To Think Outside the Box, You Have to See the Box
Our standard mental models simultaneously facilitate our learning and constrain our thinking.
We are awash in information. Even before the internet, the amount of information available to us was growing exponentially. Now we can access large swathes of this information at a moment’s notice, even as the quantity continues to skyrocket. Our ideas about the meaning of education are intimately tied to information. Most of us intuitively think of education as a process of absorbing a lot of information. We see learning and information as going hand in hand. Of course, we don’t perceive all information — or all topics of information — as being equally valuable. Therefore we expect our educational system to curate the information that a young person must absorb to become educated.
However, there are times when we acknowledge that merely absorbing information is not enough. In particular, we have long acknowledged that applying the learned information can also be crucial. Therefore students are given computational exercises in mathematics, physics, and engineering. In other subjects they may be given all manner of tasks intended to give them a taste of the practical side. But merely absorbing and applying information is not enough either. In recent years we increasingly recognize the importance of evaluating information. Not only are we awash in information, but a large quantity of that information is of dubious validity. Therefore we have begun to teach young people how to judge the quality of the information they encounter — in effect, how to separate the wheat from the chaff.
So, with these three emphases — absorbing, applying, and evaluating information — have we captured the essence of the relationship between “education” and “information”? No, not at all! Although we consider the absorption of information to be the core of learning, there is an equally important aspect that we tend to forget — organizing the information to which we are exposed. And although we might assume that people first absorb information and then organize it, it is actually the other way around — we usually have to organize the information before we can absorb it.
The issue is that we have a very hard time absorbing a new piece of information if it seems to have no connection to anything that we already know. In order for a new piece of information to “stick” in our brains, we usually have to associate it with something more familiar. For example, if you hear a random fact about an asteroid or a star that you have never heard of, then you probably won’t remember the information. But if you hear a random fact about Jupiter or Venus — familiar names — then you are much more likely to remember the information.
Therefore a key aspect of learning is the creation of organizing structures in our brains to enable us to absorb new information. And a key aspect of education is to provide advance organizers that facilitate the creation of these mental structures. These advance organizers tend to be simple models that provide a basic “big picture” of a topic, erecting a structure upon which additional information can be collected. These organizers often take the form of simple classification systems. In fact, quite a lot of which we teach kids in school is directly tied to these classification systems.
For example, consider the following topics:
- The continents of the world
- The planets of the solar system
- The colors of the rainbow
- The five senses
- The parts of speech
- The three types of rocks
- States and capitals
- The major languages of the world
- The constellations in the night sky
- The geologic eras and periods
- The phases of European classical music
- The classification of living things
- The periodic chart of elements
- The principal forms of government
- The countries of South America
The list goes on and on. In each case, we have taken an intuitively simple category and subdivided it into parts — typically a small, easily managed list of components. Thus we divide the world into continents, words into parts of speech, and the night sky into constellations. We require our students to become familiar with these lists — and often to memorize them — so that they can begin to associate information in this category with the appropriate sub-categories. This allows them to remember that Saturn is the planet with the highly visible rings, that Bach is a major composer of the Baroque period, and that basalt is a type of igneous rock.
The upshot is that these classification systems provide enormous value. By constructing organizing structures in our brains, they enable us to categorize and absorb the information that we subsequently encounter. In other words, these models enable us to learn. However, these same models also have a distinct downside, which we seldom discuss. By channeling the ways in which we think, these models not only facilitate learning, but also constrain our thinking. Each model provides us with a pre-made set of boxes ready to receive information, but thereafter we find it difficult to think in any way that contradicts these boxes.
One set of issues has to do with overgeneralization. When we assign a fact or impression (whether correct or not) to a particular sub-category in our brains, we tend to assume that it applies to nearly every example of that category. If we associate Africa with poverty, then we assume that nearly all of Africa must be impoverished. If we associate Australia with desert, then essentially all of Australia must be a desert. Such generalizations, even when they contain some truth, tend to be far less universal than we assume.
