A Brief Discussion of Human Intelligence and Learning
This article discusses some of the theory that informs the manner in which the SWT is constructed. I have certain reservations about psychology and education research, not least of which is because the researchers seem to disagree about most things. If you would like to read about my point of view, check out the article Reservations About Psychology and Education Research. If you are interested in the topics discussed below, please feel free to investigate. The Wikipedia links provided are a great place to start.
Memory
There are many different spins on how to talk about memory. We will use the terms long-term memory, short-term memory, and working memory. Working memory is the set of information you are currently manipulating, comparing, or otherwise immediately thinking about. Working memory is distinct from short-term memory, but the exact dividing line is blurry. Short-term memory is the set of information one can store temporarily (for minutes if rehearsed or actively maintained, for seconds otherwise) before recalling it to working memory for use. Long-term memory is like short-term memory, but it lasts much longer (perhaps indefinitely).
It is generally agreed that there is a lot of storage capacity in long-term memory and very little capacity in the other two types of memory. Short-term and working memory capacity is often measured in chunks. In the 1950's (when chunking was proposed), the number of chunks a person had was thought to be between 5 and 9 with most people having 7. Newer research suggests the number may actually be between 3 and 5 with most people having 4. Furthermore, the kind of data being chunked also seems to change the number of chunks that can be held in memory. As the data becomes more complex (random letters, to random small words, to random large words) the number of chunks available decreases. This is a great tradeoff though. Remembering random letters is less efficient than remembering random words, because each word usually contains many letters(i.e. 3 words have more than 4 letters in them most of the time). The amount of information you can hold in those chunks, chunking the data as efficiently as you can, is called your memory span. The number of chunks you get seems to be genetic (you can't increase the number through practice), but strategies to make the most of the chunks you have, can be learned.
Learning
Learning is the act of storing useful information in long-term memory. I see two general approaches to quickly storing this information. One is to practice remembering it. The other is to make it more memorable.
Practicing remembering is the obvious way to strengthen a memory. Practicing in intervals is the most effective practice technique. Immediately after learning a new thing a person must practice remembering it more frequently so as not to lose that information. As the memory strengthens the time intervals can be increased to make room for other activities. This is the idea behind rote learning and the mastery learning method employed by Kumon and Khan Academy. It is inherently democratic and egalitarian, as anyone can benefit from it, as long as they are willing to put in the time. A person with a stronger memory will be able to lengthen intervals more rapidly and thus outpace a person with a weaker memory. The SWT intends to employ this technique, along with others, especially in the form of an assessment app with a built-in recommender AI to suggest what interventions helped other students whose behavior looked statistically similar.
The other way to strengthen a memory is to make the memory more memorable. This complements practicing in intervals because it allows for fewer and less frequent practice sessions to yield the same quality long-term memory. There are many ways to increase memorability. Having a strong reaction (your first kiss or burning yourself on a hot stove) is one way. Usually the method is less extreme though, like learning a thing to achieve/prevent something else that is strongly desirable/undesirable. If a student believes a topic is interesting, important, or valuable, they are more likely to remember it. They are more likely to engage with it. Understanding is important to driving engagement and perceived value as well. When a person has taken an idea apart, seen how it works, and how it connects to previous knowledge, the information can be generalized (understood). This generalization means parts that were already known, do not need to be memorized again and the remaining parts are of higher value, as the value has been condensed into these fewer remaining bits. It also feels good to know how something works (how it fits together). This understanding has knock-on effects in that the next thing learned, that has some of the same generalizations, can be learned faster because of the interconnections between the old and new knowledge.
There are still more ways to increase memorability. Novelty or mystery help. New and mysterious things are interesting, because humans are curious. Solving a problem/doing something one's self also drives engagement. You have to understand something significantly, if you are going to do it alone. There is also a strong sense of accomplishment (emotional response) and often further learning of "soft/transferable skills" like methods of problem solving, creativity, perseverance, etc. It is also possible to remember something by associating it with something else that is more memorable. It can be a song, a rhythm, or a mnemonic device. To this day I can play certain songs and have equations, definitions, terms, and techniques from long past courses in abstract algebra, special relativity, or optics come flooding back.
