On Intelligence – Week 21 (26 – 30 March)

Intelligence is an interesting concept. Not until I read Chapter 11 of my Psychology textbook that I know there are alternate definitions to this word. To tell the truth, I had never even thought that definition of intelligence could be culturally determined; I thought the concept was universal. It is because in Vietnam, the definition is essential the same as that used in the West. Hence, there is an exact translation for it, sự thông minh. In addition, from what I understand, intelligence and wisdom are closely related both in English and Vietnamese. However, I do not know why that is, whether it is merely a coincidence or a (French) colonial heritage.

Nevertheless, given the conspicuous difference in terms of education, there could potentially be a subtle yet significant deviation. At least in the US system of education, critical and creative thinking are encouraged. In the current Vietnamese system, in sharp contrast, such acts are not welcome, at the very least. Students are supposed to accept whatever their teachers told them then regurgitate during an assessment. Politics is an extreme case. Strangely enough, history textbooks serve as propaganda tools for the Politburo. Given the political situation in Vietnam, those to criticize the “facts” presented to them risk severe consequences. As a general result, most people resort to silence and obedience, which, incidentally, is a cultural norm.

Interesting enough, intelligence is not included as a technical term and thus there is not an academic definition for it. Instead, our AP Psychology textbook presents four difference theories of intelligence. Personally, I find Howard Gardner’s theory the most appealing. While I remain unconvinced that naturalistic, spiritual and existential intelligences exist, I do believe that we can indeed break what Charles Spearman would call general intelligence, i.e. the g factor, down into more specific units. I have contemplated Gardner’s theory and find it a good generalization of natural phenomena related to human intelligence. While it is almost undisputed that linguistic, logical-mathematical, spatial and musical intelligences occur in nature, in my considered opinion, it is rather likely that bodily-kinesthetic, interpersonal and intrapersonal intelligences exist as well. I shall provide a few illustrations of my own.

101st Airborne

101st Airborne Insignia

From documentaries I watched and stories I have been told, paratroopers definitely possess a high degree of bodily-kinesthetic intelligence. This is at least true for the armies of France, Germany, Great Britain, the United States and South Vietnam but is probably so internationally. That makes very good sense. Whenever they jump out of an airplane, they are literally on the border separating life and death. As a result, they need to be able to skillfully control their bodies, as well as their parachutes, in order to land safely and correctly. Interpersonal intelligence – the ability to understand other people’s intentions, emotions and motivation and to effectively cooperate – appears to be closely related to emotional intelligence, whether they are the same or not. Some people exhibit remarkable interpersonal intelligence while others do not. Examples of those who command above-average interpersonal intelligence is Allied/NATO high ranking officers. As part of their jobs, they need to smoothly collaborate with people from a variety of different nations and look pass the language barrier (some may not be particularly fluent in English).

Our AP Psychology textbook goes to great length denying the existence of differences between groups. This makes much sense. All humans share up to about 99.9% genetic material. Only a tiny fraction of a percent accounts for mostly the differences in appearance. For these reasons, it is natural that there are not any significant differences, such as in intelligence between groups. The reason why early IQ tests suggested a difference in terms of intelligence between groups is because they were biased towards middle class Caucasian individuals. Those with other ancestries lacked the education and opportunities they enjoyed. As a result, early IQ tests were not valid; they did not measure what they claim to measure. Therefore, any significant differences between groups, such as IQ, are non-existent. Modern IQ tests, fortunately, have had much-improved validity and reliability. Not surprisingly, they show that the normal range of intelligence is about 100 for people from all kinds of background an ancestry. The use of IQ tests to justify racism is thus unsound.

While there is only negligible differences, if any, between groups, it is most likely another story for individuals. True, overall, most people tend towards the center of the distribution curve of human intelligence. However, for individuals, there could indeed exist major differences. That explains why history has seen so many brilliant minds and psychologists have seen the mentally challenged. To me, the boundary between group differences and individual differences is clear. In my opinion, the graph below is a wonderful piece of art as well as mathematics.

