Categories and Categorization

Question 1

Zoo Analogy

Answer 1

People visiting zoo from a faraway place - will be familiar with some concepts - permission to enter makes sense because they have the concept of exchange and private property

May not have concept of money
Have concept of animals so they will have some clear expectations about animals

Some concepts are universal - animals - while others are not

Question 2

Everyone categorizes - what are developmental changes in categorization?

Answer 2

Everyone categorizes - we group objects and events into classes of like kinds
Groupings change in age-related, predictable ways

Younger children are more likely to refer to global perceptual features that can be seen - similarity of the broad shapes of objects

Older children - feature-by-feature comparison that older children prefer

Question 3

Perceptual Category and Examples

Answer 3

An implicit classification of perceptual stimuli into discrete sets, despite a lack of physical discontinuity in the stimulus array (e.g. colors, facial expression, and consonant sounds).

EXAMPLE - Visible spectrum is physically, but not perceptually, continuous
Looks like there are dividing lines between the colours but there is no division
Even if the wavelength of the stimulus that meets our retina changes gradually from shorter to longer, our perception does not change gradually (categorical perception)

Morphed images - happy to sad - continuum - each photograph is equally physically distinct but there is a percept that there is something categorical here

Question 4

Categorical Perception & Example

Answer 4

the perception of stimuli that differs continuously as being categorically or qualitatively different
That relatively fast change in perception associated with a gradual change in the physical characteristics of the stimulus is characteristics of categorical perception.

we more easily perceive differences in two color patches that cross our category boundary (e.g., what we would call a green and a blue) than we perceive differences of equal physical magnitude (the difference in wavelength is the same) within our perceptual category (e.g., two different blues).

Another example of perceptual categorization is the perception of speech sounds: As the physical stimulus changes gradually from “ba” to “pa,” we hear a sudden categorical change, even though we cannot hear the gradual change within either category

perception of emotional facial expressions is also categorical. For example, if a facial expression changes gradually from happy to surprised, the perception of a happy face changes rather quickly to the perception of a surprised face, relative to the physical change in the stimulus

Question 5

Category

Answer 5

A mentally represented collection of entities
(objects, people, actions, or events).

psychological entity (the representation of the group) that is classified together for psychological reasons (some functional similarity)
without regard to any real-world grouping.

Question 6

The Function of a Category - wrong reasons

Answer 6

Categories allow people to behave adaptively in a way that ultimately increases survival and reproductive success.
How do categories increase fitness?

PROPOSED REASON
Reason we categorize is because our cognitive and memory capacity would be swamped by information if we did not categorize
relieve memory load - NO

DOESN’T WORK BECAUSE
1. We remember the categories and individual items - remember all people in circle despite being in categories such as family and friends from school
2. There is no reason we couldn’t remember everything - remember category of family member but still have to remember each individual family member
—-Given number of synapses you have - you could remember everything in your lifetime

Question 7

The Function of a Category - actual

Answer 7

Function is actually - inference - broader category - behave sensibly with respect to survival and reproduction - decisions that enhance fitness

Creating a category and then knowing that a particular object belongs in that category allows us to make inferences and thus provides a rich source of information regarding things that we are encountering for the first time.

Perceptually similarities but difference in category - informs behavior - house cat vs. wild cat - know what to expect from it, how it might benefit us and whether it is dangerous

Question 8

How does the size of the category influence our predictions?

Answer 8

We can make broad predictions when we have large categories (if we know that the being we just encountered is an animal, we know it will move about to seek food)

more precise predictions with smaller categories (if we know that the being we just encountered is a bongo, we know it will grow horns, that it is a herbivore, and that its offspring will be bongos

to assign a new object that we encounter to a broad category such as “animal,” we need to know relatively little about it, but in order to assign a new object to a very specific category, more information is needed

Question 9

Which types of categories are more effective for inference?

