When you teach someone , you need to understand well to transfer your knowledge.

Depends on the subject area. For example, you cannot understand math until you are be able to do math.

As long as I am unaware that I misunderstood, I believe that I understood something...

This may not be a suitable answer...

.

The function of knowledge means that the person claiming the knowledge is able to use it in some way to influence events, processes in accordance with either accepted procedures.

In mind , it started visualize that the things happen

Probably when I can find examples, applications or the relation of something with other things, it means that I have understood it.

Dear Victor P. Maiorana,

An interesting question. In my opinion, usually a person is aware that he understands something when he stops asking questions about a specific issue for which he asked questions earlier and received answers. I confirm that the role of teachers is big in this matter, ie explaining different concepts, issues, etc. But also in other professions in which representatives of various companies, public institutions explain to potential clients and contractors the offer of the organization they represent. In addition, service providers and persons representing public trust professions, such as lawyers, doctors, etc. should, in accordance with the principles of ethics, good practices, high moral standards, objectively explain the essence of the problem for clients, clients, recipients, patients, etc.

Best wishes

Levels of Understanding

What is needed in the concept of understanding is “level or depth“ of understanding.

For example, in mathematics, someone:

1. Can understand how to add and substract but not how to multiple or divide;

2. Can understand elementary logic but not higher order logics.

3. Can understand a proof having been derived by another but not prove a theorem from scratch himself or herself.

If I could able to express a term in the simplest possible way, it gives me a feeling that I have understood something!

Bloom's taxonomy can be used a a great reference for this. Six levels of cognitive learning is described, the lowest being memory recall. Unfortunately, most educators focus on this level mostly. Higher levels include understand, apply, analyze, evaluate, and create. Some examples include: If you truly understand a subject matter, you must be able to apply at various scenarios, you must be able to create new things using this as a basis. etc.

When I understand something, I can discuss it with my self and can explain it to other also.

March 2, 2019

Thank you all for replying. Comments follow.

Regards to all,

Victor Maiorana

1.

@N. Gurappa. Here, I believe, is an accurate paraphrase of your reply: “When something is explained to you, and you have not misunderstood it, then you believe you understand.” The question remains: What is about the explanation that caused you to understand it? In other words, what takes place within you – within your thinking – that brings you to a state of understanding?

2.

@Dmytro Leshchenko. Your reply is all true. But how does one come to a state where knowledge (i.e., understanding), can be claimed? What thinking process must take place to bring a person to a state of understanding?

3.

@Anjay kumar Mishra. When your mind is visualizing, what is it that you see? In other words, what thinking process takes place that supports the visualization?

4.

@Saeid Asadi. What is common among the examples, applications, or relations that allow you know that you understand? For example, what happens mentally before you are in a position to engage in application?

5.

@Dariusz Prokopowicz. Dear Dariusz Prokopowicz, Your reply gets close to the heart of the matter. What specific questions must that person ask to arrive at an understanding? Are the questions related in some way so they can be used again and again regardless of the topic at hand?

Please note re your comments on other professions and service providers: Yes, they must do the things you say. But the basic question still remains. On what mental basis do ***their*** explanations proceed?

Best wishes.

6.

@Dennis Mazur. Yes, there are levels of understanding. But what does it mean to understand? More specifically: How do you know when you understand a math topic? To say, “When I can apply it or prove it.” is an indirect answer because it does not address the explicit reasoning process that allows the application or proof to take place.

7.

@Nayan Kadam. A good general answer. Can you address what that “simplest possible way” is? What is the simplest mental process you can use to arrive at understanding?

8.

@Mariappan Jawaharial. You use the key word “Described.” Describing something is not the same as explaining it. A toothbrush can be described as a small brush attached to a short stick. But this is not an explanation of a toothbrush. According to Vygotsky (1976), “[M]ere description does not reveal the actual dynamic relations [e.g., intent-activities-consequences], that underlie [all subject matter topics]” (p. 62).

Bloom’s Cognitive Taxonomy is not an actual process to achieve understanding. It does not provide an explicit reasoning process for connecting and integrating a given topic’s facts and ideas to arrive at understanding.

In addition, Bloom’s Taxonomy is illogical. Looking at the first two “steps,” one starts with knowledge (recall of facts) and then goes directly to understand (comprehension in the original Taxonomy). But our minds do not work that way. Possession of facts and ideas does not automatically result in understanding. Something must take place between knowledge and understanding. We need to first engage in some form of reasoning that connects and integrates facts and ideas in a systematic manner. Then, understanding can emerge. Connecting and integrating facts and ideas require that we analyze, synthe­size, and evaluate in the form of a reasoning process. However, Bloom’s taxonomy shows these three mental activi­ties as coming after understanding and not between recall and understanding. Therefore, the progression is out of natural order. This was Bloom’s dilemma. Indeed, he was aware of it. Perhaps this is why Seddon (1978) placed synthesis between knowledge and comprehension.

The ability to apply something is not the same as understanding. What is the prior explicit thinking process that allows the application to take place? So, the question remains: How do you know when you understand something?

9.

@Arben J Salihu. Yes. But along what reasoning lines do your studies proceed? What do you first do mentally to show yourself that you understand, before you show/deliver that understanding to others?

10.

@Nafees Mohammad. As you say, when you can discuss it with yourself is a key condition for understanding, and for explaining to others. Can you describe the specific reasoning process you use when discussing with yourself and when explaining to others?

11.

@Monica Butnariu, @N. Gurappa, @Slavoljub Hilcenko, @Academic Accelerator, @Mubashir Ahmad, @Arben J Salihu

Thank you all for your recommendations.

Victor Maiorana

@Dmytro Leshchenko. Your reply is all true. But how does one come to a state where knowledge (i.e., understanding), can be claimed? What thinking process must take place to bring a person to a state of understanding?

@Anjay kumar Mishra. When your mind is visualizing, what is it that you see? In other words, what thinking process takes place that supports the visualization?

@Saeid Asadi. What is common among the examples, applications, or relations that allow you know that you understand? For example, what happens mentally before you are in a position to engage in application?

@Dariusz Prokopowicz. Dear Dariusz Prokopowicz, Your reply gets close to the heart of the matter. What specific questions must that person ask to arrive at an understanding? Are the questions related in some way so they can be used again and again regardless of the topic at hand?

Please note re your comments on other professions and service providers: Yes, they must do the things you say. But the basic question still remains. On what mental basis do ***their*** explanations proceed?

Best wishes.

@Dennis Mazur. Yes, there are levels of understanding. But what does it mean to understand? More specifically: How do you know when you understand a math topic? To say, “When I can apply it or prove it.” is an indirect answer because it does not address the explicit reasoning process that lead to the ability to apply or prove.

@Nayan Kadam. A good general answer. Can you address what that “simplest possible way” is? What is the simplest mental process you can use to arrive at understanding?

@Mariappan Jawaharial. You use the key word “Described.” Describing something is not the same as explaining it. A toothbrush can be described as a small brush attached to a short stick. But this is not an explanation of a toothbrush. According to Vygotsky (1976), “[M]ere description does not reveal the actual dynamic relations [e.g., intent-activities-consequences], that underlie [all subject matter topics]” (p. 62).

Bloom’s Cognitive Taxonomy is not an actual process to achieve understanding. It does not provide an explicit reasoning process for connecting and integrating a given topic’s facts and ideas to arrive at understanding.

In addition, Bloom’s Taxonomy is illogical. Looking at the first two “steps,” one starts with knowledge (recall of facts) and then goes directly to understand (comprehension in the original Taxonomy). But our minds do not work that way. Possession of facts and ideas does not automatically result in understanding. Something must take place between knowledge and understanding. We need to first engage in some form of reasoning that connects and integrates facts and ideas in a systematic manner. Then, understanding can emerge. Connecting and integrating facts and ideas require that we analyze, synthe­size, and evaluate in the form of a reasoning process. However, Bloom’s taxonomy shows these three mental activi­ties as coming after understanding and not between recall and understanding. Therefore, the progression is out of natural order. This was Bloom’s dilemma. Indeed, he was aware of it. Perhaps this is why Seddon (1978) placed synthesis between knowledge and comprehension.

The ability to apply something is not the same as understanding. What is the prior explicit thinking process that allows the application to take place? So, the question remains: How do you know when you understand something?

When my results compare well with the results of the peer-reviewed literature.

@Arben J Salihu. Yes. But along what reasoning lines do your studies proceed? What do you first do mentally to show yourself that you understand, before you show/deliver that understanding to others?

@Nafees Mohammad. As you say, when you can discuss it with yourself is a key condition for understanding, and for explaining to others. Can you describe the specific reasoning process you use when discussing with yourself and when explaining to others?

@Monica Butnariu, @N. Gurappa, @Slavoljub Hilcenko, @Academic Accelerator, @Mubashir Ahmad, @Arben J Salihu

Thank you all for your recommendations.

Victor Maiorana

@N. Gurappa. Here, I believe, is an accurate paraphrase of your reply: “When something is explained to you, and you have not misunderstood it, then you believe you understand.” The question remains: What is about the explanation that caused you to understand it? In other words, what takes place within you – within your thinking – that brings you to a state of understanding?

