Seeing vs. Visualizing

Quantifying transfer of learning is a difficult task. Many attempts to substantiate the efficacy of any particular learning theory for facilitating learning transfer have proven to be elusive. This isn’t surprising, in light of Haskell’s (2001) observation, “Transfer is the basis of mental abstraction, analogical relations, classification, generalization, generic thinking, induction, invariance, isomorphic relations, logical inference, metaphor, and constructing mental models” (p. 26). That’s a lot to be captured by a single learning theory. In reflecting on past personal educational experiences where I’m certain there was a transfer of learning, I am equally at a loss to quantify what actually facilitated the transfer. There are, however, several aspects to those experiences which, while not fully elucidating the transfer process, do provide insight into some key elements.

The example experience selected for this post involves visualizing chemical molecules and how that ability transferred to a better understanding of mathematics and martial arts. As an undergraduate biochemistry student, I struggled to understand what chemists call molecular kinetics. Basically, how the shapes of molecules influence their behavior. This is particularly important for large molecules, such as hemoglobin and DNA. When shaped one way, hemoglobin, for example, can carry oxygen. Shaped another way, it carries carbon dioxide. (There you have it. Biochemistry in two sentences.)

Experienced chemists “see” this. But how do you see a molecule? And therein lies the rub. Having a very strong preference for receiving information via the auditory channel, the idea of seeing something that couldn’t be seen was a bit of a stretch for me. The hard work to develop this skill was done in a biochemistry class which featured learning how to view stereo triptychs. Consider this example stereo triptych:

Stereo Triptych

Stereo Triptych

By training one’s brain to merge the left image with the right image, what results is an apparent third image which combines the two such that a free floating sphere is interpreted by the brain. For many people, this is easy and is the stuff 3D movies are made of. For me, it was very difficult.

Following the method described by Wood, Wilson, Benbow, and Hood (1981) and a lot of practice, I was eventually able to look at stereo triptychs of complex molecules and instantly recognize the subtle shape distinctions and changes which occur as a molecule changes state. It was a thrill to acquire this skill, like the first time you ride a bike. A whole new world opens up.

The interesting part was when I discovered this skill could be applied in mathematics. Being able to see the effects on real world events as reflected in equations for trajectory, inertia, and momentum made working through exam problems significantly easier. The best I can describe it is that the chemical symbols had been replaced by mathematical symbols in how I made sense of what was being described. Following graduation, this skill proved valuable yet again in martial arts training. The ability to rapidly assess an attack and visualize where it was going made it much easier to position myself to employ the most effective defensive technique. I recall deliberately thinking about my opponent as a giant molecule undergoing a dramatic state change.

To explore this experience in the context of educational theory, it is helpful to again consider Haskell’s (2001) observation:

Research on teaching for transfer clearly shows that for transfer to occur, the original learning must be repeatedly reinforced with multiple examples or similar concepts in multiple contexts, and I would add, on different levels and orders of magnitude. Teaching that promotes transfer, then, involves returning again and again to an idea or procedure but on different levels and in different contexts, with apparently “different” examples. (p. 26-27)

This implies that both behavioralist and constructivist approaches to learning are involved with the transfer of learning. The initial phase, repeated reinforcement with multiple examples, certainly fits within the behavioralist model. And it was certainly applicable in my experience with first learning how to visualize three dimensional representations of molecules via stereo triptychs. The multiple examples were all chemical molecules and thus provided enough variation to make the learning and transfer challenging, yet not so different as to make the task impossible.

Taking this transfer to the next level involved applying the skill in non-chemical contexts. First mathematics and later martial arts training. In this phase, the challenge involved tasks more aligned with constructivist approaches to learning. That is, building a richer understanding and deeper capabilities by synthesizing a variety of cognitive and experiential resources.


Haskell, R. E. (2001). Transfer of learning: Cognition, instruction, and reasoning. San Diego, CA: Academic Press.

Wood, W. B., Wilson, J. H., Benbow, R. M., & Hood, L. E. (1981). Biochemistry: A problems approach (2nd. ed.). Menlo Park, CA: The Benjamin/Cummings Publishing Company