Answer 9

Even more effective with respect to inference are natural kinds categories (e.g. animals), as opposed to arbitrary categories (e.g. blue rectangles)

Question 10

Categories are Functional
Krasnow Experiment

Answer 10

concepts are organized by our minds according to the value of objects where value means biological utility ex. Food
Value of should be a stronger categorization factor than how common or frequently occurring it is

-Visitors to alien planet and their job to compose a report on what they found
-taught participants two categories
of line-drawn coconut-shaped objects by presenting exemplar after exemplar and then testing how fast and accurate participants were at recognizing an example.
—-Wanted to know if people create categories by looking for
1. those items that are the most typical of the group
2. those that are the most useful or functional.

if told the category was a fruit, they were the fastest and most accurate at identifying a group member when the group member was ripe (as opposed to unripe).- evolutionary value

if not told not told that the category was fruit, then they showed the pattern consistent with the prototype view of
categorization: - most typical of the group.

Estimate of the value of items in evolutionary terms is part of what the mind uses to create categories

Question 11

Krascum and Andrews - Wug and Gillie

Answer 11

Kids come into lab and are supposed to categorize these instances into two categories

One of the groups was given a functional description but given characteristics
Other was given a characteristic description but not a functional description

Group that hears the function is better at categorizing the drawings
Better at remembering a day later

Question 12

Classic Category - Example

Answer 12

A category that can be defined by a list
of necessary and sufficient features.

is not just an idealized description of categories rather, categories are believed to
be mentally represented as definition

“raccoon,” there should be a list of necessary and sufficient features, and if all of the features are present, you have a raccoon. These features might include being four-legged, a mammal, native to North America, and furry with a dark facial mask, for example

Any entity that has all of the features should be included in the category
and any entity that lacks one or more of the features should not be included in the category.

Question 13

Classic Category Features

Answer 13

All categories were classic
All categories were equally good categories
No distinction btw psychological and real-world categories
It is always possible to say whether an item is a member of a given category

Question 14

1st PROBLEM with classic category - Wittgenstein

Answer 14

Game: What list of features includes all of these - Wittgenstein

Challenging classic view by asking what is the necessary and sufficient list that defines game

Basketball - competing, physical, teams, goal - how do we fit board games?
Has to exclude things that are not game - war, juggling, kicking ball

Question 15

2nd & 3rd problems with Classic Category

Answer 15

Not supposed to be better examples - robin is a better example than a penguin -

Ambiguous Items
If you ask someone whether an olive is a fruit, or whether curtains are furniture, they may flip-flop and give you a different answer to the same question two weeks later
Are drapes furniture ?

Question 16

Prototype View

Answer 16

viable response to Wittgenstein’s challenge to the classic view of categorization -Eleanor Rosch,

some members of a category are more central to that category than others because they more closely resemble the prototype.

More shared features - more central to the category
less prototypical member of the category if it shares features with members of other categories.

Question 17

Problem with Similarity

Answer 17

Eleanor Rosch and her colleagues talk about categories, they were talking about psychological entities, not ideal or hypothetical groupings, as Plato was

Be aware here of your own instinct blindness because when Rosch talks about the similarity (or dissimilarity) between any two things, she is not talking about the properties of the actual objects; she is talking about our perceptions. Items are similar with respect to features that we see, that we notice, that are important to us and that we use to categorize objects

Question 18

Associationists on Categorization

What evidence shows they’re wrong?

Answer 18

1- Committed to theory of classical categories

2 - Do not need to be functional

3 - Should not differ with respect to how richly inferential they are.

4 - Relies heavily on perceptual similarity.

DOESNT WORK -
1.induction studies
2. transformation studies
3. essentialism - the child’s intuition that some essence is responsible for conferring category membership to members of any natural category

Question 19

Evolutionary Psychologists on Categorization

Answer 19

psychological processes underlying the formation of categories and concepts in children were selected for by natural selection.

categories regarding living things and other natural kinds are expected to be relatively UNIFORM compared to the infinite number of possible arbitrary categories that could exist.

