Published at: www.archania.org/education/

About 2500 years ago, Socrates said this about teaching:
No one can teach, if by teaching we mean the transmission of knowledge, in any mechanical fashion, from one person to another. The most that can be done is that one person who is more knowledgeable than another can, by asking a series of questions, stimulate the other to think, and so cause him to learn for himself.
This deeply insightful quote shows why Socrates was able to educate Plato to become more or less as wise as himself, which again was able to educate Aristotle whose ideas dominated western physics until Galileo in the 16th century. Without Socrates, we might very well still be living in the middle ages, without any of the technology available today.
From Socrates to modern science
Intellectual curiosity seems to have been essential for the scientific revolution[1]. The telescope was invented in Europe in the beginning of the 17th century, but it quickly spread to China, India and the Ottoman Empire. However, none of those great civilizations were as eager as the Europeans to use the telescope to study the solar system, or to modify it into a microscope to study the microscopic world. Europeans during the 17th century seem to have been more intellectually curious and open-minded than people living in the other great civilizations of the 17th century. Therefore the telescope set in motion the scientific revolution in Europe, while not much happened in the other great civilizations of the 17th century.
Curiosity and science
Figure 1: How an intellectually curious culture seems necessary to foster scientific revolutions.
Intellectual curiosity has also been positively correlated with academic performance (0.20), together with general intelligence (0.35) and conscientiousness (0.20)[2].
Curiosity and academic performance
Figure 2: How intellectual curiosity, general intelligence, and conscientiousness seem to correlate with academic performance[2].
Intellectual curiosity seems to be essential for a child's own eagerness to learn, and might even be related to how meaningful we find our lives to be. Rather than forcing children to do their homework, we should encourage their own eagerness to learn by fostering intellectual curiosity. Humans seem to be born with intellectual curiosity, but depending on how parents and caregivers react to questions asked by their children, it might increase or decrease over time. Parents and caregivers that always react negatively to questions, are discouraging them from asking questions, and that is likely to also make them less curious. On the other hand, parents and caregivers that always react positively to questions, are encouraging them to ask questions, and that is likely to make them more curious.
Parental influence curiosity
Figure 3: How parents and caregivers might influence the development of intellectual curiosity in children.
It has been found that children are much more curious about phenomena that appear inconsistent and ambiguous to their prior knowledge, than about phenomena that appear consistent with their prior knowledge[3]. Inconsistencies motivate children to find explanations, and when they find their own explanations they acquire more in-depth understanding of the phenomena than if they just have the facts presented to themselves.
Curious about mysteries
Figure 4: How children find mysteries more interesting than facts, and how they acquire a more in-depth understanding from finding explanations by themselves.
Teenagers that are forced to memorize the multiplication table, the periodic table, or to learn a second or third language, often find it extremely boring since it involves a lot of rote memorization. Teenagers are much more interested in learning something they find meaningful. However, it can be very useful to know the multiplication table, the periodic table or to know a second or third language. According to modern research, most babies can learn up to four languages if they are exposed to it in a proper manner[4,5]. This seems to be partially because the brain is highly absorbent during the first years. According to neuroscientists, the brain develops fastest prenatally and right after birth. At birth the brain grows approximately 1% each day, until about 0.4% a day after 3 months[6]. The brain of a 2-3 year old toddler typically has about twice the synaptic density of an adult brain[7]. So instead of forcing teenagers to memorize the multiplication table, the periodic table and/or to learn a second or third language, we should focus upon teaching things that require a lot of rote memorization to toddlers.
How to teach children of different ages
Figure 5: How we should focus upon rote memorization to toddlers, physically active learning to young children, and meaningful learning to older children and teenagers.
A few years later, during early childhood, children usually become less interested in rote memorization. They are however usually much more interested in physically active learning, than about sitting calmly and listening to a teacher lecturing. We usually remember things we are interested in, since we are paying much more attention to things we are interested in. And since young children often find it much more enjoyable to play with educational toys, they might learn much more from doing that than from listening to a teacher lecturing.