The are degrees of understanding:

When one develops a set of points to describe what one has understood, there should be a 1:1 correlation between what one has understood and what the other has understood. The degree the 1:1 correlation is off, points to the fact that the understanding is off by that degree.

@Dennis Mazur. What takes place within you – within your thinking – that brings you to a state of understanding? In other words, can you describe explicitly the reasoning process you use to arrive at an understanding of any given topic?

I know that I understand when I get a message that is internally coherent. Of course understanding is subjective and the "knowing" of understanding is a matter of degree.

@Victor P. Maiorana. All processing is at a subconscious level, like a reflex.

I prefer to see understanding qualified negatively-that is a person who sees where an answer or descriptor is wrong understands it.

As your question nevertheless strangely illustrates, there are different kinds of understanding. Do lawyers, engineers and lawyers really understand or simply know?

As they used to say; teaching is the best way to master your subject. Closing the loop with accurate feedback from your students and trainees will take you to the next level of mastery!

@Muhammad M Hammami

What is it about the message that tells you it is internally coherent? Or, what do you use as a mental guide that tells you something is internally coherent?

Some topics lend themselves to subjective understanding (e.g., a work of art). But even then, the understanding is arrived at through some mental process. For most topics, understanding is objective. Otherwise, for example, men would have never landed on the moon.

Yes, understanding is a matter of degree. Can you provide an example of understanding something in degrees? It will help answer the question under discussion.

@Stanley Wilkin

To see that that an answer or descriptor is wrong means it does not comport with an understanding that you already hold. So the question remains; on what cognitive basis did you come to that understanding? What took place within you – within your thinking – that brought you to a state of understanding? In other words, can you describe explicitly the reasoning process you used to achieve understanding?

Regarding your second sentence, can you explain what you mean by different kinds of understanding? It will help focus the discussion.

Your third sentence introduces a question that can be applied to any person for any topic. The mind does not go directly from knowing to understanding. Something must take place mentally that allows mere knowledge to turn to understanding. What mental process takes place? Can you explain it explicitly?

@Mohamad-Hani Temsah

What you say is true. But it does not directly address the question. What takes place within you – within your thinking – that brings you to a state of understanding? In other words, can you describe explicitly the reasoning process you use to arrive at an understanding of any given topic?

If you prefer, the question may be asked in another way. Let’s say you ask a student to explain how they understand a topic you have taught. What, specifically, would you look for in their answer that tells you they understand?

@Dennis Mazur

Let’s say that “all processing is subconscious.” Do you think that subconscious processing is different by individual; that each human being has their own unique processing system to achieve understanding? Or is there something common in the way humans think to achieve understanding?

Let’s also say there exists some way to consciously observe that unconscious process. What system of thinking do you believe the observation would show?

@ Victor P. Maiorana The processing process may be intrinsic to the human brain and some additional animal species, but the process it heavily dependent on the individual’s past experience with the specific content of the process. One may understand elementary logic but be unable to understand higher order logics because he or she has no-little experience with them, eg, no experience with the notation of the higher order logic under consideration.

Dear Victor,

I know that understand something mainly when I am able to apply to other domains what I learned in a given domain. In other words, the more I am able to transfer the knowledge I learnt in a certain domain to other domains the more I understood what I learned.

KInd regards,

Orlando

Dear Victor P. Maiorana

I may seem very opinionated and idealistic here, but I am just going to "go for it".

Understanding:

You KNOW (and can impart it) because: True and good understanding allows more clearly right action and right discovery and continued or continuous discovery in an ever clearer/distinct area of study (and you can more reliably see necessary sequences, aka causes, of things -- certainly MUCH less personalized or idiosyncratic). You can tell when each and all of these co-related characteristics of your understanding are true -- for one thing: by a greater ability to conceptualize (which amounts to more now-usable free space in working memory ; it is all clearly related to discrimination, integration, and consolidation of concepts/skills in the Memories). Usually this free space in working memory rather soon let's you think more in ways needed about something (in the subject area you are devoted to) and find/decide-on/do what's needed. This way would be good to see good understanding and part of what's needed to impart to students (the other also-related part described in the last paragraph). And, what may or may not occur (which I bring up just since it shows , in some sense, some "outer limits"):

When you can in no way better 'see' things (benefiting less basically from help or from anything else to turn to or any other way to look at the relevant "things" ), WHEN you cannot immediately or soon become better in some OR MOST of the ways in the 1st paragraph, above, then it is possible you could say you have/sensed a small quick temporary glimpse of "Enlightenment", seeing no more that is conditional IN THAT AREA of study -- but one must make sure you set things up so this cannot occur wrongfully/artificially (though I do not consider this last concern a likely problem). NOW, to say all that again, speaking more naturalistically and more scientifically (though perhaps not more meaningfully): This is basically a relatively continuous free space in the Memories (accessed via the episodic buffer and working memory) -- and phenomenologically BEING working memory, a free space which otherwise (typically) is rather quickly well-used to progress, as indicated in the paragraph above: usually free space in working memory let's you think more in ways needed about something and THAT is what you do rather quickly or soon.

THE OTHER HALF OF THE "STORY' (in any case, with the "glimpse" or without that):

A teacher MODELS what is involved in all this by clearly having (and showing) she/he has personally evaluated (and in some best sense personally verified) all and everything she/he believes and presents to students. (This is related to EVERYTHING in the paragraphs, above.) This too is important to make clear or impart to students (perhaps maybe just by clear example).

@Dennis Mazur

03/10/2019

Your observation that “The processing process may be intrinsic [innate], to the human brain…” has meaning because it is supported by the natural science of sentence grammar.

There is basically a single structure to the sentence in the form of subject-verb-direct object. It is a structure we follow or look for naturally when speaking, listening, writing, and reading. This single and innate-to-the-mind “one-size-fits-all” sentence structure underpins all human communication. This is how we come to understand a single human thought. Even if one’s words are out-of-order, the mind is able often to sense make of them by straightening them out.

Consequentially, whatever the medium, topic, or language people can understand one another through use of a natural process of thought via the natural grammar of the sentence.

=====

Let’s say the question is, “How do you know when you understand a single thought? Then, the three paragraphs above which follow a critical reasoning process for explanation, provides an answer.

However, the question at hand is: How do you know when you understand something? The “something” could be any subject matter topic in any discipline, or any topic in the world or in one’s imagination. Understanding a topic fully requires processing not one thought, but multiple thoughts. How does one process multiple thoughts to achieve understanding?

@Orlando M Lourenco

03/10/2019

Dear Orlando,

Yes, the act of transferring knowledge from one domain to another can lead to greater understanding in both domains.

The ability to transfer (i.e., apply) knowledge gained in one topic to another topic means that you understand the first topic. That initial understanding is achieved through some reasoning process.

So, the question remains how did you achieve that initial understanding? In other words, How do ***you*** know when you understand something? What takes place mentally that tells you that you understand something?

Best wishes,

Victor

@Brad Jesness

03/10/2019

Dear Brad Jesness,

You went for it and provided a way to answer the question; and it rests in your last paragraph: “A teacher MODELS what is involved in all this by clearly having (and showing) she/he has personally evaluated (and in some best sense personally verified) all and everything she/he believes and presents to students…This too is important to make clear or impart to students (perhaps maybe just by clear example).”

This raises the question: On what mental basis do teachers model understanding of a topic? Using your active operative terms, How do teachers make clear, impart, show, evaluate, present, exemplify, provide examples of, and verify understanding? All the operative terms suggest that teachers themselves must necessarily first actively engage in some reasoning process before entering the classroom. Let’s concentrate on the showing and verifying.

Showing means teachers will illustrate (impart, present, exemplify, reveal, share, show examples of) their understanding to students in ways that are clear and explicit. This requires that teachers need to use a clear and explicit reasoning process to first explain a topic to themselves. Therefore, the immediate interest here is the reasoning process used by teachers prior to explaining a topic to students to achieve understanding.

Verifying means that students can, by themselves, apply the reasoning process or processes they have been taught to the topic at hand and to other topics as well.

===========

You may believe that reasoning for understanding is dependent on the topic at hand. If so, please consider the following:

There is basically a single structure to the sentence in the form of subject-verb-direct object. This single and innate-to-the-mind “one-size-fits-all” sentence structure underpins all human communication. This is how we come to understand a single human thought. Consequentially, whatever the medium, topic, or language people can understand one another through use of a natural process of thought via the natural grammar of the sentence. However, Understanding a given topic requires processing multiple thoughts.

So, perhaps you can take up this re-stated version of the question: “What reasoning process do teachers use to explicitly model (show, evaluate, impart, present, exemplify, reveal, share display, reveal), their understanding of something?”

Dear Victor P. Maiorana

First I would say that what I was mainly talking about before was some central, key, reoccurring topics or set of topics (to some extent, this way-it-is could well have a part of the instructor's own perspective) that an instructor must present and explain.