IQ curve

The Normal (Gaussian) Distribution Curve of Human Intelligence. (from Wikipedia).

Educational Testing – Week 20 (19 – 23 Mar)

Assessments are an inordinately important part of education.  Education is the act or process of providing individuals with useful information and help them develop necessary skills. Thus, testing is needed in order to assess how successful the students are and how effective instructional methods have been.

Those, however, are not the only purposes of testing. Today, educators and psychologists have discovered a few more uses for educational testing. First, students should be tested whether a certain educational program suits them. This type of test is used to classify students to see if they need special assistance in learning or if they are talented in any subjects. The textbook mentions that “a movement towards inclusion [i.e. putting students of significantly different aptitudes in the same class] has taken hold.” In other words, some of the faculty of special educations want their students to spend as much time in a mainstream classroom as possible. They believe that their students will benefit from the assistance offered by their “normal” peers. Personally, I partially disagree with this point of view (thanks to Mr. Marshall for correcting me here). It is truly beneficial for special needs students to spend time in a mainstream classroom with mostly average peers. Special students can receive assistance from both their classmates and teachers while students around the average level enjoy the repetition of concepts either from helping their peers or from the teachers helping their peers, which helps them do better in that class. In addition, it familiarizes students with those at different levels than they are. However, talented students will stagnate in such a class because it fails to meaningfully challenge them. While they help their peers improve, they themselves do not improve very much.

Second, tests are used as an attempt to measure aptitude and intelligence. These kinds of tests arise from the field of psychometrics, which literally means measuring the mind. Obvious examples of tests belonging to this category are the IQ Test and the SAT Reasoning Test. Even though I have never taken the official IQ Test before, I took an intelligence test when I enrolled at AIS. It said my intelligence falls into the normal range. I therefore expect to get a score of around 100 if I take the official IQ Test. The reason why I have faith in the modern IQ Test is because its method of quantifying intelligence is much more sophisticated than its classical version, which is probably too simple and thus seriously flawed. My textbook only mentions that the algorithm is similar to how teachers “grade on a curve.” However, I suspect that psychologists probably employ a more rigorous mathematical procedure to do so, for the sake of scientific credibility.

I have taken the SAT Reasoning Test twice; both times I got 1870, which is above the average score of 1500. I am genuinely impressed with this result. It shows that the SAT Reasoning Test has exceptional test-retest reliability. In fact, it is a “dead shot.” Last October, I took the PSAT at AIS. All of them in general suggest that I need to improve my reading skills and that my aptitudes in writing and mathematics are good. Their face validity is probably high; I have a lot of opportunities to work on writing and mathematics lately but not so much on voluntary reading. College Board certainly works hard to ensure the quality of every single test they administer. That can be seen by the rigor of every single question, which have one and only one correct answer. As a “veteran” of the SAT, I think it is quite valid because non-math questions therein tend to avoid American-centrism. I remember seeing questions mentioning Vietnamese culture. They also give students a sense of how well they performed on the exam statistically by giving a percentile of how they did compared to everyone who has taken it. I intend to take the SAT II Subject Test in Mathematics and Physics in the near future and add those results into my college application. I think it makes sense to do so because besides the fact that some universities require students to take both SAT I and II, SAT II attempts to assess students’ aptitude and understanding of high school materials by American standards. Of course, students may opt to take AP exams as well. Yet, these cover college-level knowledge and students are generally not expected to know topics covered in universities before they get there. In addition, both (AP and SAT) are standardized tests; this means the results ought to be both reliable and valid.

Having said that, I would like to challenge the notion of so-called SAT Words. College Board themselves never mentioned this set of vocabulary, as far as I understand. In addition, having taken multiple practice exams, I know that the likelihood of a very uncommon word appearing is quite small. For this reason, the best way to excel in the SAT is, frankly, the old fashion way: doing well in high school and reading extensively with a dictionary.

