Michele Pasin / Quotes

Conservation of number and the spread-out coins

Because preoperational children tend to believe what they see, they do not yet have a firm grasp of qualities belonging to the objects in their world. For example, they confuse “heavy” with “large.” Due to inexperience, most young children would initially be surprised that a beach ball is lighter than a baseball. Unable to separate height from age, preoperational children will insist that the tallest person is the oldest. Piaget did a classic experiment involving a conservation task to demonstrate this kind of thinking in children. He put two sets of coins on a table in two lines. Both sets had the same small number of coins, but the coins in one line were spread farther apart. When asked which line had more coins in it, preoperational children always said the line in which the coins were spread farther apart had more. They held to this belief even when the coins from the two lines were matched up to show that for each coin from the long line, there was a coin from the short line. Conservation tasks such as this one involving conservation of number show whether a child has grasped the concept that certain physical characteristics of objects remain the same, even though their outward appearance changes. Because children at this stage are dependent on their own experience, they tend to make incorrect generalizations. They base their general belief about something on a single experience, which may cause a false conclusion. One example is the girl above who believed that a dog’s barking made birds fly because she had seen birds flying when a dog barked.

Saved 12 August 2021 / www.amazon.com ↗

#child-development #thinking #perception #mathematics

Number sense is like color perception

Dehaene further likens our perception of math to how we perceive color. Color is not an objective property of the world that exists independently of human…

Beyond Zero and One (Andrew Smart) #mathematics #perception #culture #brain #evolution

Concepts describe the world, experience is of it

One may be aware of one’s concepts and mental operations but that is the result of one’s capability of being conscious of the world (and thus also of certain…

Beyond Zero and One (Andrew Smart) #concept #experience #mathematics #consciousness

Dehaene studies mathematics in the brain

Compared to Penrose, Dehaene’s approach to the issues of consciousness and math is much more empirical. Dehaene uses the tools of cognitive psychology and the…

Beyond Zero and One (Andrew Smart) #neuroscience #mathematics #consciousness

Fractional co-citation clustering

Garfield and Small both continued their research and experiments in science mapping over the decade and thereafter. In two papers published in 1985, Small…

Research Fronts 2014 : 100 Top Ranked Specialties In The Sciences And Social #field #mathematics #front

Gödel and the limits of AI

Roger Penrose argues that because humans can grasp Gödel’s theory, the mind is not a formal logical system. He argues that the source of our intuitions and…

Beyond Zero and One (Andrew Smart) #artificial-intelligence #logic #mathematics #quantum-theory

Infinitely many ways to represent numbers

Our concept of the number three can be represented as “3” in base ten, but as “0011” in binary. It is the same idea as using the word “three,” three fingers…

Beyond Zero and One (Andrew Smart) #number #mathematics #representation