However, there is a second problem — less obvious but just as noteworthy. Our culture tends to treat each of these models as unquestionable truths. Our teachers present them as absolute facts, and for the rest of our lives we accept the models as reality. We are quite accustomed to parroting back these classification systems on exams: Name the 5 senses. Name the 7 continents. Name the 7 colors of a rainbow. Name the 9 planets. But in fact, most of these models are somewhat arbitrary. In other words, a slightly different model — or even a completely different model — might be equally valid. It would have been just as “true” (if not more so) to teach us that there are 7 senses, 5 continents, 11 colors in a rainbow, and 8 planets. In each situation, our culture chose one of several possible models, elevating that one option to the level of dogmatic truth.
It is easy to see why we do this. We rely on these models to organize our knowledge, which greatly facilitates learning — so even if the models are not strictly “true”, we aren’t going to abandon them. And it would be too confusing to present two or three competing models for every category of basic knowledge. It is much easier if we all use a single standard model for teaching and discussing each of the topics in the curriculum.
Unfortunately, with each of these models, we not only facilitate learning, we also channel all subsequent thinking along certain predefined paths. We praise the idea of “thinking outside the box”, while simultaneously erecting a multitude of little boxes to direct the way we think. In a sense, it is a worthwhile tradeoff. Thinking is not particularly valuable if there is no knowledge behind it. We need a strong foundation of knowledge in order to give value to our thinking. But our means of conveying knowledge can also inhibit certain lines of thinking, while promoting other lines. So how do we escape this dilemma? How can we facilitate learning without cramping our thinking?
Perhaps the most important thing we can do is to promote awareness that the models we use to organize our knowledge are just simplified approximations of reality — and not reality itself. In most cases, other equally valid models are possible, but we have chosen one standard model to facilitate learning and communication in that subject area. Our students should be made aware of this. For older students we can go a step farther. When we teach our standard models in the higher grades, the students should learn 1) why the model was created, 2) the criteria used to create the model, and 3) how generally accepted the model is. Students should also be encouraged to discuss the strengths and weaknesses of the standard model, and perhaps even to explore alternative models.
Keep in mind that the models we teach go well beyond classification systems — but classification is by far the most common type of model we use. In the standard science curriculum, there is an eye-opening unit where we teach kids about two competing models of how light works — the wave model and the particle model. If this unit is presented well (which is not always the case), then kids learn that each model is an abstraction — a simplification of reality — that readily explains certain aspects of the behavior of light. However, neither model reflects all of the essential aspects of reality. To grasp the greater truth, we have to accept that it is not a question of which model is true. In fact, both models can be considered true, but neither model on its own is capable of conveying all of the essential truth. It would certainly be interesting to follow a similar approach with a few of our classification models.
Below are brief critiques of 6 of the common classification models we teach our kids:
Continents. There are several competing models for how to divide the world into continents. In fact, different models have been adopted as the educational standard in various parts of the world. One difference is whether America should be considered as one continent or two, and another difference is whether Eurasia is one continent or two. A more serious issue is that while the continents provide a very helpful model for organizing our knowledge about physical geography, this is not the best way to organize our knowledge about human geography. See “Are Continents Real, or a Human Invention?”
Planets. We have traditionally divided the objects in our solar system into planets, moons, asteroids, and comets. Each time we find a new object, we include it in whatever appears to be the most appropriate category. When Pluto was discovered, the best fit appeared to be “planet” — even though nearly every aspect of Pluto falls outside the normal range of parameters for a planet. Later we learned that our solar system contains many objects similar to Pluto, and they all have characteristics that set them apart from “normal” planets. Therefore whatever path we would have taken, the number of planets would no longer be 9. The agreed solution was to create a new category of astronomical object, and to put Pluto and all similar objects into this new category. So now we teach kids that there are 8 planets, not 9. See “The Day Pluto Got Demoted”.