Another part of my answer to your new question would be: well-placed, previously-justified and later-justified, PASSION. I believe I have seen this passion and, in combination with evidence well-presented, well-shown, or well-exemplified/explicated, this seems to be truly inspirational (and not fleeting). And, I think the entire exposition of the information, presentation and passion continue to be shown by such an instructor -- so all aspects of the overall issue as I addressed it before (above, in the first answer I gave, and above, with the present elaboration) are "abiding", continuing on, and they DO SHOW many of the aspects of the PROCESS: discrimination, integration, and consolidation of concepts/skills, that went on in the instructor's thought, as/how she/he developed it (and perhaps the better/best instructors are helping the students themselves to move through these processes with the "material", and individually, as needed). AND, AS PRESENTED, all that showing the individual's personal assessment/commitment in the incorporation and/or development of her/his cogent, very more-and-more apparently-worthwhile view. To put it crudely: he/she "sells it" and "sells it" well and thoroughly somehow showing many or all the aspects of processing she/he has "put into" the topic and with the importance shown with passion (and the "end result" including -- and this adds a new aspect to my answers so far: some well-developed FACILITY, this including a great ability to take and answer questions * ), and amongst the passions likely showing some JOY. This is nearly all I can think of to add to what I said before and possibly provide some answer to your new question. But, also directly to your question :

WHATEVER REASONING ALL THAT TAKES, AND OBVIOUSLY IT IS UNFOLDING in some sense -- much of this which may be, especially in an old teacher, rather thoroughly well-known. This all may seem like an ultra-idealist view, but indeed this is exactly what you want (though most of the best may do less than the ideal, I suppose).

* FOOTNOTE: In this regard, I was never a good instructor, nor was I completely or even clearly good in some of the other ideal aspects. I, frankly, do not have the strength of mind to do a lot of the ideal, but I have seen many very good professors/instructors who do show these (at least in good part, though myself inferring some).

P.S. Dear Victor P. Maiorana

After editing for about an hour (which I all too frequently do), I think the last answer of mine is done. I will value your criticism and critique

@Brad Jesness

03/11/2019

Dear Brad Jesness

I agree with all you say. The qualities you mention are wholly valid and part of good instructional (and learning) practice. Your thoughts are most insightful, and as good as they are, this reply (is again) highly abstract. The question posed on how one understands needs a concrete (i.e., operational) response that includes descriptions of an explicit process or processes (i.e., methods, means, activities).

=========

The key to answering the question again rests within your own thoughts.

1. You say, “…so all aspects of the overall issue as I addressed it before …DO SHOW many of the aspects of the PROCESS: discrimination, integration, and consolidation of concepts/skills, that went on in the instructor's thought, as/how she/he developed it (and perhaps the better/best instructors are helping the students themselves to move through these processes with the "material", and individually, as needed).”

Terms such as “discrimination, integration, and consolidation of concepts/skills” represent abstract thoughts. What is the *actual process* used? What, exactly, “…went on in the instructor’s thinking “…that constitutes the instructor’s thought process? How, exactly, do they discriminate, integrate, and consolidate concepts/skills; and what are the concepts /skills? If instructors cannot explicitly answer these questions for themselves, then they cannot explain a topic at hand to their students. They cannot help “…students themselves to move through these [thought] processes.”

2. You say, “To put it crudely: he/she "sells it" and "sells it" well and thoroughly somehow showing many or all the aspects of processing she/he has "put into" the topic

The statement “…somehow showing many or all the aspects of processing she/he has ‘put into" the topic,’ is again most abstract. How does one “…somehow [show] many or all…aspects” of the “processing” put into understanding a topic? What does the “somehow” look like? If you can provide explicitly the “somehow,” then you will have answered the question.

So, again, we come full circle to the question; here revised to include your terms: “What thought (reasoning) processes do teachers use to explicitly show, impart, present, exemplify, reveal, share, display, discriminate, integrate, and consolidate their understanding of something (e.g., a subject matter topic)?”

Thank you for your kind words.

Dear Victor P. Maiorana

Let me try to get out of your "circle".

When you want an overall general answer about problems/challenges which occur in many situations/circumstances, you can expect a general/generalized answer (thus, I thought I did pretty good). Being more specific may even be seen as a strange reply (if one tried it). Also: I believe THE SUBJECTS' BEHAVIOR IS SOMEHOW CLEARLY THE FOUNDATION OF ALL DEFINITIONS. Related to this, I do not otherwise conjure up operational definitions. In reality in different circumstances : reality IS concrete as you say (but varied) ("abstraction" not needed or needed as much).

Ask for an answer on how things show in a specific situation and circumstances: fly me to the place, put me in a class with a great instructor, and pay me and I will apply/elaborate/specify particular behaviors as instances of the general (type-of-things) answers I gave. Otherwise the work is left to the reader; the idea of me giving "operational definitions" on such things as I describe does "not fly" with me, obviously. I do not do the conjuring, like an armchair philosopher -- those "guys" being the ruin of "modern" Psychology for its whole existence; and, there is no more "distilling the essence" here from me -- no contrived hypothetico-deductive system for me to apply for you (and if there was one, I likely would not use it, because it would seem wrong) (and yet I see no other way to answer your criticism otherwise). If I cannot see something more specific that could be accurately and reasonably seen across fields of teaching/learning (better descriptions OF PARTICULARS and yet still GENERALLY SEEN across circumstances, just as clearly or more clearly than with the descriptions I provided) then it appears I missed something, and my apologies -- I think I did my best.

Perhaps you will say I should "better operationalize" this very, present response; if so, perhaps you will have to send me the notes from your counselor (if you have one). ALSO:

Some "TYPES-of-things" may actually be seen as concrete (it may be _from_ concrete things across instances and across situations and circumstances from which some "abstractions" are in-reality developed (by people, the organism, itself)); in short, they are as real for them as many other concepts that are seen as more concrete. Try to see this through an exercise: using your assessment/imagination about several particular instances with which you are familiar, try to see some "TYPES-of-things" that way. (I may not be so "abstract" as you think in a some REAL, though perhaps non-traditional way.)

Maybe someone else will work on all this for you now.

P.S. Perhaps I should ask you to provide an operational truly empirically-founded-and-based definition of "abstract". (How else would it be clear to me where my deficiencies are?) Guess what: I am the ONLY person in the field of Psychology who has done that, in part.

@Brad Jesness

03/13/2019

Dear Brad Jesness

Your reply goes in several different directions. Let’s return to the original question. Also, a suggestion for you is provided below.

Previously, you wrote that an instructor “somehow” shows students the “processing” put into understanding a topic. My response was, “What does the ‘somehow [the processing]’ look like? Answering this question provides an answer to the original question, which is: “How [not somehow, but how] do you know when you understand something.”

If instructors cannot explicitly answer this question for themselves, then they cannot explain any topic to their students. They cannot, as you say, help “…students themselves to move through these [thought] processes.” Under these conditions, instruction becomes a matter of mere description and not explanation. Describing something is not the same as explaining it. A toothbrush can be described as a small brush attached to a short stick. But this is not an explanation of a toothbrush.

To explain a topic is to apply and share with students a clear and explicit reasoning process. And, yes, you have missed something. But there is no need to apologize; the whole education culture has missed it since the first teacher set foot in the first classroom and the first author wrote the first textbook. It concerns the natural science of how the human mind innately, critically, and informally engages the world and its subject matter.

The following is excerpted from: “You’re Teaching Subject Matter Wrong - An open letter to educators from the material they teach.” (Ref.: Education Week, 01/02/2018, https://www.researchgate.net/publication/323688055_Education_Week_essay_of_01022018_You're_Teaching_Subject_Matter_Wrong_AUTHOR_SUPPLEMENT_The_Profound_Need_for_a_Core_Body_of_Knowledge_for_Critical_Instruction_to_Transform_Teacher_Education_and_Schoo

=====

[This is the world’s subject matter speaking to educators.]

“Your conscious mind has its own innate, informal grammar for thinking 

critically [i.e., for processing multiple thoughts critically]. This grammar of the mind always seeks intent, identifies the activities needed to achieve intent, and, when thinking fully, considers the consequences that follow. You use this critical pattern repeatedly throughout the day. You cannot escape it.

Your mind is responsible for bringing me to life intellectually. Therefore, it should not surprise you that I reflect your grammar of mind and that all my topics mirror the same three elements of intent, activities, and consequences. Your grammar of mind needs to be [made] explicit, formal, transparent and shared. This will make it possible to explain and comprehend me. When this need is recognized and acted upon by teacher educators, teacher candidates, [school and college teachers], education school and faculty deans, researchers, K-12 teachers, principals, assist ant principals, superintendents, professional developers, and authors of educational materials you will no longer be at a self imposed and long-standing disadvantage [that conventional roteism instruction represents].”

=====

I call our innate grammar of mind, mind grammar. To see what the “how” - what mind grammar - looks like explicitly and operationally for any and all topics, see https://criticalinstruction.com/mind-grammar-theory-and-practice/

Please take your time and consider each document carefully. Before responding, suggest that you apply the “Mind Grammar / Subject Matter Interview” to a topic of your choice.

Quite a bit of research has been done about the working of conceptual thinking.

