There are numerous similarities, as well as important differences, between solving mathematical problems, and what happens in the counselling situation. One of the similarities that I am interested in is that there are things that are below the level of what might be called 'conscious awareness' in both cases, and that the aim of both teaching and counselling is to assist the learner/client to become aware of that which is currently out of their awareness.
I am currently reading Experiencing and the Creation of Meaning by Eugene Gendlin. In the book, Gendlin describes 'felt meaning' as those meanings which may or may not be currently symbolised or symbolisable. For him, symbolising is meant in a very wide sense - words, actions, objects. We can act on that which is symbolised. Felt meanings, then, are not merely feelings, but those meanings that we can not currently symbolise.
Here is a well-known excerpt from Alice in Wonderland:
“Then you should say what you mean,” the March Hare went on.
“I do,” Alice hastily replied; “at least—at least I mean what I say—that’s the same thing, you know.”
We only say (one form of expression, which also includes bodily expression, and so on) a small part of what we mean. I am developing a diagram of meaning that currently looks something like this:
As for meaning what we say, this for me suggests the multiple (infinite) possible interpretations by another that can result from something that is said:
As a listener in a counselling situation, I must aim to place myself in reception to as much of what the speaker means as possible, and to be able to distinguish between their and my meanings. That said, I can only really know what they have expressed, and what is in my conscious awareness at that time. I can not know what their felt and unfelt meanings are, although I might be able to get a sense of them. I can only offer ways in which they might become able to symbolise those meanings that are currently outside of their awareness. There are parallels in the teaching situation.
I am in a different situation when I am solving a mathematical problem on my own. Suppose that I am stuck, there is something that is currently outside of my awareness that would help me solve this problem. I have my own felt meanings, and I need to attend to my own symbolisation and expression of these meanings in order to access that which is currently out of awareness. When solving a problem on my own, I express what I can - again and again - in the hope that this helps me bring some felt meaning to the surface. If it happens, in that moment a non-symbolised meaning becomes symbolised, comes to expression, and it feels like a moment of insight.
When solving a problem, there are things that I cannot yet know. Consider the problem I describe here, and my question "How many keys, how many locks?" I cannot know the answer to this - I cannot even draw the grids I need to draw - until some other insight - a symbol - becomes available, a missing piece of a jigsaw. In this case, it was the insight that each lock must have exactly two people who do not hold the key. This is something I can act upon. Until then, I must stay with - and struggle with - felt meanings. I must keep trying to symbolise and express, coming up with conjectures to be modified, and be alert to invariance, whilst remaining flexible - perhaps shifting between what is and what is not.
If I am completely stuck, it is useful to speak to someone else, who may be able to help me symbolise that which was out of awareness, and we are in a similar situation to the counselling situation described above. This suggests to me the importance of talking about mathematics with others in the classroom.
There are other pedagogical implications of this model. Imagine you are a teacher trying to explain something to a group of learners. Imagine a diagram as those above, but with lots of these circles. There are as many interpretations as there are people, and within that multiple meanings for any given symbol. How can you know what meanings are being symbolised by each of your learners at any moment?
I suspect there are important differences between meanings in mathematics, and those we have about ourselves. In maths, we are hoping for the realisation "Ah, yes! It must be this way!" In the counselling situation, there is not this logical certainty, and we must be content with "Ah, yes, it certainly feels that way right now!"
As the listener in the counselling situation, I am always opening myself to allow the meanings of the speaker to alter my own meanings. The speaker tries to explain what is going on for them, and I look to under-stand - to stand underneath - to allow fresh meanings to become symbolised in me, and not let my meanings stand in the way.
However, what matters as the listener is not whether I can express the felt meanings of the speaker, but rather that I can use all of the meanings that I am aware of to find ways to assist the speaker in symbolising their own felt meanings, so that they can express them to me, so that I can find other means of helping them symbolise, express... and so it goes on. Again, I think there are valuable parallels with the teacher-learner relationship here.