There are no aha moments

If we understand learning to be the developing of neural connections in the brain, then necessarily there cannot be true aha moments (or more accurately, every moment is an aha moment).

Lets suppose that a child has a (flawed) model of how something works. Each time they are presented with information, they build new connections between neurons in their brain, while also occasionally (usually while they sleep) removing connections that are not used. Over time, this gradually results in a child having competing models for understanding how something works.

At some point, the model that works best is the one that becomes used, and the neural connections that represent the unused model are eventually severed, and we might say that the child is exclusively using the new model.

At no point does a child suddenly flip from only using one model exclusively to using an entirely new model because this would require making many, many different neural connections simultaneously for the new model to function. This sudden flipping is what is commonly called an "aha" moment, and it doesn’t exist. Learning is not the sudden acquisition of new models of understanding the world, but the gradual shifting between competing models, none of which probably completely describe the world.

Aside: No one has a perfect model for understanding the world, because that requires a complete set of all possible "true" states of the world.

Different possible stimuli of the same basic information could lead to different models being used. For example, suppose I asked students to solve 4 + 5 verbally as compared to representing this symbolically in writing. It could be that students use one of their competing models to answer the verbal form of a question, and a different model to answer the written form, and in some cases arrive at different results. It could even be true that different people asking the same question results in different models being used!

When my son was in grade one, I participated in a student led conference in which he laboriously demonstrated using a regrouping method how 3 + 9 = 11. In the context of his classroom and with a written question, he answered the question with one model. I did nothing to offer feedback on his model at the time. 10 minutes later, we were driving in the car, and we played a number puzzle game where we took turns saying numbers and trying to figure out how to get that number using arithmetic operations. I said 12, and my son responded with 1 + 11 is 12, 2 + 10 is 12, 3 + 9 is 12, and so on. My son used a different model, and arrived at a different result.

If this theory is correct (and to be clear, it is just a theory), then it has implications for instruction. The first implication is that in order to help students develop models, we need to introduce all them to both different representations of ideas (ie. representations of other people’s models for understanding), from different people (ie. teachers, students, and parents), and different modes of processing that information (verbal, written, symbolically, manipulatives, etc…). It also suggests that we should not assume that because a child can respond in a way that suggests they have a solid model of understanding once, in one context, that this means that they actually have such a model. It also means that what children know how to do, or do not know how to do, is unlikely to be successfully captured by a system that assumes binary understanding of concepts (concepts are not known or unknown, we have models which seem to work in some contexts, and may not in others).

Note: It is probably worth noting that my use of the word model is a simplification of the set of neural connections we use in our to process and store information, and is almost certainly an incredible simplification of those processes.

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10 Comments

  • I’m not a neuroscientist / neurologist / neurotic / neuro-anything, so I couldn’t comment on the science of what goes on in our brains.

    I think for a lot of people, the connection between thoughts over a perceived long time period is what they understand to be ‘aha’ moments. Again, I don’t know what that brain chemistry is that actually does this, but we’ve all experienced that moment when suddenly (and it is sudden from our conscious perspective) that which was unclear is clear.

    I’ve noticed that I can trigger those ‘aha’ moments when I have looked at a problem / situation / concept from several different angles and then sleeping on it for a day. And this is what you say in the last paragraph (not the Note).

    I tend to agree that one way of instruction just can’t work and that’s simply because we all learn in materially different ways. We draw upon our experiences to help synthesize the new content being exposed to us.

    The old adage, “practice makes perfect” seems to ring true.

  • David Wees wrote:

    I think there is another explanation. After a long period of time, we become aware that our model for understanding something has changed, and so we have a moment of discovery when we realize this, which we call an ‘aha’ moment. 

  • So Archimedes didn’t have an Aha moment then ?
    More recently, I think that neuroscience should be renamed “neurospeculationism” for at least the next 30 years.

  • David Wees wrote:

    What do we know about Archimedes’ thinking before he leapt out of his bathtub? All we know is that someone told us a story of his Eureka moment; and we have no idea at all about what models he was using before then (or after then) to understand volume.