It is not that difficult to know when you have understood something. The trick is to first and foremost understand how the neocortex supports conceptual thinking and the understanding process:

https://www.researchgate.net/publication/309913950_Comprehension_Process_Overview

And this latest paper titled "The Mechanics of Conceptual Thinking":

https://doi.org/10.4236/ce.2019.102028

And finally this one:

https://www.omicsonline.org/open-access/on-the-relation-between-the-comprehension-ability-and-the-neocortexverbal-areas-2155-6180-1000331.pdf

Best Regards, André

@Andre Michaud

03/19/2019

Regarding understanding something (i.e., a concept, an idea, anything), the three links provided lead to papers that address primarily the physiological brain but not the psychological mind. The papers carry no mind-based (intellectual) answer to the operative question, “How do you know when you understand something?” In other words, the brain is an electro-biological biomass that responds to the psychological mind. The mind’s innate reasoning abilities, driven by intent, operate the biomass.

Link 1 says, “The comprehension process is a method used by the human brain… .”However, “…coherent conceptual [and arborescent] thinking” (Link 2), is a consequence of the human mind at work. The physical brain doesn’t understand or eventually comprehend; the thought-invoking mind does. Although information is stored in memory, the physical brain does not initiate exploration or questioning, the mind does. To be sure, thoughts pop to mind; but they owe their appearance to previous short and long-term concerns raised previously by the mind.

We can’t share our physical brains (But who can foretell the future?); but we can share our minds’ thoughts. The essence of education practice is explaining specific topics in classrooms, textbooks, and academic writing. Accordingly, school and college faculty, researchers, and writers need to mindfully (i.e., cognitively), know how to explicitly answer the operative question for themselves. Only then are they in a position to share understanding (i.e., explain) topics to their students and readers.

Link 3 says, "In fact, absolutely everything we think we know…have successfully understood…other[s]…have communicated to us…read… [and] feel, constitutes the raw information that we have no choice but to work with. We simply have nothing else at our disposal to understand reality.” This may have been true; but now we do have a choice. We can now understand, comprehend, and therefore explain reality objectively through what I call mind grammar.

Mind grammar (a part of critical instruction pedagogy), provides the means to objectively achieve understanding (and then comprehension) in one’s self and in students of any topic in any discipline. Here is a link to an essay that provides a conceptual overview and objective illustration of how this may be accomplished. The essay has meaning not only for textbook authors but school and college faculty, researchers, and academic writers as well.

https://www.researchgate.net/publication/327832620_Why_textbook_authors_should_be_using_critical_instruction_pedagogy

In summary, to explain a topic, one needs to first employ and then share with students explicit, formal, and objective reasoning processes that lead to one’s own understanding and comprehension. Then, explanation (i.e., instruction) can proceed. This requires using the natural science of how the human being’s conscious and innate grammar of mind critically but informally engages the world and its subject matter. To see how to engage new and revisited subject matter formally and empirically - and to try mind grammar for yourself and thus be able to answer the operative question - see mind grammar.

Best wishes, Victor

Dear Victor,

I see that you took the time to have a look at my 3 references, which is more than most do.

If you read carefully reference 2, you will see that this generally agrees with your understanding.

The actual key is the process by which multilayer neural networks are unable not to detect coherences in data sets, which is what Hebb discovered. Our conscious mind is in control as you say, but its tool to manipulate and correlate our thoughts is a 6-layer neural network that constantly correlates any set of memories that we have come to mind and cogitate about. We each have a personal and quite powerful correlator at our disposal.

I will read the reference you provided.

Best Regards, André

@Andre Michaud

03/20/2019

Dear Andre,

Two links did not make it through the 3/19/2019 reply process. Here they are.

This is one is associated with the words “critical Instruction pedagogy” that appear in the first line of the next-to-last paragraph:

https://criticalinstruction.com/core-body-of-knowledge-for-critical-instruction-pedagogy/

This one is associated with the words “mind grammar” that appear as the last two words in the last paragraph.

https://criticalinstruction.com/mind-grammar-theory-and-practice/

I believe I did not miss discussion of an explicit reasoning process that leads to understanding; but I will read your Link 2 paper again.

Best wishes, Victor

Thank you Victor for the working links. I will now have a more complete picture of your analysis.

Best Regards, André

Understanding is shown by predicting observations not yet made. If a model cannot predict - it's useless. If an observation that a model does not predict, the model is lacking. The many new observation in the realm of the standard cosmological model (dark matter, dark energy, inflation, etc.) have been post-dicted by ad hoc modifications instead of forming a new model. This implies a lack of understanding of the universe by the standard model.

@John Hodge

03/23/2019

Agreed. But the reply addresses the application of understanding.

Application responses to the operative question (How do you know when you understand something?) are not direct responses. Such responses assume that understanding already exists; they do not provide the cognitive basis for how that understanding was achieved initially.

With reference to models, there must be a conceptual cognitive foundation upon which a model is based that established understanding of a given topic. In that case, the operative question is asking “What does the model’s cognitive foundation (i.e., framework, system, scheme, structure), look like? Said another way, what reasoning process was used to establish the model intellectually and thus achieve understanding of the topic itself?

Victor P. Maiorana

People think.

Dear Victor,

You wrote: "What does the model’s cognitive foundation (i.e., framework, system, scheme, structure), look like? Said another way, what reasoning process was used to establish the model intellectually and thus achieve understanding of the topic itself?"

Any model's cognitive foundation is first and foremost a set of coherent and self-consistent conclusions, each of which is arrived at from correlating a set of premises whose coherence leads to this conclusion.

The correlating of any set of premises is an automatic process of the multilayer network that supports our thinking processes. This is what is described in the papers I referred before, which are a synthesis of the state of current research about the various aspects of the mechanics of conceptual thinking.

No independent or separate reasoning process is required to correlate a set of premises. This process is an automatic property of multi-layer neural networks.

Multi-layer neural networks are unable by structure not to detect a coherence in a data set, if such a coherence is present.

Best Regards, André

@Andre Michaud

03/30/2019

Dear Andre,

I note there has been no response to the materials sent you on 3/19 and 3/20. As opposed to descriptions of how brain mechanics are perceived to operate physiologically, the materials (see Links 4 and 6 below), provide a direct, objective, practicable, replicable and psychologically-based way answer the operative question: How do you know when you understand something?

Instead, on 3/23, you commented on my reply to @John Hodge of 3/23. You said,

“Any model's cognitive foundation is first and foremost a set of coherent and self-consistent conclusions, each of which is arrived at from correlating a set of premises whose coherence leads to this conclusion.”These key questions remain: How does one, exactly, go about correlating a set of premises? What psychological reasoning foundation is used to identify, connect, and integrate the premises that lead to a set of coherent and self-consistent conclusions?

Here is how I interpret this reply of 3/23 psychologically. The fourth paragraph is a conclusion of the three paragraphs (premises), that precede it. It states, “No independent or separate reasoning process is required to correlate a set of premises. This process is an automatic property of multi-layer neural networks.”One is moved to ask: Did the biological multi-layer neural networks write these sentences automatically or was it the psychological mind that directed they it be written, to be processed simultaneously by the biological neutral networks? And what of the three preceding paragraphs (premises)? Did neural networks automatically provide the premises, or did the conscious mind in real-time reason them into existence, to be concurrently processed neurologically?

To say, “No independent or separate reasoning process is required…[the] process is an automatic function of the neocortex,” implies and must mean that some prior psychological reasoning process exists that is always present (and, in that sense, is “automatic”). What does that reasoning process look like; meaning, what framework, system, scheme, structure, pattern, or questioning is in play?

The organization of the reply is an exampleof a conscious logical reasoning process at work. But, as in previous responses, it is not an answer to the operative question. To answer the operative question, one must describe a critical reasoning process that is objectified formally and thus can be readily used by and replicated by others. Otherwise, it cannot be used to reflect “…objective reality…[in a way that is readily verifiable by] other persons considering the same object, event, concept, or emotion…”(Ref.: Link 1 below).

--------------

Like the grammar of the sentence, there is also an innate, conscious, informal, and critical reasoning process possessed by all humans regardless of background or language. It appears early in life, before verbalization, and is always present (i.e., “automatic”). The formalization of the human grammar of mind was originated, developed, and made practicable personally. I call it mind grammar. It provides an objective basis to connect and integrate any topic’s facts and ideas to achieve comprehension. Mind grammar affords the replicative means for all learners, teachers and students, to take intellectual control of new and revisited subject matter by providing a cognitive foundation when thinking, reading, listening, writing and speaking. It is discussed below under “A Summary of The Natural Science of the Human Mind” and “Suggestion for Research Experiment.”

Coming to Terms with Comprehension

For those who are following the operative question, here are the links you kindly provided to three of your papers:

(1) https://www.researchgate.net/publication/309913950_Comprehension_Process_Overview

(2) "The Mechanics of Conceptual Thinking": https://doi.org/10.4236/ce.2019.102028

(3) https://www.omicsonline.org/open-access/on-the-relation-between-the-comprehension-ability-and-the-neocortexverbal-areas-2155-6180-1000331.pdf

Upon re-reading as you suggested previously, I did not find a definition of comprehension, or an answer to the operative question that addresses a critical reasoning process objectified formally.

For example, Paper 1 - Brief Overview of the Comprehension Process, starts with “Before intelligence, or should we rather say ‘the comprehension ability,” can be defined, it is mandatory to describe the thinking process.”Two thinking modes are identified, thinking mode by image association and thinking mode by word association.

