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What are the PreNumber Skills?
 1. Classifying (enactive)
 2. Finding the Relation between two sets (enactive)
 3. Conserving Relations (enactive to iconic)
 4. Classifying on the basis of the AsMany Relation
 5. Ordering on the basis of the MoreThan and LessThan Relations (iconic)

Why do we teach PreNumber Skills?
 1. birth to age 7
 2. skills have to have in place before being introduced to idea of number
 3. preoperational (lack ability to conserve)
 4. use measurement and quantity interchangeably when describing different sets
 5. based on a heirarchy

Four Important Understandings for Developing PreNumber Concepts
 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.

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

Finding the relation between two sets PreNumber Skill
 1. As Many As Relation
 2. MoreThan and LessThan Relation

Definition of Subitizing
 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

Classifying on the basis of AsMany Relation PreNumber Skill
children are able to match pictures of various amounts of objects to the picture of the number symbol

Ordering on the basis of MoreThan and LessThan Relations PreNumber Skill
children are able to put cards in order from least to greatest; children are able to put a card either before, middle, or end

Finding and Using the Properties of Relations
 1. Reflexive Property
 2. Symmetric
 3. Transitive

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

Symmetric Property
 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

Transitive Property
 1. A=B, B=C, then A=C
 2. require 3 sets of information
 3. Sally has seven barbies. Her mom went to WalMart 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)

One To One Matching Test in Relation with One To One Correspondence
 1. Children use the one to one matching test to determine the condition of one to one correspondence.
 2. manipulatives match up

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

Readiness Skills for Learning Numbers 110
 Step 1: associate a number with a family of sets (number / cardinality)
 Step 2: number / numeral association
 (abstract idea to written sign "4")

Counting Meaningful Skills
 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

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

Kindergarten and First Grade Counting Experiences
 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

Readiness Step for Addition and Subtration
children count from a set and must have access to model

Definition of Cardinal Numbers
 1. idea of cardinality
 2. numbers that tell how many

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

What about 0?
 1. hard to demonstrate
 2. ask questions that correspond to cardinality of "0"

Greater than 10
 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 1119 first

How to assess student performance using PREVENTATIVE TEACHING?
 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.