This little discussion prompts my interest in mathematical statistics. I may not have the resources to take that class next year. However, I will certainly have a chance to do so at university. A little peek at such a course offered at Princeton University looks exciting!

Problem Solving – Week 19 (12 – 16 Jan)

Problems arise not just in sciences but also in everyday life. As a result, learning how to deal with them is of vital importance. There are two classes of strategies for problem solving: algorithms and heuristics. Algorithms are procedures that guarantee the correct solution if properly applied. Heuristics are convenient procedures that do not necessarily yield the desired answer every single time. At first sight, algorithms seem much more preferable. However, their restrictiveness is their disadvantage. Algorithms tend to be specialized methods restricted to a single group of problems. Heuristics, on the other hand, may be applied to a variety of situations. In addition, due to their highly technical nature, algorithms may not be available to everyone.

Here is an example of a problem I recently solved. We had to use a physics simulation to guide a electrically charged particle towards the goal without colliding with any of the obstacles. The practice and first two levels of this ‘game’ are not that difficult. In fact, I believe that one does not need to be a high school student to solve the practice level problem. Nevertheless, Level 3 is truly challenging: the particle has to be directed towards the goal while avoiding up to two long barriers in the process. Here I used some heuristics my AP Psychology textbook suggested. Unfortunately, yet naturally, not all trials yielded the desired outcomes but established the foundation for my discovered solution. I tried changing the mass of the particle and directing it out of the area. (Switching the particle’s charge is another alternative. However, this will probably not make any difference.) After all, the game does not forbid the user to do these things but allows them to modify these settings. I also tried to break the problem down. I tested ways in which I can guide the ‘hockey’ away from one barrier an on a path to avoid another. This works delightfully well. The ‘hockey’ moved in a path resembling Archimedes spiral and went into the goal.

I believe this solution is beautiful for two reasons. First, it accidentally gives me a glimpse into how particle accelerators (such as the Large Hadron Collider) work. Second, it is exact. Even the slightest deviation of the positions of guiding electrically charged particles amends the path of the ‘hockey’ and usually it will miss the goal.

Guided Electric Hockey

This is my solution for Level 3 of the physics simulation called "Electric Hockey".

It took me about an hour to solve Level 3. A possible reason for this is my lack of in-depth understanding of electromagnetism. My friend, Peter, discovered that there is a single arrangement of guiding particles that works for all levels. When I asked to see his marvelous solution, however, he said he never wrote it down. His dislike of physics is probably the reason why. 😦

Language – Week 16 (5 – 9 Mar)

Language is a tool in constant usage. I agree with what Mr. Marshall says; we do not spend many thoughts on it. I have very few memories of learning either Vietnamese or English. Distant memories seem to fade away rather fast these days. Transience must be the culprit. I can only remember a few accounts my mom told me. She told me I often mispronounce (in a funny way) when I was very young. Before attending first grade, my grandfather taught me the alphabet and a few simple words. Ideally, that should not have happened because first grade is when students begin learning how to read and write. However, so-called “educational reforms” issued by the government meant that knowledge is introduced at a rate much more than the rate students can absorbed.

I excelled in spelling, both in Vietnamese and English. Till this day, I am fond of big words (in terms of spelling) in both languages. Nevertheless, in Vietnamese, the longest word ever has only 7 letters. In addition, every single word in Vietnamese, except some special ones that are not really Vietnamese but ethnic languages, contains only a single syllable. For example, Vietnam in Vietnamese is actually two words rather than one, Việt Nam. In English, however, words can be very long and multisyllabic, e.g totalitarianism. Both languages share something interesting in common: irregularities. For example, there is not a single way in both languages to convert a verb or an adjective into a noun. (If you wish for a specific example, here it is. In Vietnamese, the word buồn, meaning sad, becomes the noun nỗi buồn while the word vui, meaning happy, becomes the noun niềm vui instead of nỗi vui.) Some praise that such irregularities demonstrate how diverse English and Vietnamese are whereas others complain that they serve only to complicate the two languages and frustrate language learners. One plus for anyone learning both of these languages is that the spelling uses the Latin alphabet. I thus think that Vietnamese, though a tonal language, is much easier to learn than Mandarin Chinese.