The mental structures that support categories, concepts, and essentialism in developing children are characteristic of specialized design.

Core concepts have a long evolutionary history. Concepts that are reliably developing in infants and children are those concepts that were relevant in the EEA.

expect other species to have different categories, categories that are functional for them

Question 20

Piaget’s View on Categorization - what method did he use?

Answer 20

He believed that any category was represented psychologically as a classic category and could be defined in terms of its necessary and sufficient features - whether arbitrary or natural

Free classification method to test children’s understandings of categorization.
Give them an array of different objects - free sort - create number of categories - decide how many categories - Thematic associations - dog, dog house, horse, stable

Question 21

Piaget’s View on Categorization - what did he conclude?

Answer 21

Children in preoperational and concrete operational stages were perceptually bound -categorize based on visually perceivable features - if two red objects close - red is defining feature

—-Did not group into classic categories because they were cognitively immature - thematic - was an error and sign of immaturity

—–Children had complexes - A grouping that is more fluid and less well defined than a category and that does not rely on classic definitions.

Question 22

Basic Levels and Hierarchical Organization

Answer 22

Categories are psychologically organized into hierarchies

Superordinate category - broader category - apples - species, specific orchard -

down to an individual apple - which isnt a category but an example- subordinate level categories

Question 23

Thematic Association

Answer 23

The grouping of items based on their use
together or their prior association in a story
rather than on category membership.

Question 24

Perceptually Bound

Answer 24

Compelled to categorize objects based
on visually perceivable features, as Piaget
thought children were

Question 25

What Would Piaget Say about the Hierarchical Organization of Categories?

What was piagets experiment?

Answer 25

Piaget was interested in children’s understandings of the hierarchical relationships among categories
—-. Adults usually understand that there can never be a greater number of members of a subclass than of the superordinate class since the members that count in the subclass also count in the superordinate class.

Class-inclusion Experiment
An experiment used by Piaget and others in which children were tested to see if they would include a subset in a broader grouping.
“Could you make it so that there will be more red
flowers than flowers?

Piaget’s class-inclusion experiments led him to conclude that children were unable to reason about subordinate and superordinate classes.

Question 26

basic-level categories - 4

Answer 26

A category that is most easily processed
at a basic level, first learned by children,
and within which inferences are more
generously drawn

Childs basic level are more general than adult

Most easily visualized/brought to mind
——-Picture chair when thinking of furniture - often the shorter word is the basic level

Children’s first words
—–basic level categories have a special status psychologically
—–first words that children learn are basic-level words. In free-sorting tasks, children are more likely to group objects by basic-level categories than by other sorting schemes such as subordinate or superordinate categories

Most easily processed

Infants more easily discriminate across than within basic level categories
—Instinct blindness - even the fact that basic level categories exist
-basic-level categories have just the right blend of within-category similarity and between-category differences to allow for easy mental grouping. Basic-level categories also keep between-category exemplars mentally distinct.
———3m - infants more easily discriminate entities that belong to different basic-level categories than they discriminate entities within a basic-level category - may differ slightly than groupings used by adults - child basic level

Question 27

Basic Level at age 3

Answer 27

By the age of 3, the primacy of basic-level categories affects how children draw inferences. Not surprisingly, children are more likely to draw inferences within the basic-level categories than from a basic-level item to a superordinate-level item.

In other words, if a child is taught that a bird has a spleen, she might be quick to affirm that a new, different bird has a spleen but hesitate to say that a new animal also has a spleen

Even more cleverly, a child is more likely
to make an inference from a basic-level object to a member of the subordinate category than the reverse.
In other words, if he learns a new fact about birds (birds have gizzards), he is willing to infer that this fact is true about robins, but learning this fact about robins, he hesitates to apply it to all bird

Question 28

what do we mean when we say basic?