To define is: “the action or the power of describing, explaining, or making [something] definite and clear” (Merriam-Webster). Accordingly, one way to define something is to use a clear and coherent critical reasoning process that is objectified formally and thus can be readily replicated by others.

The paper uses a logical sequence of ideas that describe the two thinking modes. But logical thinking by itself cannot be the only basis for defining anything, including comprehension. To think logically is to discuss a topic in some orderly sequence, where the concern is the internal seral logic of the sequence itself and not the meaning, function, effect, importance, purpose, or end-in-view; and consequences; served by the logical sequence.

A logical definition cannot, by itself, serve as a critical reasoning strategy for understanding, comprehending, or explaining, which is the first mode of critical thinking. To be considered critical, the definition must be accompanied by. (a) a description of the subject matter topic’s intent (i.e., the objective of the topic itself), (b) logically arranged activities related to achieving the topic’s objective, and (c) the resultant positive and negative consequences. There are two other modes of critical thinking: argumentation and problem solving. To engage effectively in these latter two modes, one must first engage in Mode 1. It is Mode 1 of critical thinking that has long been missing in teacher education, school and college classrooms, research, and textbooks. Its absence is the reason why answering the operative question proves so difficult.

In addition, a strictly logical approach cannot serve as a critical reasoning strategy. Absent (a), and (b), and (c), purely logical discussions do not address all the critical elements (Maiorana, 2016).

A Summary of The Natural Science of the Conscious Human Mind

For those following the operative question, here are the linksI provided.

(4)https://www.researchgate.net/publication/327832620_Why_textbook_authors_[and all instructors] should_be_using_critical_instruction_pedagogy

https://criticalinstruction.com/mind-grammar-theory-and-practice/

(5)https://criticalinstruction.com/core-body-of-knowledge-for-critical-instruction-pedagogy/

(6)https://criticalinstruction.com/mind-grammar-theory-and-practice/

Based on Item (4), here is a summary of the basis for an objective psychological reasoning approach leading to comprehension.

There is an innate (natural) grammar of the sentence, and there is an innate (natural) grammar of thought. The first is called conventional grammar. The second I call mind grammar. Conventional grammar is the way words are connected and integrated to form a single complete thought. Mind grammar is the way many multiple thoughts (e.g., facts and ideas), are connected and integrated to achieve critical understanding and comprehension.

The sentence pattern takes the form of subject–verb–direct object. It is a thought pattern (i.e., form, structure, grammar, system) we all follow naturally when speaking and writing so that others may understand what they hear and read. This one-size-fits-all pattern is true of all people, languages, and subject matter topics.

The mind grammar pattern takes the form intent – activities – consequences. It is a multiple thought pattern we all follow naturally to achieve understanding and comprehension. This critical pattern is used repeatedly, implicitly, and explicitly, throughout the waking day in all endeavors. One cannot escape it. The pattern, intent(topic objective, the ‘Why?” of things) – activities(needed to achieve the intent), is used to achieve understanding. The pattern, intent – activities- consequences allows deeper exploration of a topic and is used to achieve comprehension. Just as with conventional grammar, this one-size-fits-all mind grammar pattern is true of all people, languages, and topics.

The mind is responsible for bringing subject matter to life intellectually. Therefore, it should not be surprising that the world’s subject matter reflects our grammar of mind, and that all topics in all disciplines mirror the same three elements of intent, activities, and consequences.

The conceptual, developmental, and procedural basis for objectively formalizing our grammar of mind for teacher preparation, school and college instruction and learning, research, and textbook writing can be found in Maiorana, 2015 [https://criticalinstruction.com/fixing-instruction/]; Maiorana, 2016 [https://criticalinstruction.com/preparation-for-critical-instruction/] and, Maiorana, 2017 [https://criticalinstruction.com/teach-like-the-mind-learns/]. An overview discussion of mind grammar is provided in Links 4 and 6.

These works provide the means to minimize greatly the self and student-defeating, and literacy-defeating, conventional practice of roteism instruction and learning.

Suggestion for Research Experiment

The Need for Questioning to Achieve True Objective Comprehension

Your papers make repeated references of the need for questioning to achieve comprehension. For, example, from Link 1 (underlines added):

- “the correlation process[is] always initiated by a self-questioningon [a topic]…usually resulting in the perception of a coherence…”

- “…the perception of a coherence… that is, the impression of "having understood" something following cogitationon [a topic]…does not, as such, guarantee that the subject of our cogitation has been objectively understood. Therefore, another process must be at playin order to orient our thinking towards true objective comprehension, which always is the ultimate goal.

- “…thecomprehensionprocessmandatorilyinvolvesapermanentquestioning process…”

These are all insightful and crucial observations. But they do not provide a psychologically-based answer to the operative question. Instead, they raise these questions: 1) What is the cognitive nature of the self-questioning; is it random [which Anderson (1992), has shown is of little instruction and learning value], or is it a coherent reasoning process based upon a replicable framework, system, scheme, structure, or pattern? (2) What is the reasoning nature of the cogitation, and what is the other process that is in play? (3) What is the reasoning nature of the permanent questioning process that leads to true objective comprehension?

The following provides an objective and replicative basis to answer these questions.

A Research Experiment on How to Achieve True Objective Comprehension

You have kindly read and recommended (thank you), “Why Textbooks Authors [and all instructors] Should be Using Critical Instruction Pedagogy” (Link 4). So, you have seen how mind grammar is used to develop an objectified, formal, and critical view of a topic.

I suggest we use mind grammar to develop two critical views (i.e., subject matter displays), on the topic of comprehension. Here are possible working titles. If you don’t care for the titles, we can change them. You would take the first, I the second.

- A Four-Stage MG2 Subject Matter Display of Comprehension – Neurologically-Based

- A Four-Stage MG2 Subject Matter Display of Comprehension – Psychologically-based

As we go along, we would critique each other’s display. The specific systematic questioning means to assemble a display are given in Link 6, under the heading, “The Mind Grammar / Subject Matter Interview.”Although sharing a common reasoning framework, the displays will be decidedly different in their objective, activities, consequences, and resources.

The most challenging part of the mind grammar process is identifying the objective of the subject matter topic itself; in this case, comprehension. The objective must first be pinned down clearly in order for an effective display to developed coherently.

If you decide to engage in this practical research experiment, we can start by exchanging and commenting on each other’s one-sentence subject matter objective.

Best wishes,

Victor

[Don't know why last three lines are in boldface. Could not remove.]

@John Hodge

3/30/2019

People think, but thinking is a process. The question is asking to identify the reasoning process you use to achieve understanding.

If one can’t identify an objective and replicative thinking process for one’s self, then students cannot be led to understand subject matter, and cannot learn the process for application to other subjects they study and to the world outside the classroom.

Please see again my response of 3/23.

Also, see my response of 3/30 to @Andre Michaud.

Victor P. Maiorana

A short summary would be nice (say about 2000 characters or less).

Note the question was "...WHEN..." not how.

You know when you understand something when your understanding generates more questions than you can answer.

Dear Victor,

I just took notice of your very large message. You mention and raise so many issue in a single text that I just don't know how and where to begin answering these issues.

I still work full time and sometimes have little left to interact on RG. I will try to come up with some response tomorrow. I began to read your interesting material initially, but then other activities required more urgently my attention.

As for what "understanding" means, in short, my conclusion is very close to Randy's.

I would say that we begin to understand something when what little we understand of it generates more questions than we can answer, but that when eventually we have found self-consistent answers to all of these raised questions, we are at the objective understanding level.

This is what I tried to put in perspective in the Short overview of the understanding process.

Best Regards, André

@Andre Michaud

04/05/2019

Dear Andre,

Yes, I see what you are saying. But, for purposes of classroom teaching and learning and textbook writing, the reply does not describe an objective reasoning process. The iterative questioning you refer to - if cataloged, organized, and made expressive - will inescapably reflect a universal and objective reasoning process sharable and usable by all.

If two people work together to try and understand a given topic they will inevitably have to arrive at and agree on a set of objective questions that lead to understanding. Your papers perceptively discuss the need for such questioning. For example, you make reference to the need for a “…permanent questioning process… .”

To save you time, may I suggest that your reply concentrate on the discussion found under the heading “Suggestion for Research Experiment” that appears in my reply of 03/30/2019. The suggestion addresses directly the need for and use of a permanent reasoning process.

Best wishes,

Victor

@John Hodge

04/05/2019

There cannot be a “when” unless there is a “how.”

Note, the operative question states, How do you know when you understand something? Meaning: How (i.e., by what reasoning means) do you know when (i.e., when the time arrives that) you understand something?

To date, in your replies and as previously pointed out, there has been no direct response to the operative question. I see you have read my “Why textbook authors should be using critical instruction pedagogy.” It contains an example (i.e., a display). Assembling and evaluating such a display leads one to know how and when they understand something.

For a given topic, how to use an objective reasoning process to arrive at understanding (and then comprehension), is given in:

https://criticalinstruction.com/mind-grammar-theory-and-practice/

@Randy Sorokowski

04/05/2019

Seems to me you are saying, “You know when you [don’t] understand something when your [initial] understanding generates more questions than you can answer.”

