Math Methods Chapter 0

Front 1

Philosophy

Back 1

searching for answers within the context of personal beliefs – should remain tentative and open to change as we gain experience and learn more

Front 2

Cognitive Development –

Back 2

learning that goes on in the human mind

Front 3

Internal/External
Representations

Back 3

(Golden) internal development (way of thinking)/ can be represented outside the human mind (spoken, written, demonstrated physically)

Front 4

Numberness

Back 4

an attribute of a set, attribute that describes quality

Front 5

Numeral

Back 5

symbol

Front 6

Number

Back 6

is abstract

Front 7

Conceptual –

Back 7

helping children build meaning(Constructivist)

Front 8

Rote/Procedural

Back 8

explaining, showing, telling (Behaviorist)

Front 9

Procedural (rote) learning does not

Back 9

always result in appropriate internal representations.

Front 10

Socrates:

Back 10

“real understanding must come from within. It cannot be imparted by someone else. And only the understanding that comes from within can lead to true insight.”

Front 11

Aristotle:

Back 11

believed that learning happened through sensory perceptions. Humans develop internal representations (thinking) based on classification of information taken in through the senses.

Front 12

Behaviorism:

Back 12

became prominent during the 19th century and prevailed throughout most of the 20th century. Relies on stimulus-(way of response process.

Front 13

The teaching of a process can never

Back 13

take place of the teaching of a concept

Front 14

One drawback to Behaviorist teaching

Back 14

is that it relies too heavily on teaching of procedures without concentration on the concepts that the procedures are based on.

Front 15

Constructivism:

Back 15

relies on the idea that learning happens as a result of the progressive construction and modification of logically sequenced structures in the brain.

Front 16

Piaget and Vygotsky are major contributors to

Back 16

both the philosophy and methodology of Constructivism.

Front 17

Vygotsky –

Back 17

Through enculturation we learn how to think as well as what to think.

Front 18

Zone of Proximal Development

Back 18

“readiness” for learning/ building an internal representation.

Front 19

A key idea is that children (all people actually) build

Back 19

their own knowledge, or concepts, but the learning does not happen on its own.

Front 20

The learning is mediated by

Back 20

tools (manipulatives, problems), mentors (peers, teachers, parents), and enculturation (engagement).