Colors. We teach kids that there are 7 colors in a rainbow, even though it actually contains a continuous gradient of colors. We teach kids that the primary colors are red, blue, and yellow, even though we actually use red, blue, and green as the primary colors in all of our electronic display devices. In fact, we have many different models that purport to explain colors, many of which are blatantly contradictory, and yet we tend to treat them all as truth. Is there a way to resolve these conflicting concepts? See “The Contradictions in How We Explain Colors”.
Senses. Our culture tells us that there are five human senses — sight, hearing, taste, smell, and touch. This ancient idea is based on the five obvious sense organs — eyes, ears, mouth, nose, and hands (or skin). In reality, there are seven principal external phenomena that we can sense: light (sight), sounds (hearing), airborne molecules (smell), molecules in solids and liquids (taste), external pressure (touch), temperature (hot and cold), and gravity/acceleration (balance). Some animals can detect magnetic fields or electrical fields. Therefore there are actually 7 human senses, and 9 animal senses. But if you include the ability to sense various states within our bodies, then the count goes higher still. See “The 5 Senses, or Maybe 7, Probably 9, Perhaps 11”.
Parts of Speech. We usually teach students that there are 8 parts of speech — nouns, verbs, adjectives, adverbs, pronouns, prepositions, conjunctions, and interjections. This is a perfectly adequate model for describing English and certain other languages, and it does a good job of helping kids to think about the many roles that words play in sentences or other units of communication. And yet there are several similar models that would be equally valid. For example, it is odd that pronouns are in a separate category from nouns, yet words such as “your” and “my” don’t have a separate category from adjectives. Articles such as “the” and “a” could also be considered worthy of a separate category. Numerals might be worthy of a distinct category. Plus we have lots of crossover cases where a word seems to fit in two different categories at the same time — such as the “verbal nouns”, where we use a verb in the role of a noun. (Example: “I love eating!”)
Biological Classification. Fifty years ago we were still teaching kids that there are two “kingdoms” of living things — plants and animals. But it became increasingly clear that this ancient model is a poor reflection of reality, so by the 1980s we were teaching students that there are five kingdoms of living creatures — plants, animals, fungi, protists, and bacteria. But as we continued to learn more about the many varieties of microbes in the world, this model also began to seem insufficient. Several new models now complete for designation as the best one to teach our kids. A major challenge is to select the model that provides the optimal balance of simplicity and accuracy. See “How Many Kinds of Living Thing Are There?”
Two of the above models — the five human senses and the red-yellow-blue model of primary colors — are so dubious that it seems odd that we still teach them to our kids. In two other cases — planets and the kingdoms of living things — we now teach a different standard model (or models) than we did a few decades ago. In the other two cases — continents and the parts of speech — the models we use are reasonable for their primary purposes, but other equally good models are also possible. In the case of the continent model, another issue is that we often apply it to situations where a different kind of model would be far more appropriate.
The real issue here is not to criticize one specific model or another, but to point out that all of our models are imperfect reflections of reality. The problem is not that we use simple models as substitutes for the more complex reality of the actual world — the problem is that we often confuse the model with reality, and assume that the model is reality. We teach our children by instructing them in the details of our standard models — which is good — but we fail to tell our children that these models are imperfect — which is bad. We would be far better off to admit to our kids that we are teaching them models of reality — extremely helpful and valuable models — but that other models of the same reality are possible, and sometimes even quite helpful.
The upshot is that if we want to teach our children how to “think outside the box”, then we have to teach them how to see the boxes. They need to know that our standard models are extremely useful for learning and for communicating with other people, but they certainly don’t represent the complete truth. Each model has its strengths and weaknesses, channeling our thinking in particular directions, and impeding our thinking from going in other directions. By openly acknowledging that other useful models may be possible for any given situation, we free our minds to consider other possibilities that would otherwise be closed off.
“To think outside the box, you first have to see the box.”
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