Figure 6: If we find the environment interesting, we are much more likely to think about it subsequently, and that makes us remember it much better.
When children are a bit older, they might be more interested in listening to a teacher lecturing. However, they need to find the lectures interesting, and stories seem to be something we are inclined to be interested in thinking about[8,9]. Stories usually need to have some kind of conflict between a protagonist and an antagonist[10]. When trying to teach something, the antagonist can for example be some kind of challenge, while the protagonist can be some kind of solution to the challenge. We should start with talking about the challenge, and present the solution later, after the children have been given plenty of time to speculate about possible solutions themselves. Building a conflict between some challenge and a possible solution seems to be a great way to make children interested in a topic, and the more interested children are in a topic, the better they tend to remember it. Rather than forcing children to learn at the same pace, each student should be allowed to progress at its own pace. If students acquire a higher skill level than the difficulty of what they are supposed to learn, they tend to get bored and disturb other students. While if they don't have a sufficiently high skill level for what they are supposed to learn, they tend to become anxious and might give up on what they are supposed to learn. Ideally, the skill level should be in harmony with the difficulty of what they are supposed to learn. This has been defined by the psychologist Mihaly Csikszentmihalyi as flow[11].
Figure 7: Flow is defined as when the skill level is increasing as fast as the difficulty.
It might seem challenging to let all children learn at their own pace. You might think that we would need one teacher for each pupil, which would mean much more teachers. However, we can use digital media to teach children today; such as educational games and video lectures. On the other hand, if children have access to more entertaining media, they might easily be distracted. It is therefor extremely important that they only have access to educational media on their computers. You can find educational media resources here.
Digital education
Figure 8: How we need to limit the access on educational computers, so that children are not distracted by more entertaining media.
Mixed age groups is another way to help children learn at their own pace. Instead of having one teacher for each pupil, we can let older children guide younger children. By doing this, each child gets the experience of being both the pupil during the beginning of a phase and the experience of being a guide for younger children towards the end of a phase. By being guides for younger children, they develop themselves to become more considerate and responsible, in a similar fashion to how older siblings often develop themselves to become more considerate and responsible. Children might also be better at communicating certain ideas to each other, since they might understand each other better, and have more vivid memories from when they themselves had to learn it. During the first 3 years toddlers are extremely good at forming synaptic connections, and the environment a toddler has during the first 3 years has an enormous impact for how the individual is going to become later in life[12]. We therefor need to pay a large amount of attention to toddler environments, and education should start almost immediately after birth.
Figure 9: The experiences a baby has during its first 3 years, will have huge impacts for later.
Many babies of today grow up learning only one language; the mother tongue of their parents. Babies can however learn up to four languages if they are exposed to it in a proper manner[4,5]. We should therefore have educational facilities that expose toddlers to more languages. It seems to be much easier for people to learn languages early, and individuals that learn languages early usually speak them more fluently. They also get much more time to study other subjects later, if they learn languages early.
0 3 years old
Figure 10: How a child can learn 4 different languages by relating to 4 different groups of people communicating to the child in 4 different languages.
In this system, each child will learn their mother tongue, as well as the global language (English). Children educated in this way, will be able to communicate fluently with the local population, but also with other children educated in the same way in different countries since they all learn the global language (English). In addition to these two languages, they will learn one practical language which tends to be useful in the region (for example a language of a neighboring country), and one exotic language from a faraway country, which will make it easier for the child broaden its cultural understanding later in life. During the first years of our lives, we need to develop our sensory-motor coordination[13]. Not many activities require more sensory-motor coordination than roughhousing. When wrestling with each other, toddlers need to pay attention to what the other kids are doing, and coordinate their movements in accordance[14]. In order to infer what other toddlers are up to, they need to learn how to read subtle emotional clues[15]. It has been found that toddlers release brain-derived neurotrophic factor (BDNF) during physical play; a protein which facilitates cognitive development[16]. Toddlers that are starved from physical interactions with others, tend to develop less social intelligence, and often become scared of social and physical interactions later in life.