I believe that Whorf’s linguistic relativity hypothesis has some validity, albeit to a  limited domain only. That is why it makes sense to learn both the language and culture of a country at the same time. Otherwise, it would be stiff translation from one language to another. I shall use English editions of Hanoi-controlled newspapers as an example. To me, they seem to be translation from Vietnamese into English: Their English is very dry, not fluid and, in my opinion, not enjoyable, like foreign news agencies such as the BBC or AP. Furthermore, interesting enough, Vietnamese services of foreign news agencies – e.g. VOA or BBC -, in my opinion, are more capable Vietnamese users and their Hanoi-controlled counterparts. This is probably due to the prevalent belief in freedoms of speech and press. In contrast, government-owned Vietnamese news articles tend to be monotonous and woody; their chief purpose is to be Hanoi’s mouthpiece. I thus recommend that anyone who wish to read in Vietnamese visit the Vietnamese services of those websites. Another aspect in which the linguistic relativity hypothesis may be valid is noticeable in everyday social interaction. According to my personal observation, it is more common for many Vietnamese these days to say “thank you” when they speak English. In Vietnamese, however, it is not as likely. This is some advice to anyone wishing to learn Vietnamese: learn it from elder Southern people, i.e those who have lived in South Vietnam since before 1975. I have witnessed on multiple occasions that many of these people use Vietnamese with delightful smoothness and courtesy. Their accents are not as slanted as those of people living in remote areas of North Vietnam or in the Mekong Delta.

This is an interesting topic. I shall add more later.

Memory – Week 15 (27 Feb – 2 Mar)

Last week, we were learning about learning. Now, we need to remember facts and theories on memory. Memory is any system, biological, mechanical or electronic, that encodes, stores and retrieves information. The human brain is currently ranked as having the largest memory capacity.

Although believed by many to be unlimited in storage capacity, the human brain has a finite number of neurons and a finite number of connections. For that reason, I think that human memory has a finite, though admittedly very large, “disk space.” I have been able to find some more evidence to back this view. The so-called seven “sins” of memory – transience, misattribution, blocking, bias, distortion, persistence and absent-mindedness – serve as rather strong support. Computers are able competitors to the human brain. Computer memory, just like its processing system, rarely errs; it produces the information previously stored with mathematical exactitude. On the other hand, human memory has an entire list of drawbacks as aforementioned. From an evolutionary point of view, those “sins” have adaptive values to our predecessors; they prevent them from being overwhelmed by a vast amount of data to be stored and retrieved. In addition, our sensory systems use a strategy known as selective attention when picking up data from our surroundings. That means only the details you pay attention to will be transferred into working memory, which consists of a central executive, a sketchpad and a phonological loop. Then, only some of the information in working memory will be stored in long-term memory. In all, only a small amount of stimuli detected is transferred into working memory and even a smaller amount is stored in long-term memory. Last but not least, my textbook mentions that long-term potentiation suggests that millions of neurons are involved in the storage of a single memory. Again, we have a finite number of neurons and neural connections. How can human memory capacity be unlimited when so much activity is associated with the processing of a single piece of information?

I have tested my memory of the vocabulary terms and concepts I need to remember in the above paragraph. I think my performance was satisfactory. Memory can be a very strange thing. I had a little difficulty remembering all seven “sins” of memory, on which Mr. Marshall lectured very recently. In contrast, I can solve review mathematical problems involving concepts presented last year (chapters 1 and 2 of AP Calculus) without struggling and often without having to confirm with a calculator. Furthermore, I am admittedly an absent-minded individual. I often forget where I put things. I try to resolve this issue by very regularly put them in their single designated place. For example, I always put my keys on my table as soon as I get home. That way, the possibility of leaving them in one of my pockets or elsewhere is eliminated. From that point onwards, I almost never forget my keys again.