Answer 28

When Rosch talks about basic-level categories, she is talking about a level of thinking that is created by the human mind: She is not implying that there is actually anything more basic about apples than about fruit.

A category is basic because people use the category as a basic category, not because the world is made of some categories that are more basic than others. In the real world a dog is not more of a dog than it is an animal. Again, instinct blindness masks the work that our minds are doing

you likely have the perception that the superordinate category is the most general category.

Question 29

Concepts

Answer 29

A psychological grouping together of entities, objects, events, or even characteristics on the basis of some more or less functional commonality, including some taxonomic relationship

A concept is a mental representation of that grouping. Concepts can often be named with a word or short phrase

Concepts are typically lexicalized, whereas a category can be a more arbitrary grouping (e.g., items that I bought while on vacation) - concept is a category but a richer category - much richer inferences - honesty,
Concept is everything that a word refers to

Question 30

Concepts as Theories

Answer 30

concept, like a theoretically delineated topic of study has three components:

(a) a distinct set of items that are included,
Ex. solid objects - rocks and animals included but not clouds and beliefs

(b) phenomena involving members of the set of items
Phenomena involving members of the set - collisions, falls and breaks

(c) a set of causal relationships that apply within the domain in question and explain observations within the domain, but do not apply within other domain
—A launch event that happens when one object strikes another
—-Concept and theory would both include this into

Question 31

Instinct Blind to Concepts

Answer 31

People seem to have all the right concepts to allow them to function effectively in the physical world and in social interactions - hard to imagine not having them

Do not think that useful concepts are just a small subset of all possible concepts - could be determined by color or size but instead organized into standard biological taxonomies

Uniformity in concepts that people have - between individuals and between human cultures -
Humans have similar understandings of natural things ex. water , plants, animals rocks and a remarkable number of concepts regarding social and mental phenomena - deception integrity love empathy justice

Question 32

Universality of Children’s Concepts

Answer 32

Children exposed to an enormous array of different experiences but have a surprisingly uniform set of concepts - within a culture and between cultures

An early and compelling distinction that children make is between animals that are predators and
animals that are prey, and this is true cross-culturally

This uniformity of development suggests that the developmental process of concept formation must
be constrained, privileging some hypotheses over others.
— children develop a species-typical,
universal set of concepts such as animals, plants,
—-individuals can and do develop culture-specific concepts as well: iPods, weekends, and HOV
idiosyncratic concepts - family cabin

Question 33

Natural Kinds

Answer 33

Naturally occurring categories such as “dogs,” “water,” “gold,” and “trees” are among the categories that philosophers have called natural kinds

Objects grouped together as they are perceived to be in nature.

Allow for rich inferences because members of a group have predictable characteristics in common
Rocks will sink in water
although there are entities in the real world that violate both of the above conclusions, this does not mean that the categories are not functional or that the inference is not valuable.
Inferences confer an overall benefit

Question 34

Inductive Method: Gelman and Markman

Answer 34

A research method in which a researcher asks a child what kinds of inferences he can make from one entity to another in order to probe the child’s categories in terms of membership and internal structure.

Showed 4 yr olds pictures of objects - fish and dolphin - bat and flamingo -

Then taught them new info - fish underwater, flamingos legs get cold at night and bat stays warm at night - bat is a mammal bird is not

Then showed new picture of object that was perceptually similar to one of the two original pictures but that shared a natural kinds category with the other

Responses were not percetually driven - children surprisingly adult like in their category inferences - made based on category membership

Control condition - children asked to judge the weight of each animal - made judgments based on perceptual characteristics not on category membership

Question 35

Inductive Method: Gelman and Markman CONCLUSIONS

Answer 35

It is not that children avoid using perceptual similarity in general - rather they do not rely on perceptual similarity to assign category membership or to make inductions about biological properties

Inferences are applied within category
show that children do have concepts, that the concepts they develop are relatively consistent from one child to the next concepts are not just reliant on perceptual similarity

USE CATEGORY MEMBERSHIP TO MAKE INDUCTIONS

Children are selective, and usually appropriately selective, about the inferences they will and will not make

Question 36

Inductive Method: Gelman and Markman PROBLEMATIC FOR

Answer 36

Piagetian perspective that would predict that children are perceptually bound.

also problematic for a purely associationist account, which would predict that children would only have knowledge about things they have had an opportunity to observe.

