"children understand mathematical knowledge from their environment". in the reference of the statement,as a primary teacher discuss the strategies used by children to acquire mathematica knowledge
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Children begin learning mathematics well before they enter elementary school. Starting from infancy and continuing throughout the preschool period, they develop a base of skills, concepts, and misconceptions about numbers and mathematics. The state of children’s mathematical development as they begin school both determines what they must learn to achieve mathematical proficiency and points toward how that proficiency can be acquired.
The most fundamental concept in elementary school mathematics is that of number, specifically whole number. To get a sense of both the difficulty of the concept and how much of it is taken for granted, try to define what a whole number is.
One common conception of whole number says that two sets have the same numerosity (same number of members) if and only if each member of one set can be paired with exactly one member of the other (with no members left over from either set). If one set has members left over after this pairing, then that set has a greater numerosity (more items in it) than the other does.
This definition allows one to decide whether two sets have the same number of items without knowing how many there are in either set. The Swiss psychologist Jean Piaget developed a task based in part on this definition that has been widely used to assess whether children understand the critical importance of this one-to-one correspondence in defining numerosity.1 In this task, children are shown an array like the one below, which might represent candies. They are then asked a question like the following: Are there more light candies, the same number of dark and light candies, or more dark candies?
Early research on children’s understanding of the mathematical basis for counting focused on five principles their thinking must follow if their counting is to be mathematically useful:8
One-to-one: there must be a one-to-one relation between counting words and objects;
Stable order (of the counting words): these counting words must be recited in a consistent, reproducible order;
Cardinal: the last counting word spoken indicates how many objects are in the set as a whole (rather than being a property of a particular object in the set);
Abstraction: any kinds of objects can be collected together for purposes of a count; and
Order irrelevance (for the objects counted): objects can be counted in any sequence without altering the outcome.
The first three principles define rules for how one ought to go about counting; the last two define circumstances under which such counting procedures should apply.
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Children begin learning mathematics well before they enter elementary school. Starting from infancy and continuing throughout the preschool period, they develop a base of skills, concepts, and misconceptions about numbers and mathematics. The state of children’s mathematical development as they begin school both determines what they must learn to achieve mathematical proficiency and points toward how that proficiency can be acquired.
The most fundamental concept in elementary school mathematics is that of number, specifically whole number. To get a sense of both the difficulty of the concept and how much of it is taken for granted, try to define what a whole number is.
One common conception of whole number says that two sets have the same numerosity (same number of members) if and only if each member of one set can be paired with exactly one member of the other (with no members left over from either set). If one set has members left over after this pairing, then that set has a greater numerosity (more items in it) than the other does.
This definition allows one to decide whether two sets have the same number of items without knowing how many there are in either set. The Swiss psychologist Jean Piaget developed a task based in part on this definition that has been widely used to assess whether children understand the critical importance of this one-to-one correspondence in defining numerosity.1 In this task, children are shown an array like the one below, which might represent candies. They are then asked a question like the following: Are there more light candies, the same number of dark and light candies, or more dark candies?
Early research on children’s understanding of the mathematical basis for counting focused on five principles their thinking must follow if their counting is to be mathematically useful:8
One-to-one: there must be a one-to-one relation between counting words and objects;
Stable order (of the counting words): these counting words must be recited in a consistent, reproducible order;
Cardinal: the last counting word spoken indicates how many objects are in the set as a whole (rather than being a property of a particular object in the set);
Abstraction: any kinds of objects can be collected together for purposes of a count; and
Order irrelevance (for the objects counted): objects can be counted in any sequence without altering the outcome.
The first three principles define rules for how one ought to go about counting; the last two define circumstances under which such counting procedures should apply.
Hope it helps u
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