stereo-picture

The works of Hermann J. Scheuber are one good example, in my scientific view.

Thank you for sharing with us this nice visualization of the standard model of elementary particles, Prof. Stephen I. Ternyik

I would like to share the following YouTube Channel on earthquake monitoring visualization, "Dutchsinse" recommended by a friend, Dr. Stephen L.

https://www.youtube.com/channel/UCHE92x768p8h-fMrqhsnE1Q

Pedro L. Contreras E. what a wonderful question and yes according to me you are absolutely correct about the visualization and i do agree with you on this and also i do feel there is a need to learn to see what and how we do calculate mostly by computing or coming up with a model or a tool that should be a perfect idea and i am open for any kind of research in this sector if anyone wanna join in with me

Good luck&congratulations dear dr.

Profs. Srinivas Kasulla & Faraed Salman

Thank you so much for your posts. Indeed, nowadays there are tools to present data in a visual form, that by themselves constitute an impressive advance in the development of pure and applied sciences in all fields of knowledge.

Best Regards.

I think yes, we need to learn by seeing what we calculate.

Thank you for your post, Prof. Isam Alkhalifawi

Best Regards.

Dear @P. Contreras In social science, an established fact relates to "learning by doing". Whereas in biological sciences, learning by observing (seeing) unravelled many a mystery in the past. A good observer is also a "creationist". Charles Darwin was a "creationist" and "observationist" when he sailed on the Beagle in 1831. His observations led him write "The Origin of Species" which came in 1859. Gregor Mendel (basically a mathematician and physicist), who applied mathematical theories to unravel the mystery of inheritance of biological characters, was basically a naturalist. This is clear from his words "nature is not capricious, it is orderly..." as mentioned in his original paper "Experiments in plant hybridization" which appeared in 1866. Thus my view is: visualization is important not only in "pure" sciences, but is relevant in all sciences.

Best regards, AKC

Hi. Yes of courses because it is application . What is the benefit of science without application ? Nothing.

Thank you so much for your posts, Profs. Arbind K. Choudhary , Aref Wazwaz & Esteban Rodríguez Torres

Prof. Arbind K. Choudhary you are right, nowadays visualization is also important to social sciences, let us take the example of big data and RRSS.

Best Regards.

Good morning to all, nice reading pertaining to this thread:

Article Scientific Visualization for Secondary and Post-Secondary Education

https://files.eric.ed.gov/fulltext/EJ609290.pdf

Pure sciences are the basis for most other applied sciences but in technical intelligence is probably even though it is its doing.

Indeed Prof. Nesreen Mohamed El-Said.

Thank you so much for your post. It is a good name for visualization, "technical intelligence".

Best Regards.

Thank you so much for confirming

You are most welcome, Prof. Nesreen Mohamed El-Said.

We have visualized the effect of non magnetic disorder of high Tc superconductors in the imaginary part of the self energy.

http://www.sciencepublishinggroup.com/journal/paperinfo?journalid=290&doi=10.11648/j.ep.20210501.11

We acknowledge the support by PG Science publishing group.

The following open access article is related to this thread:

Shanaka Piyatissa, M., Johar, M., & Tarofder, A. (2018). IMPACT OF VISUALIZATION ON TEACHING AND LEARNING PHYSICS AT SECONDARY SCHOOL LEVEL. European Journal of Education Studies.

doi:http://dx.doi.org/10.46827/ejes.v0i0.1621

https://oapub.org/edu/index.php/ejes/article/view/1621

The general expression " I believe it when I see it" has its roots in logical positivism and verifiability principle. As you rightly observe, visualization is very important in pure sciences; otherwise, what we learn is not subsumed into our cognition meaningfully.

Prof. Reza Biria

---> Thank you so much for your wonderful contribution. So I can consider myself following the current of the "logical positivism & verifiability principle" which I enjoy very much.

Thank you.