Within a given topic, the questioning process used to arrive at an initial understanding, if clear and objective, can be used to answer additional questions raised. This can continue on until one arrives at the desired level of understanding (referred to as “Pathway Development” in Maiorana, 2016).

To be useful in teaching, learning, textbook writing, and research, the question “How do you know when you understand something?” needs an objective operational response. Such a response can be found at:

https://www.researchgate.net/publication/327832620_Why_textbook_authors_[and all instructors] should_be_using_critical_instruction_pedagogy

and

https://criticalinstruction.com/mind-grammar-theory-and-practice/

Dear Victor,

Ok. I will try to answer some of the issues you raised in section "Suggestion for Research Experiment" as you suggest.

1) What is the cognitive nature of the self-questioning; is it random [which Anderson (1992), has shown is of little instruction and learning value], or is it a coherent reasoning process based upon a replicable framework, system, scheme, structure, or pattern?

I totally disagree with Anderson about the value of self-questioning. I think it is of critical value. It is not a coherent reasoning process as such, but it is rather what is likely to initiate a coherent reasoning process.

When thinking about a given subject, what draws our attention is typically aspects of this subject that we are uncertain about, or feel is not in harmony with the remainder of what we understand about this subject. In short, any unclear aspect of a given issue is likely to either be met with indifference on our part, it we feel that it does not really matter whether or not this unclear aspect remains unclear, or will raise our attention level to the point of wondering how this unclear aspect can be harmonized with the rest, if we feel that this should be addressed.

This when we question ourselves about an issue. This questioning will then keep us attentive to identify whatever element not previously considered might help resolve the issue, first within knowledge already accumulated by the individual, and failing finding new relevant information, will also induce the individual to search for such knowledge that could be provided by others, through reading, discussing, collaborating, etc.

A number of further questions will possibly come to mind until the issue is resolve, which process may or may not conclude, depending on whether the individual succeeds in gathering sufficient information to conclude.

(2) What is the reasoning nature of the cogitation, and what is the other process that is in play?

Cogitation is the process by which our active awareness examines a series of memories that were previously activated after some aspect of these memories struck us as odd, or as needing to be reconsidered, or needing to be reviewed, etc. Each question that we ask ourselves during this process triggers the activation of more memories to be considered in addition of the pool already activated.

When and if a new coherence is perceived, that seems more harmonious than the previous understanding of the issue that initiated the cogitation process, it will be memorized as a more satisfying solution to this issue.

(3) What is the reasoning nature of the permanent questioning process that leads to true objective comprehension?

The reasoning nature aiming at reaching objective comprehension is the process by which each memory in the set being considered is verified as whether or not it really corresponds to physical reality. Progressively, all memories found to not accurately correspond to physical reality are progressively discarded and when only memories found to really correspond to physical reality remain in the set being considered, then an objective conclusion can be reached.

I will stop here for the moment, due to other pressing activities.

Best Regards, André

When you teach someone , you need to understand well to transfer your knowledge.

Dear Dmytro,

Indeed, it is impossible to explain to someone else something that we don't understand ourselves.

1) When the next step is clear, and makes sense. Until I really understand addition, multiplication is difficult or just another stupid thing I have to memorize. I could go through life such that when I see a symbol like "3" and I see them organized as "3*3" I know to write a symbol "9". The end result is no different than translating 3*3 as the sum of three sets of three units, or nine in total. If I keep the relationship as symbols then I don't know what to do if I am told that I am using base 4 rather than base ten: one, two, three, ten, eleven, twelve, thirteen, twenty, twenty one, twenty two. So 3*3=22 in base four arithmetic. I can also extend the original problem as 3*3*3 and knowing that "3*3" is a "9" does not help me figure out what to do with "3*3*3" if all I am doing is memorizing symbols.

2) When you can write a computer program to simulate it.

The criteria might be different if I am asking how do I know that I understand plane geometry as opposed to asking how I know that I understand the mysteries of life. I am guessing that the priest will be looking for a different sort of answer relative to the mathematics professor.

Dear Timothy,

You wrote with reference to 1): "I could go through life such that when I see a symbol like "3" and I see them organized as "3*3" I know to write a symbol "9"."

I don't think that this really happens, because addition, subtraction, multiplication and division are taught to all children in primary school, if not earlier from their parents. Just like we learn articulated languages from interacting with other humans, we also learn the basics of mathematics the same way. Both need to be learned.

You wrote: "If I keep the relationship as symbols then I don't know what to do if I am told that I am using base 4 rather than base ten: one, two, three, ten, eleven, twelve, thirteen, twenty, twenty one, twenty two. So 3*3=22 in base four arithmetic."

Of course, since you are told that you are using base 4, then you know the meaning of 3*3 in this base.

You wrote: "I can also extend the original problem as 3*3*3 and knowing that "3*3" is a "9" does not help me figure out what to do with "3*3*3" if all I am doing is memorizing symbols."

I think it does, because you also assumed that "3*3" is a "9" which reveals in context that you are assuming base 10 by default. You can then easily figure out that 3*3*3 is "27" in context of this assumed base.

Assuming the most probable reference frames in context is precisely how multilayer neural networks, either artificial or living (the neocortex in our case) implement the correlation process for any set of elements considered in input.

A striking example is this sentence that was the object of much discussions a few years back on the Internet:

“Aoccdrnig to a rscheearch sdtuy at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be in the rghit pclae. The rset can be a total mses and you can sitll raed it wouthit any porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.”

The fact that the groups of letters are clearly separated by blanks (which informs our neocortex that they "may" be words in a sentence), and that they are clearly delimited by their proper first and last letter (which immediately points the network towards the few most probable solutions for each word), cause the network to automatically consider the most probable coherence for each group of letters in light of the context, that becomes clearer and clearer as decoding of the sentence proceeds.

This is put in perspective in this paper:

https://www.omicsonline.org/open-access/on-the-relation-between-the-comprehension-ability-and-the-neocortexverbal-areas-2155-6180-1000331.pdf

With reference to 2), you wrote: "When you can write a computer program to simulate it."

To my knowledge, it is not possible to program likes and dislikes as to whether a conclusion would be better than another, which is what guides our reasoning processes.

Quote: " Incidentally, it is the absence in artificial neural networks of such an uncircumventable selection mechanism of the most pleasing or alternately the less displeasing option that characterizes the neural networks of living beings, that explains why artificial neural networks are unable to draw any conclusion that they have not been trained to draw, despite the development of leading edge training techniques such as deep learning":

https://doi.org/10.4236/ce.2019.102028

The most recent techniques of "deep learning" still do not address this issue, and it doesn't seem likely that it will ever be resolved:

http://www.deeplearningbook.org/

Best Regards, André

Dear Andre,

"I don't think this really happens" is not the point. The question was "when do you know when you understand something?" One starting point is to begin with something that we all know and can agree on -- mostly, and given that we are all following some unwritten conventions like using base ten, rather than base 8 or base two or base 16 (all number bases commonly used in computer science).

You only know what to do with 3*3 in base 4 if you understand the math. If "3*3" is a symbol (no math) then knowing "3*3" has an answer of 9 in base ten does not help arrive at the correct symbol for "3*3" in base four.

3*3 is 9 in hexadecimal, or any number base greater than nine. There was one group of people that used base 60 (Babylonian: https://www.thoughtco.com/why-we-still-use-babylonian-mathematics-116679). In base 60 3*3*3 is not 27. Hexadecimal is 1, 2, 3, 4, 5,6 7, 8, 9, A, B, C, D, E, F, 10, 11, and you need to get to FF before getting to 100.

Ah, so the point is that you finally know a topic (like the English language) when it can be scrambled and you can effortlessly unscramble it. That is a good answer. I wonder if it works as well in Chinese, or German.

I do not know how to interpret the comment "It is not possible to program likes and dislikes". If the point is that being able to program is not a universal answer, then I would agree. If the suggestion is that being able to program is useless, then I disagree. The person asking the question did not specify the topic or provide context. So the scientific field of demography is about understanding how populations change over time. Computer simulation is a highly valued skill in this field, and being able to take a bunch of esoteric mathematical equations and turn them into a useful simulation is one measure of how well you understand the equations.

Dear Timothy,

I understand your point about the various bases. I am familiar with them. Understanding of the underlying logic is obviously required. Such understanding can be acquired through education, as that of all other mathematical concepts, obviously.

You wrote: "Ah, so the point is that you finally know a topic (like the English language) when it can be scrambled and you can effortlessly unscramble it."

I never thought of this this way, but this is the finest definition of understanding that I ever came across. I think this would apply to any concept.

Yes, it does work in German:

"Ncah eneir Sudite der Uinervtäist Cmabrigde ist es nhict wiecthg, in welehcr Rheigenofle die Bcuhsatebn in eeinm Wrot sheten. Whctiig ist nur, dsas der etsre und der lzttee Bcuhsbate am reigichtn Ort snid. Der Rset knan ein teloats Druhcenineadr sien und Sie keönnn es tozrtedm permobolls lseen. Deis legit daarn, dsas der msiccelnhhe Gsiet nhcit jdeen Bhcusbetan für scih lesit, sderonn das Wrot in snieer Giehtasemt."