I think Mr. Marshall’s method of maintenance rehearsal is very helpful. Besides trying to recall what a technical term means, I also try to do it in my own words. This means I also benefit from elaborative rehearsal. When I studied Mandarin Chinese, a lot of times I had to recall what a character looks like then write it on paper. In order to “help” us remember, our teacher made us copy those characters again and again. This was supposedly maintenance rehearsal. However, in practice, it was not authentically so. I often fell asleep writing those characters. My hand kept copying them but my mind was somewhere else. As a result, I had a hard time with the subject. Mr. Marshall’s method is more helpful because we had to think whenever we verbally recall a word or phrase.

Another strategy I use when learning is distributed learning plus sufficient sleep. Distributed learning prevents one from being overwhelmed by the material to be remembered. Sufficient sleep offers much needed rest for optimal functioning. I find it enjoyable as well. On weekdays, I usually sleep for 8 to 9 hours; on weekends, 10 or 11 hours is the normal number. I am certain that I usually dream about things covered in class even though I seldom remember what were in those dreams. For this reason, I believe that there is probably a connection between dreaming and memory.

Cognitive Learning – Week 13 (6 – 10 Feb)

Cognitive learning is a concept of heated debate in the past. Followers of behaviorism, i.e. behaviorists, stressed that psychology is a scientific study and therefore may only objectively investigate observable phenomena. Cognitive learning, they say, cannot be observed and since researchers must made inferences, objectiveness is compromised.

Nevertheless, evidence supporting the existence of this phenomenon has been found. In addition, these phenomena cannot be explained with neither classical conditioning or operant learning or any other branches of behaviorism. Cognitive learning must be used. How could researchers argue for the existence of the concept? They devised scientific experiments. In one of these, a rat is put into a maze. It is free to wander around and explore the maze without any reinforcements of any kind from the researcher. Afterwards, it is put on one end and food on the other. The rat negotiates its way through the maze for efficiently than one who is unaccustomed to it. Psychologists coined the term cognitive map to describe this phenomenon. The rat has created a mental model of the maze during its exploration. This cannot be explained purely in terms of classical conditioning and operant learning.

There are two other forms of cognitive learning. One is called insight learning. It occurs when the subject suddenly re-arranges its perception of the problem presented and arrives at the answer. In one famous study, a chimpanzee is put into a room with boxes and some bananas hanged from the ceiling. After some failed trials, the chimpanzee decides to put the boxes on top of one another then climb on top of them, deservedly earning its reward. The other form is called observational learning. Animals observe others then learn from them. In some cases, observing animals are indirectly reinforced just by seeing the one in action rewarded somehow. It is favorable because the process of what the best response is for a certain stimulus can be averted. Unfortunately, it is also the factor being the spread of unwanted behavior such as excessive violence.

Personally, I believe that behaviorism and cognitive learning are by no means mutually exclusive. They are simply different forms of learning. They should be united somehow in the future when neural processes, fundamental to any form of learning, are better understood. As a student, I think I use a combination of behavioral and cognitive learning. Of course, the instructor can reinforce students with praises or good marks. But the bulk of learning comes from cognitive processes because we think (a lot in some classes such as AP Calculus) rather than simply doing exactly as told.

Schedules of Reinforcement and Punishment – Week 12 (31 Jan – 3 Feb)

Schedules of reinforcement are developed based on the concept of intermittent reinforcement.Recall that continuous reinforcement is tailor-made for acquiring a new behavior. Intermittent reinforcement then offers itself as an efficient means to maintain that particular behavior. Schedules of reinforcement, therefore, are simply various strategies of intermittent reinforcement.