Question 37

Essentialism:

Answer 37

The intuition that for any given entity there is an essence–some property that every member of that kind must possess−which gives it its category membership and its category-specific features

Challenge to classic view of category

Question 38

Essence of a….

Answer 38

EX if we meet a raccoon with just three legs, we do not regard him as any less of a raccoon. Our essentialist psychology still leads us to view him as a raccoon: he still has the essence of a raccoon -gives it category membership and category specific features
This applies to natural kinds categories that are inanimate as well. No matter how you manipulate, melt, cut or re-shape gold, it is still gold.

there is an essence of a dog or a raccoon or a diamond - perceived essence as part of human psychology

Question 39

Locke Essence

Answer 39

Locke - objects, especially natural kinds, such as animals, plants, and even minerals, have essences and that these essences derive from the identity of the object and determine its properties

he was suggesting that natural kinds really had essences, an important distinction to understand

Question 40

Gelman (1988) found that children as young as 4 seem to have a different way of thinking about natural kinds and artifacts

Answer 40

4-yearolds could answer questions about which objects are made by people and which objects are not made by people,

By the age of 7 or 8, children regarded natural kinds categories as more elaborately structured than categories of artifacts, and their essentialist view of natural kinds allows for a greater number of inferences among natural kinds categories (like plants) than categories of artifacts (like crockery)

ability to make this distinction develops over time, maturing between the ages of 4 and 7 as the essentialist view of natural kinds becomes more adult-like.

Question 41

-Frank Keil’s - transformation experiment

Answer 41

the child is asked to consider an object that starts out as a member of one category (a raccoon or a coffeepot) but after a series of transformations has the outward appearance of something else (a skunk or a birdfeeder).

The child is asked what the object is: Is it a raccoon or a skunk?

First, children of all ages accept the transformation of the artifacts, as do adults. If someone has completely changed the form and function of a coffeepot so that it now functions as a birdfeeder, we all call it a birdfeeder. Why not?

In contrast, older children and adults reject the idea that natural kinds can change category membership. No matter what you do to a raccoon and what it looks like when you are finished, it is still a raccoon, most participants report

even a 4-year-old requires that the transformation be sufficiently convincing and taxonomic relation has to be close enough - raccoon to fish is too much of a stretch

Question 42

Transformation studies challenge Piaget

Answer 42

Piaget thought children would be perceptually bound
They should accept the transformation

Piaget thought that children used classical categories
So the fact that children regarded animals and artifacts differently would be a problem for piaget

Question 43

Results from studies in the tradition of Gelman, Carey and Keil suggest that children have rich concepts, whereas early Piagetian research suggested that children relied very heavily on perceptual, especially visual, similarity
Why? - 2 reasons

Answer 43

the methodologies differed dramatically and therefore measures that resulted from the tasks were different:
1—-Piaget and others whose work preceded the innovative work of Gelman and Carey and others
asked participants to sort or to tell “which ones go together.” This task was likely to yield thematic groupings as categorization and may not have mapped onto any of the child’s mental representations of categories.
————– may not have been clear to the child what the experimenter was asking him to do
—–Gelman, Carey and Keil use the transformation method or the inductive method, which can reveal what categories children hold and, importantly, what inferences are warranted within a category - naturalistic question

2—— nature of the category that was being studied.
Contemporary studies show that natural kinds categories are rich sources of inference and even compare the inferences children make within natural kinds and artificial categories.