In French:

"Sleon une édtue de l'Uvinertisé de Cmabrigde, l'odrre des ltteers dnas un mtos n'a pas d'ipmrotncae, la suele coshe ipmrotnate est que la pmeirère et la drenèire ltrtee soit à la bnnoe pclae. Le rsete peut êrte dnas un dsérorde ttoal et vuos puoevz tujoruos lrie snas porlblème. C'est prace que le creaveu hmauin ne lit pas chuaqe ltetre ivnedilvdule, mias le mot cmome un tuot."

And in Spanish also:

"Sgúen un edistduo de la Uadniisrevd de Cmabirgde, la odern de las ltaers en una plbaara no tneie icipmrotnaa, la sloa csoa itanrtopme es praa que la pmreira y la útlmia lreta etsé en el beun stiio. El rtseo pdeue esatr en un dodesren taotl y uestd pedue srpmiee leer sin pmelorba. Es pqroee el crebero hanmuo no lee cdaa lreta iivuadindl, snio la plarbaa cmoo un cotnnjuo."

...and no doubt in all languages with alphabets whose symbols represent phonemes that are meaningless when isolated and that you have to assemble in some order to represent an ideas.

I also wonder about Chinese. Doubtful in my view, since from the very limited knowledge I have of the Chinese language, each ideogram is already a complete phoneme carrying a complete idea. As for sentences, I seem to recall that the order of the ideograms is critical for proper meaning to be achieved, so any change in the order of ideograms or phonemes seems likely to make it difficult to recover any meaning other than the one provided by this different order. A Chinese speaker could certainly inform us.

About programming, you were speaking of "computer" programming. I agree with your statement that "Computer simulation is a highly valued skill in this field, and being able to take a bunch of esoteric mathematical equations and turn them into a useful simulation is one measure of how well you understand the equations."

I thought you were referring to this in context of describing reasoning. Successful reasoning seems to involve the ability to chose which option of any range of choices is the better choice all through every step of a reasoning process, however complex and elaborate it may be. This is what is out of reach of programmed neural networks.

Since they are not alive, they have no preference. Unless repeatedly trained to chose a certain type of answers in a possible range, they are likely to select any option that we would not even consider in the set of possible options.

What allows us to chose is our feelings of likes or dislikes. We tend to prefer coherence over incoherence, what feels good over what feels bad, something that seems more coherent to something that seems less coherent, something better over something simply good, etc. We understand what like and dislike are, but we are not able to program it in a computer even if we understand it. To my knowledge, this cannot be programmed into a computer.

So I think that not being unable to write a computer program to simulate likes and dislikes, that allow coherent reasoning, does not mean that we can't understand it. That's what I meant.

I prefer the definition you gave above, that is, we understand a topic when it can be scrambled and we can still effortlessly unscramble it. For example, someone could completely disassemble a car engine and spread the parts haphazardly all over the floor and an expert mechanics could still re-assemble the engine to working status.

Best Regards, André

@Dmytro Leshchenko

04/29/2019

On 04/06/2019 you wrote,

“When you teach someone, you need to understand well to transfer your knowledge.”

Yes, the first person who must understand the subject matter well is the instructor. If a school or college instructor cannot explain in a clear, formal, objective, and systematic manner how they themselves achieve understanding of a given topic, then they cannot explain it to their students. Just as important, they are therefore unable to provide students with the intellectual independence they need in their studies and in their lives.

You mention knowledge transfer. Effective instruction (i.e., explanation), and robust learning depend upon howknowledge is transferred. The profession, at all levels and in all disciplines including teacher education, continues to define itself through use of roteism instruction, which induces intellectually passive rote learning. see https://criticalinstruction.com/evidence-of-roteisms-failure/.

Roteism instruction does not and cannot show students how to take active intellectual control of the subject matter they study in classrooms and textbooks, encounter in their daily lives, and eventually in the workplace. For this, students need to be shown how to take operational intellectual control of any subject matter topic. The idea is to empower students with the formal and explicit ability to inquire (question) the subject matter itself by connecting and integrating its associated facts and ideas through thinking, reading, and writing critically. To see how this is done based on the natural science of the human mind, which provides us with a universally innate and critical grammar of mind, visit https://criticalinstruction.com/mind-grammar-theory-and-practice/.

Effective instruction begins by looking inward and asking, “How do I know when I understand something (i.e., any given topic)?” This needs to be followed by, “What specific critical thinking, reading, and writing processes am I teaching my students so they may, on their own and whether in class or out, take intellectual control of any topic, even those that are new?” Here are sample instruction and learning resources that answer the two questions:

(a) https://criticalinstruction.com. (Includes explanation of Roteism instruction and provides evidence of its continuing failure in classrooms and textbooks.)

(b) https://criticalinstruction.com/why-textbook-authors-and-teacher-educators-school-and-college-faculty-and-researchers-should-be-using-critical-instruction-pedagogy/

(c) https://criticalinstruction.com/mind-grammar-theory-and-practice/.

@Timothy A Ebert

04/29/2019

On 04/08/2019, you wrote:

1. “The person asking the question did not specify the topic or provide context.”

This ignores the descriptive material that accompanies the Question; which addresses both topic and context. The Question allows the reader to choose any topic in any discipline (as you did). The Question is clearly in the context of school, college, and classroom/textbook instruction and learning. Here is the context in summary form: “Educators…have a special responsibility. They are obligated to do more than merely tell students what they know about a given subject-matter topic. As it is the essence of education, they must also explain clearly ***how*** they know it. [This responsibility applies to:] teacher-educators; school and college faculty; students including graduate students; researchers; [and] textbook and academic authors.”

2. “The question was "when do you know when you understand something?"

This misstates the Question. The Question is “How do you know when you understand something? By ignoring the ***how*** part, one avoids providing a reasoning process for explaning how understanding of any given topic can be achieved. Indeed, no such explanation of how to reason critically to achieve understanding of a subject matter topic is found in your replies. Said another way, if a school or college instructor cannot explain in a clear, formal, objective, and systematic manner how they themselves achieve understanding of a given topic, then they cannot explain it to their students.

3. “Being able to take a bunch of esoteric mathematical equations and turn them into a useful simulation is one measure of how well you understand the equations.

This is an application of understanding and thus ignores the Question. It does not address how a mathematics instructor leads students to first gain an initial understanding of the equation or equations at hand through use of a clear, formal, objective, and systematic patterns of critical thought. Such initial understanding must precede application.

4. “…you finally know a topic (like the English language) when it can be scrambled and you can effortlessly unscramble it."

This is a soft, non-classroom and non-textbook operational, and after-the-fact answer that does not provide the instructional means or process for explaining any subject matter topic.Here is why. The ability to “unscramble” a topic presupposes the existence of a prior reasoning process that first led one to know (i.e., understand) the topic. What, explicitly, is that mental process? If you can answer this question, then the Question is also answered. See references (a) and (b) for how to answer both questions.

(a) https://criticalinstruction.com/why-textbook-authors-and-teacher-educators-school-and-college-faculty-and-researchers-should-be-using-critical-instruction-pedagogy/

(b) https://criticalinstruction.com/mind-grammar-theory-and-practice/

@Andre Michaud

04/29/2019

Dear Andre,

On 04/05/2019 you wrote:

1. “I totally disagree with Anderson about the value of self-questioning. I think it is of critical value. It is not a coherent reasoning process as such, but it is rather what is likely to initiate a coherent reasoning process.”

You may “totally disagree” with Anderson (1994, not 1992 as I originally cited), but then you are disagreeing with research evidence and common sense. Anderson (Anderson, L. W. (1994). Research on teaching and teacher education. In L. W. Anderson and L. A. Sosniak (eds.), Bloom’s Taxonomy of Educational Objectives—A Forty-Year Retrospective, Ninety-Third Yearbook of the National Society for the Study of Education (pp. 126–45). Chicago, IL: The University of Chicago Press), was simply reporting research re the weak learning impact of conventional classroom questioning by instructors in classrooms in the context of engaging new and revisited course subject matter. Questioning, including self-questioning and whether practiced by instructors or students, that is random and not coherently reasoned critically is of little instruction and learning value. You are confounding questioning or reasoning associated with argumentation (the second mode of critical thinking), with questioning or reasoning associated with understanding, comprehending, and explaining subject matter (the first mode of critical thinking, or critical instruction). To be effective, argumentation on a given topic must be preceded by and grounded in Mode 1 of critical thinking on that topic. For a discussion of the three modes of critical thinking, see https://criticalinstruction.com/critical-thinking/.

The preparation and practice of school and college faculty to engage new and revisited subject matter critically continues to be generationally weak. The reason? Preparation and practice at all levels remains rooted in roteism instruction, which is the antithesis of critical instruction. Research continues to show that school and college faculty, including teacher educators, lack knowledge of Mode 1 critical thinking and how it is applied to teaching course content as an integral part of day-to-day classroom instruction and learning. The consequential negative impact on the ability of school and college faculty and students to think, read, and write critically in the context of engaging new and revisited subject matter is also well-established. For a summary of the evidence, see https://criticalinstruction.com/evidence-of-roteisms-failure/.

