Chapter 4 Math Test 2. txt

• 1. Classifying (enactive)
• 2. Finding the Relation between two sets (enactive)
• 3. Conserving Relations (enactive to iconic)
• 4. Classifying on the basis of the As-Many Relation
• 5. Ordering on the basis of the More-Than and Less-Than Relations (iconic)

• 1. birth to age 7
• 2. skills have to have in place before being introduced to idea of number
• 3. pre-operational (lack ability to conserve)
• 4. use measurement and quantity interchangeably when describing different sets
• 5. based on a heirarchy

• 1. set of things has a number property, and the number property is stable. (CARDINALITY)
• 2. always make a set with one more or one fewer. (ORDINALITY)
• 3. whole numbers, we can determine how many objects are in a set, either by recognizing number patterns or by counting.
• 4. whole numbers, we compare two sets and find whether one set has as many as, more than, or less than the other set.

• 1. Selects objects having a SPECIFIC attitude
• 2. Sorting objects on the basis of GENERAL attitude
• 3. DUPLICATING a pattern
• 4. EXTENDING a pattern

• 1. As Many As Relation
• 2. More-Than and Less-Than Relation

• 1. being able to perceive in your brain how many in a set without having to count each individual piece
• 2. brain recognizes patterns in way elements are laid out

children are able to match pictures of various amounts of objects to the picture of the number symbol

children are able to put cards in order from least to greatest; children are able to put a card either before, middle, or end

• 1. Reflexive Property
• 2. Symmetric
• 3. Transitive

• 1. A=A
• 2. mirror images
• 3. identical sets in every way

• 1. A=B, then B=A
• 2. does not matter way they are placed, as long as same information given
• 3. green orange = orange green
• 4. numbers can be symmetric without objects being identical
• 5. five dogs + three dogs = 2 trucks + 6 trucks

• 1. A=B, B=C, then A=C
• 2. require 3 sets of information
• 3. Sally has seven barbies. Her mom went to Wal-Mart and picked out the seven outfits with seven pairs of shoes inside. (7 barbies = 7 outfits, 7 outfits = 7 shoes, then 7 barbies = 7 shoes)

• 1. Children use the one to one matching test to determine the condition of one to one correspondence.
• 2. manipulatives match up

• 1. rote counting: memorize numbers without meaning
• 2. meaningful counting: concept to number word

• Step 1: associate a number with a family of sets (number / cardinality)
• Step 2: number / numeral association
• (abstract idea to written sign "4")

• 1. count each item once and only once
• 2. have a way of keeping track of what has been counted already
• 3. know the counting sequence

knowing that the last number said represents everything that has been counted so far

• 1. count all of a set (every element of a set beginning with one)
• 2. count from a set (count on from a known number either forward or backward) = MATURATIONAL

children count from a set and must have access to model

• 1. idea of cardinality
• 2. numbers that tell how many

• 1. idea of ordinality
• 2. before, after, or next
• 3. numbers that tell position more closely related to before or after

• 1. hard to demonstrate
• 2. ask questions that correspond to cardinality of "0"

• 1. establish ones place before explaining "0"
• 2. helps develop idea of place value
• 3. good questions are a must in this activity
• 4. develop numbers 11-19 first

• 1. must be able to look through the great array of learning goals and identify those that are key.
• 2. many tools can be used to assess learning, very few of them include pencil and paper testing.
• 3. learn to collect, maintain, and study examples of student work to demonstrate mastery.
• 4. understand how children master these concepts and what difficulties they encounter when learning them.