Figure 11: Roughhousing is important for the cognitive development of toddlers.
Playing and interacting with pets can also help children to develop sensory-motor coordination and emotional intelligence. Pets have also been found to positively influence children in multiple other ways[17]. It is therefore probably a good idea to expose kids to pets from an early age.
Figure 12: Some animals that should be available to children at the educational facilities.
At this age, the child should acquire practical skills; such as counting, swimming, painting, and learning to read and write. They can also start to use tablets at this age, and should start to build molecules models with molecular building kits at this age, since it will be helpful for understanding chemistry later. You can find resources for educating kids from age 3 to 6 here. Already when kids are 3 years old, they should be able to start learning basic arithmetic operations. This can be done by teaching them to count sticks.
Arithmetic operations
Figure 13: Set for teaching children basic arithmetic operations.
Children can start making the simplest models of medicinal molecules already when they are 3 years old. As they grow older, they should be able to make more and more complex models of medicinal compounds.
Molecular models
Figure 14: Procedure for educating children to make models of medical molecules.
Common Solvents, Acids and Bases
Amino acids, Neurotransmitters, and Endogenous molecules
Vitamins, Medicines, and Health Promoting molecules
Complex Molecules
They should also start to draw the Lewis structures of these molecules. This will help them to learn how many valence electrons each element has, and how many electrons there are in different types of bonds.
Lewis structure
Figure 15: The Lewis structure of Aspirin
In art classes, kids should learn how to make beautiful makeup art. This might make them think that they can become whatever they want, and less like if they are immutable. It might also increase their self-esteem and help them to develop their unique styles. It is important that they learn to do it themselves. Having somebody else draw something on your face, doesn't give you any sense of accomplishment, no matter how beautiful it looks. By letting kids learn to do things like this to themselves, they will feel a much greater accomplishment with the result.
Makeup artist Lisa Joy Young
Figure 16: Makeup artist Lisa Joy Young (http://www.lisajoyyoung.com/)
The main objective of education should not be for the children to get good grades, but rather to foster an interest in learning. To promote an interest for learning, there should be different educational rooms. In these rooms, there should be fun games and experiments. These rooms should be open all the time, while the school is open. Pupils can choose themselves which room they want to go to, but they can only be 3 hours in a room before they need to change to a different room. They also need to have a minimum amount of hours in each room each week. There should be an adult expert in each room, but older pupils should also help younger ones. This way of teaching is similar to the Montessori approach, which has been ranked highly in studies on education efficacy[18,19]. You can find resources for educating kids from age 6 to 9 here. Mathematics often has an unfair reputation of being boring among children, maybe since it often focuses upon memorizing things, such as the multiplication table. Rather than forcing them to memorize boring things, children should start with developing an understanding of fundamental theorems, such as the Pythagorean theorem. This should be done by playing with physical building blocks, rather than by a teacher showing it on a blackboard.
Pythagoras toys
Figure 17: Sets for helping children to develop an understanding of the Pythagorean theorem.
It is also important for children to develop an understanding of π (the ratio between the circumference and the diameter of a circle). This can be done by putting beads on rings.
Beads on rings
Figure 18: How to help children develop an understanding of π (the ratio between the circumference and the diameter of a circle).
After they have attached beads to the rings, they count the number of beads around the rings, and compare it to the number of beads across the rings. They should start with attaching beads to small rings, and later bigger ones, to see that the approximation of π tends to become closer to the correct ratio of π the bigger the ring is.
Pi approximations
Figure 19: How the approximation of π tends to get closer to the real ratio the bigger the ring is.
When office computers were popularized in the 80's and 90's, the challenge was to make them easy enough to use for people that hadn't grown up with computers. In the physical world, we can move our hands in a certain pattern, and we see the same pattern with our eyes. Our hand movements correspond to what we see with our eyes. It was easiest for people to learn to use word processing software that followed the same principle; such as WordPerfect, and later Microsoft Word, and OpenOffice.