The first class of intermittent reinforcement strategies is called ratio schedules. Reinforcements in this class are issued on the basis of correct responses. Its elements are fixed ratio and variable ratio schedules. My parents use the fixed ratio schedule of reinforcement. They offer me a delicious and hearty meal after I have earned a high grade, i.e. an A, in an sizable assignment. Variable ratio schedules are obviously more irregular. For example, street vendors do not know and cannot know how long they must wait before a customer stops before them.

The second class of intermittent reinforcement strategies is called interval schedules. It is based on the amount of time elapsed since the last reinforcement. Fixed interval and variable interval schedules belong to this class. The textbook offers monthly salary as an example. My own example would be the weekend. People, myself included, often work hard during the weekdays, getting as much done as possible, so that as much of the weekend as possible could be enjoyed. Variable interval schedules are the most irregular strategy of intermittent reinforcement. One instance (which I wish is real in Vietnam) is when the Ministry of Health unexpectedly check a random food stall. Since the owners of food stall know that they are subject to an unannounced thorough check at any time, they would almost certainly follow all laid down guidelines.

Unlike reinforcement of any kind, punishments are used to remove an unwanted behavior. There are two types of punishment: positive and negative. Both types are widely known, at least in my perspective. Positive punishment is when an undesirable stimulus is issued after an unwanted response is delivered. For example, when I was little, I touched the electric outlet on one occasion. I consequently got a painful electric shock. From that point onwards, I never tough it ever again. Negative punishment is when a favorable stimulus is removed after an unwanted response is delivered. One example of this is the loss of privilege. At my school, students who are tardy on multiple occasions shall receive detention after school, a time during which they may do what they want.

Reinforcement and punishment both have one thing a common. Like medicine, they must be applied correctly and consistently. Improper applications are definitely counterproductive. Punishment, in particular, is prone to abuse (there are many sadists out there). Abuse of punishment can bring about terrible consequences.

On Operant Learning – Week 11 (16-12 Jan)

Operant learning is almost a completely new topic to me. I am familiar with the concepts of rewarding and punishing. Nonetheless, my understanding of them is trivial. When I first read this section in the book, I tend to support the behaviorists’ point of view. An organism’s behavior is clearly observable. As a result, empirical investigations can definitely be done; furthermore, conclusions drawn from these studies are more reliable, having such a strong basis. It is an arduous task to find fault with this reasoning; I would argue that that is a logical impossibility. Upon reading about cognitive learning, however, I tend to support both sides. Of course, it is hard to accurately deduce what happens in an organism’s mind. Nevertheless, strong evidence supporting the existence of cognition has been found. One example is an experiment in which psychologists put a mouse in a simple maze with food at its exit. The preferred path to the food is blocked. The motivated mouse therefore worked out the long way to the food. This phenomenon is called cognitive mapping.

Psychologist B.F Skinner, a radical behaviorist, prefers the word reinforcement to reward as a technical term. There are two types of reinforcement, one positive and the other negative. Positive reinforcement is already well-known and therefore will not be defined here. Examples of positive reinforcement include giving A’s to excellent and motivated students and giving a dog a little snack for obedience. Negative reinforcement, on the other hand, can be a bit obscure. It is the removal of an unwanted stimulus after the subject responded correctly. One example is a tax cut for companies employing a lot of new people. Another example is the removal of or slash in teaching duties for bright researchers. To be honest, I would like to have the second negative reinforcement when I complete my doctoral program. 🙂

Well, this is the end of my second post for this week.

On Classical Conditioning – Week 10 (9-13 Jan)

Classical condition is a familiar topic to me, having scratched its surface in 7th grade biology. Unfortunately, I longer have the book to recall what was covered. Still, I can remember that we did not discuss the subject in as much detail as in AP Psychology now. All I learned, as far as I can remember, was that organisms from the Animalia Kingdom could learn to respond to a new stimulus as they would do to an old one. I learned from TV that spiders can eventually learn, i.e. after eight trials, to ignore scientists’ tapping on their webs, which had a specific pattern. I thus tend to believe other animals take time to learn as well.