Nikon’s annual photomicrography competition provides a beautiful showcase for the remarkable progress made every year in imaging methods and technologies...

https://scholarlykitchen.sspnet.org/2021/08/27/back-to-the-microscopic-world-nikons-2021-small-world-winners/?informz=1

https://www.nikonsmallworld.com/

Congratulations

Thank you for your posts, Profs. Nesreen Mohamed El-Said. & Ljubomir Jacić

congratulations

Thank you so much for your posts, Profs. Radosław Walkowiak & Nesreen Mohamed El-Said.

Prof. Radosław Walkowiak I totally agree with you. Visualization helps even in those cases where theory fails to correctly diagnose and infer.

Best Regards.

Congratulations

Visualisation is helpful to grasp the theories we learn, but it's hard to visualize all the calculations we perform in mathematics and deep theoretical calculations.

Good Morning Prof. Kolita Weerasekera indeed is very difficult to visualize sometimes math calculations, it takes time and dedication, and also to learn new science, the same visualization.

Best Regards.

Thanks Dr. P. Contreras. I agree with your wise views.

Three congratulations exist on the last page! What is it about? Have I missed something? Hope that are not spammy answers.

Ups Prof. Ljubomir Jacić thank you ;)

I started this thread in May 2021, 4 months later we have reached some conclusions that are worth sharing about the importance of the visual aid in my field of research.

We will be writing a preprint soon.

God Bless All.

Dear Pedro , good luck with preprint. This resource might serve well.

Visualization in Science Education

‘Visualization in Science Education’ draws on the insights from cognitive psychology, science, and education, by experts from Australia, Israel, Slovenia, UK, and USA. It unites these with the practice of science education, particularly the ever-increasing use of computer-managed modelling packages...

https://www.springer.com/gp/book/9781402036125

Thank you for all the support, Dear Prof. Ljubomir Jacić that could be the last one, the situation here is deteriorating again very fast.

Although in God we trust.

Dear Prof Pedro L. Contreras E. - An excellent idea resembles pure sciences . Only chemistry having the ist part x ( Experimental Science ) but phys-maths resembles complex number having imaginary part ie i . Anyway very interesting !!

Indeed, Prof. Jaydip Datta thank you so much.

We had a problem in which the main two parameters were complex. And then, we realized that result will strongly depend on the way we visualize because to understand properly the calculations, visualization was eventually an aid, a plus to the research.

Best Regards.

Dear Prof. Pedro L. Contreras E. - It is very interesting that you are stating two complex para meters instead of of one - z= x + iy . But there must be another conjugate complex vatiable we have to visalise z = x- iy so that z^2 = x ^ 2 - y ^ 2 ???

I mean the following Prof. Jaydip Datta thank you for the question.

A complex function z = f(x,iy) where y =f(v,iu) is also a complex dependent function, now you get it?

Best Regards.

Very curious to know Prof. Pedro L. Contreras E. whether func linear or nonlinear and operators ie + , - etc are not known ? .

Strongly non-linear & self-consistent, so it is a real nightmare, Prof. Jaydip Datta

Physical interactions act this way sometimes...

Best Regards.

This paper is related to this thread:

Article INTEGRATING VISUALIZATIONS IN SCIENCE TEACHING: TEACHERS’ DI...

It is necessary to learn in all fields of science and knowledge

Thank you so much for your post, Prof. Hadeel Hassan , I totally agree with you

Best Regards.

A biophysicist who develops novel visualization strategies to discover the inside mechanisms of cells, Villa’s investigations embody deciphering the structure and performance of the protein referred to as leucine-rich repeat kinase 2 — the primary genetic driver of Parkinson’s illness.

Villa’s strategies assist visualize mobile equipment, just like the molecules that transport compounds inside cells and thru their membranes...

Computational instruments mix these two- dimensional photographs right into a 3D image — or tomogram — of mobile buildings of their pure surroundings.

Villa and her crew use this method — and associated cryo-electron microscopy and visualization strategies — to look at all the things from bacterial transport buildings to human proteins linked to illness...

https://us.newschant.com/us-news/san-diego/ucsd-professor-to-receive-9m-to-study-cellular-protein/

Thank you so much for providing such interesting and useful research that involves visualization, Prof. Ljubomir Jacić

Best Regards.