Old intuitive way of thinking
Figure 20: The old intuitive way of thinking. What you write is what you get.
Software engineers have however for a long time been familiar with a less intuitive way to use computers. They are used to write lines of code into computers, which is compiled into something different on the computers. Feeding information to the computer in this way, makes use of the computer's ability to process information, and can be much more efficient. A few lines of code might for example correspond to thousands of lines in the output.
New coding way of thinking
Figure 21: The new coding way of thinking. Your output can be more than you write in.
TeX and later LaTeX utilizes this approach for word processing. For people that grew up before the advent of computers, this might seem like a strange and complicated way to write documents. However, for children growing up with computers today, this might actually seem like the most appropriate way to write documents, and it is probably a good idea to teach children this way of thinking from an early age. LaTeX and HTML are particularly well suited for children to learn at an early age, to become familiar with this way of thinking. In the future, coding illiteracy might be as disadvantageous for people as normal illiteracy is for people today. Humans don't have a lot of working memory. We can only deal with a few chunks of data[20], and each chunk might only contain a few digits. We cannot necessarily keep a 12 digit number in working memory, but we can for example put it into 4 chunks containing 2 digits, into 2 chunks containing 3 digits and 1 chunk containing 2 digits, or into 2 chunks containing 4 digits:
Chunking numbers
To make it easier to calculate something difficult, we can also factorize into smaller chunks that are easier to calculate. A number of 3 digits multiplied with a number of 2 digits can for example be put into 3 chunks with 2 easy numbers to multiply, or into 2 chunks with 3 easy numbers to multiply:
Chunking equations
Chunks might also act as pointers referring to large clusters of data stored in long term memory. Experts often see connections between chunks referring to large clusters of data stored in long term memory. An expert in organic chemistry might for example be able to see how to synthesize a molecule from simpler molecules by multiple steps. Each step refers to a reaction that is stored as a cluster of data in long term memory. In order to understand chemical reactivity, they should start with learning about how the halogens and alkali metals want to be like the noble gases. You can read more about this here.
Alkali metals and halogens
Figure 22: How the alkali metals and halogens want to become like the noble gases.
Children should be thought basic ideas about morality from they are very young. Such as that stealing, lying and hurting other people is wrong. And to be helpful, respectful and considerate with other people. Much of this can be based upon the idea that you should treat other people like you want them to treat yourself, and that if all of us follow this simple rule we can make our society better for all of us.
Law of reciprocity
Figure 23: How we can make the world better for all of us if we all follow the law of reciprocity, or that we cannot expect other people to treat us well unless we show them the same courtesy.
To determine if a behavior is moral or not, we can look upon if it benefits society as a whole, or not. Behavior that benefits society as a whole, can be defined as positive-sum activity, and that can also be regarded as righteous behavior. On the other hand, behavior that is detrimental to society as a whole, can be defined as negative-sum activity, and that can also be regarded as immoral behavior.
Holism and morality
Figure 24: How the morality of behavior relates to how it affects society as a whole.
During this age, children are often interested in exotic creatures like dinosaurs, and exotic natural phenomena like black holes. They should therefore learn about cosmology and the evolutionary history of life one Earth. Other skills that should be acquired during this phase, is linear algebra, software engineering, and organic chemistry. You can find resources for educating kids from age 9 to 12 here. In the topic called evolutionary history, children should learn about how life has evolved on Earth; from the first microbes to the mammals of today. Here children will also learn about dinosaurs, and other fun creatures of the past, such as the giant shark megalodon, and the saber-toothed cat. They will also learn about how modern humans evolved from other primates. This course will focus upon the cellular changes that have occurred over time, so that the children acquire a basic understanding of cellular biology. It will also focus upon how different multicellular systems developed, such as the nervous system and the skeletal system. Interactions between different species, such as the symbiosis between flowering plants and insects, will also be covered.
Evolutionary history
Figure 25: Timeline from the first life on Earth until the appearance of anatomically modern humans.