Traditional Piagetian research assumed that all categories were classic categories, completely describable by a list of necessary and
sufficient features, and thus researchers felt free to use arbitrary, artificial categories

Question 44

Concept Development - test the inferential richness of a young child’s concepts see which kinds of objects he or she thinks can perform a given action.

McDonough and Mandler

Answer 44

showed that 14m can understand that animals - as a category - drink
Shower 14m a toy dog and the experimenter gave the dog a pretend drink from the cup then let the child manipulate the cup and another toy animal - child gave that toy a pretend drink

Question 45

Habituation Paradigm - Concept Development

Answer 45

Quinn and Eimas

• Dishabituate to a category at 3m of age - dog, dog, dog, cat
  Behl-Chadha - babies even have higher-level categories at 3.5m - Dishabituate to mammals vs non mammals - higher order categories - dog cat tiger bear fish

We don’t notice the uniformity in the concepts people have, in part because we fail to imagine the myriad other logically possible categories

infants as young as 12 months can distinguish different kinds of foods, different kinds of animals, and different kinds of furniture in a way that indicates that they have these concepts

Question 46

Functional Fixedness

Answer 46

The psychological phenomenon wherein
identifying an item as belonging to one
the category makes it difficult for a person to
think of using it for a function that is not
associated with that category.

Question 47

Duncker’s classic experiment - functional fixedness

Answer 47

subjects were given a candle, a book of matches, and a box of tacks. The solution was tacking the tack box to the board and using it as a candle holder - showed functional fixedness
Faster to arrive at solution if box was empty

Appears differently in children
—Five-year-olds did not show a facilitation of performance when the tack box was provided on its own, compared to when it was presented as a container. no functional fixedness.
—-in the most difficult situation (where the box had been used as a container), the 5-year-olds performed better than 6- and 7-year-olds and better than adults.

German and Defeyter - young children have a broader category regarding an artifacts function - reasoning is more flexible

Question 48

How would a child come to understand a new concept - conceptual change

Answer 48

Fractions
understanding of integers - well-developed by the age of 5, but does not understand fractions, ratios, decimals and proportionality.
Half of hs students struggling

Density
—Young children understand that weight can be a measure of how much matter there is; they understand some things have more matter and some things have less matter.
—Children with this initial conception don’t understand the concept of density and the relationship between volume and weight that allows objects that appear the same size to have different weights
—Weight is a measure of the extent of a specific amount of matter, whereas density is a property of the substance, regardless of how much of it you have

Gravity
Need to make conceptual shifts to understand these concepts

Question 49

Quinian Bootstrapping

Answer 49

Carey’s proposed process allowing CONCEPTUAL CHANGE

1- Create a place-holder, usual the name of the concept (e.g. memorizing word Density without understanding its meaning)

2- Make connections with the old concept (e.g. weight and volume)

3- Use models to create analogies (e.g. dots on a grid - volume allocated to each unit of weight

4- Test predictions in the real world - show them that what they understand is not making accurate predictions in the real world - how scientific understanding develops

Question 50

Who undergoes quinian bootstrapping

Answer 50

this process of Quinian bootstrapping is the process that children go through when they undergo a conceptual change, and it is the process scientists have historically gone through when creating a new concept

Question 51

Prerequisites to Quininan Bootstrapping

Answer 51

THREE characteristics of a child’s conceptual change that are associated with conceptual change, but do not explain the creation of the new conceptual structure.
Language, Memory, Information Processing Capacity

Question 52

Prerequisites to Quininan Bootstrapping - Language

Answer 52

LANGUAGE - the process of transition from one conceptual framework to another is, for children, a social process.

Children are initially introduced to new concepts and the features of the new conceptual structure explicitly from other people.

the conceptual bridge would not be possible without language

Question 53

Prerequisites to Quininan Bootstrapping - Awareness of contradiction

Answer 53

awareness of a contradiction, either among elements in the immature conceptual structure or between the immature conceptual structure and evidence in the real world.