I have been able to come up with a mathematical analogy of classical conditioning. However, for convenience, I shall state it here verbally. Let A lead to B. Thus, if A is congruent to C, then C leads to B. In this analogy, A and B are the unconditioned stimulus and response, respectively and C is the conditioned stimulus. When paired with C, however, B becomes the conditioned response. Being mathematically inclined, I find this simple analogy very helpful.

Mr. Marshall recommended that we give three examples of two concepts classical condition – acquisition and extinction – in our own lives but here I will only bring up two because I have already discussed one (on acquisition) on the previous blog post. Dog theft is currently a problem in Vietnam (guess what! Animal protection laws are virtually non-existent and many, most of them North Vietnamese, like to eat dogs). What happens is that the thieves give the house dog an apparently delicious bait, which either stuns or disables the dog. The thieves are then free to steal the dog and sell it to a dog food restaurant (in the case of a burglar, he/she has successfully overcome the house’s first line of defense). In order to prevent this, a method has been introduced. Dogs should be trained to eat from their owners only and preferably in a specific container. To do so, feed the dog in a container other than the one designated for that purpose. Add unpleasant tastes to the food, e.g that of chillies. After a few trials, the dog will shrink from food provided outside that specific container.

Another example of acquisition in classical conditioning from my personal experience is similar to Pavlov’s studies on dogs. This one, however, is accidental. We fed our dog with manufactured dog food, as well as rice. The container of the dog food, or dog snack, made a rather special noise when moved. My dog eventually acquired the association between this sound and a meal. Unfortunately, that meant she mistook the sound of human snack, such as peanuts, for her meal.

Learning – Week 9 (12-16 Dec)

In AP Psychology this week, we learned about learning. Again, we learned about learning (you’re supposed to laugh!). At first, it seems rather confusing and complicated and unfamiliar. There were just too many new words to define and remember. However, the technique of re-defining the vocabulary in one’s own words put forth by Mr. Marshall definitely helped me in remembering them. By now, my vocabulary page for Chapter 6: Learning has been completed.

It appears all three forms of learning discussed in the book, classical conditioning, operant learning and cognitive learning, all cooperate harmoniously in our everyday experience. After all, we all learn and what we learn come from by one way or the other. For academics, however, cognitive learning is the most useful, at least in my considered opinion.

A fact I am certain is of interest to everyone is that learning, no matter what form, takes time. The amount of time taken depends on the form of learning. Classical conditioning requires the neutral stimuli to be presented on multiple occasions in order to be associated with a conditioned response. Operant learning requires the consequences of a behavior to be felt before its effect is stamped upon the subject. Cognitive learning requires a considerable amount of time in order that the subject remembers the mental model created earlier.

I can remember personal experiences with classical conditioning and cognitive learning. When I had fish as pets, I used to walk very loudly out to the pond before dropping food into  it. After several times, as I was walking in normal pace towards it, the fish rose to the surface automatically, their mouths opened like o’s. They did it every time I walked out into the garden, no matter what I intended to do, i.e. going to school. I just had a delightful experience with cognitive learning very recently in math class. Last class, we covered antidifferentiation by substitution. Initially, this method of integration was unfamiliar; we needed to antidifferentiate and differentiate in the same process of deriving an algebraic formula for an integral. We hence struggled to get the classwork done. I went home a slept tight for a few days. Yesterday, when I completed homework, I could solve every single problem without much difficulty. Calculus can be bizarre sometimes; for example, Leibniz notation of the derivative dy/dx can, depending on the situation, behave like a fraction while is not so in others. That is why it is intended to be in collegiate mathematics courses and only introduced to high school as advanced placement classes (AP). An open mind is essential in learning these kinds of things.

Tet holiday is starting towards the end of next week. I am looking forward to more opportunities to pay my sleep debts. I think I need more sleep than usual after learning something challenging.