Furthermore, there are specific techniques that can be used to increase memorization rates. Dual coding presents data in a visual and verbal form at the same time. This gives the learner two chances to assimilate the same material. Interleaving is a form of practicing in intervals that also attempts to increase memorability. During interleaving, instead of studying topics in large blocks, you cycle through your topics in short blocks. For example, if you have 3 distinct topics to study and 6 hours to study, you could study topic A for 2 hours, then topic B for 2 hours, then topic C for 2 hours. Otherwise, if you interleave, you might study topic A for 20 minutes, then topic B for 20 minutes, then topic C for 20 minutes, then start again at A, repeating the cycle until the 6 hours are up. Interleaving increases memorability by artificially maintaining novelty and thus maintaining focus by staving off boredom. Its interval structure means that when you get around to the same topic again, your short-term memory should be purged. What you can recall is already heading down the road to becoming a long-term memory and recalling it further helps. What you cannot recall is what you need to focus on putting into long-term memory still. Playing is another way to learn. Skills that can be used outside the play environment can be practiced in safety. Play is fun and therefore causes a positive emotional response which makes it memorable. Particular games also tend to be repeated (practicing in intervals).
The SWT employs lots of dual coding (apps, hint system, and eventually video), play (the apps and hint system are designed to be puzzle/game like), discovery/inquiry techniques (solving problems independently, transferable skills, better understanding, sense of accomplishment), and insists on a thorough and deep understanding of the material.
You will also see SWT lessons that teach the same concept in different ways. This gives extra opportunities to understand, the opportunity to choose an explanation closer to the student's level/strengths, and is an attempt to give students of different ability levels/strengths the opportunity to see how different approaches to a problem compare. A good example is the Pythagorean Theorem lesson. A weak student may struggle with the algebra of the second explanation, but may find the task easier if the answer is already known from the first explanation. This could in turn help the student develop their algebra skills. Another important use of these multi-lessons is as classification tools. A big part of learning is knowing exactly how to classify things. Getting many varied examples of that thing, and similar things that are not that thing, help with the classification process. This really helps with identifying the core defining features of that thing in question. Consider a young child. They have a family dog named Rusty. Rusty is a Golden Retriever. The child may decide all dogs are "Rusty" and would need to be informed both of the larger category of dogs and that each dog has a name. At this point perhaps all four legged furry creatures are "dogs," the child would need to be corrected. Cats, wolves, and squirrels are not dogs (although wolves and dogs are both canines and thus more closely related than the other two). What about a chihuahua or wiener dog? They sound and act a bit like other dogs, but look very different? There are many breeds of dogs and the child must learn that there are some special cases that look very different from the others. A good example of this in action is the Area Contained in a Circle lesson (and the forthcoming lessons on fraction arithmetic). The circle area equation is being taught, but in the background the idea of limits (from calculus) is being repeatedly presented in very different ways (squares, circle sectors, and annuluses).
Intelligence
To start I will repeat the definition of human intelligence I found on Wikipedia.
- Human intelligence is the intellectual capability of humans, which is marked by complex cognitive feats and high levels of motivation and self-awareness. Through intelligence, humans possess the cognitive abilities to learn, form concepts, understand, apply logic and reason, including the capacities to recognize patterns, plan, innovate, solve problems, make decisions, retain information, and use language to communicate.
Intelligence can be broken down into two parts: fluid and crystalized intelligence.
Fluid and Crystalized Intelligence
Fluid intelligence is the ability to solve new reasoning problems (ie. comprehension, problem-solving, and learning). Examples of tasks that measure fluid intelligence include figure classifications, figural analyses, number and letter series, matrices, and paired associates. Crystallized intelligence is your prior learning (life experience). Examples of tasks that measure crystallized intelligence are vocabulary, general information, abstract word analogies, and the mechanics of language. Crystalized intelligence can be accumulated by remembering things learned with fluid intelligence or by having crystalized intelligence transferred from another person through teaching. A stronger fluid intelligence generally leads to a stronger crystalized intelligence. This is because the person will come to correct conclusions more frequently and faster (allowing for more learning overall). Furthermore, the person understands better and makes better generalizations, which can be used to supercharge future learning of related topics (as many of the generalizations are already in memory and just need to be connected to the new knowledge). It is also important to note that a stronger fluid intelligence paired with the right kind of crystalized intelligence will help a person choose authorities to accept crystalized intelligence from (ie. trusting expert opinions because most people aren't all-in-one brain surgeon-lawyer-rocket scientist-professor-mathematician-programmers).
Crystalized intelligence is stored in long-term memory, which makes a lot of sense. Fluid intelligence is highly correlated with working memory. It makes sense that being able to think about more things at once is correlated with being able to figure out new problems better and faster. One can get through more comparisons faster. Holding a larger number of results in working memory simultaneously may even make it easier to see how connections interplay.
g factor and IQ
There are a variety of cognitive tasks a person can engage in. It has been found that being good at one kind of cognitive task is strongly correlated with being good at the other cognitive tasks. Being weak at one task also made it likely a person was weak at all tasks. This lead psychologists to theorize that there was something (or a collection of things) that made people generally good or bad at all cognitive tasks. They called this thing the g factor or general intelligence. It is a number that describes how correlated performance on cognitive tasks is. It is reasonable to think of general intelligence as the combination of fluid and crystalized intelligence and it is perhaps not surprising that all three are highly correlated. As mentioned above, crystalized intelligence is basically a library that fluid intelligence writes and curates. So they are highly correlated. It then makes sense, if the g factor is the combination of these two, that it is correlated too. The data largely supports strong correlation between these three.