  • I’ve been thinking about three kinds of aha moments. The first is when, after mulling, pondering, whatever, you come to a real understanding of something or how it works (you “grok” it). Understanding the meaning of a confidence interval or the definition of a limit or a credit default swap come to mind. I guess that’s a pun. All of a sudden it makes sense. Which raises the question of what it mean to “make sense” in terms of neural connections..
    The second is when you see a solution to a problem, a solution that sometimes comes when you step away and let your mind wander a little, maybe searching through various maybe unrelated neural connections. I remember this happened to me when faced with a garbage disposal that just refused to turn on. I don’t know garbage disposals. We tried all the usual things, including the broomstick trick. Then the thought came: this is a dangerous device. Dangerous devices have – Reset Buttons. Problem solved. Again, it’s about connections, but somehow sorting through them.

    The third is when you look a situations in new ways and see meanings and models you had not seen before. It’s often a small thing that starts it, then grows with connections, and for me, it often happens in the middle of the night and start thinking about “stuff”. One started for me when I started thinking about what money is, and it went from there to (sort of) grasping what all these financial markets are about.

    But what I see connecting all these, and the ability of my AP Calculus students to solve problems different from the ones they’ve seen before, is a kind of fluidity to not just make new connections, but to rearrange, sort though, make new models, throw them out, go another way, whatever. One thing I think I grasp is that the harder one tries to force the connections, the less successful.

    Maybe it’s like all of a sudden realizing where your keys are.

  • Chris Stephens wrote:

    I assume the first sentence of paragraph seven should have “9 + 3 = 12” and not “9 + 3 = 11”. Otherwise, I’m really confused.

  • David Wees wrote:

    Nope, that’s what he said. 3 + 9 = 11. He got it wrong, that’s part of my point. With only 10 minutes apart between the two interactions, he got the wrong answer, but then got the right answer, which to me is evidence he’s using different models for understanding the same operation based on context.

  • Rob MacDuff wrote:

    David although your reasoning seems reasonable, I would strongly disagree.  It is hard to characterize aha moments in a single sentence, but my attempt would be the following.  Aha moments are associated with changes in degrees of understanding or shifts in understanding.  Needless to say it would take at least a chapter or two to unpack this simple sentence.  My only reason for mentioning this is that we have developed two programs:cognitive instruction in modeling mathematics and cognitive instruction in modeling physics (CIMM & CIMP) in which aha moments occur frequently per instructional session as we provide studens with the conceptual tools necessary for constructing their understanding and representational tools for expressing that understanding.  

    Although learning involves neural connections in the brain, it is more the coordination of the activitation of different regions of the brain. 

    cheers

    Rob

  • David Wees wrote:

    Thank you for the clarification. I’ve since thought of a neurologic way of thinking of this which would allow for aha moments; two areas of the brain being connected for the first time.

    Also, I really don’t know very much about how the neural pathways are created or used, so this is probably all nonsense anyway.

  • Rob MacDuff wrote:

    I would certainly encourage that line of thinking.  The connections necessarily need to happen in a coordinated way.  

    Student comment: “The hands-on method was very helpful for me because by wrapping the string around the pipe and marking it for each of the three different sized pipes, I was able to actually see with my eyes the length of circumference and I was able compare it with diameter a little more easily that way. By learning that as the circumference increased as the diameter increased, I was not necessarily learning anything new but I was thinking about it differently than I would usually think about it. Insead of just learning the formula, I was really seeing the relationship between circumference and diameter.”  

    Note the shift in thinking about the circumference as something round to being a length that can be compared to a diameter.  This is in essence an aha moment for this student.  Also note the terminology; thinking about it differently; seeing the relationship, …

    Student comment: “It was insaaaaaaane that the relationship between circumference and diameter ended up equaling out to be about pi. It really made me think., “Dang this clas ain’t no joke” because that can’t just be a coincidence. Before this I was a little iffy on this new way you are teaching us because it just seems so crazy that there is this whole nother world where everything seems backwards. Howeer, this new way of thinking about math is not wrong, it actually makes total sense.”

    Note the significant shifts in thinking not only about the content but also about her own thinking and these shifts being interpeted as increases in sense making.

    Unfortunately instructional the skills required to accomplish this requires significant amounts of training. 

    cheers

    Rob

     

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