When predictions fail, children can become ready for conceptual change.

Question 54

Prerequisites to Quininan Bootstrapping - domain general cognitive skills

Answer 54

development of some domain-general cognitive skills is usually necessary for conceptual change

Children must have sufficient memory and sufficient information processing capacity to get them over the gap to the mature conceptual framework.

importance of the use of analogy to support the development of the mature concept

Question 55

Moss and Case

SMITH

conceptual change and education

Answer 55

understood that 10 year old children well understand integers but did not understand fractions
developed a math curriculum that maps the integers onto a measurement of distance, like a ruler

Smith developed and tested a curriculum that lead students to conceptual change in the field of physics, by creating a placeholder for density and then modeling through experimentation how density was related to weight and volume. Importantly, one of the characteristics of Smith’s curriculum was meta-cognition: students were
made aware of what their initial conceptual understanding was and how the modeling they were doing was leading to conceptual change

Question 56

Neuropsychological Perspective on Concepts
Studies of Brain Injury Patients

Answer 56

Even with only one individual with brain damage, it is possible to make inferences about the neural organization of concepts.

Two of these patients showed stronger deficits when asked about animate things (animal) compared to non-animate things (plants and artifacts). In contrast, two of these patients had greater deficits when the task involved fruits and vegetables compared to anything that wasn’t a fruit or vegetable.

Evidence of the brain basis of these concepts
Brain damage that leads to the loss of one member of a category is more likely associated with the loss of other category members compared to non-members

Another patient showed evidence of impairment in the superordinate category but not in the basic level category

Question 57

What did Piaget think mature categorization involved?

Answer 57

(a) a person could identify which items were included and excluded from the category

(b) a person understood that membership in one category disqualified membership in another category at the same level (something cannot be both a dog and a cat), but

(c) categories are organized hierarchically,
so that members of the “dog” category and members of the “cat” category are also members of the “animal” category

Question 58

Rosch on basic level categories

Answer 58

concepts are most easily processed,

most easily brought to mind

most easily pictured

most easily discussed

the right blend of within-category similarity and between-category differences to allow for easy mental grouping.

words that we use to label basic-level categories are shorter

Question 59

concepts can be powerful sources of

Answer 59

inference, prediction and induction.

Question 60

examples of children starting with immature concepts and through explicit tutoring replacing those starting concepts with adult concepts

Answer 60

1 -child’s understanding of numbers. An understanding of integers is fairly well-developed by the age of 5 - does not understand fractions, ratios, decimals and proportionality. Indeed, half of graduating high school students are still struggling to achieve an intuitive understanding of these mathematical concepts.

2 - A second example of a child’s leap from one conceptual framework to another is in physics, specifically an understanding of matter. Young children understand that weight can be a measure of how much matter there is; they understand some things have more matter and some things less matter. But weight and density are undifferentiated in the immature concepts of physics. Children with this initial conception don’t understand the concept of density and the relationship between volume and weight that allows objects that appear the same size to have different weights

Question 61

Carey describes three characteristics of a child’s conceptual change that are associated with conceptual change, but do not explain the creation of the new conceptual structure.

Answer 61

ONE - the process of transition from one conceptual framework to another is, for children, a social process.
—introduced to new concepts and the features of the new conceptual structure explicitly from other people.
—-Thus, the conceptual bridge would not be possible without language

TWO - the transition is motivated by an awareness of a contradiction, either among elements in the immature conceptual structure or between the immature conceptual structure and evidence in the real world. When predictions fail, children can become ready for
conceptual change

THREE - development of some domain-general cognitive skills is usually necessary for conceptual change. Children must have sufficient memory and sufficient information processing capacity to get them over the gap to the mature conceptual framework. importance of the use of analogy to support the development of the mature concept.

Question 62

Conceptual change is accomplished via

Answer 62

Quinian bootstrapping