Dear Pedro L. Contreras E. , here is another example of visualization in pure science. Visualization of the 3D-reconstruction of one layer neurons... Amazing!

Cellular 3D-reconstruction and analysis in the human cerebral cortex using automatic serial sections

https://www.nature.com/articles/s42003-021-02548-6

Prof. Ljubomir Jacić, thank you so much, very nice and powerful visualization, those techniques were applied years ago in Oil & Gas industry, now they serve all sciences disciplines.

Best Regards.

Agree with Dr.Hadeel Hassan

Scientific art editors at Nature work with authors and editors to create graphics that increase comprehension and provide insight at a glance. Go behind the scenes to see how they use principles of visual communication and design to create a diagram summarizing an entire research article about a magnetic compass in the eyes of the European robin (Erithacus rubecula)...

https://www.youtube.com/watch?v=iQh63DH9H5w

Dear Pedro L. Contreras E. , I have just received this article from Science News. It is impressive!

“In nature, there are many beautiful structure colors, such as the wings of butterflies, the feathers of peacocks, the skin of chameleons and so on,” says Yanlin Song, a materials chemist at the Chinese Academy of Sciences in Beijing.

Song and colleagues printed structural colors on transparent silicone sheets using an ordinary ink-jet printer and clear polymer ink. The printer studded the silicone sheets with millions of microscopic ink domes, each of which served as a single pixel in the resulting image. Adjusting the size of a microdome changed the wavelengths of light that the dome reflected and therefore its color (SN: 3/8/19). Increasing the width of a single dome from 6.6 to 11 micrometers shifted its hue along the spectrum from blue to red and back again, the researchers report online September 22 in Science Advances...

https://www.sciencenews.org/article/transparent-ink-printer-butterflies-color-spectrum-microscale-pattern?utm_source=email&utm_medium=email&utm_campaign=latest-newsletter-v2&utm_source=Latest_Headlines&utm_medium=email&utm_campaign=Latest_Headlines

Visualisation in science should be done ethically!

Eight major publishers have issued joint guidelines for how journal editors can spot and deal with suspicious images or data. The best-practice recommendations list three categories of image manipulation, ranging from “beautified” figures to those that have been altered with an intent to mislead. The guidelines — from a group that includes Elsevier, JAMA, Wiley and Springer Nature — offer detailed, step-by-step instructions on how to deal with doctored images...

https://www.nature.com/articles/d41586-021-02610-7

Prof. Ljubomir Jacić

Thank you so much for your posts, very interesting.

Best Regards.

Dear Pedro L. Contreras E. , this is fine article.

How to make colour-blind-friendly figures

Changing the hues used in scientific graphics can make a huge difference to people with colour vision deficiencies. Try it yourself by generating the plots in R using this code, available on GitHub...

When viewed by people with protanopia, a form of red–green colour blindness, a histogram created in the programming language R using a rainbow colour scheme (left) would lose a lot of its colour, and make some data points effectively disappear (right).

However, when the Color Universal Design palette is used (left) in place of the rainbow scheme, people with colour vision deficiencies can still clearly see all the gradations (right).

https://github.com/jperkel/cvd-graphic/

Pedro L. Contreras E.

In nanotechnology we are measuring that which we cannot see but has profound effects in the large scale. Not really the 'right sort' of answer to your question but another facet...

Poor colour choices in images and figures can distort data and make them unintelligible for people with colour blindness. The size and thickness of image elements, such as dots and lines, are important, too. Thankfully, most data visualization packages include colour maps that are accessible to people with colour vision deficiencies, and tools are available online for selecting appropriate hues...

https://www.nature.com/articles/d41586-021-02696-z

Which of these phrases do you use when wanting to understand something better or find something?

"Let me touch."

"Let me hear."

"Let me smell."

"Let me taste."

"Let me see."