At this age, the amount of sexual hormones start to increase as people get into puberty. This can be a very difficult time for many teenagers, and they often become much more interested in their social environment than in education. Therefore, instead of wasting time trying to teach them things they aren't interested in, they should mostly be allowed to engage in activities they enjoy, such as dancing, theater and playing music. It is however also a period when lots of teenagers are harassed by their peers, or feel socially embarrassed because they are different. Teenagers also become extremely prone to group thinking at this age, and many parents also start to feel that their children won't listen to them anymore. It therefore seems like an appropriate time for them to have a course about cognitive biases, where they will learn about typical weaknesses in the way people usually think. You can find resources for educating students from age 12 to 15 here. While most popular action and shooter games aren't necessarily helpful to improve the brain, difficult puzzle video games have been found to improve learning skills and increase the volume of grey matter in the brain[21]. Teenagers should therefore be allowed to spend some time solving puzzles in these video games. In this course they will learn about common biased ways of thinking, in order to become more aware of weakness in their own reasoning, and more aware of weaknesses in the reasoning of other people. This might foster intellectual humility, and improve their skills in critical thinking. You can read more about cognitive biases they should learn about here. At this age, teenagers start to feel more at peace with the sexual hormones, and they are able to divert more of their attention to topics that aren't related to their social environment. Their brains are also sufficiently developed to start having more abstract topics, such as calculus, the theory of relativity and quantum chemistry. Other important topics they should learn about include information theory and Bayesian machine learning. You can find resources for educating students from age 15 to 18 here. Machine learning is used in a wide variety of fields today, such as pattern recognition, customer analytics, fraud detection and scientific research. Bayes' theorem is used in many of the most advanced machine learning algorithms, and in modern research into cognitive biases. Bayes' theorem also gives an accurate description of ideal scientific epistemology, and can therefore be regarded as a link from mathematics to science. More information about the theorem can be found here. } Information theory was traditionally developed by Claude E. Shannon for signal processing, channel coding, and data compression. Today, it is also used in quantum computing[22]and even in modern theories about black hole entropy[23]. This is because information entropy can be linked to thermodynamical entropy at a quantum scale[24]. In order to understand entropy properly, they need to understand it both from the perspective of information theory and from the perspective of thermodynamics (which they will learn about in the topic about basic physics and in the topic about basic chemistry). Information entropy relates to average of possibilities in a message. You can read more about information entropy here.
Figure 26: Entropy in information theory and thermodynamics
At this age, people are finally ready for starting to reflect on themselves and society in general. They should learn about criteria for a healthy democracy, such as: the separation of powers, freedom of the press, and investigative journalism. In the topic called history of humanity, they should analyze what made different civilizations prosper and fail, to see commonalities, so that they can understand better how to make this society prosper. They should also study discuss civil rights. You can find resources for educating students from age 18 to 21 here. In the topic called civics and politics, they should learn about criteria for a healthy democracy, such as: the separation of powers, freedom of the press, investigative journalism and civil rights. They should also learn about major political ideologies, such as: capitalism, socialism, environmentalism, nationalism, monoculturalism, multiculturalism and globalism. Furthermore, they will learn about multilateral tax treaties, the difference between a flat and progressive tax, and analyze how this might relate to entrepreneurship, innovation and the global wealth inequality. History should be taught quite late, since it is important for people to understand it properly. Older teenagers also seem to be more interested in it. Rather than learning national histories, they should learn about the history of humanity. In this topic, they should analyze what made different civilizations prosper and fail, to see commonalities, so that they can understand better how to make this society prosper. They should also try to find commonalities between periods when our understanding was advancing quickly, such as Greece in 5th century BC, the Tang dynasty in China, the Islamic Golden Age, the Italian Renaissance, the Scientific Revolution during the 17th century, the Age of Enlightenment in the 18th century, and the Civil Rights Movement in the 20th century.
Timeline civilizations
Figure 27: Timeline from the first human civilizations until today.

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