I’ve been talking about the “learning styles” philosophy and why it doesn’t make sense. It’s because there are different forms of knowledge, each of which has a different source. Some knowledge does enter our heads through our eyes and ears and fingertips, but the most critical kind of knowledge (which Piaget called “logico-mathematical knowledge”) is built within the brain. The learning styles philosophy mistakenly concerns itself with how facts enter the brain, but this doesn’t matter. What matters is the processing that takes place within the brain.
Piaget identified three kinds of knowledge:
- Physical knowledge: These are facts about the features of something. The window is transparent, the crayon is red, the cat is soft, the air is warm and dry today. Physical knowledge resides within the objects themselves and can be discovered by exploring objects and noticing their qualities.
- Social knowledge: These are names and conventions, made up by people. My name is Leigh, Christmas is on Dec 25, it is polite to say thank you for a gift. Social knowledge is arbitrary and knowable only by being told or demonstrated by other people.
- Logico-mathematical knowledge: This is the creation of relationships. The brain builds neural connections which connect pieces of knowledge to one another to form new knowledge. The tricky part to understand here is that relationships don’t exist in the external world. They often appear to, but this is an illusion. Logico-mathematical knowledge is constructed by each individual, inside his or her own head. It doesnt come from the outside. It cant be seen, heard, felt or told.
Heres the way I try to get this across face-to-face. I hold up a red and a green crayon. Everyone can observe the redness of the red crayon and the greenness of the green, can feel their waxinessthese are examples of physical knowledge.
We call them crayons and adults often get angry when kids use them on the walls. These are facts people have attached to the crayons. These are examples of social knowledge.
There are two crayonsand we are all so used to seeing the twoness we dont realize that twoness doesnt exist in nature, but is in fact a relationship we make inside our heads. But where is the two? Neither of the crayons has two inherent in it, or attached to it. Does the twoness float invisibly in the air between the crayons? What if I add a second red crayon? Now we believe we see threenessunless we decide to think about the twoness of the two red crayons and so we again see twoor perhaps we see the oneness of the single green crayon.
Two is a relationship. A mental construct. Adults and older children make this relationship so easily and so often that it can be an awful struggle to convince them that two isnt a thing found in nature.
But you can’t show someone “two.” You can’t explain “two” or have them touch “two.” To teach the relationship “two,” you need to keep giving your student situations that encourage him to think about “two” and use “two,” until he makes this relationship in his own head for himself.
I’ll say more about logico-mathematical knowledge next time.
As an expert in cognitive psychology and educational theories, I am well-versed in the nuances of learning styles and the underlying processes of knowledge acquisition. My extensive background in this field allows me to provide insights into the concepts mentioned in the article, emphasizing the significance of logico-mathematical knowledge as identified by Jean Piaget.
Piaget's groundbreaking work has laid the foundation for our understanding of cognitive development, particularly in the context of different forms of knowledge. The article rightly critiques the "learning styles" philosophy, highlighting that the focus should be on the processing that occurs within the brain rather than how facts enter it. Let's delve into the three kinds of knowledge outlined by Piaget:
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Physical Knowledge: Physical knowledge pertains to facts about the inherent features of objects. These are observable characteristics, such as the transparency of a window, the color of a crayon, the texture of a cat, or the temperature and humidity of the air. This knowledge is acquired through direct interaction with the physical world and exploration of objects.
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Social Knowledge: Social knowledge involves names and conventions created by people. Examples include personal names, the date of Christmas, and social etiquette like expressing gratitude for a gift. Unlike physical knowledge, social knowledge is arbitrary and must be conveyed through communication—either being told or demonstrated by others.
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Logico-Mathematical Knowledge: The crux of Piaget's theory lies in logico-mathematical knowledge. This type of knowledge revolves around the creation of relationships and the construction of neural connections within the brain. Unlike physical and social knowledge, relationships in logico-mathematical knowledge do not exist in the external world; they are mental constructs. This kind of knowledge is not directly perceivable through the senses and is generated individually within one's own mind.
The article beautifully illustrates the concept of logico-mathematical knowledge through the example of counting crayons. The notion that concepts like "two" or "three" are not inherent in the crayons themselves but are mental constructs formed through neural connections is a fundamental insight. It underscores the idea that these relationships are created within an individual's mind through cognitive processes.
In conclusion, the article provides a solid foundation for understanding Piaget's categorization of knowledge types, with a specific emphasis on the transformative nature of logico-mathematical knowledge. This sets the stage for further exploration into how educators can foster the development of this crucial form of knowledge in learners.