The intelligence quotient (IQ) is a number derived from a series of cognitive tests (IQ tests) in an attempt to measure the general intelligence of an individual or group. IQ tests can be designed to single out fluid intelligence or crystalized intelligence as well. IQ scores can be compared across time to see trends in society (see the Flynn effect) or between groups divided by age, gender, ethnic group, etc. The Flynn effect suggests that populations (and especially kids) with access to better education, food, and other life necessities, tend to have high IQs on average compared to populations that do not. Even air quality and the effect of banning lead in gasoline have been suggested as contributing factors. This is very similar to the growth impacts on height that nutrition has (see the rapid rise in height observed in China when its "economic miracle" raised living standards in recent decades). Fluid intelligence peaks around age 20 and slowly drops off after. Crystalized intelligence continues accruing but the rate is slowed by the drop in fluid intelligence. It is also often the case that a person gets into a routine where they do the same thing repeatedly instead of having new experiences. This hampers crystalized intelligence growth because most of the required learning has already been done. Gender differences are fairly small. Females tend to be a little better than males at verbal tasks and males tend to be a little better at spatial tasks. There is some evidence to suggest that while the averages are the same, there is more variation in male IQ scores (i.e. a larger number of males deviate farther from the mean, above and below, which cancels out in the average). Ethnic and racial differences are observed, but are easily attributable to unevenly shared participation in the Flynn effect (i.e. caused by unequal education/resource allocation and not by genetics).
It is important to acknowledge the checkered past of IQ testing. In 1905 the first IQ tests that actually succeeded in measuring intelligence were developed in France. The Binet–Simon Scale was used to test children who were considered "sick" and thus needed to be sent to the asylum. The test found that some kids were just "slow" and needed remedial education and support, and did not need to be locked up. Many kids were saved thanks to this good use of IQ testing. Malicious IQ tests were also designed to test for "feeblemindedness" and "mental retardation." The tests were designed to artificially lower the scores of minorities and thus justify forced sterilization and even euthanasia in racist eugenics programs in many countries, notably the United States and Nazi Germany. As a result of this dark heritage, the most common IQ test administered today, the SAT, eschews the title instead claiming to be an "aptitude test."
The Nature vs Nurture Debate
The nature vs nurture debate goes back thousands of years, but has been particularly in the spotlight for the last century or so. Of particular interest is the heritability of IQ. The studies suggest that IQ is partly heritable. That is genetic in the sense that the parent's intelligence is a strong indicator of what the child's intelligence will be. This makes sense because IQ is a measure of one of the three highly correlated kinds of intelligence we have discussed and fluid intelligence seems to heavily influence the other two (crystalized intelligence is largely stored results from fluid intelligence and general intelligence is the combination of fluid and crystalized intelligence). Fluid intelligence is further correlated with working memory and the amount of working memory a person has is largely determined by genetics. Training of working memory can be done, but the results are still hotly debated.
Not all of intelligence is explained by nature though. Memory span is the amount of chunks (genetically determined) and the amount of information that can be crammed into each chunk. It is the second part where teaching (the nurture side of the debate) shines. Teaching can guide students to the most information dense working memory chunks much faster than would naturally occur (if it would occur at all). One of the roles of the teacher is to encourage optimal use of the available working memory. More importantly, teaching can help with the gain of crystalized intelligence. Choosing the topics covered to maximize the utility of the content learned and the order in which it is most easily and thoroughly understood is key. This often includes scaffolding the generalizations so that insurmountable leaps do not derail the students more often than is necessary. Teaching meta strategies (ie. creative problem solving, vetting sources of knowledge, asking good questions) so students can learn on their own is also quite useful. The most important role of the teacher is in presenting and encouraging methodical techniques for learning. Patient strategic practice can make up for the disadvantages of a poor memory (although regular methodical learning and a good memory are hard to compete with).
In fact, it's quite clear that teaching/nurture is crucial in developing intelligence. One need only think about it for a moment. What would happen if a group of children were isolated from society? What would happen if they grew up with no contact with any person who could teach them? Would they create a thriving space age society? No. They would become cave people. It doesn't matter how genetically gifted a child is, they need guidance. Otherwise the best that can be reasonably hoped is they will learn to sharpen sticks to make spears.
The approach to learning here at the SWT (see the end of the learning section above) is an attempt to maximize the intelligence of the students who use the site. Regardless of what nature gave the kids, we want to nurture them to their maximum potential.