Best wishes,

Victor

@Andre Michaud

04/29/2019

Dear Andre,

The Question at hand is, “How do you know when you understand something?” We need to bear in mind the context of the Question, which is, “Educators…are obligated to do more than merely tell students what they know about a given subject-matter topic. As it is the essence of education, they must also explain clearly ***how*** they know it. [This applies to all educators including:] teacher-educators; school and college faculty; students including graduate students; researchers; [and] textbook and academic authors.”

Speaking broadly, a major responsibility of the teaching profession is to transfer through classroom and textbook instruction the knowledge that exists within the disciplines. Speaking specifically, effective instruction (i.e., explanation), and robust learning depend upon how knowledge is transferred. The profession, at all levels and in all disciplines including teacher education, continues to define itself through use of roteism instruction, which induces intellectually passive rote learning and defeats development of critical thinking, reading, and writing abilities. See https://criticalinstruction.com/evidence-of-roteisms-failure/.

Roteism instruction does not and cannot show students how to take active intellectual control of the subject matter they study in classrooms and textbooks, encounter in their daily lives, and eventually in the workplace. The professional responsibility is to empower students with the ability to inquire (question) the subject matter itself by connecting and integrating its associated facts and ideas through use of critical thinking, reading, and writing processes. All faculty and students can learn to take intellectual control of any subject matter topic using the natural science of the human mind, which provides us with a universally innate and critical grammar of mind. See: https://criticalinstruction.com/mind-grammar-theory-and-practice/.

In your referenced papers and replies to the Question, you frequently discuss the need for questioning to arrive at understanding for a given subject matter topic. Yet, nowhere in your material do you provide a coherent, formal, objective, and practical reasoning process (i.e., system, structure, framework), for use in classrooms and textbooks to achieve understanding of subject matter.

This is why I suggested (see my reply of 03/30/2019), you use mind grammar, the basis of critical instruction, to develop a critical view on the topic of comprehension itself. This, perforce, would also include the topic of understanding. You can use the coherent, formal, objective, and practical reasoning system for instruction and learning that mind grammar affords. It can be found in the link immediately above. You have not as yet responded to the suggestion.

Best wishes,

Victor

The question is unanswerable. I would guess that the people who thought the earth was flat thought that they understood how the world works. They taught a flat earth to their students. The modern perspective was that they were wrong, and from our perspective they did not understand what they thought that they understood.

@Timothy A Ebert

05/01/2019

It is ironic to reply that a question regarding how the human mind gains understanding is “unanswerable” when the reply itself uses the term “understand” or “understood” three times.

What is understood and taught in one era, and better understood and taught in another, simply means that understanding has evolved. So, saying that the Question, “How do you know when you understand something?” is “unanswerable” is to also say that old and new understandings could not be explained based on what was known and thought at the time. This clearly is not correct. After all, how did the human mind reason its way to understand that the earth is three-dimensional and not two?

All true explanations of subject matter (as opposed to mere descriptions of it), are based on current knowledge (i.e., facts, ideas), that the mind processes to achieve understanding. To better fathom, (a) the dynamic processes associated with the nature of all subject matter, (b) how the human mind is responsible for the intellectual existence of all subject matter, and (c) how the reasoned integration of the two leads to understanding and then explanation (and vice versa), suggest reading:

https://criticalinstruction.com/subject-matter-theory-principles-and-practice/

Excellent debate strategy to take a trivial element in an opponents answer and make it a key element while ignoring the point.

If there is room for understanding to evolve, then do you really understand that topic or are you blindly repeating what others have told you is factual? At the other end of the spectrum: are you always reinventing the wheel, not trusting what others have done because there is always room for understanding to evolve?

You stated

"All true explanations of subject matter are based on current knowledge..."

However, if current knowledge is wrong, then the explanation is not true.

You can claim to understand a topic (flat earth for example), and you can offer support of your claim: https://theflatearthsociety.org/home/. A round earth is all Disney video magic.

Is this really understanding the topic?

You understand a topic when you can synthesize your viewpoint and the viewpoint of the opposition and using fundamental principles (not quoting others) show how your viewpoint should be the correct answer. A part of the answer includes a clear statement of what must be assumed. As appropriate let students know if the assumption will be proven in some future class should they choose to take it. In this approach you have shown mastery of the subject and accepted that there may be flaws in your mastery. You have also given a space into which students can themselves become masters.

@Timothy A Ebert

05/05/2019

(Re your reply of 05/02/2019.)

Part 1 of 2

Let’s keep in mind the Question and its context, namely: “How do you know when you understand. something?” in the context of school and college classroom and textbook instruction and learning.

Why is it trivial to point out unsupported reasoning? In effect, you are saying, “The question ‘How do you know when you understand something,’ is “unanswerable;” but I’ll keep using the term “understand” anyway.” Is it trivial to point out reasoning that switches premises and time frames and therefore loses the basis for comparison while ignoring another conditional side, which is: If current knowledge is true, then an explanation can be true; equating knowledge of facts on a given topic with understanding that topic by using a non-sequitur regarding the evolution of understanding and then equating rote instruction and learning with understanding?; and that a conceptual and classroom-usable basis for understanding subject matter continues to be lacking in your replies; nevertheless you do not allow for another’s alternate frame of reference for understanding and instead deride, via “Disney video magic,” the Flat Earth Society when they clearly state, “we are not making the ludicrous claim that the Earth is two dimensional.” (Ref.: https://www.theflatearthsociety.org/home/index.php/blog/einsteins-relativity-proves-earth-flat). Using Newton’s and Einstein’swork,they at least provide a conceptual basis for what they mean when the say the earth can be considered flat, just as we all do implicitly when consulting two-dimensional maps. See the links provided in Part 2 of 2 for a conceptual and operational basis for understanding subject matter in all disciplines in the context of classroom and textbook teaching and learning.

------------------

Good to see that you have moved from saying the Question is “unanswerable” to providing an answer; although the answer in your last paragraph is weak.

(a) The paragraph is filled with empty rhetoric. You mention “synthesizing.” How, exactly does one synthesize facts and ideas into an integrated understandable whole? You mention “fundamental principles.” What are they? You mention “mastery.” How, explicitly, can teacher educators and school and college faculty and students reason their way to mastery of content? You don’t say. As in all your earlier postings, you do not provide a formal, objective, practical, and explicit reasoning system for accomplishing any of this that is actually classroom-usable by school and college faculty and students, academic and textbook authors, and researchers. The links in Part 2 of 2 provide classroom-usable answers to all these questions.

(b) The paragraph confounds reasoning associated with argumentation (the second mode of critical thinking), with reasoning associated with understanding, comprehending, and explaining subject matter (the first mode of critical thinking, or critical instruction). To be effective, argumentation on a given topic must be preceded by and grounded in understanding of the topic (Mode 1 of critical thinking). To learn of the three modes of critical thinking, suggest you see https://criticalinstruction.com/critical-thinking/

Note: Not sure what you mean by “not quoting others.” The conceptual, developmental, and procedural means for engaging in critical instruction and learning found at www.criticalinstruction.com are original with me. See https://criticalinstruction.com/origin-of-critical-instruction/.

*****

@Timothy A Ebert

05/05/2019

(Re your reply of 05/02/2019.)

Part 2 of 2

As mentioned in Part 1, let’s keep in mind the Question and its context, namely: “How do you know when you understand. something?” in the context of school and college classroom and textbook instruction and learning.

Good to see that you have moved from saying the Question is “unanswerable” to providing an answer; although the answer is weak and mixes argumentation with understanding (see Part 1 of 2).

------------

On 04/29/2019 I pointed out that in your reply of 04/08/2019 you, (1) misrepresented the Question, (2) said the Question lacked context when it clearly does, (3) mixed understanding with application, and (4) did not provide an explicit reasoning process for gaining understanding usable in the context of classroom and textbook instruction and learning. Indeed, to date, no such explanation of how to reason critically to achieve understanding of a subject matter topic is found in your replies. If a school or college instructor cannot explain in a clear, formal, objective, and systematic manner how they themselves achieve understanding of a given topic, then they cannot explain it to their students. You have not responded to these critiques; so, there is little alternative but to take your silence as acquiescence. There has also been no response to the material contained in these links:

(a) https://criticalinstruction.com/why-textbook-authors-and-teacher-educators-school-and-college-faculty-and-researchers-should-be-using-critical-instruction-pedagogy/

(b) https://criticalinstruction.com/mind-grammar-theory-and-practice/

(c) https://criticalinstruction.com/subject-matter-theory-principles-and-practice/

Based on the ResearchGate day-of-your-reply timeline, you appear to have spent little time reading, reflecting, and then then applying the linked material; any one of which will provide you with an answer to the Question. As a researcher or practitioner, how does one expand their knowledge base and gauge whether an idea is valid unless one first grasps and then applies it? Not to do so shows a certain lack of intellectual curiosity. You refer to yourself as an opponent (I don’t see you as such). Perhaps you can state the nature and basis of your opposition. It doesn’t appear to be the critiques or the linked material since you have not commented on either.

*****