Are you (or is your student) claiming to have aphantasia? If so, you'd have to use something external to hold the image.
Visual thinking is like other kinds of thinking, but using the visual sensory channel. It's a kind of short-term memory with limited capacity.
If you remember the days when we had to look up phone numbers in books, you might have had the experience of loading a seven-digit number into your short-term memory as an auditory loop, speaking it over and over again in your mind's voice (and hearing it in your mind's ear), long enough to dial on the phone. You could actually speak the numbers aloud for a similar effect, but most people don't have to do this to "hear" it. But a moment of distraction, especially an auditory distraction, can cause you to lose that memory.
Visual thinking is the same, but you use your mind's eye instead of ear. It's like having an imaginary whiteboard, but it requires concentration to hold an image, and a moment of distraction can erase it. You're not exactly drawing in lines either (unless you choose to). This whiteboard has limited capacity in the same way your auditory loop has a limited duration. You can choose which parts of the image to focus on, and that can have more detail (just like your real eyes can see things they're looking at directly better than things in the periphery), but if you stop focusing on an area for too long its detail fades and you lose the memory. If you try to exceed your capacity, then the part of the image you refresh might not quite have what was there before, the same way you can accidentally remember the wrong number if you try to keep too long of a string of digits in your auditory memory.
In the same way you can query your long-term memory for the sound of something, by holding the question in your mind until the sound arises (E.g. What rhymes with "muffin"? Or what does a dolphin sound like?), you can query your long-term memory for an image (E.g. What does a dolphin look like?).
And this can be done without using your mind's voice. Perhaps you can use your mind's eye to "read" the text of the question. But you don't even have to use words. You can use the concepts behind the words more directly. And sometimes these concepts are visual, or can have a visual representation. Even kinesthetic concepts have enough of a spacial component that they can be diagrammed visually in a very natural way. Many nouns correspond to visible things, and verbs correspond to visible actions. Holding such an image in memory along with the intention to query memory can cause an answer to arise to consciousness, the same way a query in words can.
The intention to query for a sound is like stopping for a moment to listen, while the intention to query for an image is like stopping to look. You have to make a space for it in your mind in the appropriate sensory channel.
You can also query your subconscious for things you've never seen before. Maybe you don't know what an ichthyosaur looks like, but someone tells you it looks like a dolphin, but with two pairs of fins instead of one. Running a hypothetical query may be enough to produce the image in your mind's eye. If that's not working, you can try to force it by "painting", which takes more effort: If you had a whiteboard (and artistic skill) you could draw a dolphin, and then draw another pair of fins in the pelvic region. You can do the same thing in the mind's eye. Start with a dolphin image, and then while concentrating to keep it refreshed in memory, make a change to it: refresh that part differently on purpose.
When I say I can't stimulate visual thinking, I more mean the problem solving element - I can construct visual thoughts in my mind with some effort, but I couldn't then work through those visualisations as a primary tool to solve problems. I'm curious as to how that works - do people who do this have a better ability to retain a visualisation in their short term memory, whether innate or practiced? Is there more to it than that?
I am bad visual thinker, but I was able to reach much higher performance on dual n back after I found the trick to write down all numbers on an imaginary board.
Say you have two distinct points x and y. Consider all points whose distance to x is the same as to y. What can you say about the location of these points in terms of the line connecting x and y?
Try to solve any geometry puzzle with only your mind and you will be forced to do visual thinking.
I've never seen any image of any kind in my mind, nor have I experienced any other imagined sense. Visual thinking is merely activity within a region of the brain associated with a visual experience. If you were to shoot a charged particle through your occipital lobe, you may experience it as a flash of light. Those with aphantasia process thought in a different region of the brain that is not associated with the experience of visualization.
Where that thought takes place will determine the structure and connections within the neural network that...
So I find I can force myself to visualise that but it would be consistently born of the concept thought first, like "oh that's a line perpendicular to the line between X and y" and then I can paint the graph in my mind. But I don't need to - I can think the concept and then apply it to paper without visualisation and I tend to find that easier.
What intrigues me precisely is visual thinking for problem solving - ie a student who can easily perform arithmetic between graphs by visualising the transformations in their mind rather than doing calculations on paper.
Setting aside the psychological and cognitive dynamics for a moment, I'd like to propose that you may be more of a visual thinker than you consider yourself to be. I would also propose that your challenge may not lie in visual thinking but in visual synthesis and visual translation. I'll explain.
1. Consider the first phrase I used, "Setting aside." These words connote a visual of some sort. In fact, language is difficult to use without word pictures that create some sort of visual in our minds. for example, "See what I mean?", "Upstream suppliers", "slower than molasses in January", "like a lead balloon", and "Pie hole." The fact that we can use these word pictures as a verbal shorthand attests to our visual thinking ability. Granted, with a nod to the symbolic interactionists, many of these may be more or less well defined in my mind than yours. They are nevertheless indispensable in our verbal communication.
2. Visual synthesis is a different matter. I believe I understand your challenge here, being somewhat challenged in that way myself. Although we know that we are not really right brain/left brain divided, I'll use those concepts to help explain. The left side of my brain is somewhat dominant. I would prefer to read a math book to a novel. Yet I have become a successful graphic recorder. And it's not due to my art skills. I have learned to hijack the analytical functions for storage and association while I role play a symbolic interaction with my critic committee and come up with a graphic that works. This is very labor intense, high calorie exercise. It costs.
3. Visual translation is another thing. While synthesis takes a significant volume of information and synthesizes it to a graphic, translation does exactly the opposite. Your brain settles on the message you want to communicate, then you must formulate a graphic to represent your thoughts. This is very risky. We often fall short. Further, no single graphic could communicate all that we want. It becomes inaccurate somewhere near the edge of context. Our internal critic committee convinces us that the graphic will fail, but live on in misunderstanding. However, if we use words, we have the opportunity to edit. Edits are cheap! So, with visual translation there is a risk we are loathe to accept. We figure that it may be better to just use good old squishy yet limited range words.
I'm curious about your saying you can't "simulate" visual thinking since visual thinking is remembering a diagram or spatial representation of something and reasoning about things on this mental map.
So, can you imagine a picture of a sailboat? Now, someone uses a visual analogy and suggests that the economy, your life goals, your relationship is like a sailboat. As soon as they start talking about, say, the business climate being the water, wouldn't you start to think ahead (from your mental picture) about what the "wind" would be, how you would tack your "sail" (and what that sail might be) in order to move the "boat" toward your goal?
Your mental model guides your reasoning by letting you use intuition and judgement about the imagined scene. The visual layout helps partition the problem into the interrelated parts, their relationships and mechanisms of interaction.
My example may not be the best one since the difference between a plain-old analogy and a visual analogy is probably that in a really rich example of visual thinking, the spatial relationships, shapes and connections between them are much more essential and informative than my sailboat example. They help you reason about causes and effects and theorize about consequences of imagined changes in a concrete and useful way.
One of my students asked me how visual thinking works. As someone who does not think in pictures, I was a bit stumped on how to explain it because I can't simulate visual thinking in my mind (I usually try to conceptualise and simulate things I haven't experienced in order to understand them better). I'm actually really interested now, myself, in understanding the mechanisms of visual thinking, and how it all works.
Are any of you here visual thinkers? How would you explain the way your visual thinking occurs in your mind to someone so they could conceptualise it in terms of both the processes and the sensations?